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WO2022199799A1 - Multi-antenna wireless transceiver and method for mimo beamforming - Google Patents

Multi-antenna wireless transceiver and method for mimo beamforming Download PDF

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Publication number
WO2022199799A1
WO2022199799A1 PCT/EP2021/057420 EP2021057420W WO2022199799A1 WO 2022199799 A1 WO2022199799 A1 WO 2022199799A1 EP 2021057420 W EP2021057420 W EP 2021057420W WO 2022199799 A1 WO2022199799 A1 WO 2022199799A1
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WO
WIPO (PCT)
Prior art keywords
channel state
channel
state information
time
wireless transceiver
Prior art date
Application number
PCT/EP2021/057420
Other languages
French (fr)
Inventor
Yoav Levinbook
Doron Ezri
Alexander KOBZANTSEV
Original Assignee
Huawei Technologies Co., Ltd.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huawei Technologies Co., Ltd. filed Critical Huawei Technologies Co., Ltd.
Priority to PCT/EP2021/057420 priority Critical patent/WO2022199799A1/en
Priority to EP21715512.6A priority patent/EP4298731A1/en
Publication of WO2022199799A1 publication Critical patent/WO2022199799A1/en

Links

Classifications

    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0619Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
    • H04B7/0636Feedback format
    • H04B7/0639Using selective indices, e.g. of a codebook, e.g. pre-distortion matrix index [PMI] or for beam selection
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202Channel estimation
    • H04L25/0204Channel estimation of multiple channels

Definitions

  • the present disclosure relates to wireless communmcations. More specifically, the present disclosure relates to a multi-antenna wireless transceiver, such as a multi-antenna wireless access point, AP, and method for MIMO beamforming.
  • a multi-antenna wireless transceiver such as a multi-antenna wireless access point, AP, and method for MIMO beamforming.
  • IEEE-802.11 -based WLANs have become popular at an unprecedented rate.
  • WLAN supports a variety of data transfer modes including (but not only) file transfer, emails, web browsing and real-time applications such as audio and video applications.
  • the evolving IEEE 802.11 standards specify several transmission (TX) schemes that can be used by a wireless transceiver.
  • TX schemes which deploy multiple TX antennas (some, but not all, also requiring multiple RX antennas on the receiver side), which are so called MIMO modes.
  • Multiple TX antennas can be utilized in different advantageous ways, such as spatial TX diversity for improving the link reliability and performance, beamforming (BF), i.e. focusing the radiated power in the direction(s) of target receiver(s) (and/or suppressing it in undesirable directions, for reducing unwanted interference to non-targeted receivers), and/or spatial multiplexing (SM), i.e. sending multiple data streams simultaneously over the same time-frequency resources, either to the same receiver or to different ones.
  • BF beamforming
  • SM spatial multiplexing
  • a multi-antenna wireless transceiver is provided.
  • the wireless transceiver may be a multi-antenna wireless access point (AP).
  • AP wireless access point
  • the wireless transceiver comprises a communication interface with an array of antennas.
  • the communication interface is configured to receive at a plurality of times channel state information from a plurality of further wireless transceivers, including channel state information at a first time and channel state information at a second time.
  • the communication interface is further configured to operate the array of antennas with an adjustable precoding configuration.
  • the plurality of further wireless transceivers may include single antenna or multi-antenna wireless stations.
  • the wireless transceiver further comprises a processing circuitry configured to perform phase alignment of the channel state information at the second time with the channel state information at the first time and to predict a channel state for an upcoming transmission at a third time based on the phase alignment of the channel state information, i.e. the phase aligned channel state information.
  • the processing circuitry of the wireless transceiver is further configured to adjust the adjustable precoding configuration for the upcoming transmission based on the predicted channel state at the third time.
  • the communication interface of the wireless transceiver is further configured to transmit at a plurality of times a channel sensing signal, in particular a NPD frame, to the plurality of further wireless transceivers for allowing the plurality of further wireless transceivers to determine the channel state information and/or transmit the channel state information to the wireless transceiver.
  • the wireless transceiver is a wireless access point or base station.
  • the wireless transceiver is configured to operate in accordance with the IEEE 802.11 WLAN standard or a standard evolved therefrom.
  • the channel state information received from the plurality of further wireless transceivers is compressed and wherein the processing circuitry is configured to decompress the compressed channel state information.
  • the communication interface is configured to communicate with the plurality of further wireless transceivers using a plurality of frequency sub-carriers and wherein the channel state information comprise channel state information only for a subset of the plurality of frequency sub-carriers.
  • the processing circuitry is configured to perform phase alignment on the channel state information for each frequency sub-carrier of the subset of the plurality of frequency sub-carriers separately.
  • the channel state information received from the plurality of further wireless transceivers at a time n is based on a singular value decomposition of a channel response matrix and comprises one or more of the first columns of the matrix V n and one or more of the first diagonal elements of the matrix S n .
  • the processing circuitry is configured to determine, based on the channel information at the time n, a partial channel response matrix , wherein k denotes a frequency sub-carrier index.
  • the processing circuitry is configured to determine a unitary matrix W that minimizes the following equation: wherein the operation diag((7) transforms a vector into a diagonal matrix whose diagonal entries equal that vector.
  • the processing circuitry is configured to determine a singular value decomposition of the matrix and to determine the unitary matrix W as .
  • the unitary matrix W is a diagonal unitary matrix.
  • the processing circuitry for aligning the channel state information the processing circuitry is configured to apply the matrix W to the partial channel response matrix . In a further possible implementation form of the first aspect, the processing circuitry is configured to predict the channel state for an upcoming transmission based on the following equation: wherein: and denote the aligned channel state information at the first and second time,
  • denotes a time difference between the first and second time
  • T denotes a time difference between the second time and the upcoming transmission
  • denotes a parameter.
  • the parameter a is a function of the aligned channel state information at the first and second time and channel estimation error variances at the first and second time.
  • the processing circuitry is configured to determine the parameter a based on the following equations: wherein: and denote the channel estimation error variances at the first and second time, N DSC denotes the decimated number of sub-carrier frequencies,
  • N r denotes the number of receiver antennas of one of the plurality of further wireless transceivers
  • N s denotes the number of spatial streams for the one of the plurality of further wireless transceivers for the upcoming transmission.
  • the processing circuitry is configured to align the channel state information at the first time and the channel state information at the second time based on a parametrized geometrical channel model and to predict the channel state for the upcoming transmission based on the parametrized geometrical channel model.
  • the parametrized geometrical channel model is defined by one or more parameters of the parametrized geometrical channel model and wherein the processing circuitry is configured to determine the one or more parameters of the parametrized geometrical channel model based on the channel state information.
  • the channel state information received from the plurality of further wireless transceivers at a time n is based on a singular value decomposition of a channel response matrix and comprises the matrices U n and V n and the diagonal elements of the matrix S n .
  • the processing circuitry is configured to determine the one or more parameters of the parametrized geometrical channel model on the basis of the following equation: wherein: ⁇ i,r denotes a complex number accounting for the i-th path complex gain with respect to the r-th antenna, s(t - T i ) T denotes the transmitted signal vector with the i-th entry corresponding to i-th antenna, denotes the angle of departure, T i denotes the time-of-flight, x( ⁇ ⁇ ) denotes the steering vector, and f m cos( ⁇ i ) denotes a term accounting for a Doppler shift of the i-th path.
  • the processing circuitry is configured to determine, based on the parametrized geometrical channel model, a plurality of candidate paths.
  • the one or more parameters of the parametrized geometrical channel model comprise an angle of departure (AOD) and a time-of-flight (TOF) associated with each candidate path, wherein the processing circuitry is configured to determine the plurality of candidate paths on the basis of a plurality of local maxima of a spectrum function (also referred to as cost function) depending on the angle of departure and the time-of-flight.
  • AOD angle of departure
  • TOF time-of-flight
  • the processing circuitry is further configured to determine a peak prominence for each of the plurality of local maxima of the function depending on the angle of departure and the time-of-flight and to determine the plurality of candidate paths on the basis of the plurality of peak prominences.
  • the one or more parameters of the parametrized geometrical channel model further comprise a complex attenuation (also referred to as complex gain) for each channel path and a Doppler shift, wherein processing circuitry is further configured to reduce the number of candidate paths on the basis of an iteratively determined least squares error.
  • the processing circuitry is further configured to correct the Doppler shifts of the plurality of candidate paths on the basis of an average of a minimum Doppler shift and a maximum Doppler shift of the plurality of candidate paths.
  • the processing circuitry is further configured to adjust the prediction of the channel state for the upcoming transmission on the basis of an adjustment between the plurality of time-of-flights of each of the plurality of candidate paths at the first time and the plurality of time-of-flights of each of the plurality of candidate paths at the second time.
  • the processing circuitry is further configured to estimate one or more model errors of the parametrized geometrical channel model at the first time and the second time and to predict the one or more model errors of the parametrized geometrical channel model for the upcoming transmission, wherein the processing circuitry is further configured to predict the channel state for the upcoming transmission based on the parametrized geometrical channel model and the one or more predicted model errors.
  • the processing circuitry is further configured to predict the one or more model errors of the parametrized geometrical channel model for the upcoming transmission using a linear temporal prediction and to weight the one or more predicted model errors by a weighting parameter b.
  • a method of operating a wireless transceiver comprising an array of antennas.
  • the method comprises the steps of: receiving at a plurality of times channel state information from a plurality of further wireless transceivers, including channel state information at a first time and channel state information at a second time; performing a phase alignment of the channel state information at the second time with the channel state information at the first time; predicting a channel state for an upcoming transmission based on the phase aligned channel state information; and adjusting, based on the predicted channel state for the upcoming transmission, a precoding configuration for operating the array of antennas.
  • Fig. 1 shows a MU-MIMO WLAN communication system, including a wireless access point in communication with a plurality of wireless stations;
  • Fig. 2 shows the dependency of the maximal total goodput on the SNR in an exemplary MU-MIMO WLAN communication system;
  • Fig. 3 is a sequence diagram illustrating exemplary sounding procedures implemented by a wireless access point according to an embodiment
  • Fig. 4 shows a further MU-MIMO WLAN communication system, including a wireless access point in communication with a plurality of wireless stations;
  • Fig. 5 shows a schematic diagram illustrating processing blocks implemented by a wireless transceiver according to an embodiment
  • Figs. 6a and 6b show schematic diagrams illustrating processing blocks implemented by a wireless transceiver according to a further embodiment
  • Fig. 7 shows a contour plot illustrating a peak search implemented by a wireless transceiver according to an embodiment
  • Figs. 8a-e illustrate the performance of a wireless transceiver according to an embodiment
  • Fig. 9 is a flow diagram illustrating a wireless transmission method according to an embodiment.
  • a disclosure in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa.
  • a corresponding device may include one or a plurality of units, e.g. functional units, to perform the described one or plurality of method steps (e.g. one unit performing the one or plurality of steps, or a plurality of units each performing one or more of the plurality of steps), even if such one or more units are not explicitly described or illustrated in the figures.
  • a specific apparatus is described based on one or a plurality of units, e.g.
  • a corresponding method may include one step to perform the functionality of the one or plurality of units (e.g. one step performing the functionality of the one or plurality of units, or a plurality of steps each performing the functionality of one or more of the plurality of units), even if such one or plurality of steps are not explicitly described or illustrated in the figures. Further, it is understood that the features of the various exemplary embodiments and/or aspects described herein may be combined with each other, unless specifically noted otherwise.
  • FIG. 1 shows a MU-MIMO WLAN communication system 100, including a wireless transceiver 110, in particular a wireless access point (or short AP) 110 according to an embodiment in communication with a plurality of wireless stations (or short ST A) 120.
  • the AP 110 is configured to transmits simultaneously to the plurality of wireless stations 120 using precoding so that the transmission to different stations 120 does not interfere with each other.
  • the precoder is calculated so that the transmission to one STA will create nulling at the other ST As (also known as null-steering).
  • the AP 110 For using MU-MIMO downlink transmission the AP 110 needs to obtain some information about the respective communication channel between the AP 110 and the STAs 120. In conventional WiFi (such as 802.11 ax) this is achieved by the sounding procedure described in the following. Sounding procedure also known as channel sounding generally refers to procedures designed to measure channel performance dynamically (on very wide channels - typically > 500 MHz wide, operating in the mmWave spectrum; 25 to greater than 50 GHz), and using MIMO and Beamforming transmissions.
  • the AP 110 transmits a short packet called NDP to the STAs 120.
  • the STAs 120 estimate the channel using the NDP.
  • the STAs 120 transmit back to the AP 110 partial channel information (more specifically the V from SVD and SNRs, in fact, quantized and decimated).
  • the AP 110 calculates a precoder based on the channel information.
  • the AP 110 uses the precoder when transmitting subsequent data packets until a more up to date channel information is available (after a new sounding procedure).
  • the time from the transmission of an NDP to the transmission of a precoded packet may take several msec. If the communication channel is static during this period of several msec, then conventional MU-MIMO works very well. However, even a relatively small mobility of 1-3 km/h (for instance, due to the motion of the AP 110 and/or one or more of the STAs 120) may turn out to cause a significant degradation of the MU-MIMO transmission.
  • the reason for the high sensitivity of DL MU-MIMO is that the nulling is very sensitive to channel variations so that the transmission to the other STAs 120 is not nulled-out and causes inter-user interference. This is different from the UL MU-MIMO case (open loop) or DL SU-MIMO, which are much more robust to mobility.
  • This approach may be regarded as a zero order hold (ZOH) scheme.
  • ZOH zero order hold
  • An AP should try to find the "sweet spot” that would maximize the overall throughput (for a given SNR), going over combinations of MCS, number of stations/users and temporal distances between NDPs. Still a conventional AP is not able to support high throughputs with this approach in even moderate mobility scenarios.
  • embodiments disclosed herein address the mobility problem described above.
  • embodiments disclosed herein are based on the idea of performing channel prediction based on the two most recent NDPs (e.g. from the two most recent sounding procedures) instead of using just the last NDP.
  • the channel may predicted for the time corresponding to the transmission of a DL MU- MIMO packet. It can be updated several times between sounding procedures, and even be updated within a data packet. Each time a new predicted channel is available, the precoder is updated (using one of possible precoding schemes such as ZF, NSP, and GMD and their possible combinations).
  • the wireless transceiver in particular wireless AP 110 illustrated in figure 1 comprises a communication interface 113 comprising the array of antennas 113a-n (in figure 1 the array of antennas comprises, by way of example, 4 antennas 113a-n).
  • the communication interface 113 of the AP 110 may further comprise analog and/or digital signal processing circuitry for processing RF and/or digital signals.
  • the communication interface 113 is configured to receive at a plurality of times channel state information from the plurality of wireless stations 120, including channel state information at a first time and channel state information at a second time, and to operate the array of antennas 113a-d with an adjustable precoding configuration, i.e. an adjustable precoder using a precoding or beamforming communication scheme, as defined, for instance, by a standard, in particular the IEEE 802.11 WLAN standard or a standard evolved therefrom.
  • an adjustable precoding configuration i.e. an adjustable precoder using a precoding or beamforming communication scheme, as defined, for instance, by a standard, in particular the IEEE 802.11 WLAN standard or a standard evolved therefrom.
