MMSE iterative equalization method of OTSM system in high-speed mobile environment

Abstract

This invention belongs to the field of communication technology, specifically relating to an MMSE iterative equalization method for OTSM systems in high-speed mobile environments. The method includes: constructing an OTSM system model, which includes a transmitter, a time-domain channel, and a receiver; processing the data output from the time-domain channel using a block-time-frequency single-tap equalizer to obtain a time-delay-time-domain information symbol prediction value; using the time-delay-time-domain information symbol prediction value as the initial estimate for the GS algorithm after decision-making for iterative detection; calculating the mean and variance based on the time-delay-time-domain information symbol estimates obtained from multiple iterations; using the mean and variance as the initial estimate for the MP algorithm for iterative detection, and outputting a decision on the transmitted symbols from the transmitter to the receiver via the time-domain channel. This invention can effectively eliminate residual symbol interference, thereby significantly improving the system's reliability and transmission quality.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to an MMSE iterative equalization method for OTSM systems in high-speed mobile environments. Background Technology

[0002] Sixth-generation (6G) wireless networks promise to provide reliable communication in high-carrier-frequency and high-mobility scenarios, such as drones, low-Earth orbit satellites, and high-speed trains. While traditional orthogonal frequency division multiplexing (OFDM) effectively reduces signal distortion and interference and boasts high spectral efficiency, the performance of OFDM-based systems degrades significantly in high-mobility communication scenarios due to high frequency dispersion caused by Doppler shift. To combat channel dispersion effects, particularly the high Doppler effect, orthogonal time-frequency-space modulation (OTFS) has been proposed. The main idea of ​​OTFS modulation is to place information symbols in the delay-Doppler (DD) domain, resulting in a 2D convolution of the information symbols with the channel in the DD domain. Studies have found that OTFS outperforms OFDM in high-Doppler communication scenarios.

[0003] like Figure 1 As shown, the OTSM system cleverly combines the characteristics of time delay and Doppler spread, allowing inter-symbol interference (ISI) to be introduced into the channel in different dimensions of time delay and sequence, with separation operations performed at the receiver. This technique can effectively suppress large-scale speckle noise and phase delay distortion caused by the Doppler effect in narrowband or broadband radar echoes, while also achieving good spectral purity and resolution. In this way, the rapidly changing time-frequency domain channel is transformed into an approximately constant non-fading channel, facilitating signal transmission and processing. Compared to OTFS, which performs IFFT in the Doppler domain, OTSM has lower complexity because the WHT transform does not involve other complex multiplications, only addition and subtraction operations, making it more efficient and simpler.

[0004] Regarding two-dimensional detection algorithms, an iterative detection algorithm based on message passing (MP) exists. This algorithm leverages the sparsity of the DD domain channel and the advantages of iterative processing to eliminate interference and improve detection performance. Furthermore, a low-complexity iterative detector, designed based on the system characteristics of OTSM, is similar to a two-stage equalizer, aiming to address interference issues in OTSM systems. To address the challenges posed by high Doppler shift wireless channels, this scheme employs an improved design. First, a single-tap minimum mean square error (MMSE) equalizer is introduced in the TF domain. This equalizer is designed to suppress inter-carrier interference and reduce the impact of Doppler shift on the signal. Next, an improved iterative detection algorithm, the Gauss-Seidel (GS) iterative detection algorithm, is used in the time domain. This algorithm further eliminates residual symbol interference through multiple iterations. Compared to the traditional GS algorithm, this improved scheme is better suited to high Doppler shift conditions. However, despite some improvements to this design, several problems remain when dealing with high Doppler shift wireless channels. Specifically, rapid channel changes and frequency spreading make channel estimation difficult, impacting the performance of the equalizer and the GS algorithm. Although the improved GS algorithm better adapts to high Doppler shifts, further optimization is needed to improve its convergence and error rate performance when facing rapidly changing wireless channels. The current design is limited in this situation, severely affecting the convergence speed and error rate performance of the GS iterative detection algorithm.

[0005] In conclusion, given the unique characteristics of high Doppler shift wireless channels, it is necessary to further improve the design of the secondary equalizer. Solving this problem is crucial for further optimizing the performance of the OTSM system and improving the reliability of data transmission. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes an iterative MMSE equalization method for OTSM systems operating in high-speed mobile environments. This method includes:

[0007] S1: Construct an OTSM system model, which includes a transmitter, a time-domain channel, and a receiver;

[0008] S2: A block-time frequency single-tap equalizer is used to process the data output from the time-domain channel to obtain the time delay-time domain information symbol prediction value;

[0009] S3: The estimated value of the time-delay-time domain information symbol is used as the initial estimate for the GS algorithm after being decided; the mean and variance are calculated based on the time-delay-time domain information symbols obtained from multiple iterations.

