UAMP-based OTSM system and equalization method thereof

Abstract

The invention belongs to the technical field of wireless communication, and relates to an orthogonal time sequence multiplexing (OTSM) system based on unitary approximate message passing (UAMP) and a balancing method of the orthogonal time sequence multiplexing (OTSM) system based on the unitary approximate message passing (UAMP). According to the method, on the basis of a ZP-OTSM system, embedded pilot frequency data and a zero filling symbol are arranged in a time delay-sequence domain of the ZP-OTSM system; the implementation process of the OTSM system equalization method is as follows: firstly, a time domain channel matrix is divided into a plurality of sub-time domain channel matrixes by using a zero filling symbol, the algorithm implementation complexity can be reduced, then singular value decomposition is performed on the plurality of sub-channel matrixes, and finally, data detection is completed in a time delay-sequence domain by using a UAMP equalization algorithm, so that the algorithm implementation complexity can be reduced. The robustness of the algorithm can be effectively exerted, and the performance is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and relates to an Orthogonal Time Sequency Multiplexing (OTSM) system based on Unitary Approximate Message Passing (UAMP) and its equalization method. Background Art

[0002] With the development of wireless communication technology, the fifth-generation mobile communication system (5G) has shown significant advantages in the modern communication field with its high data rate, high reliability, and low latency. However, in high-speed mobile communication scenarios, the traditional Orthogonal Frequency Division Multiplexing (OFDM) modulation technology faces challenges of time-selective fading and frequency-selective fading, resulting in a significant decline in system performance. To solve this problem, researchers have developed Orthogonal Time Frequency Space (OTFS) modulation technology and Orthogonal Time Frequency Sequence (OTSM) modulation technology. These technologies achieve stable transmission performance in high-speed mobile environments by converting the channel in different domains. Among them, the OTSM modulation technology modulates information symbols in the Delay-Sequency (DS) domain and uses the Walsh-Hadmard Transform (WHT), which has a lower implementation complexity compared to the Inverse Fast Fourier Transform (IFFT) of the OTFS system.

[0003] However, the existing OTSM system equalization algorithms still face significant challenges in practical applications, mainly manifested as insufficient noise suppression ability and performance instability. Specifically, this algorithm must rely on pre-acquired noise variance information, increasing the system implementation complexity, and it is difficult to maintain a stable working state in complex wireless environments. In addition, the sensitivity of the algorithm performance to communication scenarios leads to significant differences in system performance in different environments, severely restricting the overall performance optimization and application promotion of the OTSM system. Therefore, developing an equalization algorithm with stronger anti-noise ability and higher robustness is crucial for improving the performance of the OTSM system in practical applications.

[0004] In view of this, the present invention is specifically proposed. Summary of the Invention

[0005] The object of the present invention is to overcome the above-mentioned disadvantages of the prior art and provide a UAMP-based OTSM system and its equalization method.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] On the one hand, the present invention provides a UAMP-based OTSM system equalization method. Based on the ZP-OTSM system, embedded pilot data and zero-padding symbols are provided in the delay-sequence domain of the ZP-OTSM system. The execution process of the OTSM system equalization method is as follows: first, use the zero-padding symbols to divide the time-domain channel matrix into multiple sub-time-domain channel matrices, then perform singular value decomposition on the multiple sub-channel matrices, and finally complete data detection using the UAMP equalization algorithm in the delay-sequence domain.

[0008] Specifically, the specific steps of the equalization method are as follows:

[0009] Step 1. Construct a ZP-OTSM system: The ZP-OTSM system includes a transmitter, a time-domain channel, and a receiver. Among them, the transmitter modulates the information symbol data in the delay-sequence domain, inserts pilot data and zero-padding symbols, and then performs a WHT transform to the delay-time domain, and then passes through a serial-to-parallel conversion, adds a CP, and then passes through the time-domain channel. The receiver performs channel estimation by extracting the CP, serial-to-parallel conversion, and extracting pilot data, and then sends the channel estimation result to the UAMP equalization module.

[0010] Step 2. The UAMP equalization module performs unitary transformation processing on the channel estimation result and completes the reconstruction and estimation of the information symbol through the approximate message passing algorithm.