  • the wireless AP 110 further comprises a processing circuitry or a processor 111 for processing digital data.
  • the processor 111 may be implemented in hardware and/or software, which when executed causes the wireless multi-antenna transceiver 110 to perform the functions and methods described herein.
  • the hardware may comprise digital circuitry, or both analog and digital circuitry.
  • Digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field- programmable arrays (FPGAs), digital signal processors (DSPs), or general-purpose processors.
  • the wireless AP 110 may further comprise an electronic memory 115 for storing digital data, such as the channel state information received at the first time and the channel state information received at the second time.
  • the processing circuitry 111 of the AP 120 is configured to perform a phase alignment of the channel state information at the second time with the channel state information at the first time and to predict a channel state for an upcoming transmission at least at a third time based on the phase aligned channel state information.
  • the processing circuitry 111 of the AP 120 is configured to estimate, based on the information about the channel state at the first and second times, the channel state at the third time and possibly further times, such as a fourth time, a fifth time and the like.
  • the processing circuitry 111 of the AP 120 is further configured to adjust the adjustable precoding configuration for the upcoming transmission based on the predicted channel state at the third time and possibly further times.
  • the processing circuitry 111 of the AP 120 is configured to adjust, i.e. set the precoder for operating the array of antennas 113a-n at the third time and possibly further times based on the channel state predicted for the third time and the possibly further times as well as the respective time differences.
  • the first main embodiment of the wireless AP 110 is based on an advanced linear prediction (A- LP) scheme with relatively low-complexity, while the second main embodiment is based on a parametric based approach using a Sum of Sines, SOS, channel model in combination with a 2-dimensional MUSIC algorithm with spatial smoothing (also known as SpotFi algorithm).
  • A- LP advanced linear prediction
  • SOS Sum of Sines
  • SOS channel model
  • 2-dimensional MUSIC algorithm with spatial smoothing also known as SpotFi algorithm
  • the basic idea is to first estimate the TOFs (time of flight) and AODs (angle of departure) and/or AOAs (angle of arrival) of all paths using known array processing techniques (such as ESPRIT and compressed sensing) and then the remaining parameters such as the Dopplers and complex gains of the paths are estimated based on LS type estimation (several variants exist such as adding the Dopplers to the initial joint estimation).
  • array processing techniques such as ESPRIT and compressed sensing
  • the advanced linear prediction scheme implemented by the wireless AP 110 according to the first main embodiment is robust against CFO/timing offset impairments, can be applied on partial channel information (like in the WiFi standard), and essentially has no degradation when applied to low mobility/low SNR scenarios.
  • the SOS model based approach implemented by the wireless AP 110 according to the second main embodiment can handle many paths (which makes it suitable for WiFi channels) and is rather robust to deviations from the assumed model.
  • the AP 110 may use an alignment algorithm to align the partial channel information from the current sounding process with the partial channel information from a previous sounding process.
  • the AP 110 may use the (aligned) partial channel information from the last two channel sounding processes to predict, using an advanced linear based method, the partial channel at the time of transmission of the precoded packet.
  • the AP 110 may update the channel prediction also within a packet (important for long packets). For each new predicted channel, the AP 110 may update, i.e. adjust the precoder for operating the array of antennas 113a-n.
  • the prediction may be done in such a way as to guarantee that there is no degradation, i.e. negative gain in a low mobility/low MCS scenario relative to the conventional ZOH scheme.
  • the ST As 120 may compress, e.g. quantize the channel state information for decimated SCs so that the full channel may be reconstructed by the AP 110, and transmit the compressed/quantized channel state information as the feedback during the sounding procedures.
  • the AP 110 may use the feedback of the current sounding procedure to determine the full channel information for decimated SCs.
  • the AP 110 may further use an alignment algorithm (by estimating TOFs) to align the full channel from the current sounding process with that of the previous sounding process. The alignment allows to mitigate or remove CFO/timing offset impairments.
  • the AP 110 may use the SpotFi based scheme on the channel from the two last NDPs to estimate the AODs and TOFs of the candidate paths provided by the SpotFi scheme.
  • the AP 110 may use “peak prominences” and an iterative LS (least squares) estimation to decide on the true peaks and estimate the Dopplers and complex gains of the paths.
  • the AP 110 may use the estimated geometrical channel model parameters, such as AODs, TOFs, Dopplers, and complex gains to calculate model errors corresponding to the two most recent channel state information.
  • the AP 110 may use the estimated parameters of the geometrical channel model and the model errors to predict the channel at the time of transmission of the precoded packet, i.e. at the third time.
  • the AP 110 may update the channel prediction also within a packet (important for long packets).
  • the AP 110 may perform a SVD (singular value decomposition) and may update, i.e. adjust the precoder for operating the array of antennas 113a-n.
  • SVD singular value decomposition
  • the idea in this second main embodiment is to detect slowly varying parameters of the SOS geometric channel model, which are quasi constant between subsequent sounding procedures and payload (using SpotFi) and predict the channel using the geometric channel model.
  • FIG. 3 is a sequence diagram illustrating a sounding procedure implemented by the wireless transceiver, in particular wireless AP 110 according to an exemplary embodiment in compliance with the 802.11 ax WLAN standard.
  • the AP 110 uses the two most recent sounding procedures to predict the channel.
  • each sounding procedure may comprise the emission of a NDPA frame, a NDP frame and a trigger frame by the wireless AP 110 and, in response, thereto, the channel stale feedback from the STAs 120.
  • the AP 110 is configured to adjust the precoder for operating the array of antennas 113a-n and thereby sending data packets to the STAs 120 using MU-MIMO beamforming.
  • the prediction/calculation of the precoder can be updated several times, each new precoded packet or within a packet.
  • Figure 4 shows the wireless communication system 100, including the wireless AP 110 and the wireless STAs 120 in a scenario including communication with a line-of-sight
  • the scenario shown in figure 4 provides an intuitive explanation for the SOS geometrical channel model used in the second main embodiment, which may be described by the following equation: where y r is the received signal at the r-th antenna 121 , s is the transmitted signal vector with the /- th entry corresponding to the i-th TX antenna 113i, and is the steering vector of the antenna array 113a-n of the AP 110. This may be the steering vector of a ULA, but may be applicable to other arrangements of the antennas 113a-b as well, such as 2 dimensional or 3 dimensional arrangements.
  • ⁇ i,r , ⁇ i , ⁇ i , ⁇ i are all slowly varying (i.e. can be assumed to remain constant over a duration of a few msec). So although y r itself may change rapidly, it is based on a parametric model whose parameters are slowly varying.
  • ⁇ i and ⁇ i are the angle of arrival (AOD) and time of flight (TOF), respectively, corresponding to the i-th path.
  • AOD angle of arrival
  • TOF time of flight
  • ⁇ i,r is a complex number accounting for the i-th path complex gain with respect to the r-th antenna.
  • the term f m cos( ⁇ i ) accounts for the Doppler shift of the i-th path and depends on the velocity of the STA 120 and its direction with respect to the AP 110.
  • the AP 110 may comprise N T TX antennas 113a-n and initiates a sequence of sounding procedures with N a ST As 120. After the initiation of each sounding procedure, the AP 110 transmits a NDP frame to the STAs 120.
  • the following description will focus without loss of generality on the (n-1)- th and the n-th sounding procedure, whose NDPs are transmitted at times 0 (i.e. the first time) and ⁇ (i.e. the second time), respectively.
  • N s i.e. the first time
  • i.e. the second time
  • N R ⁇ N T channel matrices based on the NDP received from the AP 110.
  • the STA 120 sends as feedback the channel state information to the AP 110.
  • the STA 120 calculates for each of the decimated SCs the SVD decomposition , where U n and V n are N R ⁇ N R and N T ⁇ N R unitary matrices, respectively, and D n is a N R ⁇ N R real diagonal matrix , whose diagonal elements are ordered from the largest to the smallest.
  • AP 110 as feedback channel state information.
  • STA side can be calculated easily as — , where is the estimated noise variance during the transmission of the NDP, N LTF is the number of LTF symbols used for the NDP, and ⁇ is the frequency- domain (FD) channel estimation processing gain.
  • AP 110 as , where is an estimate for the noise variance at the STA 120 calculated by the AP 110 based on the SNR values per SCs or average SNR already transmitted by the STA 120 according to the WiFi standard, and is a typical value for the FD channel estimation processing gain in WiFi (such as a value of 4).
  • Figure 5 shows a schematic diagram illustrating processing blocks implemented by the wireless AP 110 for the first main embodiment, i.e. where the AP 110 uses an alignment scheme to align the partial channel information from the current sounding process with the partial channel information from a previous sounding process (herein referred to as advanced linear prediction, A-LP).
  • A-LP advanced linear prediction
  • the STA 120 takes from V n the first N s columns, denoted , and the first N s diagonal elements of D n denoted (corresponding to SNR per stream) compresses and quantizes them, possibly (but not necessarily) in the same manner as in the current WiFi standard.
  • the compressed/quantized quantities and are reduced partial channel information. Compression can be done such that the last row of is real-valued.
  • the AP receives the partial channel state information from the STA and decompresses it (processing block 501). This may yield for the n-th sounding procedure and for the /c-th decimated SC.
  • the processing circuitry 111 of the AP 110 may implement an alignment procedure between the n-th NDP and (n-1)- th NDP (as illustrated in processing block 503 of figure 5).
  • the alignment allows compensating for the possible discontinuities caused by the STA 120 when determining the SVD and/or compressing .
  • the alignment implemented by processing block 503 may also handle a phase/slope offset between these NDPs caused by impairments such as CFO and timing offset. Indeed, CFO and timing offset may cause a common phase and slope error in the channel in the FD, respectively, both of which may advantageously be removed by the alignment algorithm described in the following.
  • the alignment algorithm as implemented by the processing block 503 may be done separately per each decimated SC as follows.
  • the processing circuitry 111 of the AP 110 may be configured to determine a unitary matrix A k that minimizes the following equation: where the diag operation on a vector gives a diagonal matrix whose diagonal equals that vector.
  • the solution to this minimization problem is to perform the singular value decomposition, SVD, U' , S' , V' of , where U' and V' are unitary matrices and S' is a diagonal matrix (all are N s ⁇ N s matrices).
  • a k U'V' H .
  • This alignment algorithm implemented by the processing circuitry 111 of the AP 110 according to an embodiment has a low complexity since N s , i.e. the number of streams per STA is usually small.
  • an even lower complexity alignment algorithm may be implemented by the AP 110 according to an embodiment, namely an algorithm that does not require the SVD by further restricting the matrix A to be a diagonal matrix (but at the price of some performance loss).
  • This simpler alignment algorithm amounts to finding a diagonal matrix A with unit magnitude diagonal elements such that the equation above is minimized. This is equivalent to finding a phase ⁇ i per stream i such that is maximized, where denotes the i-th column of .
  • the channel prediction can be performed. Let and . Let T denote the time the channel is predicted for (i.e., the time difference to the (n-1)-th NDP). Let denote the (partial) channel prediction for time T .
  • the processing circuitry 111 of the AP 110 may be configured to determine ⁇ on the basis of the following equation: where ⁇ is a function of (k goes over all decimated SCs) and is some measure of the variations in the channel between the two NDPs and ⁇ min is a non-positive number.
  • the processing circuitry 111 of the AP 110 may be configured to determine a using the equation above, but separately for each TX antenna or per stream (or both).
  • the processing circuitry 111 of the AP 110 may be configured to determine ⁇ using ⁇ min based on the following equation: In a further embodiment based on the A-LP scheme, the processing circuitry 111 of the AP 110 may be configured to determine ⁇ using ⁇ based on the following equation: wherein N DSC denotes the number of decimated SCs, and ⁇ is a function of (and k goes over all decimated SCs).
  • the processing circuitry 111 of the AP 110 may be configured to determine a using the following equation:
  • the above choices for ⁇ described above may eliminate negative gain in the case the channel estimation error is not negligible relative to channel variations (low mobility/low SNR). An ⁇ close to 1 may be obtained for high mobility and SNR. Indeed, if the channel variations are significantly larger than the channel estimation error variance, then and ⁇ ⁇ 1.
  • may assume a negative value, which accounts for some averaging between the NDPs.
  • the processing circuitry 111 of the AP 110 may use this information for interpolated to all SCs to yield . However, before this interpolation in the frequency domain (FD) is done, the processing circuitry 111 of the AP 110 may be configured to perform a phase alignment over the SCs (dubbed "FD alignment") compensating for the phase discontinuities caused by the SVD, similarly to the case of the ZOH scheme.
  • FD alignment phase alignment over the SCs
  • the AP 110 is configured to determine the precoder on the basis thereof, which is used for subsequent transmissions of data packets until a new prediction is available. Whatever precoding scheme that is applicable in the ZOH case is also applicable here. Note that the AP 110 may be configured to update for each DL
  • Figures 6a and 6b show schematic diagrams illustrating processing blocks implemented by the wireless AP 110 for the second main embodiment, i.e. where the AP 110 determines slowly varying parameters of the model SOS geometric channel model using, for instance, the SpotFi algorithm, and predicts the channel state on the basis thereof.
  • the processing blocks 613, 615, 617 and 618 relate to the SpotFi algorithm
  • the processing blocks 601 , 605 and 611 are related to impairment (CFO/timing) corrections
  • the processing blocks 607 and 621-629 are related to additional processing stages providing further improvements, such as the ability to handle many paths and making the scheme more robust with respect to deviations from the SOS channel model.
  • the STA 120 takes the full matrices U n , V n and the vector d combat containing the diagonal of D n compresses and quantizes them, and send them to the AP 110 as feedback.
  • the quantization of V n and d n can be done possibly in a similar manner as done in the current WiFi standard.
  • the compressed/quantized quantities U n , V n , and d fit are reduced full channel information.
  • the AP 110 receives the full channel state information and decompresses it.
  • the AP 110 calculates for the NDPs of the (n-1)-th and the n-th sounding procedures, the full channel estimates and , respectively.
  • an alignment procedure between the n-th NDP and n-1-th NDP is performed by the AP 110.
  • the alignment may be advantageous, in case there is a phase offset and slope difference between these NDPs due to impairments such as CFO and timing offset.
  • the processing circuitry 111 of the AP 110 implements a pre-processing stage that estimates the phase and delay change (slope) between the NDPs and compensate for these impairments, for instance, the FFT based PSC (phase and slope correction) block 601 described in more detail in the following.
  • a pre-processing stage that estimates the phase and delay change (slope) between the NDPs and compensate for these impairments, for instance, the FFT based PSC (phase and slope correction) block 601 described in more detail in the following.
  • the FFT based PSC (phase and slope correction) block 601 is configured to find a solution for the following LS (least squares) problem: Mathematically, it can be shown that this is equivalent to the following problem:
  • This problem can be decomposed into two parts, namely (a) determine where , and (b) then calculate
  • N OSFFT MN FFT for some M . Then can be searched on a grid (unit is samples in original sampling rate) by performing an oversampled IFFT of size N OSFFT and finding the maximum of the magnitude.
  • This solution is an approximation and may require a large IFFT to provide accurate results.
  • f k may be extended from decimated SCs to oversampled FFT size by zero padding.