[0010] S4: Use the mean and variance as the initial estimates of the MP algorithm for iterative detection, and output the decision of the transmitted symbols that have reached the receiver after passing through the time domain channel.

[0011] Preferably, the process of processing the time-domain channel output data using a block-based time-frequency single-tap equalizer includes:

[0012] The time-domain vector output from the time-domain channel is divided into N time-domain blocks, and each block is subjected to an M-point FFT to obtain N frequency-domain blocks.

[0013] MMSE equalization is performed on each frequency domain block to obtain information symbols for multiple frequency domain blocks;

[0014] Perform an M-point IFFT on the information symbols of each frequency domain block to obtain the time delay-time domain information symbol estimate.

[0015] Preferably, in step S3, the iterative detection process using the GS algorithm includes:

[0016] S31: The symbol vector of each time-domain block is determined to obtain the time-domain information symbol; the time-domain information symbol is subjected to matched filtering to obtain the time-domain input-output relationship;

[0017] S32: Use the GS method to iteratively solve the least squares solution corresponding to the time-domain input-output relationship to obtain the time delay-time-domain information symbol estimate for the current iteration;

[0018] S33: Perform hard decision on the least squares solution obtained through iterative solution to obtain the delayed sequence field information symbol in each iteration process;

[0019] S34: Relax and scale the delayed sequence domain information symbols to obtain new time-delay-time domain information symbols and use them as the initial values ​​in the next iteration process. Repeat steps S32 to S34 until the preset number of iterations is reached.

[0020] Preferably, in step S4, the process of using the mean and variance as initial estimates for the MP algorithm for iterative detection includes:

[0021] S41: Initialize the probability mass function;

[0022] S42: The observation node passes the mean and variance to the variable node;

[0023] S43: The variable node updates the probability mass function using the current probability mass function, mean, and variance, and passes the new probability mass function to the observation node;

[0024] S44: Calculate the convergence indicator and update the mean and variance;

[0025] S45: If the current convergence indicator is greater than the convergence indicator of the previous iteration, then update the transmission symbol according to the current probability mass function;

[0026] S46: Determine whether the convergence indicator meets the stopping criteria. If the convergence indicator meets the stopping criteria or the number of iterations reaches the maximum number of iterations, output the transmission symbol; otherwise, return to step S42.

[0027] Furthermore, the formula for updating the probability mass function is:

[0028]

[0029] in, The symbol a represents the information passed from variable node c to observation node d in the i-th iteration. j The posterior probability, where α represents the damping factor, a j Represents the j-th symbol. The symbol a represents the information passed from variable node c to observation node d in the i-th iteration. j The estimated value, The symbol 'a' represents the symbol passed from variable node c to observation node d in the (i-1)th iteration. j The posterior probability.

[0030] Furthermore, the formula for calculating the convergence indicator is:

[0031]

[0032] Where, η (i) This represents the convergence indicator for the i-th iteration, where N represents the number of symbols in the system, M represents the number of subcarriers in the system, and a j Represents the j-th symbol. In the i-th iteration, the symbol a j At position c, the probability value is represented by γ, which indicates the threshold. I represents the symbol set, and I(·) represents the indicator function.

[0033] Furthermore, the formulas for updating the mean and variance are as follows:

[0034]

[0035] in, In the i-th iteration, the symbol a j Statistical mean of the estimated values The symbol a represents the information passed from any intermediate node e to the observation node d in the (i-1)th iteration. j The posterior probability, aj Let H[d,e] represent the j-th symbol, H[d,e] represent the channel matrix, Q represent a constant normalized over all possible symbols, and I(d) represent the indicator function. In the i-th iteration, the symbol a j The statistical variance of the estimated value, σ 2 This represents the noise variance.

[0036] Furthermore, the formula for updating the transmission symbols is:

[0037]

[0038] in, This represents the sign estimate at the c-th position. In the i-th iteration, the symbol a j At position c, the probability value a j Represents the j-th symbol. Represents a set of symbols.

[0039] Furthermore, the stopping criterion is that the convergence indicator is 1 or the following condition is met:

[0040] η (i) <η (i*) -ε

[0041] Where, η (i) η represents the convergence indicator for the i-th iteration. (i*) ε represents the maximum convergence indicator, and ε represents a small constant.

