CN115277335A - Symbol detection method of orthogonal time sequence multiplexing system - Google Patents

Symbol detection method of orthogonal time sequence multiplexing system Download PDF

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CN115277335A
CN115277335A CN202210862776.9A CN202210862776A CN115277335A CN 115277335 A CN115277335 A CN 115277335A CN 202210862776 A CN202210862776 A CN 202210862776A CN 115277335 A CN115277335 A CN 115277335A
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CN115277335B (en
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龙锟
李国军
叶昌荣
谢文希
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Chongqing University of Post and Telecommunications
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    • 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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2649—Demodulators
    • H04L27/26532—Demodulators using other transforms, e.g. discrete cosine transforms, Orthogonal Time Frequency and Space [OTFS] or hermetic transforms
    • 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
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/01—Equalisers
    • 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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2689—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
    • H04L27/2691—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation involving interference determination or cancellation
    • 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
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Abstract

The invention belongs to the field of communication, and particularly relates to a symbol detection method of an orthogonal time sequence multiplexing system; after receiving the time domain vector at a receiving end, performing MMSE equalization block by block in the time domain by utilizing the channel characteristics to obtain an estimated symbol vector of each time domain block; in order to further eliminate the interference of residual symbols, estimated symbol vectors are judged and then are used as initial values of a Gauss-Saider iterative detection algorithm for iterative detection, so that estimated values of each time domain block vector are obtained, and the estimated values of the original transmitted symbol vectors are obtained after vector matrixing and Walsh-Hadamard transformation. The invention can solve the problem that in a high-speed mobile environment, doppler spread introduces interference in each block and the performance of a single-tap frequency domain equalizer is limited when facing high Doppler frequency shift.

Description

Symbol detection method of orthogonal time sequence multiplexing system
Technical Field
The invention belongs to the field of communication, and particularly relates to a symbol detection method of an orthogonal time sequence multiplexing system.
Background
Future wireless communication systems require reliable data transmission in various emerging applications, such as low earth orbit satellites, high speed trains, unmanned aerial vehicles, and other high speed mobile scenarios. However, high doppler shift exists in high mobility wireless communication systems, and the currently widely adopted Orthogonal Frequency Division Multiplexing (OFDM) system suffers from severe Inter-Carrier Interference (ICI). Orthogonal Time Frequency Space (OTFS) modulation has excellent performance in a fast fading channel, and has the advantages of high spectral efficiency, low peak-to-average power ratio and the like. The OTFS modulates the information symbols in a delay-Doppler domain instead of a traditional time-frequency domain, so that the symbols in each data frame experience an approximately constant delay-Doppler domain non-fading channel, and the defects of the OFDM in a high-speed mobile environment are well overcome. Although OTFS may provide good error performance, two-dimensional precoding in the time-frequency domain may increase the modulation complexity of the transceiver.
Recently, thaj et al proposed a novel two-dimensional modulation scheme: orthogonal Time Multiplexing (OTSM) modulation, the key idea of which is to modulate information symbols in the delay-sequence domain. As shown in fig. 1, the OTSM performs Inverse Walsh-hadamard Transform (IWHT) along a sequence domain to convert information symbols placed in a delay-sequence domain into a delay-time domain, and finally performs signal transmission and reception in a time domain. Compared to OTFS performing IFFT along the doppler domain, the Walsh-hadamard Transform (WHT) involves only addition and subtraction operations, and therefore OTSM has a lower modulation complexity. Meanwhile, the OTSM has the performance similar to that of the OTFS, and a low-complexity modulation scheme is provided for realizing reliable communication of a high-mobility wireless channel.
In 2018, raviteja et al propose an iterative detection algorithm based on Message Passing (MP) by using the sparsity of a delay-Doppler domain channel, but the MP algorithm needs to continuously approach to the optimal performance through a large number of iterations, and the calculation complexity is extremely high. In 2020, thaj et al proposed a low complexity iterative Decision Feedback Equalizer (DFE) based on Maximum Ratio Combining (MRC) for OTFS. Simulation results show that compared with the most advanced MP detector at present, the detector is greatly improved in performance and complexity. In 2021, thaj et al proposed a low-complexity iterative detector for OTSM, and designed a single-tap least mean square equalizer in the time-frequency domain to suppress inter-carrier interference, and then used gaussian-Seidel (GS) iterative detection in the time domain to further eliminate residual symbol interference. However, in a high doppler frequency shift wireless channel, the performance of a single-tap least mean square equalizer is very limited, and the convergence speed and the error code performance of the GS iterative detection algorithm are seriously influenced.
