CN115514606B - High-precision timing estimation method based on mutual quality sampling - Google Patents
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Abstract
The invention discloses a high-precision timing estimation method based on mutual quality sampling, and belongs to the field of communication signal processing. The implementation method of the invention comprises the following steps: based on a mutual quality sampling theory, designing a mutual quality relation between a frequency interval and a receiver sampling frequency, and constructing a sparse multitone training sequence meeting the mutual quality sampling relation in a frequency domain; the spectrum mapping relation is utilized at a receiving end to realize the undistorted reconstruction of the signal when the bandwidth is far greater than the sampling rate at the sub-Nyquist sampling rate; estimating a broadband channel where the signal is based on a least square principle, and converting an estimation result into a time domain; and then carrying out peak detection on the channel time domain information obtained in the channel estimation process to obtain a timing position estimation value. The invention utilizes the characteristic of large bandwidth of the signal recovered by the intersubstance sampling, improves the signal bandwidth which can be recovered without distortion under the same sampling rate of the receiver, and improves the time domain resolution in timing estimation according to the information of the broadband channel, so as to improve the timing estimation precision of the OFDM communication system.
Description
Technical Field
The invention relates to a high-precision timing estimation method based on mutual quality sampling, in particular to a high-precision timing estimation method based on mutual quality sampling in an OFDM system, and belongs to the field of communication signal processing.
Background
Orthogonal Frequency Division Multiplexing (OFDM) is a communication technology that is currently widely used, and is effective against frequency selective fading. OFDM techniques are susceptible to symbol timing synchronization shifts, resulting in misalignment of the fast fourier transform windows of the signal and severely degrading communication performance. In addition, the demands of communication systems for communication perception integration are gradually increasing nowadays, and if the communication systems under waveform integration realize radar functions such as high-precision ranging, the timing precision at the current nyquist sampling rate often cannot meet the precision requirement for ranging. Conventional OFDM timing synchronization often employs a timing estimation algorithm based on a training sequence, and an increase in the timing accuracy requirement increases the training sequence bandwidth to achieve sufficiently high time-domain resolution. The increase of the signal bandwidth puts higher demands on the sampling rate of the ADC at the receiving end, so that research on a timing estimation algorithm with high timing accuracy under the condition of low sampling rate has important significance.
Disclosure of Invention
Under nyquist sampling, the sampling rate limits the signal bandwidth, and therefore the time-domain resolution, the timing synchronization accuracy is often on the order of the sampling interval, and the accuracy cannot be further improved. On the one hand, for an OFDM system, carrier synchronization and subsequent signal demodulation have higher requirements on timing precision; on the other hand, if the communication system is expected to perform further sensing functions such as ranging positioning through timing synchronization, the timing accuracy of the sampling point level cannot meet the requirement.
Aiming at the technical defects of the conventional OFDM system timing estimation method, the main purpose of the invention is to provide a high-precision timing estimation method based on mutual quality sampling, wherein a multi-tone training sequence with sparsity is constructed in a frequency domain, and the frequency interval between multi-tones and the sampling frequency of a receiver meet the mutual quality sampling relation; and constructing a spectrum mapping relation before and after sampling at the receiving end group according to the mutual quality relation, and realizing signal undistorted reconstruction when the bandwidth is far greater than the sampling rate at the sub-Nyquist sampling rate by using the spectrum mapping relation. Based on the undistorted reconstructed signal, estimating a broadband channel in which the signal is positioned based on a least square principle, and converting an estimation result into a time domain; and then carrying out peak detection on the channel time domain information obtained in the channel estimation process to obtain a timing position estimation value, namely realizing high-precision timing estimation. The invention utilizes the characteristic of large bandwidth of the signal recovered by the intersubstance sampling, improves the signal bandwidth which can be recovered without distortion under the same sampling rate of the receiver, and further improves the time domain resolution in timing estimation according to the information of the broadband channel, so as to improve the timing estimation precision of the OFDM communication system.
The invention aims at realizing the following technical scheme:
the invention discloses a high-precision timing estimation method based on mutual quality sampling, which comprises the following steps:
step 1, based on a mutual quality relation between a designed frequency interval of a mutual quality sampling theory and a sampling frequency of a receiver, constructing a sparse multitone training sequence meeting the mutual quality sampling relation in a frequency domain.
