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EP2130341A2 - Atténuation d'un déséquilibre en quadrature à l'aide de séquences d'apprentissage sans biais - Google Patents

Atténuation d'un déséquilibre en quadrature à l'aide de séquences d'apprentissage sans biais

Info

Publication number
EP2130341A2
EP2130341A2 EP08731756A EP08731756A EP2130341A2 EP 2130341 A2 EP2130341 A2 EP 2130341A2 EP 08731756 A EP08731756 A EP 08731756A EP 08731756 A EP08731756 A EP 08731756A EP 2130341 A2 EP2130341 A2 EP 2130341A2
Authority
EP
European Patent Office
Prior art keywords
training sequence
unbiased
symbol
generating
symbols
Prior art date
Legal status (The legal status 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 status listed.)
Withdrawn
Application number
EP08731756A
Other languages
German (de)
English (en)
Inventor
Rabih Chrabieh
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Qualcomm Inc
Original Assignee
Qualcomm Inc
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
Priority claimed from US11/684,566 external-priority patent/US8428175B2/en
Priority claimed from US11/755,719 external-priority patent/US8290083B2/en
Priority claimed from US11/853,809 external-priority patent/US8081695B2/en
Priority claimed from US11/853,808 external-priority patent/US8064550B2/en
Application filed by Qualcomm Inc filed Critical Qualcomm Inc
Publication of EP2130341A2 publication Critical patent/EP2130341A2/fr
Withdrawn legal-status Critical Current

Links

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2602—Signal structure
    • H04L27/261—Details of reference signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/05—Electric or magnetic storage of signals before transmitting or retransmitting for changing the transmission rate
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/38—Demodulator circuits; Receiver circuits
    • H04L27/3845—Demodulator circuits; Receiver circuits using non - coherent demodulation, i.e. not using a phase synchronous carrier
    • H04L27/3854—Demodulator circuits; Receiver circuits using non - coherent demodulation, i.e. not using a phase synchronous carrier using a non - coherent carrier, including systems with baseband correction for phase or frequency offset
    • H04L27/3863—Compensation for quadrature error in the received signal
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H04L2027/0016—Stabilisation of local oscillators
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0224—Channel estimation using sounding signals
    • H04L25/0226—Channel estimation using sounding signals sounding signals per se

Definitions

  • Patent Application No. 11/684,566 entitled QUADRATURE MODULATION ROTATING TRAINING SEQUENCE, filed March 9, 2007, wherein its status is pending, Attorney Docket No. 060395, and assigned to the assignee hereof and hereby expressly incorporated by reference herein.
  • This invention relates generally to communication channel estimation and, more particularly, to systems and methods for using a quadrature modulation unbiased training sequence in the training of receiver channel estimates.
  • FIG. 1 is a schematic block diagram of a conventional receiver front end (prior art).
  • a conventional wireless communications receiver includes an antenna that converts a radiated signal into a conducted signal. After some initial filtering, the conducted signal is amplified. Given a sufficient power level, the carrier frequency of the signal may be converted by mixing the signal (down-converting) with a local oscillator signal. Since the received signal is quadrature modulated, the signal is demodulated through separate I and Q paths before being combined. After frequency conversion, the analog signal may be converted to a digital signal, using an analog-to- digital converter (ADC), for baseband processing. The processing may include a fast Fourier transform (FFT).
  • FFT fast Fourier transform
  • a unique direction in the constellation (e.g., the I path) is stimulated, while the other direction (e.g., the Q path) is not.
  • the same type of unidirectional training may also be used with pilot tones. Note: scrambling a single modulation channel (e.g., the I channel) with ⁇ 1 symbol values does not rotate the constellation point, and provides no stimulation for the quadrature channel.
  • FIG. 2 is a schematic diagram illustrating quadrature imbalance at the receiver side (prior art). Although not shown, transmitter side imbalance is analogous.
  • the Q path is the reference.
  • the impinging waveform is cos(wt + ⁇ ), where ⁇ is the phase of the channel.
  • the Q path is down-converted with — sin(wt).
  • the I path is down-converted with (l+2 ⁇ )cos(wt+ 2 ⁇ ).
  • 2 ⁇ and 2 ⁇ are hardware imbalances, respectively a phase error and an amplitude error.
  • the low pass filters Hi and HQ are different for each path.
  • the filters introduce additional amplitude and phase distortion. However, these additional distortions are lumped inside 2 ⁇ and 2 ⁇ . Note: these two filters are real and affect both +w and —w in an identical manner. [0008] Assuming the errors are small:
  • the first component on the right hand side, cos(wt), is the ideal I path slightly scaled.
  • the second component, - 2A ⁇ .sin(wt), is a small leakage from the Q path. After down-conversion of the impinging waveform: in the I path: (l+2£)cos(#) + 2£.sin(#). in the Q path: sin(#).
  • Wireless communication receivers are prone to errors caused by a lack of tolerance in the hardware components associated with mixers, amplifiers, and filters. In quadrature demodulators, these errors can also lead to imbalance between the I and Q paths, resulting in improperly processed data.
  • a training signal can be used to calibrate receiver channels.
  • a method for transmitting an unbiased communications training sequence.
  • the method generates an unbiased training sequence in a quadrature modulation transmitter.
  • the unbiased training sequence represents a uniform accumulated power evenly distributed in the complex plane. More explicitly, training information in the time domain is sent via an in-phase (I) modulation path having an accumulated power. Training information in the time domain is sent via a quadrature (Q) modulation path having an accumulated power equal to the I modulation path power.
  • the unbiased training sequence is generated as a signal pair including a complex value reference signal (p) at frequency +f and a complex value mirror signal (p m ) at frequency — f.
  • the method nullifies the product (p-p m ).
  • a method is also provided for calculating an unbiased channel estimate.
  • the method accepts an unbiased training sequence in a quadrature demodulation receiver.
  • the unbiased training sequence includes predetermined reference signals (p) representing a uniform accumulated power evenly distributed in the complex plane.