Disclosure of Invention
Based on the problems in the prior art, in order to realize reliable transmission of data in a high-mobility wireless channel, the invention provides a new secondary equalizer for an OTSM (optical transport short message system) system to realize detection and estimation of a transmitted symbol vector. MMSE detection is first performed on the received time domain blocks in the time domain block by block, and then the residual symbol interference is further eliminated by using GS iterative algorithm. In order to further reduce the complexity of the system, the invention also utilizes the sparsity and the banded structure of the channel matrix to carry out low-complexity LU decomposition on the estimated symbol vector, and avoids matrix inversion operation by forward replacement and backward replacement algorithms.
The invention provides the following technical scheme to realize the technical purpose:
a method of symbol detection for an orthogonal time sequence multiplexing system, the method comprising:
after receiving the time domain vectors, carrying out MMSE equalization processing on each time domain block by block to obtain a symbol vector of each time domain block;
judging the symbol vector of each time domain block, and then performing iterative detection by taking the symbol vector of each time domain block as an initial value of a Gauss-Saider iterative detection algorithm to obtain an estimated value of the symbol vector of each time domain block;
after the symbol vector of each time domain block is matrixed, a time delay-time domain information symbol is obtained;
and carrying out Walsh-Hadamard transform on the time delay-time domain information symbols to obtain an estimated value of the transmitted time delay-sequence domain information symbols.
Further, the process of obtaining the symbol vector of each time domain block includes:
carrying out LU matrix decomposition on the banded matrix subjected to MMSE equalization processing to obtain a lower triangular matrix L and an upper triangular matrix U; the strip matrix comprises a channel matrix and a noise matrix;
according to the received time domain vector and the inverse matrix U of the upper triangular matrix U-1Solving a first time domain vector by using a reverse substitution algorithm of the strip matrix;
according to the solved first time domain vector and the inverse matrix L of the lower triangular matrix L-1Solving a second time domain vector by using a forward substitution algorithm of the banded matrix;
and solving the symbol vector of each time domain block by using sparse matrix vector multiplication according to the solved second time domain vector and the channel matrix of the time domain block.
Further, the formula adopted for MMSE equalization processing for each time domain block is represented as:
Figure BDA0003757327640000031
wherein the content of the first and second substances,
Figure BDA0003757327640000032
a symbol vector representing the estimated nth time domain block; r isnRepresents the nth received time domain block; hnRepresenting the channel matrix of the nth time domain block, and the superscript H represents the conjugate transpose of the matrix;
Figure BDA0003757327640000033
represents the variance of Gaussian white noise, and
Figure BDA0003757327640000034
is a ribbon matrix.
Further, the strip matrix in the process of MMSE equalization processing is processed
Figure BDA0003757327640000035
After LU matrix decomposition, symbol vector
Figure BDA0003757327640000036
Expressed as:
Figure BDA0003757327640000037
wherein, it is made
Figure BDA0003757327640000038
Figure BDA0003757327640000039
An nth time domain block representing the first time domain vector, and
Figure BDA00037573276400000310
Figure BDA00037573276400000311
an nth time domain block representing a second time domain vector.
Further, the solving of the first time domain vector by using the inverse substitution algorithm of the strip matrix comprises respectively calculating a first time domain vector with an interval of [1, α -1] and a first time domain vector with an interval of [ α, M-1] by using a first segmentation formula; wherein the first segmentation formula is represented as:
Figure BDA00037573276400000312
alpha denotes the channel delay spread length, M denotes each time domain block vector rnLength of (a) rnRepresents the nth received time domain block; r is(1)(k) Denotes a first time domain vector of length k, r (k) denotes a received time domain vector of length k, L (k, k-i) denotes a value of k-i column of k-th row of the lower triangular matrix, r(1)(k-i) denotes a first time-domain vector of length (k-i), M>α。
Further, the solving of the second time domain vector by the forward substitution algorithm using the strip matrix comprises using a second segmentation formula to obtain a second time domain vector with an interval of [ M-1, M-alpha ] and a second time domain vector with an interval of [ M-alpha-1, 0 ]; wherein the first segmentation formula is represented as:
Figure BDA0003757327640000041
r(2)(k) Representing a second time domain vector of length k, U (k, k) representing the value of the k-th row k-column of the lower triangular matrix, and U (k, k + i) representing the value of the k-th row k-i-column of the lower triangular matrix; r is(2)(k + i) denotes a second time domain vector of length (k + i).
Further, the symbol vector of each time domain block is estimated as:
Figure BDA0003757327640000042
wherein, P represents the number of propagation paths of the time-varying channel;
Figure BDA0003757327640000043
represents the path gain of the ith path, represents the complex conjugate,
Figure BDA0003757327640000044
circ represents a circulant matrix, T represents a transposition, and MN represents the total number of sending symbols;
Figure BDA0003757327640000045
diag denotes taking the diagonal of the matrix element; r is(2)Representing a second time domain vector.