[0011] Further, step 1 is specifically as follows:

[0012] Step 1.1. The transmitter places multiple QAM symbol vectors modulated by the symbol modulation module in the delay-sequence domain grid X of size M×N (M is the number of rows, N is the number of columns), X = [x0, x1,..., x M-1 T , ( represents the complex domain Complex), m = 0, 1, 2,..., M - 1, and the QAM symbols altogether occupy the first M' rows, M' = M - (2l max +1), l max is the maximum discrete delay spread of the current OTSM system;

[0013] Step 1.2. Place the pilot data P at the delay-sequence domain index, and define the position of the index as (m p , n p ​), and at the same time, it is required that the length of the inserted zero-padding symbol is not less than l max , to ensure that there is no interference between data blocks and facilitate subsequent time-domain channel matrix block processing; where m p = M - l max - 1;

[0014] Step 1.3. First, transform the symbol matrix X in the delay-sequence domain grid into a delay-time domain symbol matrix through the WHT transformation module and W N is an N-point WHT transformation matrix; then perform a serial-to-parallel conversion by column to obtain a time-domain transmission vector represents a time-domain data block, n = 0, 1, 2,..., N - 1, and vec(·) represents column-wise vectorization of a matrix; before data transmission, the l max + 1 symbols at the end of the frame are added to the frame header as CP, and the CP includes 1 pilot data and l max ZPs;

[0015] Step 1.4. At the receiving end, first extract the CP of the received data, and define the time-domain received vector as r MN×1 = G·s + n, where G MN×MN is the time-domain channel matrix, is additive complex Gaussian white noise with a mean of 0 and a variance of ;

[0016] Then, transform the time-domain received vector to the delay-time domain through a serial-to-parallel conversion, that is where represents vectorizing into a matrix of dimension M×N, m = 0, 1, 2,..., M - 1;

[0017] Next, extract the pilot information in the current matrix and perform time-domain channel estimation together with the CP to obtain the estimated time-domain channel matrix

[0018] Then, transform the delay-time domain symbol matrix into a delay-sequence domain symbol matrix through the WHT transformation that is

[0019] Finally, obtain the delay-sequence domain received vector through a parallel-to-serial conversion and send it to the delay-sequence domain symbol detection module for UAMP equalization to obtain the transmitted symbol matrix

[0020] Furthermore, in Step 1.3, define the relationship at the transmitting end in matrix form as where P is a row-column interleaving matrix, IM is an M×M identity matrix, represents the Kronecker product.

[0021] Furthermore, in step 1.4, the relationship at the receiver in matrix form is defined as With T being the transpose symbol, the input-output relationship in the time-delay sequence domain for the OTSM system is where, is the Gaussian white noise in the time-delay sequence domain.

[0022] Specifically, step 2 includes:

[0023] Step 2.1: Divide the time-domain channel matrix into multiple sub-time-domain channel matrices G using the zero-padding symbol, where

[0024]

[0025] In equation (1), represents the sub-time-domain channel matrix corresponding to the nth time-domain data block, where n = 0, 1, 2,..., N - 1;

[0026] Step 2.2: Perform singular value decomposition on the sub-time-domain channel matrix block by block:

[0027]

[0028] In equation (2), matrices U, S, and V are respectively represented as follows:

[0029]

[0030] In equation (4), S n is an M×M diagonal matrix;

[0031] Step 2.3: According to the singular value decomposition result and the input-output relationship in the time-sequence domain, apply unitary transformation to obtain where, The noise remains additive complex Gaussian white noise with a mean of 0 and a variance of after being processed by unitary transformation.

[0032] Furthermore, the unitary transformation process in step 2.3 specifically includes:

[0033] Step 2.3.1: Data initialization, and the specific process is as follows:

[0034] Input data: the received signal after unitary transformation QAM modulation order M mod , the maximum number of iterations T uamp , λ = d·d *, where \(d = diag(S)\), \(d\) * denotes the conjugate of vector \(d\), and \(\cdot\) denotes the dot product;

[0035] Output data: transmitted signal vector

[0036] Recovery vector Intermediate variable \(k\) (0) \(= 0\), noise variance precision Mean of posterior probability variance Set of information symbols Iteration number \(t = 0\);

[0037] Step 2.3.2: Calculate vectors and where,

[0038] Step 2.3.3: Calculate intermediate variables and where \(\. / \) denotes element-wise division;

[0039] Step 2.3.4: Update noise variance precision

[0040] Step 2.3.5: Calculate intermediate variables and \(k\) (t) \(= v\) k \(\cdot (r - p)\);

[0041] Step 2.3.6: Calculate intermediate variable \(v\) q \(= MN / \lambda\) T \(v\) k and where

[0042] Step 2.3.7: Calculate the mean and variance of the posterior probability, where \(j\in\{1,2,\cdots,MN\}\) is the data symbol index, \(\xi\) j,a \(=\exp(-|\alpha\) a \(- q\) j |\) 2 / v\) q );

[0043] Step 2.3.8: Update the mean of the posterior probability variance

[0044] Step 2.3.9: Iteration number \(t = t + 1\), if \(t\geq T\) uamp , stop iteration and output Otherwise, go to Step 2.3.2.