  • the maximum peak location accounts for the fractional timing offset and the phase of the peak accounts for phase offset.
  • the channel of second NDP may be corrected by the processing circuitry 111 of the AP 11o as follows for the decimated SCs:
  • the FFT based PSC block 601 advantageously performs the coarse phase/timing correction.
  • a further processing stage may be added, whose purpose it is to further align the NDPs timing relative to each other (i.e. resolve the small residual slope difference).
  • this additional stage may be provided by the "Advanced Slope correction" block 605 shown in figure 6a and described in more detail in the following.
  • NAOD normalized AOD
  • NTOF normalized TOF
  • Doppler shift of the i-th path respectively
  • the antenna arrays 113a-n of the AP 110 is ULA (as is apparent from the expression for v AOD ).
  • the processing circuitry 111 of the AP 110 is configured to estimate the N path NAOD ⁇ i and NTOF ⁇ i using the SpotFi algorithm (i.e. a well-known array signal processing algorithm based on MUSIC algorithm). Further details about the SpotFi algorithm may be found, for instance, in M. Kotaru, K. Joshi, D. Bharadia, and S. Katti, "Spotfi: Decimeter level localization using WiFi," in Proc. ACM Conf. Special Interest Group Data Commun., 2015, pp. 269-282.
  • SCs in jumps of N g not all are available, e.g., the zero SCs around the DC tone.
  • the processing circuitry 111 is configured to perform interpolation so that the channel estimates will be available on each N g SCs except on the guard bands. This may be done using linear interpolation for example.
  • the resulting number of SCs after the interpolation is denoted here as N sc .
  • the processing circuitry 111 of the AP 110 implementing the SpotFi algorithm is configured to determine candidate paths of the channel in the NAOD and NTOF domain by performing the steps described in the following in more detail.
  • the SpotFi-based scheme is based on , which are the outputs of the Advance Slope correction block 605, where and are the aligned channel estimates for SC k at time 0 and ⁇ , respectively, i.e., corresponding to the (n-1)- th and n-th NDPs, respectively.
  • C k be a N R ⁇ N T matrix, which in an embodiment is the input to the SpotFi algorithm implemented by the processing circuitry 111 of the AP 110, where k is the SC index.
  • C k is a function of .
  • One option is for
  • NDP n-1 and for NDP n are identical and for NDP n.
  • Another option is to use , which is expected to be good for moderate
  • Doppler shifts and gaps For example, assume a velocity of 3 km/h, which implies a Doppler shift ⁇ 16Hz (at the high 5Ghz band), and 8 ms gap. Then the rotation in degrees during the 8 ms gap is about 45 degrees. This means that when averaging 2 NDPs, the noise is reduced by factor of 3dB and averaging of each path behaves like .
  • the SpotFi algorithm implemented by the processing circuitry 111 of the AP 110 is configured to create the correlation matrix of the smoothed CSI.
  • the smoothing of the CSI or channel estimates may be done on both the SCs and the antennas (spatial smoothing). Spatial smoothing assumes an antenna array 113a-n in the form of a ULA or other specific arrays, which can be transformed to a ULA.
  • CSI SS H .
  • Ris a matrix of size M SC M T by M SC M T .
  • R 2 may be created by flipping R 1 from left to right and from up to down. This latter calculation of the matrix R is referred to as symmetric smoothed CSI.
  • S may be constructed by the processing circuitry 111 of the AP 110 as , where S i is constructed from the CSIs related to the i-th STA antenna as in the case for 1 antenna 121 of the STA 120 described above.
  • N sig i.e. the number of signals for which NAOD and NTOF is estimated, where N sig should desirably equal the number of channel paths.
  • MDL Minimum Description Length
  • AIC Alignment Information Criterion
  • a more heuristic approach may be employed by determining N sig as the number of eigenvalues that are above a threshold, provided that this number does not exceed another threshold.
  • the eigenvectors corresponding to the remaining eigenvalues i.e., after excluding the N sig largest eigen- values
  • the processing circuitry 111 of the AP 110 may be configured to calculate the matrix v that is created by concatenating the N sig eigenvectors corresponding to the N sig largest eigenvalues.
  • V is the output of the PCA of R in which the dimension of R is reduced to N sig .
  • the processing circuitry 111 of the AP 110 may compute a spectrum as where ( is Kronecker product).
  • v TOF ( ⁇ ) denotes the vector whose entries ar e , where k goes over all active SCs.
  • the processing circuitry 111 of the AP 110 may use the matrix v (which reduces complexity) for determining the SpotFi spectrum, because it can be shown that the following equation holds: '
  • processing circuitry 111 of the AP 110 is configured to determine the local maxima of the spectrum q( ⁇ , ⁇ ) . To this end, in an embodiment, the processing circuitry
  • the 111 of the AP 110 is configured to determine q( ⁇ , ⁇ ) on a dense grid of the parameters ⁇ , ⁇ .
  • the processing circuitry 111 of the AP 110 is configured to determine the local maxima, i.e. peaks of the function q( ⁇ , ⁇ ) .
  • these peaks may be restricted to be above a certain threshold, e.g., 60dB or less below the global maximum. The reason is that there may be many small false peaks due to, for instance, the noise.
  • the processing circuitry 111 of the AP 110 may consider the peaks determined in the previous stage as candidate peaks, wherein N CAP denotes the number of candidate peaks.
  • Figure 7 shows a typical, but exemplary contour plot of the function q( ⁇ , ⁇ ) in the AOD-
  • TOF parameter plane In figure 7 un-normalized AOD and TOF values are used so that the physical interpretation is clear.
  • the respective true location of each AOD-TOF paths is shown as a circle, and is unknown to the AP.
  • the dots show the estimated AOD-TOF peaks.
  • the channel is TGac-D NLOS having 26 true paths.
  • the processing circuitry 111 of the AP 110 may implement additional processing blocks that are not part of the standard SpotFi algorithm.
  • SpotFi algorithm the person skilled in the art will appreciate that the same functionality may be provided by other available algorithms as well, such as other related array processing algorithms (such as 2-dimensional root MUSIC or ESPRIT) that can provide the candidate channel paths.
  • Embodiments disclosed herein make use of the SpotFi algorithm since it provides the spectrum function q( ⁇ , ⁇ ) , while other algorithms provide the candidate channel paths location but not necessarily a spectrum associated with them. However, clearly q( ⁇ , ⁇ ) can be calculated on the candidate paths location even if they are first found by another algorithm.
  • some of the candidate peaks determined by the processing circuitry 111 of the AP 110 implementing, for instance, the SpotFi algorithm may be false peaks. It turns out that it is not necessarily the peak strength (magnitude of
  • the processing circuitry 111 of the AP 110 may be configured to approximate the peak prominence heuristically, wherein the prominence of the i -th candidate peak may be denoted as p i .
  • the approximated prominence p is in fact an upper-bound of the true prominence.
  • the contour line encircling the /- th peak must intersect the line connecting the /-th peak with any higher peak.
  • a lower contour line may intersect this line but not encircle the i-th peak (this is why it is an upper bound on the prominence). The reason for choosing the closest higher peak is to make the probability of the latter case smaller. If the candidate channel paths are not determined by the SpotFi algorithm, but by another related array processing algorithm, and q( ⁇ , ⁇ ) is not available on the line connecting peaks, it can be calculated on the fly where it is necessary.
  • the processing circuitry 111 of the AP 110 may be configured to reduce the number of candidate peaks from N CAP candidate peaks to N p peaks , and the remaining parameters f i and ⁇ i (corresponding to the I -th peak) are estimated.
  • the idea is to use peak prominence and an iterative LS estimation to find the peaks that improve the LS error and remove the false peaks.
  • f denote the vector whose i -th entry is .
  • the LS based estimation, calculating and the estimates for f and A may be implemented by the processing circuitry 111 in the following way: Step 1 : construct and , where dim(x) is the dimension of the vector x .
  • Step 2 calculate , where o denotes Hadamard product.
  • Step 3 calculate , where lis a vector with all entries equal 1 .
  • Step 4 calculate
  • Step 6 calculate
  • the above function measures the least squares error over the 2 NDPs.
  • the 1s and gf functions may be used in iterative way described below.
  • p th denote the low prominence threshold.
  • a peak ( ⁇ i , ⁇ i ) is said to be a low prominence peak if p i ⁇ p th .
  • Puncturing the entry of a scalar gives the empty vector (whose dimension is 0).
  • the parameter / used below is the LS refinement threshold, whose value is less than 1 (e.g., 0.79). Let and be constructed from the prominent peaks by setting their i -th entry to ⁇
  • Step 5 Calculate and Step 6: If go to Step 12
  • Step 7 Calculate
  • Step 8 puncture the s entry from r and put in r m Step 9: , and
  • the iterative LS estimation process may end, when either r m is empty or no peak in r m decreases the LS error by the specified threshold.
  • the processing circuitry 111 of the AP 110 may be configured to implement an efficient calculation of the LS from one iteration to the following by using the block matrix inversion formula.
  • An initial is iteration may be done in Step 2 and one obtains , and .
  • m ⁇ 1 the block matrix inversion formula
  • each LS iteration may be stored, for instance, in the memory 115 to be used in the next iteration.
  • the processing circuitry 111 of the AP 110 is further configured to implement a processing block for the geometrical channel estimation and prediction.
  • this block is configured to calculate , based on , and using 0, respectively, where are the shifted Dopplers, which are calculated by the Advance Phase correction block described below.
  • the geometrical channel estimation and prediction block provides a prediction for the channel.
  • this prediction may be not robust and may suffer from missed paths, in particular for channels with a large number of paths.
  • the errors provided by the channel model may be used. This approach is based on the idea to consider the resulting estimation error in each NDP, i.e. , where is an output of the Phase Correction block (see below). These errors may contain missed paths, the noise, and in some cases false peaks detected by the SpotFi algorithm. Instead of ignoring these errors, a linear extrapolation may be performed in the following form:
  • the processing circuitry 111 of the AP 110 is further configured to use the model predicted error in the final prediction: where ⁇ is a function of .
  • ⁇ ⁇ 1 is advantageous is two-fold.
  • the linear interpolation may be biased, i.e., the result is over estimated (on average) by some scaling factor.
  • E T which originated from the linear interpolation of , which, in turn, originated from the SOS Geometrical channel prediction, without compensating for the scaling does not improve performance.
  • the SOS geometrical channel prediction estimates all the paths sufficiently well (which can happen in channels with few paths), the addition of the E T -term only adds noise and causes degradation.
  • the processing circuitry 111 of the AP 110 may use the value , where: and ⁇ is a function of , and approaches 0 when the model errors are mainly due to the channel estimation errors and approaches 1 when the model errors are significantly larger than the channel estimates errors.
  • the processing circuitry 111 of the AP 110 is further configured to implement an advance slope correction processing block.
  • This block may use a MUSIC type algorithm for each of the NDPs for finding the TOFs of each NDP and trying to compensate for the slope difference between NDPs and also centers of the TOFs relative to the SpotFi grid used later.
  • the MUSIC algorithm implemented in the preprocessing stage is 1 -dimensional, only on the TOF (The TX antennas are averaged).
  • the output for the nth NDP is TOFs and prominence of each candidate peak .
  • the TOFs and of the (n-1)- th and n-th NDP, respectively may be merged, in the sense of finding i, j such that and correspond to the same path. For each pair also a prominence may be calculated as .
  • L denote the number of such pairs (which can be a smaller number than the number of peaks found in each of the NDPs). Note that for these pairs, in general, and should differ due to a residual slope difference.
  • the pairs for which their prominence is above a certain threshold are used to calculate vectors ⁇ ⁇ and ⁇ ⁇ whose entries are and , respectively. If no pair has a prominence above the threshold, only the peak with the largest prominence is used.
  • the median m of ⁇ ⁇ may be calculated as well as s such that is found, where g T is the grid step for
  • the slope of the (n-1 )-th and n-th NDP may be corrected as follows: As described above, the timing impairment causing a slope error may be handled by the Advance slope correction processing block, but the phase error so far is corrected only by the FFT based PSC. It turns out that this simple pre-processing stage may be usually sufficient for the SpotFi algorithm since the rotation between NDPs is sufficiently small. However, after the SpotFi algorithm and subsequent LS estimation is done and the Doppler shifts are found, it may be advantageous to add another compensation for the phase offset so that the channel prediction, which also uses linear estimation on the model errors, will be even more accurate. This compensation may be implemented rather simply.
  • the processing circuitry 111 of the AP 110 may be configured to determine the maximum estimated Doppler shifts and the minimum estimated Doppler shifts over all paths that are considered real paths (after iterative LS estimation), and to take the average thereof.
  • the channel prediction may be compensated for this average Doppler shift, i.e.:
  • the embodiments described above may be extended for handling antenna polarization as well.
  • the odd TX antennas may support a polarization (say horizontal H), while the even TX antennas support an orthogonal polarization (say vertical V).
  • the odd RX antennas may support a polarization, while the even RX antennas support an orthogonal polarization (in general, not aligned with the TX side).
  • the SOS model gives: where and are N R x 1 vectors corresponding to the channel complex phasor from TX antennas with first and second polarization, respectively, to the RX antennas.
  • the vector is a N T / 2 ⁇ 1 steering vector corresponding to N T /2 antennas with the same polarization.
  • the vector ⁇ r denotes a column vector with all entries zero except the r-th entry that is 1. The idea behind this approach is to cast the problem with polarization to a different problem that is equivalent to the single polarization case.
  • ar ⁇ 6 redefine as a matrix whose ( r,q )- th entry is the channel from 2 q -1 + mod(r, 2) TX antenna to RX antenna. This leads to: with ⁇ i a vector and v AOD ( ⁇ i ) a vector.
  • the processing circuitry 111 of the AP 110 may be configured to apply the SpotFi based scheme on the new problem, but with different values for M sc and M T than for the single polarization case.
  • the results are also valid when the AP 110 has dual-polarized antennas 113a-n (each element has the H and V components) and/or the ST As 120 have dual-polarized antennas 121 , where each antenna with dual polarization is regarded as two antennas at the same position each with a single polarization. For example, if the AP 110 has dual polarized antennas 113a-n, N T is taken as twice the number of physical antennas, and then is the number of physical antennas.
  • the processing circuitry 111 of the AP 110 is configured to update the precoder for each new predicted channel.
  • the channel may be updated either each new downlink transmission or within a transmission. Since in the second main embodiment the full channel is predicted, SVD is beneficial prior to precoding.
  • the SVD may be similar to the SVD done in the STAs 120 only that it is done on the predicted channel.
  • FIGS 8a to 8e illustrate the performance gains of the wireless transceiver 110 according to different embodiments provided in particular in mobile scenarios.
  • the AP 110 can achieve a good PER (packet error rate) performance with a 3 km/h velocity and approach the performance of the ZOH scheme in the case of 0 km/h.
  • the performance of the AP 110 according to an embodiment implementing the A-LP scheme described above further improves.
  • Figure 8a presented the performance gain provided by an embodiment of the AP 110 in terms of the PER for a chosen MCS.
  • a further exemplary scenario is described illustrating the performance gain provided by an embodiment of the AP 110 in terms of the actual throughput.