The training sequence is composed of a plurality of pilot symbols. Recording the data subcarrier interval as delta f and the training sequence length as T in OFDM system sym And has the same length as the OFDM symbol of the data, and satisfies T sym =1/Δf. The number of pilot symbols contained in each training sequence is K, and each pilot symbol is identical and is the subcarrier spacing Deltaf p And length T p Is satisfied with Deltaf p ＝K△f，T p ＝T sym and/K. Before the first training sequence there is a length T sym Cyclic prefix of/4. The training sequence is in the form of periodic multitone signal, and the number of carriers is N sc Total bandwidth bw=mk Δf.
Based on the inter-quality sampling theory, the sampling rate and the training sequence subcarrier interval are normalized relative to a certain frequency value and then inter-quality, so that the sampling rate f s The method meets the following conditions:
f s ＝M·△f (1)
therefore, when constructing training sequence, the selected K value must be compatible with M, the number of sub-carriers N sc The maximum value is M. The wideband training sequence sent by the transmitter shows periodicity, each pilot symbol in the training sequence is a segment of subcarrier with the number of N sc The baseband signal expression of the OFDM signal of (a) is:
wherein X is k Representing the modulated symbols on the kth subcarrier, f k Represents the frequency of the kth subcarrier, satisfies f k = kK Δf. Deriving the frequency of the pilot signal from the above formThe domain expression is:
because the front end of the radio frequency has a band-pass filter with the bandwidth being the bandwidth of the received signal, the value range of f is more than or equal to 0 and less than or equal to N sc K.DELTA.f, for ease of description, is denoted herein as a single-sided spectrum signal, in effect taking on a range of values-N sc K△f/2≤f≤N sc The bilateral spectrum signal of K delta f/2 is equivalent to the bilateral spectrum signal. When the minimum frequency of the bilateral spectrum signal is taken as the center frequency, the bilateral spectrum can be converted into a unilateral spectrum.
The sequence satisfying the time domain form of the formula (2) and the frequency domain form of the formula (3) is the constructed sparse multitone training sequence.
And 2, constructing a spectrum mapping relation before and after sampling on the receiving end based on the mutual quality relation obtained in the step 1, wherein the mapping relation can be converted into a mapping lookup table in advance before the OFDM communication system works so as to avoid hardware resource consumption in the online search calculation process, and realizing signal undistorted reconstruction when the bandwidth is far greater than the sampling rate at the sub-Nyquist sampling rate by using the spectrum mapping relation.
Step 2.1, the received signal firstly passes through a high-speed sampling holder T/H at the receiving end, and the sampling holder is used for improving the input bandwidth of the OFDM communication system and simultaneously ensuring the signal stability during the subsequent ADC sampling.
And 2.2, sampling the signal by using a sampling rate which has a mutual quality relation with the training sequence subcarrier spacing to obtain a digital signal.
After the training sequence passes through the channel, the training sequence is affected by multipath and noise:
y(t)＝h(t)*x(t)+n(t) (4)
where h (t) represents the channel impulse response and n (t) represents the noise signal. Since the cyclic prefix is inserted in the front end of the training sequence, the spectrum of the received pilot symbol is expressed as:
Y(f)＝H(f)·X(f)+N(f) (5)
the received signal spectrum is expressed as:
wherein H is k Representing the channel frequency response of the kth subcarrier. The received signal in expression (6) contains N sc The bars have sparse spectral lines and thus are able to sample the received signal using a sampling rate well below the total bandwidth of the signal.
Because M and K are mutually prime, the pilot subcarrier spacing Δf p Is K.DELTA.f, thus ensuring f s And Deltaf p Normalized to Δf. The time domain expression after signal sampling is:
the spectral expression of the sampled signal is:
as seen from the form of the above formula, R (f) has periodicity, f s Is periodic. All the information of R (f) is contained in the main value interval, and the expression of the main value interval of R (f) is as follows:
in the above formula, N' (f) is a noise spectrum in the main value interval, and the spectrum is a result of superposition of the spectrum period continuation of N (f) in the main value interval in the sampling process. The expression is as follows:
from the form of formula (9), the frequency point f 'of the effective signal spectral line in the main value interval' k The method comprises the following steps:
f′ k ＝mod(k·K△f,M△f),k＝0,1,...,N sc -1 (11)
and 2.3, rearranging the frequency domain signals to restore the signals.
k 'represents the line number of the interval Δf in the main value interval after the intersubstance sampling, k' =0, 1. After introducing k', formula (11) can be rewritten as:
f′ k ＝k′△f (12)
wherein:
k′＝mod(kK,M) (13)
the above equation (13) establishes a mapping relationship of spectrum sequences before and after the mutual mass sampling, and k 'K, M can be searched in a range of 0, 1..m-1 to obtain a spectral line position k before the corresponding sampling as known at a receiving end k'. In an actual implementation of the OFDM communication system, after the mapping relationship between k 'and k is calculated in advance, a lookup table from k' to k is established, so that the consumption of hardware resources in the online search calculation process can be avoided.