[0045] In addition, the present invention also provides an OTSM system applying the above-described equalization method in part or in whole, including:

[0046] Transmitter: operating in the time-delay sequence domain, placing multiple QAM symbol vectors modulated by a symbol modulation module in a time-delay sequence domain grid X of size M×N, X = [x0, x1, …, x M-1 T , placing pilot data P at the time-delay sequence domain index, defining the position at the index as (m p , n p ), and at the same time requiring that the length of the inserted zero-padding symbols is not less than l max to ensure that there is no interference between data blocks and facilitate subsequent time-domain channel matrix block processing;

[0047] First WHT transformation module: transforming the transmitter time-delay sequence domain symbol matrix X into a time-delay time domain symbol matrix

[0048] Second WHT transformation module: transforming the receiver time-delay time domain symbol matrix into a time-delay sequence domain symbol matrix

[0049] Processing module and receiver: performing "parallel-to-serial conversion → adding CP → pulse shaping → DAC conversion" processing on the time-delay time domain symbol matrix and then transmitting it through the time-domain channel, and after "ADC conversion → matched filtering → extracting CP → serial-to-parallel conversion" processing, outputting in two paths. One path of the output symbols is sent to the UAMP equalization module after being processed by the second WHT transformation module, and the other path of the output symbols is subjected to channel estimation by extracting pilots and CP to obtain a channel estimation result, and the channel estimation result is sent to the UAMP equalization module;

[0050] UAMP equalization module: performing unitary transformation processing on the received channel estimation result and the output symbols processed by the second WHT transformation module, and completing the reconstruction and estimation of information symbols through an approximate message passing algorithm.

[0051] Among them, the information symbols after reconstruction and estimation can directly perform QAM demodulation processing; the total number of rows occupied by the QAM symbol vectors is the first M′ rows, M′ = M - (2l max + 1), and l max is the maximum discrete delay spread of the current OTSM system.

[0052] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0053] ​The equalization method provided by the present invention is based on the ZP-OTSM system. By using the zero-padding (ZP) symbols inserted in the DS (delay-sequence) domain grid, the time-domain channel matrix is divided into multiple sub-time-domain channel matrices. The singular value decomposition is performed on the sub-time-domain channel matrices, and then the UAMP equalization algorithm is used for data detection in the DS domain, which facilitates subsequent work such as symbol demodulation based on the equalization result. The UAMP equalization algorithm can self-estimate the noise variance accuracy during the iterative process, and the complexity of the singular value decomposition can be greatly reduced through the division of the sub-time-domain channel matrices, improving the algorithm operation efficiency. Description of the Drawings

[0054] The drawings herein are incorporated into the specification and constitute a part of this specification, and are used together with the specification to explain the principles of the present invention.

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0056] Figure 1 It is a flowchart of the OTSM system equalization method based on UAMP provided by the present invention;

[0057] Figure 2 It is a schematic block diagram of the OTSM system principle based on UAMP provided by the present invention;

[0058] Figure 3 It is a schematic diagram of the transmission relationship of the OTSM system based on UAMP provided by the present invention;

[0059] Figure 4 It is the bit error rate of the UAMP algorithm and other traditional algorithms in an uncoded system with ideal time-domain channel gain and 4QAM modulation;

[0060] Figure 5 It is the bit error rate of the UAMP algorithm and other traditional algorithms in an uncoded system with ideal time-domain channel gain and 16QAM modulation;

[0061] Figure 6 It is the bit error rate of the UAMP algorithm and other traditional algorithms under 1 / 2 LDPC coding with ideal time-domain channel gain and 4QAM modulation;

[0062] Figure 7 It is the bit error rate of the UAMP algorithm and other traditional algorithms under 1 / 2 LDPC coding with ideal time-domain channel gain and 16QAM modulation;

[0063] Figure 8 The bit error rates of the UAMP algorithm and other traditional algorithms under LDPC coding, with estimated channel gain and 4QAM modulation;

[0064] Figure 9 The bit error rates of the UAMP algorithm and other traditional algorithms under LDPC coding, with estimated channel gain and 16QAM modulation. Specific embodiments

[0065] Here, the exemplary embodiments will be described in detail. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. On the contrary, they are only examples consistent with some aspects of the present invention detailed in the appended claims.