Further, the process of obtaining the estimated value of the transmitted delay-sequence domain information symbol includes obtaining a time domain information symbol after the symbol vector of each time domain block after the low-complexity MMSE equalization processing is judged, and obtaining a time domain input-output relationship after the time domain information symbol is subjected to matched filtering operation; then, solving a least square solution corresponding to the time domain input-output relation through iteration; carrying out hard decision on the least square solution of the iterative solution to obtain a time delay-sequence information symbol in each iterative process; and (4) taking the time delay-sequence information symbol after the hard decision as an initial value in the next iteration process after relaxation and scaling until the iteration is completed, and outputting an estimated value of the transmitted symbol vector.
Further, the delay-sequence information symbol after the relaxation scaling update is represented as:
Figure BDA0003757327640000051
wherein the content of the first and second substances,
Figure BDA0003757327640000052
representing an estimated symbol of an nth time domain block in the (i + 1) th iteration, wherein delta represents a relaxation parameter, and vec represents matrixing;
Figure BDA0003757327640000053
estimated symbol representing the nth time-domain block in the ith iteration, X(i)Time delay-sequence field information symbol, W, representing the ith iterationNRepresenting an N-point walsh-hadamard transform.
The invention has the beneficial effects that:
1. the invention carries out block processing on the information symbols sent at the receiving end, obtains the initial estimation symbols by adopting accurate MMSE equalization, and can solve the problems that in a high-speed mobile environment, doppler expansion introduces interference in each block, and a single-tap frequency domain equalizer has limited performance when facing high Doppler frequency shift.
2. The invention utilizes the sparsity and the banded structure of the channel matrix to carry out low-complexity LU matrix decomposition on the banded matrix in the MMSE equalization processing process, avoids matrix inversion operation by a forward replacement algorithm and a backward replacement algorithm, and can effectively reduce the complexity.
3. The invention multiplexes information symbols in time delay and sequence domains by means of cascaded time division and walsh-hadamard (WHT) multiplexing. Since the WHT does not need to perform complex multiplication operations during the modulation and demodulation process, the WHT has lower modulation complexity compared to Orthogonal Time Frequency Space (OTFS) modulation.
4. The invention adopts Gauss-Saider (GS) iterative detection to carry out iterative detection processing on the estimated value of the time delay-sequence domain information symbol after WHT transformation and judgment, and further eliminates residual symbol interference.
5. Simulation results show that compared with the traditional GS iterative detection based on single-tap equalization, the method has remarkable performance improvement, and when 4QAM modulation is adopted and the error rate is 10-6The time performance gain is 1.211dB, 16QAM modulation is adopted, and the error rate is 10-4The time performance gain is 1.785dB.
Drawings
FIG. 1 is a diagram of the relationship between different discrete information symbol domains and corresponding modulation schemes in the prior art;
FIG. 2 is a diagram of a transmit-receive model of an OTSM system employed in the present invention;
FIG. 3 is a flow chart of a symbol detection method for an orthogonal time division multiplexing system according to the present invention;
fig. 4 is a flow chart of receiver signal processing according to the present invention;
FIG. 5 is a simulation diagram of error code performance of the OTSM system according to the present invention under different detection algorithms;
FIG. 6 is a simulation diagram of error code performance of the OTSM system according to the present invention under different system parameters;
FIG. 7 is a simulation graph of GS iterative detection based on single tap equalization and error code performance comparison of the present invention at different speeds;
FIG. 8 is a simulation diagram of GS iteration OTSM and OTFS detection based on single tap equalization and error code performance comparison of the present invention;
fig. 9 is a simulation diagram of error performance under different user moving speeds and signal-to-noise ratios.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 2 is a diagram of a transmit-receive model of an OTSM system, as shown in fig. 2, for convenience of description, the OTSM system model is represented in a matrix form in the present invention, and it is assumed that
Figure BDA0003757327640000061
Respectively representing transmitted information symbols and received information symbols, wherein MN is the total number of the transmitted symbols, N is the number of symbol vectors, M is the length of each symbol vector, and the duration and the bandwidth of an OTSM signal frame are respectively Tf= NT and B = M Δ f, where Δ f =1/T.
At the transmitting end, the information symbols
Figure BDA0003757327640000062
Is divided into M symbol vectors
Figure BDA0003757327640000063
Then put it in the time delay-sequence domain matrix
Figure BDA0003757327640000064
Wherein, the indexes of the column and the row of the delay-sequence domain matrix respectively represent the delay and the sequence tap index of the delay-sequence grid, and the superscript T represents the transposition of the matrix.