After preliminary timing synchronization is recorded, the time domain vector of the first training sequence under the mutual quality sampling is as follows:
y cs ＝[y cs (0) y cs (1) … y cs (M-1)] T (14)
the frequency domain vector of the received signal is recorded as:
Y sc ＝[Y cs (0) Y cs (1) … Y cs (M-1)] T (15)
due to the presence of cyclic prefix, subcarrier orthogonality is not destroyed, Y cs And y is cs The relation of (2) is as follows:
Y cs ＝DFT(y cs ) (16)
after the inter-quality sampling, the signal spectrum is reordered, and the spectrum needs to be reconstructed in order to obtain the actual received signal spectrum. Equation (13) gives the mapping relation of spectrum reordering and reconstruction. Mapping matrix of spectrum reorder is P cs The method comprises the following steps:
wherein Y is a received signal spectrum vector before the inter-quality sampling spectrum rearrangement, and the expression is as follows:
Y＝[Y(0) Y(1) … Y(M-1)] T (18)
P cs the expression of (2) is:
P cs the elements in (a) obey the following formula:
N sc the number of subcarriers for transmitting pilot symbols. Since the elements in Y satisfy:
based on the relation of the mutual mass sampling frequency spectrum rearrangement, Y cs The elements of the method are as follows:
when reconstructing the original signal spectrum, due to P cs Is orthogonal to each other, the received signal can be reconstructed by:
step 3, based on the signal after distortion-free reconstruction, estimating a broadband channel where the signal is located based on a Least Square (LS) principle, and converting an estimation result into a time domain; and then, carrying out peak detection on the channel time domain information obtained in the channel estimation process to obtain a timing position estimation value with timing error far lower than a sampling interval, thereby improving the timing estimation precision of the OFDM communication system.
And 3.1, carrying out wideband channel estimation based on a least square principle to obtain an estimation result.
Since the symbols modulated on each subcarrier in the pilot symbols are known at the receiving end, the least squares estimate of the channel frequency response on each subcarrier can be calculated, namely:
obtaining:
the matrix form is expressed as:
wherein the method comprises the steps ofIs composed of->The component vectors, expressed as:
is a diagonal matrix consisting of the inverse of the non-zero elements in X, where the elements satisfy:
the time delay position of the channel tap under the direct channel can represent the relative position between the signal starting point and the current reference point, and the fine timing synchronization estimated value can be further obtained by solving the time domain tap h (n) of the channel.
And 3.2, performing IDFT on the LS channel estimation result to obtain a time domain tap of the channel estimation result.
The least square estimation result of the channel spectrum is thatThe IDFT result is the channel impulse response estimation resultAnd can be calculated +.>Input to IDFT at the time->Zero padding is performed, the fence effect of IDFT is relieved, the accuracy of subsequent fine timing estimation is improved, and therefore:
the number of the IDFT points after zero padding is N IFFT Wherein isThe method comprises the following steps:
by aligningThe position of the maximum value in (2) can be used for carrying out fine timing estimation on the signal.
And 3.3, carrying out peak detection on the time domain tap of the LS channel estimation result, improving the time domain resolution by utilizing the characteristic of large bandwidth of the training sequence, obtaining a timing position estimation value with timing error far lower than a sampling interval, and improving the timing estimation precision of the OFDM communication system.
For a pair ofPerforming peak detection to obtain a fine timing estimation value, and recording that the peak position captured in the timing estimation based on the mutual quality sampling is delta n, wherein the peak position is:
the time interval between each point in the system is 1/N IFFT △f p Fine timing position deviation estimate +.>The method comprises the following steps:
a symbol positive indicates that the initial timing position is advanced to the symbol start position and vice versa. Due to the signal bandwidth N sc △f p Far greater than f s ，/>The precision of the method is far higher than the sampling interval, and compared with the traditional OFDM timing precision, the method has obvious improvement.
The beneficial effects are that:
1. the invention discloses a high-precision timing estimation method based on mutual quality sampling, which utilizes a wideband training sequence constructed based on a mutual quality theory to realize reconstruction of wideband signals under a sub-Nyquist sampling rate and realize high-precision timing estimation. The method can effectively reduce the requirement of the ADC sampling rate on the premise of no distortion recovery signal so as to solve the problem of insufficient ADC sampling rate in the current large-bandwidth signal recovery.