[0066] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0067] Embodiment 1

[0068] See Figures 1 to 3 As shown, this embodiment provides an OTSM system equalization method based on UAMP. Based on the ZP-OTSM system, the time-delay sequence domain of the ZP-OTSM system is provided with embedded pilot data and zero-padding symbols; the execution process of the OTSM system equalization method is as follows: first, the time-domain channel matrix is divided into multiple sub-time-domain channel matrices by using the zero-padding symbols, then the singular value decomposition is performed on the multiple sub-channel matrices, and finally, the data detection is completed by using the UAMP equalization algorithm in the time-delay sequence domain.

[0069] Furthermore, the specific steps of the equalization method are as follows:

[0070] Step 1, construct a ZP-OTSM system: The ZP-OTSM system includes a transmitter, a time-domain channel, and a receiver; among them, the transmitter modulates the information symbol data in the time-delay sequence domain, inserts the pilot data and zero-padding symbols, and then performs a WHT transformation to the time-delay time domain, and then passes through the time-domain channel after serial-to-parallel conversion and adding CP; the receiver performs channel estimation by extracting CP, parallel-to-serial conversion, and extracting pilot data, and then sends the channel estimation result to the UAMP equalization module;

[0071] Step 2, the UAMP equalization module performs unitary transformation processing on the channel estimation result, and completes the reconstruction and estimation of the information symbols through the approximate message passing algorithm.

[0072] Furthermore, the above Step 1 is specifically as follows:

[0073] Step 1.1: The transmitting end places multiple QAM symbol vectors modulated by the symbol modulation module in the time delay-sequence domain grid X of size M×N (M rows and N columns), where X = [x0, x1, …, x M-1 T , The QAM symbol vectors altogether occupy the first M′ rows, where M′ = M - (2l max + 1), and l max is the maximum discrete time delay spread of the current OTSM system;

[0074] Step 1.2: The pilot data P is placed at the time delay-sequence domain index, and the defined index position is (m p , n p ). Meanwhile, to ensure that the time delay spread generated by the time domain data block and the pilot symbol P after passing through the time domain channel does not affect the subsequent data, it is required that the length of the inserted zero-padding symbols is not less than l max to ensure that there is no interference between data blocks and facilitate subsequent time domain channel matrix block processing; where m p = M - l max - 1;

[0075] Step 1.3: First, the symbol matrix X in the time delay-sequence domain grid is transformed into a time delay-time domain symbol matrix through the WHT transformation module and W N is an N-point WHT transformation matrix; then, the column-by-column serial-to-parallel conversion is performed to obtain the time domain transmission vector represents the time domain data block, n = 0, 1, 2, …, N - 1, and vec(·) represents the column-wise vectorization of the matrix; before data transmission, the l max + 1 symbols at the end of the frame are added to the frame header as the CP, and the CP includes 1 pilot data and l max ZPs;

[0076] Step 1.4: The receiving end first extracts the CP of the received data, and the received vector is defined as r MN×1 = G·s + n, where G MN ×MN is the time domain channel matrix, is additive complex Gaussian white noise with a mean of 0 and a variance of ;

[0077] Then, the time delay-sequence domain vector is transformed to the time delay-time domain through serial-to-parallel conversion, that is where represents the vectorized into a matrix of dimension M×N, m = 0, 1, …, M - 1;

[0078] Then, the pilot information in the current matrix ​Extract it and perform time-domain channel estimation together with the CP to obtain the estimated time-domain channel matrix

[0079] Then, transform the delay-time domain symbol matrix through the WHT transform into a delay-sequence domain symbol matrix That is

[0080] Finally, obtain the delay-sequence domain received vector through serial-to-parallel conversion And send it to the delay-sequence domain symbol detection module for UAMP equalization to obtain the transmitted symbol matrix

[0081] Furthermore, in step 1.3, the relationship at the transmitter in matrix form is defined as where P is a row-column interleaving matrix, and I M is an M×M identity matrix, represents the Kronecker product

[0082] Furthermore, in step 1.4, the relationship at the receiver in matrix form is defined as T is the transpose symbol, then the input-output relationship in the delay-sequence domain corresponding to the OTSM system is where is Gaussian white noise in the delay-sequence domain

[0083] Further, step 2 includes:

[0084] Step 2.1: Use zero-padding symbols to divide the time-domain channel matrix into multiple sub-time-domain channel matrices G, where

[0085]

[0086] In formula (1), G n ∈C M×M represents the sub-time-domain channel matrix corresponding to the nth time-domain data block, n = 0, 1, 2,..., N - 1;

[0087] Step 2.2: Perform singular value decomposition on the sub-time-domain channel matrix block by block:

[0088]

[0089] In formula (2), the matrices U, S, and V are respectively represented as follows:

[0090]

[0091] In formula (4), S n is an M×M diagonal matrix;

[0092] Step 2.3. Apply unitary transformation based on the singular value decomposition result and the input-output relationship in the time-series domain to obtain where After the noise is processed by the unitary transformation, it remains additive complex Gaussian white noise with a mean of 0 and a variance of .