  • Figure 8b provides a comparison between the maximum goodput provided by the AP 110 according to different embodiments of the first main group of embodiments implementing the A-LP scheme with the maximum goodput provided by a conventional AP using the ZOH scheme.
  • Figures 8c and 8d provide comparisons between the maximum goodput provided by the AP 110 according to different embodiments of the second main group of embodiments implementing the geometric channel model with the maximum goodput provided by a conventional AP using the ZOH scheme.
  • Figure 8e shows that in comparison with a conventional AP an embodiment of the AP 110 implementing the A-LP scheme does not result in a negative gain, i.e. no performance degradation in low mobility/low SNR scenarios. More specifically, figure 8e compares the performance of an embodiment of the AP 110 implementing the A-LP scheme in terms of PER with that of a conventional AP implementing the ZOH scheme in the case that there is no mobility, i.e., 0 km/h velocity. As can be taken from figure 8e, there is no negative gain (i.e., no degradation relative to ZOH).
  • FIG. 9 is a flow diagram illustrating a method 900 of operating the wireless transceiver, in particular AP 110.
  • the method 900 comprises the steps of: receiving 901 at a plurality of times channel state information from the plurality of further wireless transceivers, including channel state information at a first time and channel state information at a second time; performing 903 a phase alignment of the channel state information at the second time with the channel state information at the first time; predicting 905 a channel state for an upcoming transmission at a third time based on the phase aligned channel state information; and adjusting 907 an adjustable precoding configuration based for operating the array of antennas based on the predicted channel state for the upcoming transmission.
  • the disclosed system, apparatus, and method may be implemented in other manners.
  • the described embodiment of an apparatus is merely exemplary.
  • the unit division is merely logical function division and may be another division in an actual implementation.
  • a plurality of units or components may be combined or integrated into another system, or some features may be ignored or not performed.
  • the displayed or discussed mutual couplings or direct couplings or communication connections may be implemented by using some interfaces.
  • the indirect couplings or communication connections between the apparatuses or units may be implemented in electronic, mechanical, or other forms.
  • the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the objectives of the solutions of the embodiments.
  • functional units in the embodiments of the invention may be integrated into one processing unit, or each of the units may exist alone physically, or two or more units are integrated into one unit.

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Abstract

A wireless transceiver (110), in particular wireless access point comprises a communication interface (113) comprising an array of antennas (113a-d), wherein the communication interface (113) is configured to receive at a plurality of times channel state information from a plurality of further wireless transceivers (120), including channel state information at a first time and channel state information at a second time, and to operate the array of antennas (113a-d) with an adjustable precoding configuration. Furthermore, the wireless transceiver (110) comprises a processing circuitry (111) configured to perform a phase alignment of the channel state information at the second time with the channel state information at the first time and to predict a channel state for an upcoming transmission based on the phase aligned channel state information. The processing circuitry (111) is further configured to adjust the adjustable precoding configuration for the upcoming transmission based on the predicted channel state.

Description

Multi-antenna wireless transceiver and method for MIMO beamforming
TECHNICAL FIELD
The present disclosure relates to wireless communmcations. More specifically, the present disclosure relates to a multi-antenna wireless transceiver, such as a multi-antenna wireless access point, AP, and method for MIMO beamforming.
BACKGROUND
IEEE-802.11 -based WLANs have become popular at an unprecedented rate. WLAN supports a variety of data transfer modes including (but not only) file transfer, emails, web browsing and real-time applications such as audio and video applications. For efficiently supporting high throughputs, the evolving IEEE 802.11 standards specify several transmission (TX) schemes that can be used by a wireless transceiver. Particularly useful for increasing the link throughput are TX schemes which deploy multiple TX antennas (some, but not all, also requiring multiple RX antennas on the receiver side), which are so called MIMO modes. Multiple TX antennas, often with each antenna being accompanied by a dedicated TX processing chain including a Power Amplifier (PA), can be utilized in different advantageous ways, such as spatial TX diversity for improving the link reliability and performance, beamforming (BF), i.e. focusing the radiated power in the direction(s) of target receiver(s) (and/or suppressing it in undesirable directions, for reducing unwanted interference to non-targeted receivers), and/or spatial multiplexing (SM), i.e. sending multiple data streams simultaneously over the same time-frequency resources, either to the same receiver or to different ones.
SUMMARY
It is an objective of the present disclosure to provide an improved multi-antenna wireless transceiver and method for MIMO beamforming.
The foregoing and other objectives are achieved by the subject matter of the independent claims. Further implementation forms are apparent from the dependent claims, the description and the figures. According to a first aspect a multi-antenna wireless transceiver is provided. In an embodiment, the wireless transceiver may be a multi-antenna wireless access point (AP).
The wireless transceiver comprises a communication interface with an array of antennas. The communication interface is configured to receive at a plurality of times channel state information from a plurality of further wireless transceivers, including channel state information at a first time and channel state information at a second time. The communication interface is further configured to operate the array of antennas with an adjustable precoding configuration. The plurality of further wireless transceivers may include single antenna or multi-antenna wireless stations.
The wireless transceiver further comprises a processing circuitry configured to perform phase alignment of the channel state information at the second time with the channel state information at the first time and to predict a channel state for an upcoming transmission at a third time based on the phase alignment of the channel state information, i.e. the phase aligned channel state information.
The processing circuitry of the wireless transceiver is further configured to adjust the adjustable precoding configuration for the upcoming transmission based on the predicted channel state at the third time.
In a further possible implementation form of the first aspect, the communication interface of the wireless transceiver is further configured to transmit at a plurality of times a channel sensing signal, in particular a NPD frame, to the plurality of further wireless transceivers for allowing the plurality of further wireless transceivers to determine the channel state information and/or transmit the channel state information to the wireless transceiver.
In a further possible implementation form of the first aspect, the wireless transceiver is a wireless access point or base station.
In a further possible implementation form of the first aspect, the wireless transceiver is configured to operate in accordance with the IEEE 802.11 WLAN standard or a standard evolved therefrom.
In a further possible implementation form of the first aspect, the channel state information received from the plurality of further wireless transceivers is compressed and wherein the processing circuitry is configured to decompress the compressed channel state information. ln a further possible implementation form of the first aspect, the communication interface is configured to communicate with the plurality of further wireless transceivers using a plurality of frequency sub-carriers and wherein the channel state information comprise channel state information only for a subset of the plurality of frequency sub-carriers.
In a further possible implementation form of the first aspect, the processing circuitry is configured to perform phase alignment on the channel state information for each frequency sub-carrier of the subset of the plurality of frequency sub-carriers separately.
In a further possible implementation form of the first aspect, the channel state information received from the plurality of further wireless transceivers at a time n is based on a singular value decomposition of a channel response matrix and comprises
Figure imgf000005_0001
one or more of the first columns
Figure imgf000005_0002
of the matrix Vn and one or more of the first diagonal elements of the matrix Sn.
In a further possible implementation form of the first aspect, the processing circuitry is configured to determine, based on the channel information at the time n, a partial channel response matrix , wherein k denotes a frequency sub-carrier index.
Figure imgf000005_0003
In a further possible implementation form of the first aspect, for aligning the channel state information the processing circuitry is configured to determine a unitary matrix W that minimizes the following equation:
Figure imgf000005_0004
wherein the operation diag(...) transforms a vector into a diagonal matrix whose diagonal entries equal that vector.
In a further possible implementation form of the first aspect, for aligning the channel state information the processing circuitry is configured to determine a singular value decomposition
Figure imgf000005_0006
of the matrix and to determine the
Figure imgf000005_0005
unitary matrix W as .
Figure imgf000005_0007
In a further possible implementation form of the first aspect, the unitary matrix W is a diagonal unitary matrix.
In a further possible implementation form of the first aspect, for aligning the channel state information the processing circuitry is configured to apply the matrix W to the partial channel response matrix
Figure imgf000005_0008
. In a further possible implementation form of the first aspect, the processing circuitry is configured to predict the channel state for an upcoming transmission based on the following equation:
Figure imgf000006_0001
wherein: and denote the aligned channel state information at the first and second time,
Δ denotes a time difference between the first and second time,
T denotes a time difference between the second time and the upcoming transmission, and α denotes a parameter. In a further possible implementation form of the first aspect, the parameter a is a function of the aligned channel state information at the first and second time and channel estimation error variances at the first and second time.
In a further possible implementation form of the first aspect, the processing circuitry is configured to determine the parameter a based on the following equations:
Figure imgf000006_0002
wherein: and denote the channel estimation error variances at the first and second time, NDSC denotes the decimated number of sub-carrier frequencies,
Nr denotes the number of receiver antennas of one of the plurality of further wireless transceivers, and Ns denotes the number of spatial streams for the one of the plurality of further wireless transceivers for the upcoming transmission.
In a further possible implementation form of the first aspect, the processing circuitry is configured to align the channel state information at the first time and the channel state information at the second time based on a parametrized geometrical channel model and to predict the channel state for the upcoming transmission based on the parametrized geometrical channel model.
In a further possible implementation form of the first aspect, the parametrized geometrical channel model is defined by one or more parameters of the parametrized geometrical channel model and wherein the processing circuitry is configured to determine the one or more parameters of the parametrized geometrical channel model based on the channel state information.
In a further possible implementation form of the first aspect, the channel state information received from the plurality of further wireless transceivers at a time n is based on a singular value decomposition of a channel response matrix and comprises
Figure imgf000007_0001
the matrices Un and Vn and the diagonal elements of the matrix Sn.
In a further possible implementation form of the first aspect, the processing circuitry is configured to determine the one or more parameters of the parametrized geometrical channel model on the basis of the following equation:
Figure imgf000007_0002
wherein: αi,r denotes a complex number accounting for the i-th path complex gain with respect to the r-th antenna, s(t - Ti)T denotes the transmitted signal vector with the i-th entry corresponding to i-th antenna, denotes the angle of departure, Ti denotes the time-of-flight, x(θί) denotes the steering vector, and fmcos(φi) denotes a term accounting for a Doppler shift of the i-th path.
In a further possible implementation form of the first aspect, the processing circuitry is configured to determine, based on the parametrized geometrical channel model, a plurality of candidate paths.
In a further possible implementation form of the first aspect, the one or more parameters of the parametrized geometrical channel model comprise an angle of departure (AOD) and a time-of-flight (TOF) associated with each candidate path, wherein the processing circuitry is configured to determine the plurality of candidate paths on the basis of a plurality of local maxima of a spectrum function (also referred to as cost function) depending on the angle of departure and the time-of-flight.
In a further possible implementation form of the first aspect, the processing circuitry is further configured to determine a peak prominence for each of the plurality of local maxima of the function depending on the angle of departure and the time-of-flight and to determine the plurality of candidate paths on the basis of the plurality of peak prominences.
In a further possible implementation form of the first aspect, the one or more parameters of the parametrized geometrical channel model further comprise a complex attenuation (also referred to as complex gain) for each channel path and a Doppler shift, wherein processing circuitry is further configured to reduce the number of candidate paths on the basis of an iteratively determined least squares error.
In a further possible implementation form of the first aspect, the processing circuitry is further configured to correct the Doppler shifts of the plurality of candidate paths on the basis of an average of a minimum Doppler shift and a maximum Doppler shift of the plurality of candidate paths.
In a further possible implementation form of the first aspect, the processing circuitry is further configured to adjust the prediction of the channel state for the upcoming transmission on the basis of an adjustment between the plurality of time-of-flights of each of the plurality of candidate paths at the first time and the plurality of time-of-flights of each of the plurality of candidate paths at the second time.
In a further possible implementation form of the first aspect, the processing circuitry is further configured to estimate one or more model errors of the parametrized geometrical channel model at the first time and the second time and to predict the one or more model errors of the parametrized geometrical channel model for the upcoming transmission, wherein the processing circuitry is further configured to predict the channel state for the upcoming transmission based on the parametrized geometrical channel model and the one or more predicted model errors.
In a further possible implementation form of the first aspect, the processing circuitry is further configured to predict the one or more model errors of the parametrized geometrical channel model for the upcoming transmission using a linear temporal prediction and to weight the one or more predicted model errors by a weighting parameter b.
According to a second aspect a method of operating a wireless transceiver comprising an array of antennas is provided. The method comprises the steps of: receiving at a plurality of times channel state information from a plurality of further wireless transceivers, including channel state information at a first time and channel state information at a second time; performing a phase alignment of the channel state information at the second time with the channel state information at the first time; predicting a channel state for an upcoming transmission based on the phase aligned channel state information; and adjusting, based on the predicted channel state for the upcoming transmission, a precoding configuration for operating the array of antennas.
Details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will be apparent from the description, drawings, and claims.
BRIEF DESCRIPTION OF THE DRAWINGS
In the following, embodiments of the present disclosure are described in more detail with reference to the attached figures and drawings, in which:
Fig. 1 shows a MU-MIMO WLAN communication system, including a wireless access point in communication with a plurality of wireless stations; Fig. 2 shows the dependency of the maximal total goodput on the SNR in an exemplary MU-MIMO WLAN communication system;
Fig. 3 is a sequence diagram illustrating exemplary sounding procedures implemented by a wireless access point according to an embodiment; Fig. 4 shows a further MU-MIMO WLAN communication system, including a wireless access point in communication with a plurality of wireless stations;
Fig. 5 shows a schematic diagram illustrating processing blocks implemented by a wireless transceiver according to an embodiment;
Figs. 6a and 6b show schematic diagrams illustrating processing blocks implemented by a wireless transceiver according to a further embodiment;
Fig. 7 shows a contour plot illustrating a peak search implemented by a wireless transceiver according to an embodiment;
Figs. 8a-e illustrate the performance of a wireless transceiver according to an embodiment; and Fig. 9 is a flow diagram illustrating a wireless transmission method according to an embodiment.
In the following, identical reference signs refer to identical or at least functionally equivalent features. DETAILED DESCRIPTION OF THE EMBODIMENTS
In the following description, reference is made to the accompanying figures, which form part of the disclosure, and which show, by way of illustration, specific aspects of embodiments of the present disclosure or specific aspects in which embodiments of the present disclosure may be used. It is understood that embodiments of the present disclosure may be used in other aspects and comprise structural or logical changes not depicted in the figures. The following detailed description, therefore, is not to be taken in a limiting sense, and the scope of the present disclosure is defined by the appended claims.
For instance, it is to be understood that a disclosure in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa. For example, if one or a plurality of specific method steps are described, a corresponding device may include one or a plurality of units, e.g. functional units, to perform the described one or plurality of method steps (e.g. one unit performing the one or plurality of steps, or a plurality of units each performing one or more of the plurality of steps), even if such one or more units are not explicitly described or illustrated in the figures. On the other hand, for example, if a specific apparatus is described based on one or a plurality of units, e.g. functional units, a corresponding method may include one step to perform the functionality of the one or plurality of units (e.g. one step performing the functionality of the one or plurality of units, or a plurality of steps each performing the functionality of one or more of the plurality of units), even if such one or plurality of steps are not explicitly described or illustrated in the figures. Further, it is understood that the features of the various exemplary embodiments and/or aspects described herein may be combined with each other, unless specifically noted otherwise.