X＝[x0,x1,…,xM-1]T (1)
And setting the last alpha row symbol vector in X as a zero vector, wherein alpha represents the delay spread length of the discrete channel. As shown in fig. 2, zero Padding (ZP) helps to avoid inter-block interference caused by channel delay spread. For the symbol vector xmPerforming N-point WHT (after normalization, IWHT equivalence is performed along the sequence domain) to obtain a time delay-time domain matrix
Figure BDA0003757327640000065
Figure BDA0003757327640000066
Wherein the content of the first and second substances,
Figure BDA0003757327640000067
representing the transmitted symbol vector after N-point WHT transformation,
Figure BDA0003757327640000068
m＝0,...,M-1，WNrepresenting N-point Walsh-Hadamard transforms, pair matrices
Figure BDA0003757327640000071
Vectorizing column by column to obtain symbol vector
Figure BDA0003757327640000072
Expressed as:
Figure BDA0003757327640000073
the symbol vector s at the transmitting end is transmitted to a wireless channel in the form of s (t) after pulse shaping and digital-to-analog conversion.
At a receiving end, a time domain vector is obtained after the received time domain signal r (t) is subjected to analog-to-digital conversion
Figure BDA0003757327640000074
Obtaining a time delay-time domain matrix by matrixing r
Figure BDA0003757327640000075
Figure BDA0003757327640000076
For matrix
Figure BDA0003757327640000077
When N point WHT is receivedDelay-sequence field information symbol:
Figure BDA0003757327640000078
wherein, ymRepresenting the received symbol vector after N-point WHT transformation,
Figure BDA0003757327640000079
m＝0,...,M-1。
for the channel, and the input-output relationship between the transmitting end and the receiving end, the invention considers a time-varying channel with P propagation paths, where hi，τiAnd viPath gain, delay and doppler shift of the ith path, respectively. Let τ bemaxAnd vmaxRespectively represents the maximum delay spread and the Doppler shift in the channel, and the delay spread length and the Doppler spread length of the channel are respectively
Figure BDA00037573276400000710
And
Figure BDA00037573276400000711
wherein
Figure BDA00037573276400000712
Is an rounding-up function. Assuming that an OTSM system with a carrier frequency of 4GHz and a subcarrier spacing of 15KHz, N =128, and M =512 is considered, an Extended vehicle channel model (EVA) proposed by 3GPP is adopted, and the delay-doppler spread length can be calculated as α =20<<MN＝65536，β＝16<<MN＝65536。
The channel impulse response based on the delay-doppler domain can be represented as follows:
Figure BDA00037573276400000713
the corresponding continuous time-varying channel impulse response function can be expressed as:
g(τ,t)＝∫vh(τ,v)ej2πv(t-τ)dv (7)
the received time domain signal r (t) may be represented as:
Figure BDA00037573276400000714
therefore, the time domain input-output relationship in matrix form can be expressed as:
r＝H·s+w (9)
wherein
Figure BDA0003757327640000081
Is a mean of 0 and a variance of
Figure BDA0003757327640000082
The white gaussian noise of (a) is,
Figure BDA0003757327640000083
for the time domain discrete channel matrix:
Figure BDA0003757327640000084
wherein the content of the first and second substances,
Figure BDA0003757327640000085
based on the above analysis, as shown in fig. 2, ZP prevents time domain inter-block interference, and the time domain input-output relationship in equation (9) can be expressed as:
rn＝Hn·sn+wn,n＝0,…,N-1 (11)
wherein the content of the first and second substances,
Figure BDA0003757327640000086
Hnis the nth time domain block channel matrix.