[0093] Furthermore, the unitary transformation process in Step 2.3 specifically includes:

[0094] Step 2.3.1. Data initialization, the specific process is as follows:

[0095] Input data: The received signal after unitary transformation QAM modulation order M mod , the maximum number of iterations T uamp , λ = d·d * , where d = diag(S), d * denotes taking the conjugate of vector d, and · denotes dot product;

[0096] Output data: Transmitted signal vector

[0097] Recovery vector Intermediate variable k (0) = 0, noise variance precision Mean of the posterior probability variance Set of information symbols Iteration number t = 0;

[0098] Step 2.3.2. Calculate vectors and where

[0099] Step 2.3.3. Calculate intermediate variables and where. / denotes point division;

[0100] Step 2.3.4. Update the noise variance precision

[0101] Step 2.3.5. Calculate intermediate variables and k (t) = v k ·(r - p);

[0102] Step 2.3.6. Calculate intermediate variable v q = MN / λ T v k and where

[0103] Step 2.3.7, calculate the mean of the posterior probability and variance where j ∈ {1, 2,..., MN} is the data symbol index, ξ j,a = exp(-|α a -q j | 2 / v q );

[0104] Step 2.3.8, update the mean of the posterior probability variance

[0105] Step 2.3.9, the iteration number t = t + 1, if t ≥ T uamp , stop the iteration and output Otherwise, go to Step 2.3.2.

[0106] It should be noted that the information symbols after reconstruction and estimation can be directly subjected to QAM demodulation processing.

[0107] In addition, this embodiment also provides an OTSM system applying the above partial or all of the equalization methods, including

[0108] Transmitter: working in the delay-sequence domain, placing multiple QAM symbol vectors modulated by the symbol modulation module in the delay-sequence domain grid X of size M×N, X = [x0, x1,..., x M-1 T , the pilot data P is placed at the delay-sequence domain index, and the defined index position is (m p , n p ), and at the same time, it is required that the length of the inserted zero-padding symbol is not less than l max to ensure that there is no interference between data blocks and facilitate subsequent time-domain channel matrix block processing;

[0109] The first WHT transformation module: transforming the symbol matrix X in the transmitter delay-sequence domain grid into a delay-time domain symbol matrix

[0110] The second WHT transformation module: transforming the received-end delay-time domain symbol matrix into a delay-sequence domain symbol matrix

[0111] The processing module and the receiver: for the said delay-time domain symbol matrix ​After performing the processing of "parallel-to-serial conversion → adding CP → pulse shaping → DAC conversion", it passes through the time-domain channel, and then after the processing of "ADC conversion → matched filtering → extracting CP → serial-to-parallel conversion", it is output in two paths. One path of the output symbols is sent to the UAMP equalization module after being processed by the second WHT transformation module, and the other path of the output symbols is subjected to channel estimation by extracting the pilot and CP to obtain the channel estimation result, and the channel estimation result is sent to the UAMP equalization module;

[0112] UAMP equalization module: Perform unitary transformation processing on the received channel estimation result and the output symbols processed by the second WHT transformation module, and complete the reconstruction and estimation of the information symbols through the approximate message passing algorithm.

[0113] Further, the QAM symbol vector altogether occupies the first M' rows, M' = M - (2l max +1), where l max is the maximum discrete delay spread of the current OTSM system.

[0114] To further verify the effectiveness of the technical solution provided by the present invention, 1 group of algorithm complexity comparison and 3 groups of simulation experiments are designed. Among them, the 3 groups of simulation experiments are respectively:

[0115] 1) In the uncoded system, the bit error rate performance under ideal time-domain channel gain, 4QAM and 16QAM modulations;

[0116] 2) In the 1 / 2 code rate LDPC coded system, the bit error rate performance under ideal time-domain channel gain, 4QAM and 16QAM modulations;

[0117] 3) In the 1 / 2 code rate LDPC coded system, the bit error rate performance under the time-domain channel gain output by channel estimation, 4QAM and 16QAM modulations.

[0118] In each group of simulation experiments, the Single-Tap algorithm, Gauss-Seidel (GS) algorithm, Maximal Ratio Combining (MRC) iterative algorithm, Turbo-MRC algorithm and time-domain block LMMSE algorithm are compared simultaneously. Among them, since Turbo iteration requires a coding and decoding module, the Turbo-MRC algorithm is not compared in the uncoded system.