2. The high-precision timing estimation method based on the mutual quality sampling, disclosed by the invention, utilizes the large bandwidth characteristic of the reconstructed signal to obtain the wideband channel information, and can improve the time domain resolution of the receiver to the signal under the condition of certain sampling frequency, thereby completing high-precision timing estimation. This timing estimate can be used to both provide a signal start position for subsequent receiver demodulation processes and to implement sensing functions such as ranging.
3. And (2) constructing a spectrum mapping relation before and after sampling on the receiving end based on the inter-quality relation obtained in the step (1), wherein the mapping relation can be converted into a mapping lookup table in advance before the OFDM communication system works so as to avoid hardware resource consumption in the online search calculation process, and the signal undistorted reconstruction when the bandwidth is far greater than the sampling rate at the sub-Nyquist sampling rate is realized by using the spectrum mapping relation.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description will briefly introduce the drawings that are required to be used in the embodiments or the prior art descriptions, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of high-precision timing estimation based on mutual quality sampling according to the present invention;
FIG. 2 is a schematic diagram of a wideband training sequence structure according to the present invention;
FIG. 3 is a schematic diagram of the spectrum before and after the intersubstance sampling;
FIG. 4 is a schematic diagram of the spectrum sequence before and after the intersubstance sampling;
FIG. 5 is a comparison of time domain waveform reconstruction performance based on inter-mass sampling;
FIG. 6 is a schematic diagram of time domain taps based on a wideband channel estimate of inter-quality sampling;
fig. 7 is a timing estimation result RMSE performance diagram based on the mutual quality sampling.
Detailed Description
For a better description of the objects and advantages of the present invention, the following description will be given with reference to the accompanying drawings and examples.
Example 1:
as shown in fig. 1, the high-precision timing estimation method based on the mutual quality sampling disclosed in this embodiment includes the following steps:
step 1, based on a mutual quality relation between a designed frequency interval of a mutual quality sampling theory and a sampling frequency of a receiver, constructing a sparse multitone training sequence meeting the mutual quality sampling relation in a frequency domain.
Sampling rate f in the present embodiment s For 15.36MHz, OFDM data subcarrier spacing is Deltaf=15KHz, based on the mutual prime sampling theory, the sampling rate and training sequence subcarrier spacing are required to normalize relative to a certain frequency value and then mutually prime, in the invention, let M=1024, then the sampling rate f s The method meets the following conditions:
f s ＝M·△f＝1024×15KHz (33)
the training sequence is composed of a plurality of pilot symbols as shown in fig. 2. Training sequence length T sym =66.7us, and is the same as the data OFDM symbol length, satisfying T sym =1/Δf. The number of pilot symbols included in each training sequence is k=11, which is comparable to the value of M in this embodiment. Each pilot symbol is identical and is the subcarrier spacing delta f p =165 KHz and length T p =6.06 us OFDM symbols, satisfying Δf p ＝K△f，T p ＝T sym and/K. Before the first training sequence there is a length T sym Cyclic prefix of/4=16.7us. The training sequence is in the form of periodic multitone signal, and the number of carriers is N sc =1024, total bandwidth bw= 168.96MHz.
When constructing training sequence, the number of subcarriers N sc The maximum value is M. Emission ofThe wideband training sequence sent by the machine shows periodicity, each pilot frequency symbol in the training sequence is a section of subcarrier with the number of N sc An OFDM signal of=1024, whose baseband signal expression is:
wherein X is k Representing the modulated symbols on the kth subcarrier, f k Represents the frequency of the kth subcarrier, satisfies f k =k.165 KHz. The frequency domain expression of the pilot signal is derived from the above form:
because the front end of the radio frequency has a band-pass filter with the bandwidth being the bandwidth of the received signal, the value range of f is more than or equal to 0 and less than or equal to 15.36MHz, and for convenience of discussion, the band-pass filter is represented as a single-side spectrum signal, and in fact, a double-side spectrum signal with the value range of more than or equal to-7.68 MHz and less than or equal to 7.68MHz is equivalent to the single-side spectrum signal. When the minimum frequency of the bilateral spectrum signal is taken as the center frequency, the bilateral spectrum can be converted into a unilateral spectrum.
The sequence satisfying the time domain form of the formula (34) and the frequency domain form of the formula (35) is the constructed sparse multitone training sequence.