  • the method processes the unbiased training sequence and generates processed symbols (y) representing complex plane information in the unbiased training sequence.
  • the processed symbols (y) are multiplied by the conjugate of the corresponding reference signal (p*), and an unbiased channel estimate (h u ) is obtained.
  • FIG. 1 is a schematic block diagram of a conventional receiver front end (prior art).
  • FIG. 2 is a schematic diagram illustrating quadrature imbalance at the receiver side (prior art).
  • FIG. 3 is a schematic block diagram depicting an exemplary data transmission system.
  • FIG. 4 is a schematic block diagram of a system or device for transmitting an unbiased communications training sequence.
  • Fig. 5A is a diagram depicting an unbiased training sequence represented in both the time and frequency domains.
  • FIGS. 5B and 5C are diagrams depicting the uniform accumulation of power evenly distributed in a complex plane.
  • FIG. 6 is a diagram depicting an unbiased training sequence enabled as a sequence of pilot tones in the time domain.
  • FIG. 7 is a diagram depicting an unbiased training sequence enabled as a preamble preceding non-predetermined communication data.
  • FIG. 8 is a diagram depicting an unbiased training sequence enabled by averaging symbols over a plurality of messages.
  • FIG. 9 is a schematic block diagram depicting a processing device for transmitting an unbiased communications training sequence.
  • FIG. 10 is a schematic block diagram of a system for calculating an unbiased channel estimate.
  • FIG. 11 is a schematic block diagram depicting a processing device for calculating an unbiased channel estimate.
  • Fig. 12 depicts the performance achieved by applying the above- described algorithms to the WiMedia UWB standard.
  • Fig. 13 is a flowchart illustrating a method for transmitting an unbiased communications training sequence.
  • Fig. 14 is a flowchart illustrating a method for calculating an unbiased channel estimate.
  • a component may be, but is not limited to being, a process running on a processor, generation, a processor, an object, an executable, a thread of execution, a program, and/or a computer.
  • an application running on a computing device and the computing device can be a component.
  • One or more components can reside within a process and/or thread of execution and a component may be localized on one computer and/or distributed between two or more computers.
  • these components can execute from various computer readable media having various data structures stored thereon.
  • the components may communicate by way of local and/or remote processes such as in accordance with a signal having one or more data packets (e.g., data from one component interacting with another component in a local system, distributed system, and/or across a network such as the Internet with other systems by way of the signal).
  • a signal having one or more data packets (e.g., data from one component interacting with another component in a local system, distributed system, and/or across a network such as the Internet with other systems by way of the signal).
  • data packets e.g., data from one component interacting with another component in a local system, distributed system, and/or across a network such as the Internet with other systems by way of the signal.
  • DSP digital signal processor
  • ASIC application specific integrated circuit
  • FPGA field programmable gate array
  • a general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine.
  • a processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.
  • a software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
  • a storage medium may be coupled to the processor such that the processor can read information from, and write information to, the storage medium.
  • the storage medium may be integral to the processor.
  • the processor and the storage medium may reside in an ASIC.
  • the ASIC may reside in the node, or elsewhere.
  • the processor and the storage medium may reside as discrete components in the node, or elsewhere in an access network.
  • FIG. 3 is a schematic block diagram depicting an exemplary data transmission system 300.
  • a baseband processor 302 has an input on line 304 to accept digital information form the Media Access Control (MAC) level.
  • the baseband processor 302 includes an encoder 306 having an input on line 304 to accept digital (MAC) information and an output on line 308 to supply encoded digital information in the frequency domain.
  • An interleaver 310 may be used to interleave the encoded digital information, supplying interleaved information in the frequency domain on line 312.
  • the interleaver 310 is a device that converts the single high speed input signal into a plurality of parallel lower rate streams, where each lower rate stream is associated with a particular subcarrier.
  • An inverse fast Fourier transform (IFFT) 314 accepts information in the frequency domain, performs an IFFT operation on the input information, and supplies a digital time domain signal on line 316.
  • a digital-to-analog converter 318 converts the digital signal on line 316 to an analog baseband signal on line 320.
  • a transmitter 322 modulates the baseband signal, and supplies a modulated carrier signal as an output on line 324.
  • alternate circuitry configurations capable of performing the same functions as described above would be known by those with skill in the art.
  • a receiver system would be composed of a similar set of components for reverse processing information accepted from a transmitter.
  • FIG. 4 is a schematic block diagram of a system or device for transmitting an unbiased communications training sequence.
  • the system 400 comprises a transmitter or transmission means 402 having an input on line 404 to accept digital information. For example, the information may be supplied from the MAC level.
  • the transmitter 402 has an output on line 406 to supply a quadrature modulation unbiased training sequence representing a uniform accumulated a power evenly distributed in a complex plane.
  • the transmitter 402 may include a transmitter subsystem 407, such as a radio frequency (RF) transmitter subsystem that uses an antenna 408 to communicate via an air or vacuum media.
  • RF radio frequency
  • the transmitter subsystem 407 includes an in-phase (I) modulation path 410, or a means for generating I modulation training information in the time domain having an accumulated power.
  • the transmitter subsystem 407 also includes a quadrature (Q) modulation path 412, or a means for generating Q modulation training information in the time domain having an accumulated power equal to the I modulation path power.
  • I path information on line 404a is upconverted at mixer 414 with carrier fc, while Q path information on line 404b is upconverted at mixer 416 with a phase shifted version of the carrier (fc + 90°).
  • the I path 410 and Q path 412 are summed at combiner 418 and supplied on line 420.
  • the signal is amplified at amplifier 422 and supplied to antenna 408 on line 406, where the unbiased training sequences are radiated.
  • the I and Q paths may alternately be referred to as I and Q channels.
  • a unbiased training sequence may also be referred to as a rotating training signal, a quadrature balanced training sequence, balanced training sequence, balanced training sequence, or unbiased training signal.