[0119] Complexity comparison:

[0120] In terms of computational complexity, step 2.3.7 needs to complete the calculation according to the specific modulation method, and the complexity of this step is O(MNM mod) Except for Steps 2.2.2 and 2.2.6, the remaining steps only involve dot multiplication and dot division operations. In these two steps, the matrix V is a block diagonal matrix, and all elements except for some elements on the block diagonal are 0. Therefore, the computational complexity of Steps 2.2.2 and 2.2.6 is O(M 2 N), and the computational complexity of a single iteration of the UAMP algorithm is O(M 2 N)+O(MNM mod ). The comparison of the computational complexity with other algorithms is shown in Table 1 below.

[0121] Table 1 Comparison of algorithm complexities

[0122]

[0123]

[0124] Among them, L represents the number of channel delay taps, and T GS , T MRC and T uamp represent the number of iterations corresponding to the GS algorithm, MRC algorithm, and UAMP algorithm respectively.

[0125] Simulation experiment 1)

[0126] Compare the bit error rate performance of different algorithms under 4QAM and 16QAM modulations in an uncoded system with ideal time-domain channel gains. The parameter settings are shown in Table 2 below, and the simulation results are as shown in Figure 4 and Figure 5 .

[0127] Table 1 Simulation parameter settings for Experiment 1)

[0128]

[0129] It can be seen from Figure 4 that in the uncoded system, under 4QAM modulation, the bit error rate performance of the UAMP algorithm is better than that of other algorithms. Taking the bit error rate of 10 -4 as the boundary, the UAMP algorithm can reach it at about 18.2 dB, while the MRC algorithm and GS algorithm reach it at 19 dB and 19.5 dB respectively. It can be seen from Figure 5 that in the uncoded system, under 16QAM modulation, the bit error rate performance of the UAMP algorithm is also better than that of other algorithms, and taking the bit error rate of 10 -4 as the boundary, the performance of the UAMP algorithm is improved by more than 2 dB compared with the MRC algorithm and GS algorithm. This shows that the UAMP algorithm performs better than other algorithms in the uncoded system, and even has a greater performance improvement under 16QAM.

[0130] Simulation experiment 2)

[0131] Compare the BER performance of different algorithms under 4QAM and 16QAM modulations using 1 / 2 rate LDPC coding and ideal time-domain channel gains. Carry out simulation experiment 2) with other simulation parameters unchanged. The results are as Figure 6 and Figure 7 shown.

[0132] From Figure 6 it can be seen that in the 1 / 2 rate LDPC coding system, the BER performance of each algorithm under 4QAM modulation has been greatly improved compared to the uncoded system. At the same time, the UAMP algorithm is superior to other algorithms. Taking 10 -4 as the boundary, the UAMP algorithm can reach it at about 13dB, while the time-domain block LMMSE algorithm reaches it at 14dB. The remaining algorithms require an SNR of more than 14dB. From Figure 7 it can be seen that in the case of 16QAM modulation, the performance of the UAMP algorithm is superior to other algorithms and has a relatively large performance advantage. Taking 10 -4 as the boundary, UAMP can reach it at about 19.5dB, while other algorithms require an SNR of more than 22dB, indicating that the UAMP algorithm has better anti-interference and anti-noise performance. At the same time, in Figure 6 and Figure 7 it can be found that in this experimental case, the MRC, GS, and LMMSE algorithms are not stable enough. Under 4QAM, LMMSE is superior to MRC and GS algorithms. Under 16QAM, MRC and GS are superior to the LMMSE algorithm. And UAMP can perform excellently in both modulation methods, proving that the UAMP algorithm has good robustness.

[0133] Simulation experiment 3)

[0134] Carry out simulation with channel estimation. The time-domain channel gain is estimated by the channel estimation module, and the equalization algorithms all use the results estimated by the channel estimation to equalize the received symbols. The pilot uses the embedded pilot P, and the pilot energy E p is set to 4 times the average energy E s of the data symbols, that is, E p = 4E s , where E s = sqrt[(M mod -1) / 6×d 2 , d = 2. The channel estimation module uses the CP and the pilot for LS channel estimation, and the rest of the simulation settings remain unchanged.

[0135] The simulation results are as Figure 8 and Figure 9 shown. From Figure 8It can be seen that under 4QAM modulation, when the channel gain obtained by channel estimation is adopted, the performance of UAMP equalization and LMMSE equalization is approximate. Taking 10 -4 as the boundary, both reach around 18 dB, while the other several algorithms need to reach above 20 dB. It can be seen from Figure 8 that when 16QAM is adopted, the performance of the UAMP algorithm is still the best. Taking 10 -4 as the boundary, the UAMP algorithm has a performance improvement of about 2 dB compared with Turbo-MRC, and the bit error rate of the UAMP algorithm drops to 0 when above 26 dB. This shows that: 1) The UAMP algorithm has strong anti-interference and anti-noise performance and can still perform well even under the condition of non-ideal channel gain; 2) The robustness of the UAMP algorithm is relatively high. From the simulation results in the above various cases, it can be seen that the adaptability of the UAMP algorithm is better than that of the other several algorithms, and the bit error rate performance is stable.