And 2, constructing a spectrum mapping relation before and after sampling on the receiving end based on the mutual quality relation obtained in the step 1, wherein the mapping relation can be converted into a mapping lookup table in advance before the OFDM communication system works so as to avoid hardware resource consumption in the online search calculation process, and realizing signal undistorted reconstruction when the bandwidth is far greater than the sampling rate at the sub-Nyquist sampling rate by using the spectrum mapping relation.
Step 2.1, the received signal firstly passes through a high-speed sampling holder T/H at the receiving end, and the sampling holder is used for improving the input bandwidth of the OFDM communication system and simultaneously ensuring the signal stability during the subsequent ADC sampling.
And 2.2, sampling the signal by using a sampling rate which has a mutual quality relation with the training sequence subcarrier spacing to obtain a digital signal.
After the training sequence passes through the channel, the training sequence is affected by multipath and noise:
y(t)＝h(t)*x(t)+n(t) (36)
where h (t) represents the channel impulse response and n (t) represents the noise signal. Since the cyclic prefix is inserted in the front end of the training sequence, the spectrum of the received pilot symbol is expressed as:
Y(f)＝H(f)·X(f)+N(f) (37)
the received signal spectrum is expressed as:
wherein H is k Representing the channel frequency response of the kth subcarrier. The received signal in expression (38) contains N sc =1024 sparse spectral lines, so the received signal can be sampled using a sampling rate well below the total bandwidth of the signal.
Because m=1024 and k=11 are mutually prime, the pilot subcarrier spacing Δf p Is K.DELTA.f, thus ensuring f s And Deltaf p Normalized to Δf. The time domain expression after signal sampling is:
the spectral expression of the sampled signal is:
as seen from the form of the above formula, R (f) has periodicity, f s =15.36 MHz as period. All the information of R (f) is contained in the main value interval, and the expression of the main value interval of R (f) is as follows:
in the above formula, N' (f) is a noise spectrum in the main value interval, and the spectrum is a result of superposition of the spectrum period continuation of N (f) in the main value interval in the sampling process. The expression is as follows:
from the form of formula (9), the frequency point f 'of the effective signal spectral line in the main value interval' k The method comprises the following steps:
f′ k ＝mod(k·11△f,1024△f),k＝0,1,...,1023 (43)
a schematic diagram of the signal spectrum before and after sampling is shown in fig. 3.
And 2.3, rearranging the frequency domain signals to restore the signals.
k 'represents the line number of the interval Δf in the main value interval after the intersubstance sampling, k' =0, 1,..1023. After introducing k', formula (43) can be rewritten as:
f′ k ＝k′△f (44)
wherein:
k′＝mod(11k,1024) (45)
the above equation (45) establishes a mapping relationship between the spectrum sequence before and after the inter-mass sampling, and the schematic diagram of the spectrum sequence before and after the inter-mass sampling is shown in fig. 4. As is known at the receiving end K', k=11, m=1024, K can be searched for the corresponding pre-sampling spectral line position K by a search in the range 0, 1. In an actual implementation of the OFDM communication system, after the mapping relationship between k 'and k is calculated in advance, a lookup table from k' to k is established, so that the consumption of hardware resources in the online search calculation process can be avoided.
After preliminary timing synchronization is recorded, the time domain vector of the first training sequence under the mutual quality sampling is as follows:
y cs ＝[y cs (0) y cs (1) … y cs (1023)] T (46)
the frequency domain vector of the received signal is recorded as:
Y sc ＝[Y cs (0) Y cs (1) … Y cs (1023)] T (47)
due to the presence of cyclic prefix, subcarrier orthogonality is not destroyed, Y cs And y is cs The relation of (2) is as follows:
Y cs ＝DFT(y cs ) (48)
after the inter-quality sampling, the signal spectrum is reordered, and the spectrum needs to be reconstructed in order to obtain the actual received signal spectrum. Equation (45) gives the mapping of the spectral re-ordering and reconstruction. Mapping matrix of spectrum reorder is P cs The method comprises the following steps:
wherein Y is a received signal spectrum vector before the inter-quality sampling spectrum rearrangement, and the expression is as follows:
Y＝[Y(0) Y(1) … Y(1023)] T (50)
P cs the expression of (2) is:
P cs the elements in (a) obey the following formula:
when reconstructing the original signal spectrum, due to P cs Is orthogonal to each other, the received signal can be reconstructed by:
at this point the receiver uses f s Sample frequency of 15.36MHz, signal of training sequence with total bandwidth bw= 168.96MHz is losslessly recovered, compared with nyquist band-pass samplingThe recoverable signal bandwidth is greatly improved, and the time domain signal pair recovered based on the intersubstance sampling and the time domain signal pair recovered under the Nyquist sampling is shown in FIG. 5, so that the former can still recover the signal without damage although the former has larger noise variance, and the required sampling rate is greatly reduced. By means of the lossless recovered wideband signal, wideband channel estimation and fine timing position estimation can be accomplished.