Before describing different embodiments in more detail, in the following some technical background as well as terminology concerning wireless transceivers in accordance with the IEEE 802.11 WLAN standard will be introduced making use of one or more of the following abbreviations:
AID Association Identifier
AOA Angle of arrival
AOD Angle of departure
AP Access Point
BF Beam-forming
BSS Basic Service Set
BW Bandwidth
CA Certification Authority / Collision Avoidance / Carrier Aggregation
CCA Clear Channel Assessment
CSMA Carrier Sense Multiple Access
HD High Density HEW High Efficient Wi-Fi
IP Internet Protocol
MAC Medium Access Control MCS Modulation and Coding Scheme MIMO Multiple Input Multiple Output MU Multi-User NDP Null Data Packet NDPA NDP Announcement OBSS Overlapping Basic Service Set PER Packet Error Ratio / Packet Error Rate PHY Physical Layer PPDU PHY Protocol Data Unit RRM Radio Resource Management RX Receive Or Receiver SIFS Short Inter-frame Space SINR Signal to Interference plus Noise Ratio SR Spatial Reuse STA Station TOF Time of flight TX T ransmit or T ransmitter TxOP Tx Opportunity VHD Very High Density
WLAN Wireless local area network based on IEEE 802.11 and related standards Figure 1 shows a MU-MIMO WLAN communication system 100, including a wireless transceiver 110, in particular a wireless access point (or short AP) 110 according to an embodiment in communication with a plurality of wireless stations (or short ST A) 120. In MU-MIMO the AP 110 is configured to transmits simultaneously to the plurality of wireless stations 120 using precoding so that the transmission to different stations 120 does not interfere with each other. The precoder is calculated so that the transmission to one STA will create nulling at the other ST As (also known as null-steering).
For using MU-MIMO downlink transmission the AP 110 needs to obtain some information about the respective communication channel between the AP 110 and the STAs 120. In conventional WiFi (such as 802.11 ax) this is achieved by the sounding procedure described in the following. Sounding procedure also known as channel sounding generally refers to procedures designed to measure channel performance dynamically (on very wide channels - typically > 500 MHz wide, operating in the mmWave spectrum; 25 to greater than 50 GHz), and using MIMO and Beamforming transmissions. The AP 110 transmits a short packet called NDP to the STAs 120. The STAs 120 estimate the channel using the NDP. The STAs 120 transmit back to the AP 110 partial channel information (more specifically the V from SVD and SNRs, in fact, quantized and decimated). The AP 110 calculates a precoder based on the channel information. The AP 110 uses the precoder when transmitting subsequent data packets until a more up to date channel information is available (after a new sounding procedure).
The time from the transmission of an NDP to the transmission of a precoded packet may take several msec. If the communication channel is static during this period of several msec, then conventional MU-MIMO works very well. However, even a relatively small mobility of 1-3 km/h (for instance, due to the motion of the AP 110 and/or one or more of the STAs 120) may turn out to cause a significant degradation of the MU-MIMO transmission. The reason for the high sensitivity of DL MU-MIMO is that the nulling is very sensitive to channel variations so that the transmission to the other STAs 120 is not nulled-out and causes inter-user interference. This is different from the UL MU-MIMO case (open loop) or DL SU-MIMO, which are much more robust to mobility.
In figure 2, for each SNR point the number of stations/users and the modulation and coding scheme, MCS, maximizing the goodput is found and the corresponding goodput is shown. As can be taken from figure 2, even though the gap between NDP and DL MU- MIMO transmission is small, namely just 4ms, the degradation for a mobility of 3km/h is rather huge and it is not possible to support large number of streams/users using the conventional schemes described above. The problem of DL MU-MIMO transmission in mobility scenarios has not been solved to date. As already described above, in WiFi devices a precoder based on channel information from the last feedback is used and fixed throughout MU-MIMO transmissions until new feedback based on the next sounding procedure becomes available. This approach may be regarded as a zero order hold (ZOH) scheme. Using this ZOH scheme, higher mobility may be supported by decreasing the gap between NDPs (i.e., the gap between sounding procedures). Unfortunately, decreasing this gap comes with the drawback of increasing the signalling overhead, as already described above. For instance, the time duration of feedback transmissions may take 2 ms in some cases. If the gap is 4 ms, the MAC throughput is at least 50% less than the PHY throughput. Decreasing the gap further will significantly decrease the MAC throughput and lead to very poor spectral efficiency. An AP should try to find the "sweet spot" that would maximize the overall throughput (for a given SNR), going over combinations of MCS, number of stations/users and temporal distances between NDPs. Still a conventional AP is not able to support high throughputs with this approach in even moderate mobility scenarios.
As will be described in more detail in the following, embodiments disclosed herein address the mobility problem described above. Generally, embodiments disclosed herein are based on the idea of performing channel prediction based on the two most recent NDPs (e.g. from the two most recent sounding procedures) instead of using just the last NDP. The channel may predicted for the time corresponding to the transmission of a DL MU- MIMO packet. It can be updated several times between sounding procedures, and even be updated within a data packet. Each time a new predicted channel is available, the precoder is updated (using one of possible precoding schemes such as ZF, NSP, and GMD and their possible combinations).
More specifically, according to an embodiment the wireless transceiver, in particular wireless AP 110 illustrated in figure 1 comprises a communication interface 113 comprising the array of antennas 113a-n (in figure 1 the array of antennas comprises, by way of example, 4 antennas 113a-n). In addition to the array of antennas 113a-n the communication interface 113 of the AP 110 may further comprise analog and/or digital signal processing circuitry for processing RF and/or digital signals.
The communication interface 113 is configured to receive at a plurality of times channel state information from the plurality of wireless stations 120, including channel state information at a first time and channel state information at a second time, and to operate the array of antennas 113a-d with an adjustable precoding configuration, i.e. an adjustable precoder using a precoding or beamforming communication scheme, as defined, for instance, by a standard, in particular the IEEE 802.11 WLAN standard or a standard evolved therefrom.
As illustrated in figure 1 , the wireless AP 110 further comprises a processing circuitry or a processor 111 for processing digital data. The processor 111 may be implemented in hardware and/or software, which when executed causes the wireless multi-antenna transceiver 110 to perform the functions and methods described herein. The hardware may comprise digital circuitry, or both analog and digital circuitry. Digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field- programmable arrays (FPGAs), digital signal processors (DSPs), or general-purpose processors. The wireless AP 110 may further comprise an electronic memory 115 for storing digital data, such as the channel state information received at the first time and the channel state information received at the second time.
As will be described on more detail below, the processing circuitry 111 of the AP 120 is configured to perform a phase alignment of the channel state information at the second time with the channel state information at the first time and to predict a channel state for an upcoming transmission at least at a third time based on the phase aligned channel state information. In other words, the processing circuitry 111 of the AP 120 is configured to estimate, based on the information about the channel state at the first and second times, the channel state at the third time and possibly further times, such as a fourth time, a fifth time and the like. Moreover, the processing circuitry 111 of the AP 120 is further configured to adjust the adjustable precoding configuration for the upcoming transmission based on the predicted channel state at the third time and possibly further times. In other words, the processing circuitry 111 of the AP 120 is configured to adjust, i.e. set the precoder for operating the array of antennas 113a-n at the third time and possibly further times based on the channel state predicted for the third time and the possibly further times as well as the respective time differences.
In the following two main embodiments of the wireless AP 110 will be described. The first main embodiment of the wireless AP 110 is based on an advanced linear prediction (A- LP) scheme with relatively low-complexity, while the second main embodiment is based on a parametric based approach using a Sum of Sines, SOS, channel model in combination with a 2-dimensional MUSIC algorithm with spatial smoothing (also known as SpotFi algorithm). The basic idea is to first estimate the TOFs (time of flight) and AODs (angle of departure) and/or AOAs (angle of arrival) of all paths using known array processing techniques (such as ESPRIT and compressed sensing) and then the remaining parameters such as the Dopplers and complex gains of the paths are estimated based on LS type estimation (several variants exist such as adding the Dopplers to the initial joint estimation). Further background about the parametric based approach using the SOS channel model may be found, for instance, in I. C. Wong and B. L. Evans, "Sinusoidal Modeling and Adaptive Channel Prediction in Mobile OFDM Systems," in IEEE Transactions on Signal Processing; R. O. Adeogun, P. D. Teal and P. A. Dmochowski, "Extrapolation of MIMO Mobile-to-Mobile Wireless Channels Using Parametric-Model-Based Prediction," in IEEE Transactions on Vehicular Technology; and S. Uehashi, Y. Ogawa, T. Nishimura and T. Ohgane, "Prediction of Time-Varying Multi- User MIMO Channels Based on DOA Estimation Using Compressed Sensing," in IEEE Transactions on Vehicular Technology.
The advanced linear prediction scheme implemented by the wireless AP 110 according to the first main embodiment is robust against CFO/timing offset impairments, can be applied on partial channel information (like in the WiFi standard), and essentially has no degradation when applied to low mobility/low SNR scenarios. The SOS model based approach implemented by the wireless AP 110 according to the second main embodiment can handle many paths (which makes it suitable for WiFi channels) and is rather robust to deviations from the assumed model.
In the first main embodiment, the AP 110 may use an alignment algorithm to align the partial channel information from the current sounding process with the partial channel information from a previous sounding process. Before the transmission of a precoded packet to the ST As 120, the AP 110 may use the (aligned) partial channel information from the last two channel sounding processes to predict, using an advanced linear based method, the partial channel at the time of transmission of the precoded packet. The AP 110 may update the channel prediction also within a packet (important for long packets). For each new predicted channel, the AP 110 may update, i.e. adjust the precoder for operating the array of antennas 113a-n. The prediction may be done in such a way as to guarantee that there is no degradation, i.e. negative gain in a low mobility/low MCS scenario relative to the conventional ZOH scheme.
In the second main embodiment, the ST As 120 may compress, e.g. quantize the channel state information for decimated SCs so that the full channel may be reconstructed by the AP 110, and transmit the compressed/quantized channel state information as the feedback during the sounding procedures. After the completion of a current sounding procedure, the AP 110 may use the feedback of the current sounding procedure to determine the full channel information for decimated SCs. The AP 110 may further use an alignment algorithm (by estimating TOFs) to align the full channel from the current sounding process with that of the previous sounding process. The alignment allows to mitigate or remove CFO/timing offset impairments. The AP 110 may use the SpotFi based scheme on the channel from the two last NDPs to estimate the AODs and TOFs of the candidate paths provided by the SpotFi scheme. The AP 110 may use “peak prominences” and an iterative LS (least squares) estimation to decide on the true peaks and estimate the Dopplers and complex gains of the paths. The AP 110 may use the estimated geometrical channel model parameters, such as AODs, TOFs, Dopplers, and complex gains to calculate model errors corresponding to the two most recent channel state information. Before the transmission of a precoded packet to the STAs 120, the AP 110 may use the estimated parameters of the geometrical channel model and the model errors to predict the channel at the time of transmission of the precoded packet, i.e. at the third time. The AP 110 may update the channel prediction also within a packet (important for long packets). For each new predicted channel, the AP 110 may perform a SVD (singular value decomposition) and may update, i.e. adjust the precoder for operating the array of antennas 113a-n. The idea in this second main embodiment is to detect slowly varying parameters of the SOS geometric channel model, which are quasi constant between subsequent sounding procedures and payload (using SpotFi) and predict the channel using the geometric channel model.
Figure 3 is a sequence diagram illustrating a sounding procedure implemented by the wireless transceiver, in particular wireless AP 110 according to an exemplary embodiment in compliance with the 802.11 ax WLAN standard. As already described above, the AP 110 uses the two most recent sounding procedures to predict the channel. As illustrated in figure 3, each sounding procedure may comprise the emission of a NDPA frame, a NDP frame and a trigger frame by the wireless AP 110 and, in response, thereto, the channel stale feedback from the STAs 120. Based on the predicted channel the AP 110 is configured to adjust the precoder for operating the array of antennas 113a-n and thereby sending data packets to the STAs 120 using MU-MIMO beamforming. The prediction/calculation of the precoder can be updated several times, each new precoded packet or within a packet.
Figure 4 shows the wireless communication system 100, including the wireless AP 110 and the wireless STAs 120 in a scenario including communication with a line-of-sight,
LOS, component as well as scattered components. As will be described in more detail below, the scenario shown in figure 4 provides an intuitive explanation for the SOS geometrical channel model used in the second main embodiment, which may be described by the following equation:
Figure imgf000018_0001
where yr is the received signal at the r-th antenna 121 , s is the transmitted signal vector with the /- th entry corresponding to the i-th TX antenna 113i, and
Figure imgf000018_0002
is the steering vector of the antenna array 113a-n of the AP 110. This may be the steering vector of a ULA, but may be applicable to other arrangements of the antennas 113a-b as well, such as 2 dimensional or 3 dimensional arrangements.
In the equation above describing the geometric channel model the quantities αi,riii are all slowly varying (i.e. can be assumed to remain constant over a duration of a few msec). So although yr itself may change rapidly, it is based on a parametric model whose parameters are slowly varying. In the equation above θi and τi are the angle of arrival (AOD) and time of flight (TOF), respectively, corresponding to the i-th path. In addition, αi,r is a complex number accounting for the i-th path complex gain with respect to the r-th antenna. Finally, the term fmcos(φi) accounts for the Doppler shift of the i-th path and depends on the velocity of the STA 120 and its direction with respect to the AP 110.
In an embodiment, the AP 110 may comprise NT TX antennas 113a-n and initiates a sequence of sounding procedures with Na ST As 120. After the initiation of each sounding procedure, the AP 110 transmits a NDP frame to the STAs 120. The following description will focus without loss of generality on the (n-1)- th and the n-th sounding procedure, whose NDPs are transmitted at times 0 (i.e. the first time) and Δ (i.e. the second time), respectively. Consider one of the STAs 120 that has NR RX antennas 121 and the number of spatial streams intended for this STA 120 is Ns . The STA 120 estimates the
NR × NT channel matrices based on the NDP received from the AP 110. The STA 120 sends as feedback the channel state information to the AP 110. This channel station information may not be send for each subcarrier, SC, but roughly for each Ng SC (also referred to as "decimated SCs"). For instance, the standard value Ng = 4 may be used, but the non-standardized Ng = 8 may also be a good choice.
The STA 120 calculates for each of the decimated SCs the SVD decomposition , where Un and Vn are NR × NR and NT × NR unitary matrices,
Figure imgf000019_0001
respectively, and Dn is a NR × NR real diagonal matrix , whose diagonal elements are ordered from the largest to the smallest.
Let denote estimates for the channel estimation error variance for (n-1)- th and n-
Figure imgf000019_0002
th NDP, respectively. In one embodiment may be transmitted by the STA 120 to the
Figure imgf000019_0003
AP 110 as feedback channel state information. At the STA side
Figure imgf000019_0004
can be calculated easily as — , where is the estimated noise variance during the transmission
Figure imgf000019_0006
Figure imgf000019_0005
of the NDP, NLTF is the number of LTF symbols used for the NDP, and γ is the frequency- domain (FD) channel estimation processing gain.
In another embodiment may be approximated by the processing circuitry 111 of the
Figure imgf000019_0008
AP 110 as , where is an estimate for the noise variance at the STA 120
Figure imgf000019_0009
Figure imgf000019_0007
calculated by the AP 110 based on the SNR values per SCs or average SNR already transmitted by the STA 120 according to the WiFi standard, and
Figure imgf000019_0010
is a typical value for the FD channel estimation processing gain in WiFi (such as a value of 4).