  • the unbiased training sequence may be initially sent via the I modulation path 410, with training information subsequently sent via the Q modulation path 412. That is, the training signal may include information, such as a symbol or a repeated series of symbols sent only via the I modulation path, followed by the transmission of a symbol or repeated series of symbols sent only via the Q modulation path. Alternately, training information may be sent initially via the Q modulation path, and subsequently via the I modulation path. In the case of single symbols being sent alternately through the I and Q paths, the transmitter sends a rotating training signal. For example, the first symbol may always be (1,0), the second symbol may always be (0,1), the third symbol (-1,0), and the fourth symbol (0-1).
  • the transmitter may send training information simultaneously through both the I and Q modulation paths, and combine I and Q modulated signals.
  • the above-mentioned rotating type of unbiased training sequence which initially sends training signal via Oust) the I modulation path, may be accomplished by energizing the I modulation path, but not energizing the Q modulation path. Then, the transmitter sends a training signal via the Q modulation path by energizing the Q modulation path, subsequent to sending training information via the I modulation path.
  • the training symbols can also be rotated by supplying symbols, each with both I and Q components, as is conventionally associated with quadrature modulation.
  • the transmitter 402 also sends quadrature modulated (non-predetermined) communication data.
  • the unbiased training sequence is used by a receiver (not shown) to create unbiased channel estimates, which permit the non-predetermined communication data to be recovered more accurately.
  • the quadrature modulated communication data is sent subsequent to sending the unbiased training sequence.
  • the unbiased training sequence is sent concurrently with the communication data in the form of pilot signals. The system is not limited to any particular temporal relationship between the training signal and the quadrature modulated communication data.
  • the symbol values associated with any particular subcarrier may periodically vary.
  • a message is a grouping of symbols in a predetermined format.
  • a message has a duration of several symbols periods. One or more symbols may be transmitted every symbol period.
  • Some messages include a preamble preceding the main body of the message. For example, a message may be formed as a long packet containing many OFDM symbols. Each OFDM symbol contains many subcarriers.
  • the message preamble includes the unbiased training sequence.
  • the unbiased training sequence is a sequence of pilot signals that are transmitted simultaneously with the non-predetermined communication data.
  • a methodology that rotates the phase of the symbol by 90 degrees every period is not always useful.
  • a 60- degree or 120- degree rotation may be used to evenly distribute the symbol
  • a 180/5-degree or 360/5- degree rotation may be used.
  • combination solutions can be used. For example, if there are a total of 7 symbols in a message, then a rotation of 90 degrees may be used for the first 4 symbols, and a rotation of 120 (or 60) degrees for the next three symbols.
  • the unbiased training sequence may be averaged over more than one message. For example, if a message includes 3 training symbols, then the combination of 2 messages includes 6 symbols. In the context of a 6-symbol training signal, a rotation of 90 degrees may be used between symbols.
  • the power associated with a symbol vector at angle ⁇ in complex space may also be considered to be the power at ( ⁇ + 180).
  • the accumulated power at an angle of 60 degrees is the same as the power at 240 degrees.
  • the power associated with a symbol at angle ⁇ may be summed with the power at angle ( ⁇ + 180).
  • Fig. 5A is a diagram depicting an unbiased training sequence represented in both the time and frequency domains.
  • the transmitter generates a signal pair including a complex value reference signal (p) at frequency +f and a complex value mirror signal (p m ) at frequency — f, with a nullified product (P 1 P 1n ).
  • P 1 P 1n a nullified product
  • p and p m are complex values with amplitude and phase components.
  • the transmitter may nullify the sum of the products (pi ⁇ i m ) by generating information as a complex value that remains constant for every occurrence, to represent p.
  • the transmitter may generate information as a complex value that rotates 180 degrees every occurrence.
  • the transmitter generates i occurrences of reference signal (p) and mirror signal (p m ), and a product (pi ⁇ i m ) for each occurrence. The transmitter pairs occurrences and nullifies the sum of the products from each paired occurrence.
  • one or more messages may contain a temporal sequence of N pilot tones, for a given subcarrier f, with N pilot tones for the mirror subcarrier — f.
  • N pilot tones
  • Pi ⁇ i m + P2"P2m 0-
  • the unbiased training sequence may include:
  • Time 1 pi for +f and p ⁇ m for -f;
  • the unbiased training sequence can be obtained by averaging.
  • the principle of unbiased training sequence dictates that the pilot must satisfy:
  • the unbiased training sequence can be organized as follows:
  • FIGS. 5B and 5C are diagrams depicting the uniform accumulation of power evenly distributed in a complex plane.
  • the complex plane can be used to represent real axis (R) and imaginary axis (I) information.
  • the circle represents the boundary of uniform power or energy with a normalized value of 1.
  • the unbiased training sequence is formed from 3 symbols: a first symbol (A) at 0 degrees; a second symbol (B) at 120 degrees; and a third symbol (C) at 240 degrees.
  • the exact same power distribution is obtained when the first symbol (A) remains at 0 degrees, the second symbol (B') is at 60 degrees, and the third symbol (C) is at 120 degrees.
  • the power associated with each symbol is 1.
  • the unbiased training sequence is formed from 5 symbols: 2 symbols at 0 degrees, each with a power of 0.5, so that the accumulated power is 1; a symbol at 90 degrees with a power of 1: a symbol at 180 degrees with a power of 1; and a symbol at 270 degrees with a power of 1.
  • FIG. 6 is a diagram depicting an unbiased training sequence enabled as a sequence of pilot tones in the time domain.
  • the transmitter may generate the unbiased training sequence by supplying P pilot symbols per symbol period, in a plurality of symbol periods. Each pulse in the figure represents a symbol.
  • the transmitter generates (N — P) quadrature modulated communication data symbols per symbol period, and simultaneously supplies N symbols per symbol period, in the plurality of symbol periods.
  • FIG. 7 is a diagram depicting an unbiased training sequence enabled as a preamble preceding non-predetermined communication data.
  • the transmitter generates quadrature modulated communication data and supplies the unbiased training sequence in a first plurality of symbol periods (e.g., at times 1-4), followed by the quadrature modulated communication data in a second plurality of symbol periods (e.g., at times 5 through N).