[0136] It should be emphasized that the higher the energy of the pilot symbol, the closer the channel estimation result is to the ideal channel gain. In this experiment, embedded pilots with lower energy are adopted. If pilots with higher energy are adopted, the simulation results will be better. However, high pilot energy will lead to an increase in the peak-to-average power ratio at the transmitter, which will lead to an increase in the system implementation complexity. In an actual system, the size of the pilot symbol energy and the peak-to-average power ratio should be weighed.

[0137] The above are only specific implementation manners of the present invention, enabling those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention.

[0138] It should be understood that the present invention is not limited to the above-described content and can be variously modified and changed without departing from its scope. The scope of the present invention is only limited by the appended claims.

Claims

1. An equalization method for an OTSM system based on UAMP, characterized in that, Based on the ZP-OTSM system, embedded pilot data and zero-padding symbols are provided in the delay-sequence domain of the ZP-OTSM system; the execution process of the OTSM system equalization method is as follows: first, the time-domain channel matrix is divided into multiple sub-time-domain channel matrices by using the zero-padding symbols, then singular value decomposition is performed on the multiple sub-channel matrices, and finally data detection is completed by using the UAMP equalization algorithm in the delay-sequence domain.

2. The OTSM system equalization method based on UAMP according to claim 1, wherein The specific steps are as follows: Step 1. Construct a ZP-OTSM system: The ZP-OTSM system includes a transmitter, a time-domain channel, and a receiver; among them, the transmitter modulates the information symbol data in the delay-sequence domain, inserts pilot data and zero-padding symbols, and then performs a WHT transform to the delay-time domain, and then passes through the time-domain channel after serial-to-parallel conversion and adding CP; the receiver performs channel estimation by extracting CP, serial-to-parallel conversion, and extracting pilot data, and then sends the channel estimation result to the UAMP equalization module; Step 2. The UAMP equalization module performs unitary transformation processing on the channel estimation result, and completes the reconstruction and estimation of the information symbol through the approximate message passing algorithm.

3. The OTSM system equalization method based on UAMP according to claim 2, characterized in that, Step 1 is specifically as follows: Step 1.1: The transmitter places multiple QAM symbol vectors modulated by the symbol modulation module in a time delay-sequence domain grid X of size M×N, X = [x0, x1,..., x M-1 T , where m = 0, 1, 2,..., M - 1, and the QAM symbols totally occupy the first M' rows, M' = M - (2l max + 1), and l max is the maximum discrete delay spread of the current OTSM system;​ Step 1.2: Place the pilot data P at the time delay-sequence domain index, and define the position of the index as (m p , n p ), and at the same time, require that the length of the inserted zero-padding symbol is not less than l max to ensure that there is no interference between data blocks and facilitate subsequent time-domain channel matrix block processing; where m p = M - l max - 1; Step 1.3: First, transform the symbol matrix X in the delay-sequence domain grid into a symbol matrix in the delay-time domain through the WHT transformation module and W N is an N-point WHT transformation matrix; then, perform a serial-to-parallel conversion by column to obtain a time-domain transmission vector represents a time-domain data block, n = 0, 1, 2,..., N - 1, and vec(·) represents column-wise vectorization of a matrix; before data transmission, add the l max +1 symbols at the end of the frame to the frame header as the CP, and the CP includes 1 pilot data and l max ZPs; Step 1.4: The receiver first extracts the CP of the received data and defines the time-domain received vector as r MN×1 = G·s + n, where G MN×MN is the time-domain channel matrix, is additive complex Gaussian white noise with a mean of 0 and a variance of ; Then, through serial-to-parallel conversion, the time-domain received vector is transformed into the delay-time domain, that is where represents the matrix obtained by vectorizing into dimensions M×N, where m = 0, 1, 2, ..., M - 1; Next, extract the pilot information in the current matrix and perform time-domain channel estimation together with the CP to obtain the estimated time-domain channel matrix Then, the time-delay - time domain symbol matrix is transformed through the WHT into the time-delay - sequence domain symbol matrix That is Finally, through serial-to-parallel conversion, the time-delay sequence domain received vector is obtained and it is sent to the time-delay sequence domain symbol detection module for UAMP equalization to obtain the transmitted symbol matrix 4. The equalization method of the OTSM system based on UAMP according to claim 3, characterized in that, In Step 1.3, the relationship at the transmitting end in matrix form is defined as where P is a row-column interleaving matrix, and I M is an M×M identity matrix, represents the Kronecker product.