Step 3, based on the signal after distortion-free reconstruction, estimating a broadband channel where the signal is located based on a Least Square (LS) principle, and converting an estimation result into a time domain; and then, carrying out peak detection on the channel time domain information obtained in the channel estimation process to obtain a timing position estimation value with timing error far lower than a sampling interval, thereby improving the timing estimation precision of the OFDM communication system.
And 3.1, carrying out wideband channel estimation based on a least square principle to obtain an estimation result.
Since the symbols modulated on each subcarrier in the pilot symbols are known at the receiving end, the least squares estimate of the channel frequency response on each subcarrier can be calculated, namely:
obtaining:
the matrix form is expressed as:
wherein the method comprises the steps ofIs composed of->The component vectors, expressed as:
is a diagonal matrix consisting of the inverse of the non-zero elements in X, where the elements satisfy:
the time delay position of the channel tap under the direct channel can represent the relative position between the signal starting point and the current reference point, and the fine timing synchronization estimated value can be further obtained by solving the time domain tap h (n) of the channel.
And 3.2, performing IDFT on the LS channel estimation result to obtain a time domain tap of the channel estimation result.
The least square estimation result of the channel spectrum is thatThe IDFT result is the channel impulse response estimation resultAnd can be calculated +.>Input to IDFT at the time->Zero padding is performed, the fence effect of IDFT is relieved, the accuracy of subsequent fine timing estimation is improved, and therefore:
the number of the IDFT points after zero padding is N IFFT =4096, then thereinThe method comprises the following steps:
time domain taps based on the wideband channel estimation of the inter-quality samples are shown in fig. 6. By aligningThe position of the maximum value in (2) can be used for carrying out fine timing estimation on the signal.
And 3.3, carrying out peak detection on the time domain tap of the LS channel estimation result, improving the time domain resolution by utilizing the characteristic of large bandwidth of the training sequence, obtaining a timing position estimation value with timing error far lower than a sampling interval, and improving the timing estimation precision of the OFDM communication system.
For a pair ofPerforming peak detection to obtain a fine timing estimation value, and recording that the peak position captured in the timing estimation based on the mutual quality sampling is delta n, wherein the peak position is:
the time interval between each point in the process is 1/4096 delta f p Fine timing position deviation estimate +.>The method comprises the following steps:
a symbol positive indicates that the initial timing position is advanced to the symbol start position and vice versa. Due to the signal bandwidth N sc △f p = 168.96MHz far greater than f s ＝15.36MHz，/>The precision of the method is far higher than the sampling interval, and compared with the traditional OFDM timing precision, the method has obvious improvement.
Fig. 7 illustrates comparison between timing estimation accuracy based on intersubstance sampling and timing accuracy under traditional nyquist sampling under two channels of COST207RA/TU, wherein an ordinate RMSE in the timing estimation simulation results is a result obtained by normalizing an estimation deviation to a 15.36MHz down-sampling interval, and the unit is the number of sampling points (Sa) under 15.36 MHz. Simulation results show that the RMSE of the timing estimation is less than 10 when the signal to noise ratio is more than 5dB under the two channel conditions -3 Sa has very high timing estimation accuracy, and the RMSE of the timing estimation under the traditional Nyquist sampling is larger than 10 -2 The former has a distinct advantage over the latter in terms of timing accuracy. If the ranging function is implemented based on timing estimation, the ranging accuracy in the order of centimeters can be achieved in this embodiment by calculation, considering the receiver sampling rate of 15.36MHz in this embodiment.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (2)
1. A high-precision timing estimation method based on mutual quality sampling is characterized in that: the method comprises the following steps:
step 1, based on a mutual quality relation between a designed frequency interval of a mutual quality sampling theory and a sampling frequency of a receiver, constructing a sparse multitone training sequence meeting the mutual quality sampling relation in a frequency domain;
step 2, constructing a spectrum mapping relation before and after sampling on a receiving end based on the inter-quality relation obtained in the step 1, wherein the mapping relation can be converted into a mapping lookup table in advance before the OFDM communication system works so as to avoid hardware resource consumption in the online search calculation process, and realizing signal undistorted reconstruction when the bandwidth is far greater than the sampling rate at the sub-Nyquist sampling rate by using the spectrum mapping relation;