In the conventional symbol detection method, assuming that the channel matrix of each time domain block is a circulant matrix at low doppler shift, it can be diagonalized in the frequency domain. The received time frequency signal can be processed by performing M-point FFT operation on the time domain block:
Figure BDA0003757327640000087
MMSE equalization is then performed on each block:
Figure BDA0003757327640000088
wherein M =0, \8230, M-1, N =0, \8230, N-1, the frequency domain channel coefficients are:
Figure BDA0003757327640000089
wherein diag [ A ]]Representing a column vector containing diagonal elements of the square matrix a. As shown in fig. 1, the estimation value of the delay-sequence domain information symbol can be estimated through the time-frequency domain
Figure BDA00037573276400000810
Performing M-point IFFT and N-point WHT to obtain:
Figure BDA00037573276400000811
wherein
Figure BDA00037573276400000812
After being judged, the matrix is used as an initial value of a GS iterative detection algorithm to carry out iterative detection, and the matrix input-output relationship in the formula (11) after matched filtering operation can be expressed as follows:
Figure BDA00037573276400000813
wherein
Figure BDA00037573276400000814
GS iterationThe algorithm is used to iteratively solve a least squares solution of the M-dimensional linear system of equations in equation (16):
Figure BDA0003757327640000091
let DnAnd LnAre each RnThe diagonal element matrix and the lower triangular element matrix of the GS iterative algorithm, and the GS iterative algorithm solves each iteration
Figure BDA0003757327640000092
The method can be as follows:
Figure BDA0003757327640000093
Figure BDA0003757327640000094
Figure BDA0003757327640000095
wherein
Figure BDA0003757327640000096
For the GS iteration matrix is the matrix that is,
Figure BDA0003757327640000097
representing the symbol estimates for the nth time domain block in the ith iteration. The delay-sequence field information symbol for the ith iteration may be obtained by:
Figure BDA0003757327640000098
wherein
Figure BDA0003757327640000099
It is meant that a hard decision is made,
Figure BDA00037573276400000910
the decision symbols are then converted back to the time domain as the initial estimate for the next iteration:
Figure BDA00037573276400000911
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00037573276400000912
representing an estimated symbol of an nth time domain block in the (i + 1) th iteration, delta representing a relaxation parameter for improving the convergence of a high-order modulation scheme detector, and vec representing matrixing;
Figure BDA00037573276400000913
an estimated symbol representing the nth time-domain block in the ith iteration, X(i)Time delay-sequence field information symbol, W, representing the ith iterationNRepresenting an N-point walsh-hadamard transform.
In a high-speed mobile environment, doppler spreading introduces interference in each block, and a single-tap frequency domain equalizer has limited performance in the face of high doppler shifts. In view of this, the invention adopts more accurate time domain block equalization in the initial equalization, and as shown in fig. 3, the symbol detection method of the orthogonal time sequence multiplexing system of the invention includes:
s1, after receiving time domain vectors, carrying out MMSE equalization processing on each time domain block by block, and estimating to obtain a symbol vector of each time domain block;
receiving a time domain block r of a time domain vector rnThereafter, MMSE equalization is performed for each time domain block:
Figure BDA00037573276400000914
wherein the content of the first and second substances,
Figure BDA00037573276400000915
a symbol vector representing the estimated nth time domain block; r isnDenotes the n-th connectionA received time domain block; hnRepresenting the channel matrix of the nth time domain block, and the superscript H represents the conjugate transpose of the matrix;
Figure BDA0003757327640000101
represents the variance of Gaussian white noise, and
Figure BDA0003757327640000102
in the form of a ribbon matrix.
The direct calculation of equation (23) requires a higher complexity, but ZP makes
Figure BDA0003757327640000103
Based on the banded matrix structure, the invention adopts low-complexity LU decomposition. The LU decomposed equation (23) can be simplified as:
Figure BDA0003757327640000104
wherein, it is made
Figure BDA0003757327640000105
Figure BDA0003757327640000106
An nth time domain block representing the first time domain vector, and
Figure BDA0003757327640000107
Figure BDA0003757327640000108
an nth time domain block representing a second time domain vector;
Figure BDA0003757327640000109
and
Figure BDA00037573276400001010
the calculation can be performed by using algorithm 1 and algorithm 2 in table 1, respectively, where algorithm 1 is a reverse replacement algorithm and algorithm 2 is a forward replacement algorithm.
Table 1 forward and backward substitution algorithms
Figure BDA00037573276400001011
Fig. 4 shows the low complexity receiver signal processing flow proposed by the present invention, and as shown in fig. 4, it will be described
Figure BDA00037573276400001012
After low-complexity LU decomposition is carried out, a lower triangular matrix L and an upper triangular matrix U are obtained through decomposition; inverse matrix U of matrix U-1Combining the received time domain vector, and solving a first time domain vector by using a reverse substitution algorithm of a banded matrix; according to the solved time domain vector in the initial iteration process and the inverse matrix L of the matrix L-1Solving a second time domain vector by using a forward substitution algorithm of the banded matrix; a sparse matrix vector multiplication (i.e., equation 27) is used to solve the symbol vector for each time domain block based on the solved second time domain vector and the channel matrix for the time domain block.