Figure 5 shows a schematic diagram illustrating processing blocks implemented by the wireless AP 110 for the first main embodiment, i.e. where the AP 110 uses an alignment scheme to align the partial channel information from the current sounding process with the partial channel information from a previous sounding process (herein referred to as advanced linear prediction, A-LP).
The STA 120 takes from Vn the first N s columns, denoted
Figure imgf000019_0011
, and the first Ns diagonal elements of Dn denoted (corresponding to SNR per stream) compresses and
Figure imgf000019_0014
quantizes them, possibly (but not necessarily) in the same manner as in the current WiFi standard. The compressed/quantized quantities and are reduced partial channel
Figure imgf000019_0012
information. Compression can be done such that the last row of is real-valued.
Figure imgf000019_0013
The AP receives the partial channel state information from the STA and decompresses it (processing block 501). This may yield for the n-th sounding procedure and for
Figure imgf000020_0001
Figure imgf000020_0002
the /c-th decimated SC. As already described above, the processing circuitry 111 of the AP 110 may implement an alignment procedure between the n-th NDP and (n-1)- th NDP (as illustrated in processing block 503 of figure 5). The alignment allows compensating for the possible discontinuities caused by the STA 120 when determining the SVD and/or compressing . The alignment implemented by processing block 503 may also handle a
Figure imgf000020_0003
phase/slope offset between these NDPs caused by impairments such as CFO and timing offset. Indeed, CFO and timing offset may cause a common phase and slope error in the channel in the FD, respectively, both of which may advantageously be removed by the alignment algorithm described in the following.
The alignment algorithm as implemented by the processing block 503 may be done separately per each decimated SC as follows. To this end, in an embodiment, the processing circuitry 111 of the AP 110 may be configured to determine a unitary matrix Ak that minimizes the following equation:
Figure imgf000020_0004
where the diag operation on a vector gives a diagonal matrix whose diagonal equals that vector. The solution to this minimization problem is to perform the singular value decomposition, SVD, U' , S' , V' of , where U' and V' are
Figure imgf000020_0005
unitary matrices and S' is a diagonal matrix (all are Ns × Ns matrices). Then Ak = U'V'H . This alignment algorithm implemented by the processing circuitry 111 of the AP 110 according to an embodiment has a low complexity since Ns , i.e. the number of streams per STA is usually small.
Nevertheless, an even lower complexity alignment algorithm may be implemented by the AP 110 according to an embodiment, namely an algorithm that does not require the SVD by further restricting the matrix A to be a diagonal matrix (but at the price of some performance loss). This simpler alignment algorithm amounts to finding a diagonal matrix A with unit magnitude diagonal elements such that the equation above is minimized. This is equivalent to finding a phase θi per stream i such that
Figure imgf000020_0006
is maximized, where denotes the i-th column of .
Figure imgf000021_0001
Figure imgf000021_0002
Once the partial channel is aligned, the channel prediction can be performed. Let and . Let T denote the time the channel is
Figure imgf000021_0003
Figure imgf000021_0004
predicted for (i.e., the time difference to the (n-1)-th NDP). Let denote the (partial)
Figure imgf000021_0005
channel prediction for time T . In an embodiment of the A-LP scheme the processing circuitry 111 of the AP 110 may be configured to use with
Figure imgf000021_0006
a being a function of (where the index k runs over all decimated SCs) and
Figure imgf000021_0007
. Note that the case α = 1 corresponds to a linear prediction, α = 0 corresponds
Figure imgf000021_0008
to the conventional ZOH scheme, and corresponds to averaging the
Figure imgf000021_0009
two NDPs according to the corresponding channel estimates error variances. Thus, a proper choice of α may provide the benefits of a linear prediction for the case of a non- negligible mobility, while eliminating a negative gain in the case of low mobility/low SNR.
In an embodiment based on the A-LP scheme, the processing circuitry 111 of the AP 110 may be configured to determine α on the basis of the following equation:
Figure imgf000021_0010
where β is a function of (k goes over all decimated SCs) and is some measure of
Figure imgf000021_0011
the variations in the channel between the two NDPs and αmin is a non-positive number.
In a further embodiment based on the A-LP scheme, the processing circuitry 111 of the AP 110 may be configured to determine a using the equation above, but separately for each TX antenna or per stream (or both).
In a further embodiment based on the A-LP scheme, the processing circuitry 111 of the AP 110 may be configured to determine α using αmin based on the following equation:
Figure imgf000021_0012
In a further embodiment based on the A-LP scheme, the processing circuitry 111 of the AP 110 may be configured to determine α using β based on the following equation:
Figure imgf000022_0001
wherein NDSC denotes the number of decimated SCs, and λ is a function of (and
Figure imgf000022_0002
k goes over all decimated SCs).
In a further embodiment based on the A-LP scheme, the processing circuitry 111 of the AP 110 may be configured to determine a using the following equation:
Figure imgf000022_0003
As will be appreciated, the above choices for α described above may eliminate negative gain in the case the channel estimation error is not negligible relative to channel variations (low mobility/low SNR). An α close to 1 may be obtained for high mobility and SNR. Indeed, if the channel variations are significantly larger than the channel estimation error variance, then and α → 1.
Figure imgf000022_0004
If, on the other hand, the channel is static relative to the channel estimation error variance, α may assume a negative value, which accounts for some averaging between the NDPs.
Once is available on decimated SCs, the processing circuitry 111 of the AP 110 may use this information for interpolated to all SCs to yield
Figure imgf000022_0005
. However, before this interpolation in the frequency domain (FD) is done, the processing circuitry 111 of the AP 110 may be configured to perform a phase alignment over the SCs (dubbed "FD alignment") compensating for the phase discontinuities caused by the SVD, similarly to the case of the ZOH scheme.
Once is available on all SCs, the AP 110 is configured to determine the precoder on the basis thereof, which is used for subsequent transmissions of data packets until a new prediction is available. Whatever precoding scheme that is applicable in the ZOH case is also applicable here. Note that the AP 110 may be configured to update
Figure imgf000022_0006
for each DL
MU-MIMO transmission and even during a transmission. Since is an estimate of the
Figure imgf000022_0007
partial channel and has the dimension Ns × NT no further SVD is necessary prior to the precoder determination in this case.
Figures 6a and 6b show schematic diagrams illustrating processing blocks implemented by the wireless AP 110 for the second main embodiment, i.e. where the AP 110 determines slowly varying parameters of the model SOS geometric channel model using, for instance, the SpotFi algorithm, and predicts the channel state on the basis thereof. As will be described in more detail below, the processing blocks 613, 615, 617 and 618 relate to the SpotFi algorithm, the processing blocks 601 , 605 and 611 are related to impairment (CFO/timing) corrections, and the processing blocks 607 and 621-629 are related to additional processing stages providing further improvements, such as the ability to handle many paths and making the scheme more robust with respect to deviations from the SOS channel model.
The STA 120 takes the full matrices Un, Vn and the vector d„ containing the diagonal of Dn compresses and quantizes them, and send them to the AP 110 as feedback. The quantization of Vn and dn can be done possibly in a similar manner as done in the current WiFi standard. The compressed/quantized quantities Un , Vn , and d„ are reduced full channel information.
The AP 110 receives the full channel state information and decompresses it. The AP 110 calculates for the NDPs of the (n-1)-th and the n-th sounding procedures, the full channel estimates and , respectively. In an embodiment, an alignment procedure between
Figure imgf000023_0001
the n-th NDP and n-1-th NDP is performed by the AP 110. The alignment may be advantageous, in case there is a phase offset and slope difference between these NDPs due to impairments such as CFO and timing offset. In an embodiment, for handling these impairments the processing circuitry 111 of the AP 110 implements a pre-processing stage that estimates the phase and delay change (slope) between the NDPs and compensate for these impairments, for instance, the FFT based PSC (phase and slope correction) block 601 described in more detail in the following.
The FFT based PSC (phase and slope correction) block 601 is configured to find a solution for the following LS (least squares) problem:
Figure imgf000023_0002
Mathematically, it can be shown that this is equivalent to the following problem:
Figure imgf000024_0001
This problem can be decomposed into two parts, namely (a) determine
Figure imgf000024_0002
where , and (b) then calculate
Figure imgf000024_0003
Figure imgf000024_0004
Let NOSFFT = MNFFT for some M . Then can be searched on a grid
Figure imgf000024_0005
(unit is samples in original sampling rate) by performing
Figure imgf000024_0006
an oversampled IFFT of size NOSFFT and finding the maximum of the magnitude. This solution is an approximation and may require a large IFFT to provide accurate results. When performing the IFFT fk may be extended from decimated SCs to oversampled FFT size by zero padding. As will be appreciated, the maximum peak location accounts for the fractional timing offset and the phase of the peak accounts for phase offset. To avoid a too large IFFT, one can first perform an IFFT with smaller oversampling factor, find the peak, and then perform an IFFT in the region of the peak to improve the resolution. While this is not equivalent to performing a complete IFFT, it provides similar results.
In an embodiment, the channel of second NDP may be corrected by the processing circuitry 111 of the AP 11o as follows for the decimated SCs:
Figure imgf000024_0007
For the second main embodiment based on the SOS geometric channel model, the FFT based PSC block 601 advantageously performs the coarse phase/timing correction. However, it turns out that there may be a small residual slope error between the NDPs, which still degrades the performance. Therefore, in a further embodiment, a further processing stage may be added, whose purpose it is to further align the NDPs timing relative to each other (i.e. resolve the small residual slope difference). In an embodiment, this additional stage may be provided by the "Advanced Slope correction" block 605 shown in figure 6a and described in more detail in the following.
In an embodiment, the processing circuitry 111 of the AP 110 implements a SOS channel model, where the NR × NT channel matrix for subcarrier k at time t is described as
Figure imgf000025_0002
Figure imgf000025_0001
where Npath is the number of channel paths, θii and fi are the normalized AOD (NAOD), normalized TOF (NTOF), and Doppler shift of the i-th path, respectively,
Figure imgf000025_0003
and αi is a NR × 1 vector for i = 1,...,N path . As will be appreciated, the above expression strictly holds for a single polarization, but may be easily extended to polarized antennas.
In this embodiment, it is assumed that the antenna arrays 113a-n of the AP 110 is ULA (as is apparent from the expression for vAOD).
In an embodiment, the processing circuitry 111 of the AP 110 is configured to estimate the Npath NAOD θi and NTOF τi using the SpotFi algorithm (i.e. a well-known array signal processing algorithm based on MUSIC algorithm). Further details about the SpotFi algorithm may be found, for instance, in M. Kotaru, K. Joshi, D. Bharadia, and S. Katti, "Spotfi: Decimeter level localization using WiFi," in Proc. ACM Conf. Special Interest Group Data Commun., 2015, pp. 269-282. The SpotFi algorithm works on the channel estimates performed on the NDPs at the ST As side and transmitted to the AP 110. This may provide estimates of the vectors vAODi) and . Then αi and f (for
Figure imgf000025_0004
i i = 1,...,N path ) may be estimated using a LS type estimation.
Let , where , and are the estimates
Figure imgf000025_0007
Figure imgf000025_0005
Figure imgf000025_0006
for θi , τi , fi , and αi , respectively. In WiFi generally the channel estimates are available on decimated SCs, which are roughly each Ng SC. However, when one considers the
SCs in jumps of Ng not all are available, e.g., the zero SCs around the DC tone. As a first step the processing circuitry 111 is configured to perform interpolation so that the channel estimates will be available on each Ng SCs except on the guard bands. This may be done using linear interpolation for example. The resulting number of SCs after the interpolation is denoted here as Nsc .
In an embodiment, the processing circuitry 111 of the AP 110 implementing the SpotFi algorithm is configured to determine candidate paths of the channel in the NAOD and NTOF domain by performing the steps described in the following in more detail. The SpotFi-based scheme is based on
Figure imgf000026_0001
, which are the outputs of the Advance Slope correction block 605, where
Figure imgf000026_0002
and
Figure imgf000026_0003
are the aligned channel estimates for SC k at time 0 and Δ , respectively, i.e., corresponding to the (n-1)- th and n-th NDPs, respectively.
Let Ck be a NR × NT matrix, which in an embodiment is the input to the SpotFi algorithm implemented by the processing circuitry 111 of the AP 110, where k is the SC index. There are several options for Ck , which is a function of . One option is for
Figure imgf000026_0004
Figure imgf000026_0005
NDP n-1 and for NDP n.
Figure imgf000026_0006
Another option is to use , which is expected to be good for moderate
Figure imgf000026_0007
Doppler shifts and gaps. For example, assume a velocity of 3 km/h, which implies a Doppler shift ~16Hz (at the high 5Ghz band), and 8 ms gap. Then the rotation in degrees during the 8 ms gap is about 45 degrees. This means that when averaging 2 NDPs, the noise is reduced by factor of 3dB and averaging of each path behaves like .
Figure imgf000026_0008
Thus, even if all paths have a maximal Doppler shift the power is , whence there is at least a 2.31 dB improvement of the
Figure imgf000026_0009
SNR. Even if the Doppler shift or the gap size are further doubled, then the averaging of 2 NDPs is at least as good as using just one NDP. Yet, another option is to add also the Doppler shift to the MUSIC estimation (in addition to AOD and TOF).
In the following an embodiment, wherein the second option is adopted, i.e.,
Figure imgf000027_0001
will be described in more detail in the following.
In a first stage, the SpotFi algorithm implemented by the processing circuitry 111 of the AP 110 is configured to create the correlation matrix of the smoothed CSI. The smoothing of the CSI or channel estimates may be done on both the SCs and the antennas (spatial smoothing). Spatial smoothing assumes an antenna array 113a-n in the form of a ULA or other specific arrays, which can be transformed to a ULA.
In the following equations will be presented for the exemplary case of 1 antenna 121 of the station 120, which may be readily generalized to more antennas 121 . Let CkJ denote the l-th entry of Ck (corresponding to the l-th TX antenna 113a-n). Let Msc and MT denote the SCs and antenna block size, respectively. Note that MT < NT when performing spatial smoothing.
In order to create the correlation matrix let s denote the matrix whose i-th column
( i = 0, 1, ... , (Nsc - Msc + 1) (NT - MΤ + 1) - 1 ) is g iven below:
, where k = mod(i, Nsc -Msc +1) and
Figure imgf000027_0003
Figure imgf000027_0002
The length of the above vector is MSCMT . Then the correlation matrix of the smoothed
CSI is R = SSH . Note that Ris a matrix of size MSCMT by MSCMT . In an embodiment, a symmetry may be utilized and the smoothing from the last SC/last antenna may be performed in the opposite direction. This corresponds to
Figure imgf000028_0001
where R1 = SSH and R2 may be created by flipping R1 from left to right and from up to down. This latter calculation of the matrix R is referred to as symmetric smoothed CSI.
When the number of STA antennas is NR > 1 , S may be constructed by the processing circuitry 111 of the AP 110 as , where Si is constructed from the CSIs
Figure imgf000028_0005
related to the i-th STA antenna as in the case for 1 antenna 121 of the STA 120 described above.