  • the pulses in the figure represent symbols.
  • an Ultra Wideband (UWB) system uses 6 symbols transmitted prior to the transmission of communication data or a beacon signal. Therefore, 3 consecutive symbols may be generated on the I modulation path followed by 3 consecutive on the Q modulation path. Using this process, the Q channel need only be activated briefly, for 3 symbols, before returning to sleep. However, there are many other combinations of symbols that may be used to generate an unbiased training sequence.
  • the transmitter generates a temporal sequence of complex plane symbols with equal accumulated power in a plurality of directions (in the complex plane).
  • direction refers to the summation of vectors at each angle ⁇ and ( ⁇ +180).
  • the power associated with a symbol at 0 degrees is accumulated with the power from a symbol at 180 degrees, as 0 and 180 degrees are the same direction.
  • the temporal sequence of symbols in the unbiased training sequence have a cumulative power associated with real axis information in the time domain, and an equal cumulative power associated with imaginary axis information in the time domain, as supplied in a plurality of symbols periods by the transmitter.
  • the "dot" between the a ⁇ an( j a ⁇ symbols is intended to represent a conventional multiplication operation between scalar numbers.
  • a ⁇ is typically a subcarrier with a periodic waveform, there is no one particular value for a. That is, a ⁇ varies with time, and could be represented as a-[(t).
  • the symbol may be expressed as a ⁇ (kT), or a ⁇ (k), assuming T is normalized to 1.
  • T is normalized to 1.
  • the power in direction ⁇ is:
  • integral a ⁇ -a ⁇ integral ⁇ pi. pi exp(j4 ⁇ ft)
  • FIG. 8 is a diagram depicting an unbiased training sequence enabled by averaging symbols over a plurality of messages.
  • a symbol (or more than one, not shown) is generated in a first symbol period in a first message.
  • a symbol is generated in a second symbol period in a second message, subsequent to the first message.
  • a training information symbols are generated in a plurality (n) messages.
  • the transmitter generates the unbiased training sequence by creating equal power in a plurality of complex plane directions, as accumulated over the plurality of messages.
  • a preamble type training sequence is shown, similar to FIG. 7, the same type of analysis applied to pilot-type unbiased training sequence.
  • FIG. 9 is a schematic block diagram depicting a processing device for transmitting an unbiased communications training sequence.
  • the processing device 900 includes a transmitter module 902 for accepting digital information on line 904 and supplying a quadrature modulation unbiased training sequence on line 906.
  • the unbiased training sequence represents a uniform accumulation of power evenly distributed in the complex plane.
  • the functionality associated with the processing device 900 is similar to the transmitter described in FIGS. 3 through 8 above, and will not be repeated here in the interest of brevity.
  • FIG. 10 is a schematic block diagram of a system for calculating an unbiased channel estimate.
  • the system 1000 comprises a quadrature demodulation receiver or receiving means 1002 having an input on line 1004 to accept an unbiased training sequence.
  • the receiver 1002 may be an RF device connected to an antenna 1005 to receive radiated information.
  • the receiver may alternately receive the unbiased training sequence via a wired or optical medium (not shown).
  • the unbiased training sequence includes predetermined reference signals (p) representing a uniform accumulated power evenly distributed in the complex plane, as defined above.
  • the receiver 1002 generates processed symbols (y) on line 1006 representing complex plane information in the unbiased training sequence, which is sent to multiplier 1008. Since the value of p is predetermined, a multiplier 1008 is able to multiply each processed symbol (y) by the (predetermined) conjugate of the corresponding reference signal (p*), and supply an unbiased channel estimate (h u ) at an output on line 1010.
  • the conjugate information may, for example, be stored in memory 1012 and supplied to the multiplier 1008 on line 1014.
  • the receiver 1002 accepts an unbiased training sequence with a plurality of simultaneously accepted predetermined reference signals (p n ).
  • the receiver may accept a message with P pilot symbols (per symbol period), see FIG. 6.
  • the receiver 1002 generates a plurality of processed symbols (y n ) from the corresponding plurality of reference signals, multiplies each processed symbol by its corresponding reference signal conjugate, obtains a plurality of channel estimates (h un ), and averages the channel estimate (h un ) for each value of n.
  • P unbiased channels estimates are obtained.
  • the methodology for determining channel estimates is well known in the art.
  • the present invention receiver is able to calculate extremely accurate unbiased type of channel estimate using predetermined data.
  • a receiver subsystem 1016 has an in-phase (I) demodulation path 1018 or a means for accepting I demodulation training information in the time domain having an accumulated power.
  • a quadrature (Q) demodulation path 1020 or a means for accepting Q demodulation training information in the time domain has an accumulated power equal to the I modulation path power.
  • the receiver 1002 accepts an unbiased training sequence with temporal sequence of n predetermined reference signals (p n ).
  • the receiver 1002 generates a temporal sequence of n processed symbols (y n ) from the temporal sequence of reference signals and multiplies each processed symbol in the temporal sequence by its corresponding reference signal conjugate.
  • P processed symbols (y) are generated each symbol period.
  • the receiver 1002 obtains a temporal sequence of n channel estimates (h un ), and averages the n channel estimates.
  • the receiver 1002 accepts the unbiased training sequence as a signal pair including a complex value reference signal (p) at frequency +f and a complex value mirror signal (p m ) at frequency -f, where the product (p-p m ) is null, see FIG. 5. Further, the receiver may accept the unbiased training sequence as i occurrences of the reference signal (p) and the mirror signal (p m ), where the sum of the products (pi ⁇ i m ) is null. In one variation, the receiver 1002 accepts i occurrences of the reference signal and mirror signal, where the signal pair values p and p m vary for every occurrence.
  • the receiver accepts the unbiased training sequence as i occurrences of the reference signal (p) and mirror signal (p m ), and generates a product (pi ⁇ i m ) for each occurrence.
  • the receiver pairs occurrences and generates a processed symbol by nullifying the sum of the products from each paired occurrence.