Specifically, solving the first time domain vector by using the reverse substitution algorithm of the strip matrix comprises respectively calculating the first time domain vector with the interval [1, alpha-1 ] and the first time domain vector with the interval [ alpha, M-1] by using a first segmentation formula; wherein the first segmentation formula is represented as:
Figure BDA0003757327640000111
alpha denotes the channel delay spread length and M denotes the length of the symbol vector, where M corresponds to each time-domain block vector rnLength of (a) r(1)(k) Denotes a first time domain vector of length k, r (k) denotes a received time domain vector of length k, L (k, k-i) denotes a value of k-i column of k-th row of the lower triangular matrix, r(1)(k-i) denotes a first time-domain vector of length (k-i), M>α。
Specifically, solving the second time domain vector by using a forward substitution algorithm of the strip matrix comprises adopting a second segmentation formula to obtain the second time domain vector with an interval of [ M-1, M-alpha ] and the second time domain vector with an interval of [ M-alpha-1, 0 ]; wherein the second segmentation formula is represented as:
Figure BDA0003757327640000112
r(2)(k) Representing a second time domain vector of length k, U (k, k) representing the value of the k-th row k-column of the lower triangular matrix, and U (k, k + i) representing the value of the k-th row k-i-column of the lower triangular matrix; r is(2)(k + i) denotes a second time domain vector of length (k + i).
Second time domain vector r of the results calculated by algorithm 1 and algorithm 2(2)Into the formula (24), wherein
Figure BDA0003757327640000113
According to the sparsity of the channel matrix H, a second time domain vector r(2)After cyclic shift, and
Figure BDA0003757327640000114
obtained by multiplication
Figure BDA0003757327640000117
Figure BDA0003757327640000115
Wherein, P represents the number of propagation paths of the time-varying channel;
Figure BDA0003757327640000116
represents the path gain of the ith path, represents the complex conjugate,
Figure BDA0003757327640000121
circ denotes a circulant matrix, T denotes transpose;
Figure BDA0003757327640000122
diag denotes taking the diagonal of the matrix elements.
S2, after the symbol vector of each time domain block is judged, the symbol vector of each time domain block is used as an initial value of a Gauss-Saider iterative detection algorithm to carry out iterative detection, and an estimated value of the symbol vector of each time domain block is obtained;
in the embodiment of the invention, the symbol vector of each time domain block is judged and then used as the initial value of the Gauss-Saider iterative detection algorithm to carry out iterative detection to obtain the estimated value of the time domain information symbol, and then the estimated value of the transmitted symbol vector is obtained according to the steps S3 and S4.
In the embodiment of the invention, symbol vectors of each time domain block after low-complexity MMSE equalization processing are judged to obtain time domain information symbols, and the time domain information symbols after time domain estimation after low-complexity MMSE equalization judgment are obtained are subjected to matched filtering operation to obtain a time domain input-output relation; then solving a least square solution corresponding to the time domain input-output relation through Gauss-Saider iteration; performing hard decision on the least square solution of the iterative solution to obtain a time delay-sequence information symbol in each iterative process; and (3) taking the time delay-sequence information symbol after the hard decision as an initial value in the next iteration process after the time delay-sequence information symbol is subjected to loose scaling, repeatedly executing the processes of formulas (16) to (22) until the iteration is completed, and finally converting the time domain signal into the time delay-sequence domain symbol through the steps S3 and S4 so as to obtain an estimation value of the transmitted symbol vector.
S3, matrixing the symbol vector of each time domain block to obtain a time delay-time domain information symbol;
in the embodiment of the invention, the symbol vector of each time domain block obtained by the Gaussian-Saider iterative detection algorithm estimation
Figure BDA0003757327640000123
Performing matrixing, symbol vector
Figure BDA0003757327640000124
The time delay-time domain information symbols can be obtained by matrixing:
Figure BDA0003757327640000125
and S4, carrying out Walsh-Hadamard transformation on the time delay-time domain information symbol to obtain an estimated value of the time delay-sequence domain information symbol.
In the embodiment of the invention, the time delay-sequence domain information symbol obtained in the step S3 is subjected to
Figure BDA0003757327640000127
Performing N-point WHT to obtain a delay-sequence domain information symbol:
Figure BDA0003757327640000126
this embodiment will analyze the computational complexity of the present invention and the GS iterative detection algorithm based on a single-tap equalizer, and table 2 shows the number of complex multiplications required for each operation of the low complexity receiver in fig. 4. The number of complex multiplications required for a single-tap frequency domain equalizer can be given by equation (13) as NM [ alpha +2log2(M)+3]. Since OTSM does not require complex multiplication in modem, the computational complexity required at each GS iteration is only O (NM).