the implementation method of the step 2 is that,
step 2.1, a receiving signal firstly passes through a high-speed sampling retainer T/H at a receiving end, wherein the sampling retainer is used for improving the input bandwidth of an OFDM communication system and simultaneously ensuring the signal stability during the subsequent ADC sampling;
step 2.2, sampling the signal by using a sampling rate with a mutual quality relation with the training sequence subcarrier spacing to obtain a digital signal;
after the training sequence passes through the channel, the training sequence is affected by multipath and noise:
y(t)＝h(t)*x(t)+n(t) (4)
where h (t) represents the channel impulse response and n (t) represents the noise signal; since the cyclic prefix is inserted in the front end of the training sequence, the spectrum of the received pilot symbol is expressed as:
Y(f)＝H(f)·X(f)+N(f) (5)
the received signal spectrum is expressed as:
wherein H is k Representing the channel frequency response of the kth subcarrier; x is X k Representing the modulated symbols on the kth subcarrier, f k Represents the frequency of the kth subcarrier, satisfies f k = kK Δf; the received signal in expression (6) contains N sc The bars have sparse spectral lines and can therefore be used far below the signalSampling the received signal at the sampling rate of the total bandwidth of the signal;
because M and K are mutually prime, the pilot subcarrier spacing Δf p Is K delta f, thus ensuring f s And Δf p Normalized relative to Δf, the mutual mass; the time domain expression after signal sampling is:
the spectral expression of the sampled signal is:
m is the number N of subcarriers sc Maximum value, K, is the number of pilot symbols contained in each training sequence, R (f) has periodicity, as seen from the form of the above equation, f s Is a period; all the information of R (f) is contained in the main value interval, and the expression of the main value interval of R (f) is as follows:
in the above, N' (f) is the noise spectrum in the main value interval, and the spectrum is the result of superposition of the spectrum period continuation of N (f) in the main value interval in the sampling process; the expression is as follows:
from the form of formula (9), the frequency point f 'of the effective signal spectral line in the main value interval' k The method comprises the following steps:
f′ k ＝mod(k·KΔf,MΔf),k＝0,1,...,N sc -1 (11)
step 2.3, rearranging the frequency domain signals and recovering signals;
k 'represents the spectral line number of the interval Δf in the main value interval after the intersubstance sampling, k' =0, 1, & gt, M-1; after introducing k', formula (11) can be rewritten as:
f′ k ＝k′Δf (12)
wherein:
k′＝mod(kK,M) (13)
the above formula (13) establishes a mapping relationship of spectrum sequences before and after the intersubstance sampling, and k can be searched in a range of 0,1, M-1 to obtain a spectral line position k before the corresponding sampling as known at a receiving end k', K, M; in the practical implementation of the OFDM communication system, after the mapping relation between k 'and k can be calculated in advance, a lookup table from k' to k is established, so that the consumption of hardware resources in the online searching and calculating process can be avoided;
after preliminary timing synchronization is recorded, the time domain vector of the first training sequence under the mutual quality sampling is as follows:
y cs ＝[y cs (0) y cs (1) … y cs (M-1)] T (14)
the frequency domain vector of the received signal is recorded as:
Y cs ＝[Y cs (0) Y cs (1) … Y cs (M-1)] T (15)
due to the presence of cyclic prefix, subcarrier orthogonality is not destroyed, Y cs And y is cs The relation of (2) is as follows:
Y cs ＝DFT(y cs ) (16)
after the inter-quality sampling, the signal spectrum is reordered, and in order to obtain the actual received signal spectrum, the spectrum needs to be reconstructed; the mapping relation of spectrum reordering and reconstruction is given in the formula (13); mapping matrix of spectrum reorder is P cs The method comprises the following steps:
wherein Y is a received signal spectrum vector before the inter-quality sampling spectrum rearrangement, and the expression is as follows:
Y＝[Y(0) Y(1) … Y(M-1)] T (18)
P cs the expression of (2) is:
P cs the elements in (a) obey the following formula:
N sc the number of subcarriers for transmitting pilot symbols; since the elements in Y satisfy:
based on the relation of the mutual mass sampling frequency spectrum rearrangement, Y cs The elements of the method are as follows:
when reconstructing the original signal spectrum, due to P cs Is orthogonal to each other, the received signal can be reconstructed by:
step 3, based on the signal after distortion-free reconstruction, estimating a broadband channel in which the signal is positioned based on a least square principle, and converting an estimation result into a time domain; performing peak detection on channel time domain information obtained in the channel estimation process to obtain a timing position estimation value with timing error far lower than a sampling interval, and improving the timing estimation precision of the OFDM communication system;