  • the receiver may accept a signal pair, where the sum of the products (pi ⁇ i m ) is nulled, as follows.
  • Information is accepted as a complex value that remains constant for every occurrence, representing p.
  • Information representing p m is accepted as a complex value that rotates 180 degrees every occurrence. [0073] Contrasting FIGS.
  • the receiver accepts the unbiased training sequence as P pilot symbols per symbol period, in a plurality of symbol periods, and obtains P unbiased pilot channel estimates.
  • the receiver simultaneously accepts (N — P) quadrature modulated communication data symbols in each symbol period, generating a processed symbol (y c ) for communication data in each symbol period. That is, (N-P) processed symbols are generated.
  • the receiver extrapolates channels estimates for each processed symbol (y c ), derived from the unbiased pilot channel estimates, and multiplies each processed symbol by the extrapolated channel estimate to derive a transmitted symbol (x).
  • the symbol x is the unknown symbol value that is transmitted as communication data.
  • the receiver 1002 accepts quadrature modulated communication data in symbol periods, subsequent to accepting the unbiased training sequence.
  • the receiver generates a processed symbol (y c ) for each communication data symbol and multiplies each processed symbol by the unbiased channel estimate to derive a transmitted symbol (x).
  • the receiver accepts a temporal sequence of complex plane symbols with equal accumulated power (as defined above) in a plurality of directions in the complex plane.
  • the temporal sequence of unbiased training sequence symbols has a cumulative power associated with real axis information in the time domain, and an equal cumulative power associated with imaginary axis information in the time domain.
  • the receiver may accept the unbiased training sequence as symbols in a plurality of messages, having an equal power in a plurality of complex plane directions, as accumulated over the plurality of messages.
  • FIG. 11 is a schematic block diagram depicting a processing device for calculating an unbiased channel estimate.
  • the processing device 1100 comprises a quadrature demodulation receiving module 1102 having an input on line 1104 to accept an unbiased training sequence having predetermined reference signals (p) representing a uniform accumulated power evenly distributed in the complex plane.
  • the receiver module 1102 generates processed symbols (y) representing complex plane information in the unbiased training sequence supplied on line 1106.
  • a multiplication module 1108 multiplies the processed symbols (y) by the conjugate of the corresponding reference signals (p*), and supplies an unbiased channel estimate (h u ) at an output on line 1110.
  • Many features of the process device 1100 are shared in common with the receiver of FIG. 10, and will not be repeated here in the interest of brevity.
  • Training sequences are similar in that the information content of transmitted data is typically predetermined or "known" data that permits the receiver to calibrate and make channel measurements.
  • the data itself When receiving communication (non-predetermined) data, there are 3 unknowns: the data itself, the channel, and noise. The receiver is unable to calibrate for noise, since noise changes randomly.
  • Channel is a measurement commonly associated with delay and multipath. For relatively short periods of time, the errors resulting from multipath can be measured if predetermined data is used, such as training or pilot signals. Once the channel is known, this measurement can be used to remove errors in received communication (non- predetermined) data. Therefore, some systems supply a training signal to measure a channel before data decoding begins.
  • the channel can change, for example, as either the transmitter or receiver moves in space, or the clocks drift. Hence, many systems continue to send more "known” data along with the "unknown” data in order to track the slow changes in the channel.
  • the transmitter of FIG. 3 and the receiver of FIG. 10 may be combined to form a transceiver.
  • the transmitter and receiver of such a transceiver may share elements such as an antenna, baseband processor, and MAC level circuitry.
  • the explanations made above are intended to describe a transceiver that both transmits unbiased training sequences and calculates unbiased channel estimates based upon the receipt of unbiased training sequences from other transceivers in a network of devices.
  • Modern high data rate communication systems transmit signals on two distinct channels, the in-phase and quadrature-phase channels (I and Q).
  • the two channels form a 2D constellation in a complex plane.
  • QPSK and QAM are examples of constellations.
  • the I and Q channels may be carried by RF hardware that cannot be perfectly balanced due to variations in RF components, which results in IQ imbalance.
  • the imbalance issued are even greater.
  • IQ imbalance distorts the constellation and results in crosstalk between the I and Q channels: the signal interferes with itself. Increasing transmission power does not help, since self-generated interference increases with the signal power.
  • the signal-to-noise ratio reaches an upper bound that puts a limit on the highest data rate attainable with a given RF hardware.
  • SINR signal-to-noise ratio
  • a costly solution is to use fancier, more expensive hardware.
  • a possibly less costly solution is to digitally estimate IQ imbalance and compensate for it.
  • the concepts of digital estimation and compensation algorithms have been previously advanced in the art. However, the solutions tend to be expensive because they do not rely on a special type of training sequence. These solutions often only consider imbalance at one side, usually at the receiver.
  • OFDM Orthogonal Frequency Division Multiplexing
  • time domain systems which study end-to-end imbalance, from transmitter to receiver.
  • OFDM Orthogonal Frequency Division Multiplexing
  • the imbalance is modeled as a function of frequency, taking into account variations in the frequency response of the filters.
  • Two kinds of enhancements are presented: one with zero cost that eliminates the interference from the channel estimate by using an unbiased training sequence. Substantial gains are achieved because the error of the channel estimate is often more detrimental to performance than the error in the data itself.
  • a second, relatively low cost, enhancement compensates for data distortion, if more gain is needed.
  • a model of the IQ imbalance is provided below. Analysis is provided to show how conventional channel estimation using unbiased training sequences can mitigate part of the IQ imbalance. Then, a straightforward extension is provided to calculate the IQ imbalance parameters, proving that the algorithms are effective. Using the estimated parameters, a simple compensation algorithm is presented to mitigate data distortion. Simulation results for WiMedia's UWB are also given, as well as suggestions to amend the standard.
  • IQ imbalance arises when the power (amplitude) balance or the orthogonality (phase) between the in-phase (I) and quadrature-phase (Q) channels is not maintained. IQ imbalance is therefore characterized by an amplitude imbalance 2 ⁇ and a phase imbalance 2 ⁇ .