Table 2 shows the computational complexity of the different operations of the receiver of the invention
Figure BDA0003757327640000131
In the embodiment, the proposed equalization algorithm is compared with the OTSM iterative detection algorithm based on the single-tap equalizer in a simulation manner, and the simulation parameters in table 3 are adopted without any special description. Assuming that the channel information is completely known, each point in the BER graph sends a frame, and the Doppler shift of the channel is given by the Jakes formula vi＝vmaxcos(θi) Generation vmaxAt the maximum moving speed, θiIn the range of [ - π, π]Are uniformly distributed.
TABLE 3 simulation parameters
Figure BDA0003757327640000132
Fig. 5 compares the Single tap frequency domain equalization and time domain Block equalization algorithms required for iteration, and also compares the error code performance of the GS Iterative detection (Single tap Iterative) based on the Single tap frequency domain equalization and the GS Iterative detection algorithm (Block LMMSE Iterative) based on the time domain Block equalization proposed in the present invention in different modulation modes. Simulation results show that the performance of the single-tap frequency domain equalizer is very limited in a high-speed moving environment, the convergence speed and the error code performance of the GS iterative algorithm are seriously influenced, and the performance of the algorithm is remarkably improved compared with the GS iterative detection algorithm based on the single-tap equalizer under the condition of high signal-to-noise ratio. Adopts 4QAM modulation and has the error rate of 10-6The time performance gain is 1.211dB, 16QAM is adopted for modulation, and the error rate is 10-4The time performance gain is 1.785dB. Meanwhile, the algorithm still shows remarkable performance improvement even under high-order modulation.
Figure 6 shows the error performance of the OTSM system under different system parameters. Due to the fact that the resolution ratio of the time delay-sequence domain grid is low, the performance of the GS iterative detection algorithm based on the single-tap frequency domain equalization and the algorithm provided by the invention are reduced at different levels along with the reduction of M and N. This is because the receiver parses out fewer channel paths, resulting in lost diversity. It can also be seen from the figure that the proposed algorithm still shows a certain level of gain as M and N change.
Fig. 7 compares the SNR at 25dB and 30dB respectively based on the GS iterative detection of single-tap frequency domain equalization and the error performance of the algorithm proposed by the present invention at different user moving speeds (i.e. various maximum doppler shifts). Simulation results show that the error code performance of the algorithm provided by the invention is obviously superior to GS iterative detection based on single-tap frequency domain equalization along with the increase of the moving speed of a user. It can also be seen from the figure that the error performance is lower when the user moving speed is small than when the user moving speed is large. This result is surprising for conventional modulation schemes that require quasi-static channels. Indeed, modulation in the delay-sequence domain may benefit from a larger doppler shift, since the receiver may resolve more channel paths by doppler shift.
Fig. 8 compares the error performance of the algorithm provided by the present invention and GS iterative detection based on single tap frequency domain equalization adopted in OTSM and OTFS systems. It can be found from the figure that the performance of the OTSM and the OTFS modulation scheme is very close when the same detection algorithm is adopted, but because of WHT, the OTSM does not need to perform complex multiplication operation in the modulation and demodulation process, and compared with the OTFS, the OTSM has lower modulation complexity, and is very suitable for a low-complexity transceiver.
In order to further intuitively feel the error code performance of the algorithm under different user moving speeds and signal-to-noise ratios, the invention carries out three-dimensional analysis on the detection method, as shown in fig. 9. It can be seen from fig. 9 that the error code performance of the OTSM system is better and better as the moving speed of the user increases, and the OTSM system can benefit from larger doppler shift, so that the OTSM system can well meet the requirements of the future wireless mobile communication system.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (9)

1. A method for symbol detection in an orthogonal time division multiplexing system, the method comprising:
after receiving the time domain vector, performing low-complexity MMSE equalization processing on each time domain block by block to obtain a symbol vector of each time domain block;
after the symbol vector of each time domain block is judged, the symbol vector of each time domain block is used as an initial value of a Gauss-Saider iterative detection algorithm to carry out iterative detection, and an estimated value of the symbol vector of each time domain block is obtained;
after the symbol vector of each time domain block is matrixed, a time delay-time domain information symbol is obtained;
and carrying out Walsh-Hadamard transform on the time delay-time domain information symbols to obtain an estimated value of the transmitted time delay-sequence domain information symbols.
2. The method of claim 1, wherein the obtaining the symbol vector of each time domain block comprises:
performing LU matrix decomposition on the banded matrix subjected to MMSE equalization processing to obtain a lower triangular matrix L and an upper triangular matrix U; the strip matrix comprises a channel matrix and a noise matrix;
according to the received time domain vector and the inverse matrix U of the upper triangular matrix U-1Solving a first time domain vector by using a reverse substitution algorithm of the strip matrix;
according to the solved first time domain vector and the inverse matrix L of the lower triangular matrix L-1Solving a second time domain vector by using a forward substitution algorithm of the banded matrix;
and solving the symbol vector of each time domain block by using sparse matrix vector multiplication according to the solved second time domain vector and the channel matrix of the time domain block.