the implementation method of the step 3 is that,
step 3.1, carrying out wideband channel estimation based on a least square principle to obtain an estimation result;
since the symbols modulated on each subcarrier in the pilot symbols are known at the receiving end, the least squares estimate of the channel frequency response on each subcarrier can be calculated, namely:
obtaining:
the matrix form is expressed as:
wherein the method comprises the steps ofIs composed of->The component vectors, expressed as:
is a diagonal matrix consisting of the inverse of the non-zero elements in X, where the elements satisfy:
the time delay position of the channel tap under the direct channel can represent the relative position between the signal starting point and the current reference point, and the fine timing synchronization estimated value can be further obtained by solving the time domain tap h (n) of the channel;
step 3.2, performing IDFT on the LS channel estimation result to obtain a time domain tap of the channel estimation result;
the least square estimation result of the channel spectrum is thatThe IDFT result is the estimated result of the channel impulse response +.>And can be calculated +.>Input to IDFT at the time->Zero padding is performed, the fence effect of IDFT is relieved, the accuracy of subsequent fine timing estimation is improved, and therefore:
the number of the IDFT points after zero padding is N IFFT Wherein isThe method comprises the following steps:
by aligningThe position of the maximum value in the (b) can carry out fine timing estimation on the signal;
step 3.3, carrying out peak detection on the time domain tap of the LS channel estimation result, improving the time domain resolution by utilizing the characteristic of large bandwidth of the training sequence, obtaining a timing position estimation value with timing error far lower than a sampling interval, and improving the timing estimation precision of the OFDM communication system;
for a pair ofPerforming peak detection to obtain a fine timing estimation value, and recording that the peak position captured in the timing estimation based on the mutual quality sampling is delta n, wherein:
the time interval between each point in the system is 1/N IFFT Δf p Fine timing position deviation estimate +.>The method comprises the following steps:
a positive sign indicates that the initial timing position is earlier than the sign starting position, whereas it indicates that the initial timing position is later than the sign starting position; due to the signal bandwidth N sc Δf p Far greater than f s ，/>Is a essence of (2)The degree is far higher than the sampling interval, and compared with the traditional OFDM timing precision, the precision is obviously improved.
2. The high-precision timing estimation method based on the mutual quality sampling as claimed in claim 1, wherein: the implementation method of the step 1 is that,
the training sequence is composed of a plurality of pilot symbols; recording the data subcarrier spacing as delta f and the training sequence length as T in OFDM system sym And has the same length as the OFDM symbol of the data, and satisfies T sym =1/Δf; each pilot symbol is identical and is the subcarrier spacing deltaf p And length T p Is satisfied with Δf p ＝KΔf，T p ＝T sym K; before the first training sequence there is a length T sym Cyclic prefix of/4; the training sequence is in the form of periodic multitone signal, and the number of carriers is N sc Total bandwidth bw=mkΔf;
based on the inter-quality sampling theory, the sampling rate and the training sequence subcarrier interval are normalized relative to a certain frequency value and then inter-quality, so that the sampling rate f s The method meets the following conditions:
f s ＝M·Δf (1)
therefore, when constructing the training sequence, the selected K value must be compatible with M; the wideband training sequence sent by the transmitter shows periodicity, each pilot symbol in the training sequence is a segment of subcarrier with the number of N sc The baseband signal expression of the OFDM signal of (a) is:
the frequency domain expression of the pilot signal is derived from the above form:
because the front end of the radio frequency has a band-pass filter with the bandwidth being the bandwidth of the received signal, the value range of f is more than or equal to 0 and less than or equal to N sc KΔf, for ease of description, is denoted herein as a single-sided spectrum signal, in effect taking on a range of values-N sc KΔf/2≤f≤N sc A double-sided spectrum signal of K delta f/2 is equivalent to the double-sided spectrum signal; when the minimum frequency of the bilateral spectrum signal is taken as the center frequency, the bilateral spectrum can be converted into a unilateral spectrum;
the sequence satisfying the time domain form of the formula (2) and the frequency domain form of the formula (3) is the constructed sparse multitone training sequence.
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