  • a complex symbol x is transmitted and received via the I and Q channels.
  • the symbol x is received intact. But in the presence of IQ imbalance, a noisy or distorted version is likely received.
  • Nonlinear model (1) is linearized via the vector form
  • B is the imbalance matrix.
  • the second row is obsolete since it is a duplicate version of the first row. But it gives a same size and type input and output so imbalance blocks at transmitter and receiver can be concatenated, as described below.
  • the imbalance matrix at the transmitter is defined by Bt, and at the receiver it is defined by B 1 -.
  • a one-tap channel is considered, suitable for OFDM.
  • a one-tap channel h in appropriate matrix form is
  • IQ imbalance and channel combine to create a global channel h', plus an undesired distortion or interference characterized by a global imbalance parameter ⁇ '.
  • the global imbalance parameter ⁇ ' changes when the channel changes, and may need to be estimated regularly.
  • the condition is considered where the symbol x, rather than spanning the entire complex plane, is restricted to a given (ID) axis.
  • the axis may be associated with BPSK modulation, the real axis, the imaginary axis, or any axis in between.
  • x * kx may be written, where k is a complex constant (a rotation), and
  • IQ imbalance vanishes, becoming an integral part of an overall channel response.
  • the interference created by IQ imbalance does not show up at the same frequency f, but rather at the mirror frequency — f, and vice versa. What is transmitted at -f creates interference on frequency +f. If signal x m is the signal transmitted at frequency -f, where index m denotes a quantity at mirror frequency — f, then at frequency — f the following is obtained
  • the IQ imbalance parameters ⁇ and ⁇ are here a function of frequency. This models an imbalance due to different low-pass (base-band) or band-pass (IF) filters in the system.
  • the I and Q paths cannot have the exact same filters and, hence, the imbalance varies with frequency.
  • This kind of imbalance exists but it is very expensive to compensate.
  • An equalizer and an extension of the model to deal with different convolutions on different channels are required. So in the time domain, bulk or average imbalance is used. Frequency domain systems are able to take advantage of the plain equalizer structure and model the imbalance on a per frequency basis.
  • the second row is no longer obsolete.
  • the model deals, in one shot, with a pair of mirror frequencies.
  • a one-tap channel h at frequency f, and h m at frequency -f is modeled by the matrix
  • h', h m ' are the global channel taps, and ⁇ ', ⁇ m ' are the global imbalance parameters.
  • the imbalance parameters change when the channels change and may need to be estimated regularly.
  • the model (12) is stimulated with pilot tones. At frequency +f, the pilot p is transmitted, and at frequency — f, the pilot p m . Assuming, without loss of generality, that the pilots have a unit norm (the channel carries the effective power), the conventional channel estimate at frequency f is obtained by de-rotating by p *
  • the training sequence consists of an even number of symbols, and it is enough to ensure each pair adds up to zero
  • Examples of simple sequences that satisfy the condition are given in Table 1. These types of training sequences are denoted as unbiased training sequences because, on one hand, unbiased channel estimates are produced, and on the other, the training signals equally spans the I and Q dimensions of the complex plane in time domain. For example, an unbiased training sequence is not concentrated along just the real axis.
  • the channel estimate may be smoothed over adjacent subcarriers within one symbol.
  • the cyclic prefix is designed to be short, and the channel is supposed to vary slowly from tone to tone.
  • the filters in the RF chain should have short temporal response and their frequency response also varies slowly, i.e., the IQ imbalance varies slowly across subcarriers.
  • the same channel smoothing techniques can be used to smooth and improve the imbalance parameter estimate.
  • unbiased training sequences there is no interaction between the channel estimate and the imbalance estimate.
  • Each estimated can be independently smoothed.
  • a nearly unbiased training sequence can be obtained by applying the summation from equation (14) over groups of 2 or more adjacent subcarriers. Then smoothing automatically cancels all or part of the interference from mirror frequencies.
  • One solution is to rotate the pilot by 90 degrees on the adjacent subcarrier (moving in mirror directions on the positive and negative frequencies).
  • L transmissions Xi, L noise terms Ni and L observations Y i may be respectively concatenated into the 2 by L matrices
  • the unknown is H'.
  • the LS estimator is
  • Model (17) can be viewed as unknown information H' sent via 2 consecutive transmissions over 2 vectors (rows of A ) in an L dimension space. We denote by ⁇ ), Mj and J j respectively row j of ⁇ , * %and J, where j * ⁇ 1,2 ⁇ . Models (12) and (17) can be written
  • each transmission there are 2 transmissions, each involving the 2 vectors ⁇ i, J ' 2, and where each vector is carrying complex amplitude information to be estimated.
  • the LS estimator consists of projecting onto each vector, in a parallel way to the other vector in order to cancel interference. A very good result is obtained when the 2 vectors are orthogonal, i.e., when dot product (14) is zero.
  • Unbiased training sequences are by definition, training sequences that verify this condition. Other sequences use non-orthogonal vectors and suffer a loss of performance function of the angle between the vectors .Y 1 and J'2.
  • Many OFDM systems currently use a very poor kind of training sequences where .T 1 ,. Y2 are collinear, and it is impossible to properly estimate the 4 entries in H'. These training sequences tend to estimate noisier versions of the channels h' and h' m .
  • This is a 2 by 2 matrix, i.e., 4 error values.
  • Each value can be isolated by multiplying left and right with combinations of the vectors (*• ® fi and M-' *) ⁇ .
  • Assuming is an identity matrix, or more generally a diagonal matrix with elements ⁇ 2 and ⁇ m 2 , it can be shown that the MSE of h' and ⁇ • compose/ are, respectively, the first and second diagonal elements of O 2 OTA H )- 1 .
  • the MSE are, respectively, the first and second diagonal element of ⁇ m 2 (,Y.Y H )-i_
  • tr(,Y.t' H ) 2L.
  • ⁇ IAj subject to ⁇ ⁇ j is constant.