3. The symbol detection method of an orthogonal time-division multiplexing system as claimed in claim 1 or 2, wherein the formula for MMSE equalization processing for each time domain block is represented as:
Figure FDA0003757327630000011
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003757327630000012
a symbol vector representing the estimated nth time domain block; r isnRepresents the nth received time domain block; hnRepresenting the channel matrix of the nth time domain block, and the superscript H represents the conjugate transpose of the matrix;
Figure FDA0003757327630000013
represents the variance of Gaussian white noise, and
Figure FDA0003757327630000014
in the form of a ribbon matrix.
4. The symbol detection method of claim 3, wherein the symbol detection method is applied to the strip matrix in the MMSE equalization process
Figure FDA0003757327630000021
After LU matrix decomposition, symbol vector
Figure FDA0003757327630000022
Expressed as:
Figure FDA0003757327630000023
wherein, it is made
Figure FDA0003757327630000024
Figure FDA0003757327630000025
An nth time domain block representing the first time domain vector, and
Figure FDA0003757327630000026
Figure FDA0003757327630000027
an nth time domain block representing a second time domain vector.
5. The symbol detection method of an orthogonal time division multiplexing system as claimed in claim 2, wherein the solving of the first time domain vector by the inverse substitution algorithm using the strip matrix comprises calculating the first time domain vector with interval [1, α -1] and the first time domain vector with interval [ α, M-1] by using a first segmentation formula; wherein the first segmentation formula is expressed as:
Figure FDA0003757327630000028
alpha represents the channel delay spread length, M represents each time domain block vector rnLength of (a), rnRepresents the nth received time domain block, r(1)(k) Denotes a first time domain vector of length k, r (k) denotes a received time domain vector of length k, L (k, k-i) denotes a value of k-i column of k-th row of the lower triangular matrix, r(1)(k-i) denotes a first time-domain vector of length (k-i), M>α。
6. The symbol detection method of an orthogonal time division multiplexing system of claim 5, wherein the solving of the second time domain vector by the forward substitution algorithm using the strip matrix comprises using a second section formula with a second time domain vector having a section of [ M-1, M- α ] and a second time domain vector having a section of [ M- α -1,0 ]; wherein the second segmentation formula is represented as:
Figure FDA0003757327630000029
r(2)(k) Representing a second time domain vector of length k, U (k, k) representing the values of the k row and k column of the lower triangular matrix, U (k, k + i) representing the values of the k row and k + i column of the lower triangular matrix; r is(2)(k + i) denotes a second time domain vector of length (k + i).
7. The method of claim 6, wherein the symbol vector of each time domain block is estimated as:
Figure FDA0003757327630000031
wherein, P represents the number of propagation paths of the time-varying channel;
Figure FDA0003757327630000032
represents the path gain of the ith path, represents the complex conjugate,
Figure FDA0003757327630000033
circ represents a circulant matrix, T represents a transposition, and MN represents the total number of sending symbols;
Figure FDA0003757327630000034
diag denotes taking the diagonal of the matrix element; r is a radical of hydrogen(2)Representing a second time domain vector.
8. The symbol detection method of an orthogonal time sequence multiplexing system according to claim 1, wherein the process of obtaining the estimated value of the transmitted delay-sequence field information symbol comprises obtaining the time field information symbol after the symbol vector of each time field block after the low complexity MMSE equalization processing is judged, and obtaining the time field input-output relationship after the matched filtering operation is performed on the time field information symbol; then solving a least square solution corresponding to a time domain input-output relation through Gauss-Saider iteration; carrying out hard decision on the least square solution of the iterative solution to obtain a time delay-sequence information symbol in each iterative process; and (4) taking the time delay-sequence information symbol after the hard decision as an initial value in the next iteration process after relaxation and scaling until the iteration is completed, and outputting an estimated value of the transmitted symbol vector.
9. The symbol detection method of claim 8, wherein the time delay-sequence information symbol after the relaxed scaling update is represented as:
Figure FDA0003757327630000035
wherein the content of the first and second substances,
Figure FDA0003757327630000036
to representEstimating symbols of an nth time domain block in the (i + 1) th iteration, wherein delta represents a relaxation parameter, and vec represents matrixing;
Figure FDA0003757327630000037
an estimated symbol representing the nth time-domain block in the ith iteration, X(i)Time delay-sequence field information symbol, W, representing the ith iterationNRepresenting an N-point walsh-hadamard transform.
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