In the next stage, after the calculation of the smoothed CSI correlation matrix R is to perform an eigen decomposition (i.e. a PCA) and find Nsig , i.e. the number of signals for which NAOD and NTOF is estimated, where Nsig should desirably equal the number of channel paths. In order to perform this number of paths determination one may use MDL (Minimum Description Length) or AIC (Akaike Information Criterion) informative criteria.
In a further embodiment, a more heuristic approach may be employed by determining Nsig as the number of eigenvalues that are above a threshold, provided that this number does not exceed another threshold. In the standard SpotFi algorithm, the eigenvectors corresponding to the remaining eigenvalues (i.e., after excluding the Nsig largest eigen- values) are concatenated to give a matrix N . According to a variant, the processing circuitry 111 of the AP 110 may be configured to calculate the matrix v that is created by concatenating the Nsig eigenvectors corresponding to the Nsig largest eigenvalues. Thus,
V is the output of the PCA of R in which the dimension of R is reduced to Nsig . Note that an equivalent (but not equal) N can be calculated as N = I-VVH.
Once N is available the processing circuitry 111 of the AP 110 may compute a spectrum as
Figure imgf000028_0002
where ( is Kronecker product). vTOF (τ) denotes the
Figure imgf000028_0003
vector whose entries ar e , where k goes over all active SCs.
Figure imgf000028_0004
In an alternative embodiment, the processing circuitry 111 of the AP 110 may use the matrix v (which reduces complexity) for determining the SpotFi spectrum, because it can be shown that the following equation holds: '
Figure imgf000029_0001
In embodiment, processing circuitry 111 of the AP 110 is configured to determine the local maxima of the spectrum q(θ, τ) . To this end, in an embodiment, the processing circuitry
111 of the AP 110 is configured to determine q(θ, τ) on a dense grid of the parameters θ,τ .
Having calculated the values for q(θ, τ) over the grid and stored these values, for instance, in the memory 115, the processing circuitry 111 of the AP 110 is configured to determine the local maxima, i.e. peaks of the function q(θ, τ) . In an embodiment, these peaks may be restricted to be above a certain threshold, e.g., 60dB or less below the global maximum. The reason is that there may be many small false peaks due to, for instance, the noise.
In an embodiment, the processing circuitry 111 of the AP 110 may consider the peaks determined in the previous stage as candidate peaks, wherein NCAP denotes the number of candidate peaks. The i -th candidate peak (for i = 1,...,NCAP ) defines a pair .
Figure imgf000029_0002
Figure 7 shows a typical, but exemplary contour plot of the function q(θ, τ) in the AOD-
TOF parameter plane. In figure 7 un-normalized AOD and TOF values are used so that the physical interpretation is clear. The respective true location of each AOD-TOF paths is shown as a circle, and is unknown to the AP. The dots show the estimated AOD-TOF peaks. The channel is TGac-D NLOS having 26 true paths.
As will be from the exemplary results shown in figure 7, when considering the candidate peaks, there may be several false peaks and missed peaks. It is mainly these false peaks and missed peaks that make it difficult to handle a channel that has many different paths. Therefore, once the candidate peaks are found, the processing circuitry 111 of the AP 110 may implement additional processing blocks that are not part of the standard SpotFi algorithm. Although embodiments described herein make use of the SpotFi algorithm, the person skilled in the art will appreciate that the same functionality may be provided by other available algorithms as well, such as other related array processing algorithms (such as 2-dimensional root MUSIC or ESPRIT) that can provide the candidate channel paths. Embodiments disclosed herein make use of the SpotFi algorithm since it provides the spectrum function q(θ, τ) , while other algorithms provide the candidate channel paths location but not necessarily a spectrum associated with them. However, clearly q(θ, τ) can be calculated on the candidate paths location even if they are first found by another algorithm.
As already mentioned above, some of the candidate peaks determined by the
Figure imgf000030_0001
processing circuitry 111 of the AP 110 implementing, for instance, the SpotFi algorithm may be false peaks. It turns out that it is not necessarily the peak strength (magnitude of
) that implies if it is a real peak or not. For example, there can be several true
Figure imgf000030_0002
strong peaks located closely to each other that create false peaks between them. The strength of the false peaks can be rather large, but they are not very prominent relative to the true peaks. So, it turns out that the topographical prominence of the peak can be a better measure, i.e. the magnitude of the peak relative to the lowest counter line encircling it, but encircling no other peak with larger magnitude. Since calculating topographical prominence is a rather difficult task, the processing circuitry 111 of the AP 110 may be configured to approximate the peak prominence heuristically, wherein the prominence of the i -th candidate peak may be denoted as pi .
In an embodiment, the processing circuitry 111 of the AP 110 may be configured to determine the values of pi for i = 1,...,NCAP in the following way. Let ai denote the index of i -th maximal candidate peak, then
1. = ∞ (the prominence of the tallest peak is infinity).
2. m = 2
3. Let (closest peak with higher
Figure imgf000030_0003
prominence), where m is a configurable positive real scalar.
4. Go on a straight line between the peaks and on the SpotFi grid
Figure imgf000030_0004
Figure imgf000030_0005
(NAOD-NTOF plane) and find the minimum on this line.
Figure imgf000030_0006
5.
Figure imgf000031_0001
6. m = m + 1
7. If m ≤ NCAP go to Step 3.
The mod operation used for the distance of Step 3 is done because the NAOD axis is cyclic (this means that NAOD=0.5 and NAOD=-0.5 are the same).
The approximated prominence p,. is in fact an upper-bound of the true prominence.
Indeed, the contour line encircling the /- th peak, but encircling no higher peak, must intersect the line connecting the /-th peak with any higher peak. On the other hand, a lower contour line may intersect this line but not encircle the i-th peak (this is why it is an upper bound on the prominence). The reason for choosing the closest higher peak is to make the probability of the latter case smaller. If the candidate channel paths are not determined by the SpotFi algorithm, but by another related array processing algorithm, and q(θ, τ) is not available on the line connecting peaks, it can be calculated on the fly where it is necessary. In a following stage (Iterative LS estimation) the processing circuitry 111 of the AP 110 may be configured to reduce the number of candidate peaks from NCAP candidate peaks to Np peaks , and the remaining parameters fi and αi (corresponding to
Figure imgf000031_0002
Figure imgf000031_0003
the I -th peak) are estimated. The idea is to use peak prominence and an iterative LS estimation to find the peaks that improve the LS error and remove the false peaks. Let f denote the vector whose i -th entry is .
Let A denote the matrix whose i -th row is .
Figure imgf000031_0004
Given the channel estimates NAODsθ , and NTOFs τ , the LS based
Figure imgf000031_0005
estimation, calculating
Figure imgf000031_0006
and
Figure imgf000031_0007
the estimates for f and A , respectively, may be implemented by the processing circuitry 111 in the following way: Step 1 : construct and
Figure imgf000032_0001
, where dim(x) is the dimension of
Figure imgf000032_0002
the vector x .
Step 2: calculate , where o denotes Hadamard
Figure imgf000032_0003
product.
Step 3: calculate , where
Figure imgf000032_0004
lis a vector with all entries equal 1 .
Step 4: calculate
Figure imgf000032_0005
Step 5: A is calculated as follows for
Figure imgf000032_0006
i =1,..., dim(θ) , r = 1,...,NR .
Step 6: calculate
Figure imgf000032_0007
The above LS based estimation steps may be denoted as a function
Figure imgf000032_0008
Let be a function defined as follows:
Figure imgf000032_0009
Figure imgf000032_0010
where .
Figure imgf000032_0011
The above function measures the least squares error over the 2 NDPs. The 1s and gf functions may be used in iterative way described below. Let pth denote the low prominence threshold. A peak (θii) is said to be a low prominence peak if pi<pth .
Construct the vector r0 containing the indices of the low prominence peaks ordered according to their prominence, from most prominent to least prominent. Given a vector r , if dim(r) >1 , puncturing the s entry from r means to construct the vector
Figure imgf000033_0001
Puncturing the entry of a scalar, gives the empty vector (whose dimension is 0).
The parameter / used below is the LS refinement threshold, whose value is less than 1 (e.g., 0.79). Let and be constructed from the prominent peaks by setting their i -th entry to
Figure imgf000033_0002
·
Let for i = 1,...,NProm denote the prominent peaks. Let θ0 and τ0 be such that
Figure imgf000033_0003
their i -th entries are , respectively.
Figure imgf000033_0004
Step 1 : Put m = 0 Step 2: Calculate and
Figure imgf000033_0005
Figure imgf000033_0006
Step 3: Put s = 1
Step 4: Let
Figure imgf000033_0007
Step 5: Calculate and
Figure imgf000033_0008
Figure imgf000033_0009
Step 6: If go to Step 12
Figure imgf000033_0010
Step 7:
Figure imgf000034_0007
Step 8: puncture the s entry from r and put in rm Step 9: , and
Figure imgf000034_0001
Figure imgf000034_0002
Step 10: If dim(rm) = 0(i.e., rm is empty), m = m + 1 and go to Step 14 Step 11 :m = m + 1 ; go to Step 3
Step 12: if s = dim(rm) , go to Step 14
Step 13: s = s + 1 and go to Step 4
Step 14:
Figure imgf000034_0003
In an embodiment, the iterative LS estimation process may end, when either rm is empty or no peak in rm decreases the LS error by the specified threshold.
In an embodiment, the processing circuitry 111 of the AP 110 may be configured to implement an efficient calculation of the LS from one iteration to the following by using the block matrix inversion formula. An initial is iteration may be done in Step 2 and one obtains
Figure imgf000034_0004
, and
Figure imgf000034_0005
. Then for m ≥ 1 :
Figure imgf000034_0006
Figure imgf000035_0001
This means that for each LS iteration may be stored,
Figure imgf000035_0002
Figure imgf000035_0003
for instance, in the memory 115 to be used in the next iteration. In another variant, may be stored instead of for the updates:
Figure imgf000035_0004
Figure imgf000035_0005
Figure imgf000035_0006
where
Figure imgf000035_0007
This may be written as.
Figure imgf000036_0001
The equations above follow from each other and the fact that
Figure imgf000036_0002
In an embodiment, the processing circuitry 111 of the AP 110 is further configured to implement a processing block for the geometrical channel estimation and prediction. In an embodiment, this block is configured to calculate , based on , and
Figure imgf000036_0004
Figure imgf000036_0005
Figure imgf000036_0003
using 0, respectively, where are the
Figure imgf000036_0006
Figure imgf000036_0007
shifted Dopplers, which are calculated by the Advance Phase correction block described below.
The geometrical channel estimation and prediction block provides a prediction for the channel. However, this prediction may be not robust and may suffer from missed paths, in particular for channels with a large number of paths. In order to efficiently handle missed paths the errors provided by the channel model may be used. This approach is based on the idea to consider the resulting estimation error in each NDP, i.e.
Figure imgf000036_0008
, where
Figure imgf000036_0009
is an output of the Phase Correction block (see below). These errors may contain missed paths, the noise, and in some cases false peaks detected by the SpotFi algorithm. Instead of ignoring these errors, a linear extrapolation may be performed in the following form:
Figure imgf000036_0010
In an embodiment, the processing circuitry 111 of the AP 110 is further configured to use the model predicted error in the final prediction:
Figure imgf000037_0001
where β is a function of .
Figure imgf000037_0002
The reason why β ≠ 1 is advantageous is two-fold. First, the linear interpolation may be biased, i.e., the result is over estimated (on average) by some scaling factor. Adding the term ET , which originated from the linear interpolation of
Figure imgf000037_0003
, which, in turn, originated from the SOS Geometrical channel prediction, without compensating for the scaling does not improve performance. Secondly, if the SOS geometrical channel prediction estimates all the paths sufficiently well (which can happen in channels with few paths), the addition of the ET-term only adds noise and causes degradation.
However, properly choosing β can lead to huge gains relative to β = 0 in the case of WiFi channels, which have many paths, yet have no degradation in the case of channels with a small number of paths.
In an embodiment, the processing circuitry 111 of the AP 110 may use the value
Figure imgf000037_0004
, where: and γ is a function of , and
Figure imgf000037_0006
Figure imgf000037_0005
approaches 0 when the model errors
Figure imgf000037_0007
are mainly due to the channel estimation errors and approaches 1 when the model errors
Figure imgf000037_0008
are significantly larger than the channel estimates errors.
The motivation for the above choice of is that it removes from the linear prediction the
Figure imgf000037_0009
linear prediction of the residue. This gives the linear prediction of the part of the channel that the SOS model based prediction predicted. The scaling factor between the SOS model-based prediction and the corresponding linear extrapolation may be found as and be compensated for by multiplying ET by .
Figure imgf000037_0011
Figure imgf000037_0010
As far as γ is concerned, in one embodiment it may be defined as follows:
Figure imgf000038_0001
In an embodiment, the processing circuitry 111 of the AP 110 is further configured to implement an advance slope correction processing block. This block may use a MUSIC type algorithm for each of the NDPs for finding the TOFs of each NDP and trying to compensate for the slope difference between NDPs and also centers of the TOFs relative to the SpotFi grid used later. The MUSIC algorithm implemented in the preprocessing stage is 1 -dimensional, only on the TOF (The TX antennas are averaged). The output for the nth NDP is TOFs and prominence of each candidate peak . Next the TOFs
Figure imgf000038_0002
Figure imgf000038_0003
and of the (n-1)- th and n-th NDP, respectively, may be merged, in the sense of finding i, j such that
Figure imgf000038_0004
and correspond to the same path. For each pair also a
Figure imgf000038_0005
prominence may be calculated as .
Figure imgf000038_0006
Let L denote the number of such pairs (which can be a smaller number than the number of peaks found in each of the NDPs). Note that for these pairs, in general,
Figure imgf000038_0007
and
Figure imgf000038_0008
should differ due to a residual slope difference. The pairs for which their prominence is above a certain threshold are used to calculate vectors Δτ and ητ whose entries are and , respectively. If no pair has a prominence above the
Figure imgf000038_0009
Figure imgf000038_0010
threshold, only the peak with the largest prominence is used. In the next step the median m of Δτ may be calculated as well as s such that is found, where gT is the grid step for
Figure imgf000038_0011
TOF used by the SpotFi algorithm.
Then the slope of the (n-1 )-th and n-th NDP may be corrected as follows:
Figure imgf000038_0012
As described above, the timing impairment causing a slope error may be handled by the Advance slope correction processing block, but the phase error so far is corrected only by the FFT based PSC. It turns out that this simple pre-processing stage may be usually sufficient for the SpotFi algorithm since the rotation between NDPs is sufficiently small. However, after the SpotFi algorithm and subsequent LS estimation is done and the Doppler shifts are found, it may be advantageous to add another compensation for the phase offset so that the channel prediction, which also uses linear estimation on the model errors, will be even more accurate. This compensation may be implemented rather simply. For instance, in an embodiment, the processing circuitry 111 of the AP 110 may be configured to determine the maximum estimated Doppler shifts and the minimum estimated Doppler shifts over all paths that are considered real paths (after iterative LS estimation), and to take the average thereof. The channel prediction may be compensated for this average Doppler shift, i.e.:
Figure imgf000039_0001
As already described above, the embodiments described above may be extended for handling antenna polarization as well. By way of example, the odd TX antennas may support a polarization (say horizontal H), while the even TX antennas support an orthogonal polarization (say vertical V). Similarly, the odd RX antennas may support a polarization, while the even RX antennas support an orthogonal polarization (in general, not aligned with the TX side). It can be shown that the SOS model gives:
Figure imgf000039_0002
where and are NR x 1 vectors corresponding to the channel complex phasor from
Figure imgf000039_0003
TX antennas with first and second polarization, respectively, to the RX antennas. The vector is a NT / 2 × 1 steering vector corresponding to NT /2 antennas with the same polarization. The vector δr denotes a column vector with all entries zero except the r-th entry that is 1. The idea behind this approach is to cast the problem with polarization to a different problem that is equivalent to the single polarization case.