  • the total MSE has been minimized, and the resulting MSE per element is either ⁇ 2 /L or ⁇ m 2 /L. But this MSE per element is likely to be the best that can be obtained, even if a unique vector transmission is used. The MSE is unlikely to be improved for a 2 vector transmissions, and therefore the MSE per element has been minimized.
  • the unbiased training sequences plus conventional channel estimator are the MMSE of all LS estimators.
  • the IQ imbalance parameters may be estimated (as described previously) and applied to compensate for data distortion.
  • the model is the same as any 2-tap channel with cross-correlations. Any channel equalization algorithm can be fitted.
  • a simple equalization algorithm is presented suitable for the ubiquitous bit-interleaved coded QAM and fading channels.
  • the ZF technique consists of computing
  • Table 3 summarizes the ZF algorithm with noise enhancement avoidance.
  • Fig.12 depicts the performance achieved by applying the above- described algorithms to the WiMedia UWB standard.
  • the highest data rate, 480 Mbps, is simulated in IEEE 802.15.3's channel model CM2 (indoor pico- environment of about 4 meters). Shadowing and band hopping are turned off.
  • the figure shows the Packet Error Rate (PER) as a function of Eb/No. The performance degrades quickly without any form of compensation.
  • Table 4 lists the loss of various algorithms with respect to ideal case.
  • End-to-end IQ imbalance and channel combine to form a global 2 by 2 channel matrix.
  • the use of unbiased training sequences achieves considerable gains at no cost.
  • the unbiased training sequences automatically cancel end-to-end self-generated interference from the channel estimate.
  • such training sequences are ideal for estimating IQ imbalance parameters, and a simple algorithm is given to compensate for data distortion: Zero- Forcing with noise enhancement avoidance.
  • WiMedia UWB benefits from the following enhancement: the conventional biased training sequence that consists of 6 symbols exclusively transmitted on the I channel can be divided in 2 halves to create an unbiased sequence. The first 3 symbols are sent on the I channel, and the last 3 symbols are sent on the Q channel. By uniformly spanning the complex plane, an unbiased training sequence is created with large gains for high data rates. For backward compatibility, this scheme may be reserved for high data rate modes and signaled via the beacons, or the training sequence type may be blindly detected.
  • the subcarriers f and -f can be assigned to different users. Considerable interference can arise if power control drives one user to high power level. It is therefore a good idea to locate the pilots of different users on mirror subcarriers. The pilots should satisfy the unbiased training sequence criterion. Each user automatically benefits without any extra effort. The pilots may hop to different locations while maintaining mirror positions.
  • OFDMA e.g., WiMAX
  • Fig. 13 is a flowchart illustrating a method for transmitting an unbiased communications training sequence. Although the method is depicted as a sequence of numbered steps for clarity, the numbering does not necessarily dictate the order of the steps. It should be understood that some of these steps may be skipped, performed in parallel, or performed without the requirement of maintaining a strict order of sequence. The method starts at Step 1300.
  • Step 1302 generates an unbiased training sequence in a quadrature modulation transmitter, with the unbiased training sequence representing a uniform accumulation of power evenly distributed in the complex plane, as defined above.
  • Step 1304 transmits the unbiased training sequence.
  • the terms "generating”, “deriving”, and “multiplying” refer to processes that may be enabled through the use of machine-readable software instructions, hardware, or a combination of software and hardware.
  • generating the unbiased training sequence in Step 1302 includes substeps.
  • Step 1302a generates training information in the time domain sent via an in-phase (I) modulation path having an accumulated power.
  • Step 1302b generates training information in the time domain sent via a quadrature (Q) modulation path having an accumulated power equal to the I modulation path power.
  • generating the unbiased training sequence in Step 1302 includes the following substeps.
  • Step 1302c generates a signal pair including a complex value reference signal (p) at frequency +f and a complex value mirror signal (p m ) at frequency -f.
  • Step 1302d nullifies the product (P-Pm).
  • i occurrences of the reference signal (p) and mirror signal (p m ) may be generated, and the sum of the products (pi ⁇ i m ) is nullified.
  • the generation of i occurrences of the reference signal and mirror signal may include generating signal pair values p and pm that vary for every occurrence.
  • the sum of the products (pi ⁇ i m ) may be nullified by generating information as a complex value that remains constant for every occurrence, to represent p.
  • information may be generated as a complex value that rotates 180 degrees every occurrence.
  • i occurrences of reference signal (p) and mirror signal (p m ) may be generated, and a product (pi ⁇ i m ) may be generated for each occurrence.
  • the occurrences may then be paired, and the sum of the products nullified from each paired occurrence.
  • generating the unbiased training sequence in Step 1302 includes generating P pilot symbols per symbol period, in a plurality of symbol periods. Then, Step 1303 generates (N — P) quadrature modulated communication data symbols per symbol period. Transmitting the unbiased training sequence in Step 1304 includes simultaneously transmitting N symbols per symbol period, in the plurality of symbol periods. [00123] In another aspect, Step 1303 generates quadrature modulated communication data. Step 1304 transmits the unbiased training sequence in a first plurality of symbol periods, followed by the quadrature modulated communication data in a second plurality of symbol periods.
  • Step 1302 generates symbols in a plurality of messages having an equal power in a plurality of complex plane directions, as accumulated over the plurality of messages.
  • Fig. 14 is a flowchart illustrating a method for calculating an unbiased channel estimate.
  • the method starts at Step 1400.
  • Step 1402 accepts an unbiased training sequence in a quadrature demodulation receiver, the unbiased training sequence having predetermined reference signals (p) representing a uniform accumulated power evenly distributed in the complex plane.
  • Step 1404 processes the unbiased training sequence, generating processed symbols (y) representing complex plane information in the unbiased training sequence.
  • Step 1406 multiplies the processed symbols (y) by the conjugate of the corresponding reference signals (p*).
  • Step 1408 obtains an unbiased channel estimate (h u ).
  • accepting the unbiased training sequence in Step 1402 includes accepting an unbiased training sequence with a plurality of simultaneously accepted predetermined reference signals (p n ).