5. The equalization method of the OTSM system based on UAMP according to claim 4, wherein In Step 1.4, the receiver relationship in matrix form is defined as Let \(T\) be the transpose symbol, then the input-output relationship in the time-delay sequence domain corresponding to the OTSM system is where is the Gaussian white noise in the time-delay sequence domain.

6. The OTSM system equalization method based on UAMP according to claim 2, wherein, Step 2 includes: Step 2.

1. Use the zero-padding symbols to divide the time-domain channel matrix into multiple sub-time-domain channel matrices G, where In formula (1), represents the sub-time domain channel matrix corresponding to the nth time domain data block, where n = 0, 1, 2,..., N - 1; Step 2.

2. Perform block singular value decomposition on the sub-time-domain channel matrix: In formula (2), the matrices U, S, and V are respectively represented as follows: In formula (4), S n is an M×M dimensional diagonal matrix; Step 2.

3. According to the singular value decomposition result and the input-output relationship in the time-series domain, apply unitary transformation to obtain where After the noise is processed by unitary transformation, it is still additive complex Gaussian white noise with a mean of 0 and a variance of .

7. The equalization method of the OTSM system based on UAMP according to claim 6, characterized in that The unitary transformation processing in step 2.3 specifically includes: Step 2.3.

1. Data initialization, the specific process is as follows: Input data: Received signal after unitary transformation QAM modulation order M mod , maximum number of iterations T uamp , λ = d·d * , where d = diag(S), d * denotes the conjugate of vector d, and · denotes dot product; Output data: transmission signal vector Recovery vector Intermediate variable k (0) = 0, noise variance precision Mean of posterior probability variance Set of information symbols Iteration number t = 0; Step 2.3.2, calculate the vectors and where Step 2.3.3, calculate the intermediate variables and where. / represents division by point; Step 2.3.4, Update the noise variance precision Step 2.3.5, calculate the intermediate variable and k (t) = v k ·(r - p); Step 2.3.6, calculate the intermediate variable v q = MN / λ T v k and where Step 2.3.7, calculate the mean of the posterior probability and variance where j ∈ {1, 2,..., MN} is the data symbol index, Step 2.3.8, Update the mean of the posterior probability variance Step 2.3.9, the iteration number t = t + 1. If t ≥ T uamp , stop the iteration and output Otherwise, go to Step 2.3.

2.

8. An OTSM system applying the equalization method according to any one of claims 1 to 7, characterized in that, Including, Transmitter: It is used to work in the time-delay sequence domain and place multiple QAM symbol vectors modulated by a symbol modulation module in a time-delay sequence domain grid X of size M×N, where X = [x0, x1,..., x M-1 T , The pilot data P is placed at the time-delay sequence domain index, and the position of the index is defined as (m p , n p ). At the same time, it is required that the length of the inserted zero-padding symbols is not less than l max to ensure that there is no interference between data blocks and facilitate subsequent time-domain channel matrix block processing;​ First WHT transformation module: transforming the delay-sequence domain symbol matrix X at the transmitting end into a delay-time domain symbol matrix Second WHT transformation module: transforming the received symbol matrix in the delay-time domain into a symbol matrix in the delay-sequence domain Processing module and receiving end: For the delay-time domain symbol matrix After performing the processing of "parallel-to-serial conversion → adding CP → pulse shaping → DAC conversion", it passes through the time-domain channel, and then after the processing of "ADC conversion → matched filtering → extracting CP → serial-to-parallel conversion", it is output in two paths. One path of the output symbols is processed by the second WHT transformation module and then sent to the UAMP equalization module. The other path of the output symbols is subjected to channel estimation by extracting pilots and CP to obtain the channel estimation result, and the channel estimation result is sent to the UAMP equalization module; UAMP equalization module: Perform unitary transformation processing on the received channel estimation result and the output symbol processed by the second WHT transformation module, and complete the reconstruction and estimation of the information symbol through the approximate message passing algorithm.

9. The OTSM system according to claim 8, characterized in that, The information symbol after reconstruction and estimation can be directly subjected to QAM demodulation processing.

10. The OTSM system according to claim 8, characterized in that, The QAM symbol vector occupies the first M' rows in total, where M' = M - (2l max + 1), and l max is the maximum discrete delay spread of the current OTSM system.

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