We define , ar\6 redefine as a matrix whose ( r,q )-
Figure imgf000040_0001
Figure imgf000040_0002
Figure imgf000040_0003
th entry is the channel from 2q -1 + mod(r, 2) TX antenna to RX antenna. This
Figure imgf000040_0008
leads to:
Figure imgf000040_0004
with αi a vector and vAODi) a vector. The processing circuitry 111 of the
Figure imgf000040_0005
Figure imgf000040_0006
AP 110 may be configured to apply the SpotFi based scheme on the new problem, but with different values for Msc and MT than for the single polarization case. The results are also valid when the AP 110 has dual-polarized antennas 113a-n (each element has the H and V components) and/or the ST As 120 have dual-polarized antennas 121 , where each antenna with dual polarization is regarded as two antennas at the same position each with a single polarization. For example, if the AP 110 has dual polarized antennas 113a-n, NT is taken as twice the number of physical antennas, and then is the number of physical
Figure imgf000040_0007
antennas.
As already described above, the processing circuitry 111 of the AP 110 is configured to update the precoder for each new predicted channel. The channel may be updated either each new downlink transmission or within a transmission. Since in the second main embodiment the full channel is predicted, SVD is beneficial prior to precoding. The SVD may be similar to the SVD done in the STAs 120 only that it is done on the predicted channel.
Figures 8a to 8e illustrate the performance gains of the wireless transceiver 110 according to different embodiments provided in particular in mobile scenarios.
As can be taken from figure 8a, with the plain vanilla ZOH scheme it is impossible to accommodate the modulation and coding scheme MCS7, when the AP is equipped with 8 TX antennas transmitting to 6 STAs equipped with 1 RX antenna each and the velocity of the STAs is 3 km/h (there is a complete collapse). However, the AP 110 according to an embodiment (using the A-LP scheme described above) can achieve a good PER (packet error rate) performance with a 3 km/h velocity and approach the performance of the ZOH scheme in the case of 0 km/h. When the velocity is 1 km/h, the performance of the AP 110 according to an embodiment implementing the A-LP scheme described above further improves.
Figure 8a presented the performance gain provided by an embodiment of the AP 110 in terms of the PER for a chosen MCS. In the following a further exemplary scenario is described illustrating the performance gain provided by an embodiment of the AP 110 in terms of the actual throughput. In this exemplary scenario the AP 110 according to an embodiment comprises 8 TX antennas and is configured to transmit a packet in DL-MU- MIMO mode to several ST As 120 with NR=1 RX antennas for a certain fixed SNR. For each SNR value, all possible MCSs are determined and the MCS is found that maximizes the goodput. Figure 8b provides a comparison between the maximum goodput provided by the AP 110 according to different embodiments of the first main group of embodiments implementing the A-LP scheme with the maximum goodput provided by a conventional AP using the ZOH scheme. As can be taken from figure 8b, the AP 110 according to different embodiments provides a very significant gain in goodput for high SNR, e.g., a 90 % throughput gain at SNR=30dB.
Figures 8c and 8d provide comparisons between the maximum goodput provided by the AP 110 according to different embodiments of the second main group of embodiments implementing the geometric channel model with the maximum goodput provided by a conventional AP using the ZOH scheme. In this exemplary scenario the AP 110 according to an embodiment comprises 8 TX antennas and is configured to transmit a packet in DL- MU-MIMO mode to several ST As 120 with NR=1 RX antenna (Figure 8c) and NR=2 RX antennas (Figure 8d) for a certain fixed SNR.
Figure 8e shows that in comparison with a conventional AP an embodiment of the AP 110 implementing the A-LP scheme does not result in a negative gain, i.e. no performance degradation in low mobility/low SNR scenarios. More specifically, figure 8e compares the performance of an embodiment of the AP 110 implementing the A-LP scheme in terms of PER with that of a conventional AP implementing the ZOH scheme in the case that there is no mobility, i.e., 0 km/h velocity. As can be taken from figure 8e, there is no negative gain (i.e., no degradation relative to ZOH). In this context it may be noted that the embodiments of the AP 110 implementing the A-LP scheme have a low computational complexity, which is linear in the number of TX antennas, RX antennas, and number of SCs. Thus, the complexity increase relative to a conventional AP implementing the ZOH scheme is negligible. Figure 9 is a flow diagram illustrating a method 900 of operating the wireless transceiver, in particular AP 110. The method 900 comprises the steps of: receiving 901 at a plurality of times channel state information from the plurality of further wireless transceivers, including channel state information at a first time and channel state information at a second time; performing 903 a phase alignment of the channel state information at the second time with the channel state information at the first time; predicting 905 a channel state for an upcoming transmission at a third time based on the phase aligned channel state information; and adjusting 907 an adjustable precoding configuration based for operating the array of antennas based on the predicted channel state for the upcoming transmission.
The person skilled in the art will understand that the "blocks" ("units") of the various figures (method and apparatus) represent or describe functionalities of embodiments of the present disclosure (rather than necessarily individual "units" in hardware or software) and thus describe equally functions or features of apparatus embodiments as well as method embodiments (unit = step).
In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus, and method may be implemented in other manners. For example, the described embodiment of an apparatus is merely exemplary. For example, the unit division is merely logical function division and may be another division in an actual implementation. For example, a plurality of units or components may be combined or integrated into another system, or some features may be ignored or not performed. In addition, the displayed or discussed mutual couplings or direct couplings or communication connections may be implemented by using some interfaces. The indirect couplings or communication connections between the apparatuses or units may be implemented in electronic, mechanical, or other forms.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the objectives of the solutions of the embodiments. In addition, functional units in the embodiments of the invention may be integrated into one processing unit, or each of the units may exist alone physically, or two or more units are integrated into one unit.

Claims

1. A wireless transceiver (110), comprising: a communication interface (113) comprising an array of antennas (113a-d), wherein the communication interface (113) is configured to receive at a plurality of times channel state information from a plurality of further wireless transceivers (120), including channel state information at a first time and channel state information at a second time, and to operate the array of antennas (113a-d) with an adjustable precoding configuration; and a processing circuitry (111) configured to perform a phase alignment of the channel state information at the second time with the channel state information at the first time and to predict a channel state for an upcoming transmission based on the phase aligned channel state information, wherein the processing circuitry (111) is further configured to adjust the adjustable precoding configuration for the upcoming transmission based on the predicted channel state for the upcoming transmission.
2. The wireless transceiver (110) of claim 1 , wherein the communication interface (113) is further configured to transmit at a plurality of times a channel sensing signal to the plurality of further wireless transceivers (120) for allowing the plurality of further wireless transceivers (120) to determine the channel state information and/or to transmit the channel state information to the wireless transceiver (110).
3. The wireless transceiver (110) of any one of the preceding claims, wherein the wireless transceiver (110) is a wireless access point (110) or base station (110).
4. The wireless transceiver (110) of any one of the preceding claims, wherein the wireless transceiver (110) is configured to operate in accordance with the IEEE 802.11 WLAN standard or a standard evolved therefrom.
5. The wireless transceiver (110) of any one of the preceding claims, wherein the channel state information received from the plurality of further wireless transceivers (120) is compressed and wherein the processing circuitry (111) is configured to decompress the compressed channel state information.
6. The wireless transceiver (110) of any one of the preceding claims, wherein the communication interface (113) is configured to communicate with the plurality of further wireless transceivers (120) using a plurality of frequency sub-carriers and wherein the channel state information comprise channel state information for a subset of the plurality of frequency sub-carriers.
7. The wireless transceiver (110) of claim 6, wherein the processing circuitry (111) is configured to perform the phase alignment on the channel state information for each frequency sub-carrier of the subset of the plurality of frequency sub-carriers separately.
8. The wireless transceiver (110) of any one of the preceding claims, wherein the channel state information received from the plurality of further wireless transceivers (120) at a time n is based on a singular value decomposition of a channel response matrix
Figure imgf000045_0001
Figure imgf000045_0002
and comprises one or more of the first columns of the matrix Vn and one or
Figure imgf000045_0003
more of the first diagonal elements
Figure imgf000045_0004
of the matrix Sn.
9. The wireless transceiver (110) of claim 8, wherein the processing circuitry (111) is configured to determine, based on the channel information at the time n, a partial channel response matrix , wherein k denotes a frequency sub-carrier index.
Figure imgf000045_0005
10. The wireless transceiver (110) of claim 9, wherein for aligning the channel state information the processing circuitry (111) is configured to determine a unitary matrix W that minimizes the following equation:
Figure imgf000045_0006
wherein the operation diag(...) transforms a vector into a diagonal matrix whose diagonal entries equal that vector.
11 . The wireless transceiver (110) of claim 9 or 10, wherein for aligning the channel state information the processing circuitry (111) is configured to determine a singular value decomposition
Figure imgf000045_0007
of the matrix and to determine the
Figure imgf000045_0008
unitary matrix W as
Figure imgf000045_0009
H.
12. The wireless transceiver (110) of claim 10, wherein the unitary matrix W is a diagonal unitary matrix.
13. The wireless transceiver (110) of any one of claims 10 to 12, wherein for aligning the channel state information the processing circuitry (111) is configured to apply the matrix W to the partial channel response matrix .
14. The wireless transceiver (110) of any one of claims 9 to 13, wherein the processing circuitry (111) is configured to predict the channel state for an upcoming
Figure imgf000046_0001
transmission based on the following equation:
Figure imgf000046_0002
wherein: and denote the aligned channel state information at the first and second time, Δ denotes a time difference between the first and second time,
T denotes a time difference between the second time and the upcoming transmission, and α denotes a parameter.
15. The wireless transceiver (110) of claim 14, wherein the parameter α is a function of the aligned channel state information at the first and second time and channel estimation error variances at the first and second time.
16. The wireless transceiver (110) of claim 14 or 15, wherein the processing circuitry (111 ) is configured to determine the parameter α based on the following equations:
Figure imgf000046_0003
wherein: and denote the channel estimation error variances at the first and second time,
NDSC denotes the decimated number of sub-carrier frequencies, Nr denotes the number of receiver antennas of one of the plurality of further wireless transceivers (120), and
Ns denotes the number of spatial streams for the one of the plurality of further (120) wireless transceivers for the upcoming transmission.
17. The wireless transceiver (110) of any one of claims 1 to 7, wherein the processing circuitry (111) is configured to align the channel state information at the first time and the channel state information at the second time based on a parametrized geometrical channel model and to predict the channel state for the upcoming transmission based on the parametrized geometrical channel model.
18. The wireless transceiver (100) of claim 17, wherein the parametrized geometrical channel model is defined by one or more parameters of the parametrized geometrical channel model and wherein the processing circuitry is configured to determine the one or more parameters of the parametrized geometrical channel model based on the channel state information.
19. The wireless transceiver (110) of claim 18, wherein the channel state information received from the plurality of further wireless transceivers (120) at a time n is based on a singular value decomposition of a channel response matrix and comprises
Figure imgf000047_0001
the matrices Un and Vn and the diagonal elements of the matrix Sn.
20. The wireless transceiver (110) of any one of claims 17 to 19, wherein the processing circuitry (111) is configured to determine the one or more parameters of the parametrized geometrical channel model on the basis of the following equation:
Figure imgf000047_0002
wherein: αi, r denotes a complex number accounting for the i-th path complex gain with respect to the r-th antenna, s(t - Ti)T denotes the transmitted signal vector with the i-th entry corresponding to i-th antenna, θi denotes the angle of departure, ti denotes the time-of-flight, x(θi) denotes the steering vector, and fm co s(φ i) denotes a term accounting for a Doppler shift of the i-th path.
21 . The wireless transceiver (110) of any one of claims 17 to 20, wherein the processing circuitry (111) is configured to determine, based on the parametrized geometrical channel model, a plurality of candidate paths.
22. The wireless transceiver (110) of claim 21 , wherein the one or more parameters of the parametrized geometrical channel model comprise an angle of departure and a time- of-flight [associated with each candidate path] and wherein the processing circuitry (111) is configured to determine the plurality of candidate paths on the basis of a plurality of local maxima of a spectrum function depending on the angle of departure and the time-of- flight.
23. The wireless transceiver (110) of claim 22, wherein the processing circuitry (111) is further configured to determine a prominence for each of the plurality of local maxima of the function depending on the angle of departure and the time-of-flight and to determine the plurality of candidate paths on the basis of the plurality of prominences.
24. The wireless transceiver (110) of claim 23, wherein the one or more parameters of the parametrized geometrical channel model further comprise an antenna gain for each antenna of the array of antennas (113a-d) and a Doppler shift and wherein processing circuitry (111) is further configured to reduce the number of candidate paths on the basis of an iteratively determined least squares error.
25. The wireless transceiver (110) of claim 24, wherein the processing circuitry (111) is further configured to correct the Doppler shifts of the plurality of candidate paths on the basis of an average of a minimum Doppler shift and a maximum Doppler shift of the plurality of candidate paths.
26. The wireless transceiver (110) of any one of claims 22 to 25, wherein the processing circuitry (111) is further configured to adjust the prediction of the channel state for the upcoming transmission on the basis of an adjustment between the plurality of time- of-flights of each of the plurality of candidate paths at the first time and the plurality of time-of-flights of each of the plurality of candidate paths at the second time.
27. The wireless transceiver (110) of any one of claims 17 to 26, wherein the processing circuitry (111) is further configured to estimate one or more model errors of the parametrized geometrical channel model at the first time and the second time and to predict the one or more model errors of the parametrized geometrical channel model for the upcoming transmission, wherein the processing circuitry (111) is further configured to predict the channel state for the upcoming transmission based on the parametrized geometrical channel model and the one or more predicted model errors.
28. The wireless transceiver (110) of claim 27, wherein the processing circuitry (111 ) is further configured to predict the one or more model errors of the parametrized geometrical channel model for the upcoming transmission using a linear prediction and to weight the one or more predicted model errors by a weighting parameter b.
29. A method (900) of operating a wireless transceiver (110) comprising an array of antennas (113a-d), wherein the method (900) comprises: receiving (901) at a plurality of times channel state information from a plurality of further wireless transceivers (120), including channel state information at a first time and channel state information at a second time; performing (903) a phase alignment of the channel state information at the second time with the channel state information at the first time; predicting (905) a channel state for an upcoming transmission based on the phase aligned channel state information; and adjusting (907), based on the predicted channel state for the upcoming transmission, a precoding configuration for operating the array of antennas.
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