  • Generating the processed symbol (y) in Step 1404 includes generating a plurality of processed symbols (y n ) from the corresponding plurality of reference signals.
  • Multiplying the processed symbol (y) by the conjugate of the reference signal (p*) in Step 1406 includes multiplying each processed symbol by its corresponding reference signal conjugate.
  • Step 1408 obtains the channel estimate by obtaining a plurality of channel estimates (h un ), and averages the channel estimate (h un ) for each value of n.
  • Step 1402 accepts the unbiased training sequence by accepting training information in the time domain via an in-phase (I) modulation path having an accumulated power, as well as accepting training information in the time domain via a quadrature (Q) modulation path having an accumulated power equal (as defined above) to the I modulation path power.
  • I in-phase
  • Q quadrature
  • Step 1402 accepts an unbiased training sequence with temporal sequence of n predetermined reference signals (p n ) having a cumulative power associated with real axis information in the time domain, and with an equal amount of cumulative power associated with imaginary axis information in the time domain.
  • Step 1404 generates a temporal sequence of n processed symbols (y n ) from the temporal sequence of reference signals.
  • Step 1406 multiplies each processed symbol in the temporal sequence by its corresponding reference signal conjugate.
  • obtaining the channel estimate h in Step 1408 includes: obtaining a temporal sequence of n channel estimates (h un ); and, averaging the n channel estimates.
  • Step 1402 accepts the unbiased training sequence as a signal pair including a complex value reference signal (p) at frequency +f and a complex value mirror signal (p m ) at frequency -f, where the product (P ⁇ m) i ⁇ nu ll-
  • a complex value reference signal (p) at frequency +f and a complex value mirror signal (p m ) at frequency -f
  • i occurrences of the reference signal (p) and the mirror signal (p m ) may be accepted, where the sum of the products (pi ⁇ i m ) is null.
  • the signal pair values p and P 1n that vary for every occurrence.
  • the sum of the products (pi ⁇ i m ) is nulled by accepting information as a complex value that remains constant for every occurrence, representing p; and, accepting information as a complex value that rotates 180 degrees every occurrence, representing p m .
  • i occurrences of the reference signal (p) and mirror signal (p m ) may be accepted and a product (pi ⁇ i m ) generated for each occurrence. The occurrences are then paired, and the sum of the products from each paired occurrence is nullified.
  • Step 1402 accepts the unbiased training sequence as P pilot symbols per symbol period, in a plurality of symbol periods, and Step 1408 obtains P unbiased pilot channel estimates.
  • Step 1403 simultaneously accepts (N — P) quadrature modulated communication data symbols in each symbol period.
  • Step 1405 generates a processed symbol (y c ) for communication data in each symbol period.
  • Step 1410 extrapolates channels estimates for each processed symbol (y c ), derived from the unbiased pilot channel estimates.
  • Step 1412 multiplies each processed symbol (y c ) by the extrapolated channel estimate to derive a transmitted symbol (x).
  • Step 1403 accepts quadrature modulated communication data in symbol periods, subsequent to accepting the unbiased training sequence.
  • Step 1405 generates a processed symbol (y c ) for each communication data symbol, and Step 1414 multiplies each processed symbol by the unbiased channel estimate to derive a transmitted symbol (x).
  • Step 1402 accepts a temporal sequence of complex plane with equal accumulated power in a plurality of directions in the complex plane.
  • accepting the unbiased training sequence in Step 1402 includes accepting symbols in a plurality of messages, having an equal power in a plurality of complex plane directions, as accumulated over the plurality of messages.
  • the above- described flowchart may also be interpreted as an expression of a machine-readable medium having stored thereon instructions for calculating an unbiased channel estimate.
  • the instructions for calculating the unbiased channel estimate would correspond to Steps 1400 through 1414, as explained above.

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Abstract

L'invention concerne un système et un procédé pour émettre une séquence d'apprentissage de communications sans biais. Le procédé génère une séquence d'apprentissage sans biais dans un émetteur à modulation à quadrature. La séquence d'entraînement sans biais représente une puissance accumulée uniforme répartie de façon régulière dans le plan complexe. Par suite, des informations d'apprentissage dans le domaine temporel sont envoyées via un trajet de modulation en phase (I), ayant une puissance accumulée. Des informations d'apprentissage dans le domaine temporel sont envoyées via un trajet de modulation en quadrature (Q) ayant une puissance accumulée égale à la puissance du trajet de modulation I. L'invention concerne également un système et un procédé pour calculer une estimation de canal sans biais à partir d'une séquence d'apprentissage sans biais reçue.
EP08731756A 2007-03-09 2008-03-07 Atténuation d'un déséquilibre en quadrature à l'aide de séquences d'apprentissage sans biais Withdrawn EP2130341A2 (fr)

Applications Claiming Priority (5)

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US11/684,566 US8428175B2 (en) 2007-03-09 2007-03-09 Quadrature modulation rotating training sequence
US11/755,719 US8290083B2 (en) 2007-03-09 2007-05-30 Quadrature imbalance mitigation using unbiased training sequences
US11/853,809 US8081695B2 (en) 2007-03-09 2007-09-11 Channel estimation using frequency smoothing
US11/853,808 US8064550B2 (en) 2007-03-09 2007-09-11 Quadrature imbalance estimation using unbiased training sequences
PCT/US2008/056327 WO2008112587A2 (fr) 2007-03-09 2008-03-07 Atténuation d'un déséquilibre en quadrature à l'aide de séquences d'apprentissage sans biais

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EP08731756A Withdrawn EP2130341A2 (fr) 2007-03-09 2008-03-07 Atténuation d'un déséquilibre en quadrature à l'aide de séquences d'apprentissage sans biais

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BRPI0808676A2 (pt) 2014-08-12
KR101109797B1 (ko) 2012-04-06
WO2008112587A3 (fr) 2009-02-05
CA2790073C (fr) 2016-01-12
TWI393399B (zh) 2013-04-11

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