[0042] The beneficial effects of this invention are as follows: Considering the high Doppler frequency shift caused by high-speed mobile environments and inter-symbol interference caused by multipath transmission, this invention first employs block-by-block MMSE detection in the time-frequency domain to accurately recover and demodulate the signal, suppressing inter-carrier interference and reducing the impact of Doppler frequency shift on the signal. Then, a certain number of iterations of the Gauss-Seidel (GS) method with matched filtering are used as the initial estimate. Next, Bayesian networks and Markov random fields are used between observation nodes and variable nodes to capture the direct and indirect dependencies between variables, and information is updated for iterative detection. The computational efficiency of the GS iterative method effectively reduces the number of message passing (MP) iterations while providing a better initial estimate, thereby reducing the overall computational load and improving bit error rate performance. The system of this invention can effectively eliminate residual symbol interference, thus significantly improving the system's reliability and transmission quality. Simulation results show that, compared with the traditional GS iterative detection method based on single-tap equalization and the MP iterative detection method based on single-tap equalization, the algorithm proposed in this invention achieves a significant improvement in bit error rate performance. Attached Figure Description

[0043] Figure 1 The relationship between different discrete signal symbol domains and corresponding modulation schemes;

[0044] Figure 2 This is a flowchart of the MMSE iterative equilibrium method in this invention;

[0045] Figure 3 This is a transceiver model diagram of the OTSM system in this invention;

[0046] Figure 4 This is an information graph of the observation nodes and variable nodes in this invention;

[0047] Figure 5 The graph shows the bit error rate performance of the OTSM system under different equalization algorithms in this invention.

[0048] Figure 6 The error rate performance of the OTSM system in this invention under different detection algorithms;

[0049] Figure 7 To compare the bit error rate performance of the present invention with that of the comparison algorithm under different speeds and signal-to-noise ratios. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] This invention proposes an iterative MMSE equalization method for OTSM systems in high-speed mobile environments, such as... Figure 2 As shown, the method includes the following:

[0052] S1: Construct an OTSM system model, which includes a transmitter, a time-domain channel, and a receiver.

[0053] Construct an OTSM system model, representing the OTSM system using the following matrix / vector representation. Let... These are the information symbols for transmission and reception, respectively. For OTSM signal frame transmission, the total frame duration is set to T. f =NT, bandwidth is B=MΔf, where Δf=1 / T, the signal is sampled strictly according to the pulse-shaped waveform, and N is selected as a power of 2. Figure 3 The transmission model of the OTSM system is demonstrated.

[0054] At the sending end, information symbols Divided into m symbol vectors Each symbol vector x m All symbolic vectors are neatly arranged in the m-th row of the matrix. The column index and row index are used to represent the delay index and sequence index of the delayed sequence grid, respectively.

[0055] X = [x0, x1, ..., x M-1 ] T (1)

[0056] Then X last l max The row is set as the zero vector, where l max This represents the discrete channel delay spread index. For example... Figure 3 As shown, zero-padding (ZP) along the delay domain helps avoid inter-block interference caused by channel delay spread. For each symbol vector x m Perform an N-point WHT transform to convert it to the delay time domain:

[0057]

[0058] matrix It contains time-delay samples, which are vectorized to obtain time-delay domain symbol vectors. Finally, it is sent to the channel, where each symbol vector represents a signal sample at a specific time delay.

[0059]

[0060] At the receiving end, after analog-to-digital conversion and sampling, the time-domain signal r(t) is demodulated into the received time-domain vector following the reverse steps compared to the transmitting end. Let... This is the time-domain vector after RF front-end processing and ADC sampling. The received information symbols y are arranged into a matrix by columns. Each column corresponds to a received symbol vector.

[0061]

[0062] right Perform N-point WHT transformations to obtain the information symbol Y in the DS domain, where:

[0063]

[0064] In the time-domain channel part, the baseband equivalent channel model includes P propagation paths, each with a different gain v. i Delay offset τ i and Doppler frequency shift v i Let the maximum delay spread of the channel be τ. max The maximum Doppler extension is v maxThe corresponding Doppler spread length and channel delay spread length are α = [v max NT] and β = [τ] max [MΔf]. In an OTSM system with a carrier frequency of 4 GHz and a subcarrier spacing of 15 kHz, it is assumed that an extended vehicle channel model (EVA) is used. Under this setting, the delay-Doppler spread length α = 10 and β = 3 are significantly smaller than the number of sampling points NM of the system.

[0065] Since the number of propagation paths P in a time-delay-Doppler domain channel is usually finite, the time-delay-Doppler domain channel response can be expressed as:

[0066]

[0067] The corresponding continuous time-varying channel impulse response function can be expressed as:

[0068] g(τ,v)=∫ v h(τ,v)e jπ2v(t-τ) dv (7)

[0069] Starting with the received time-domain signal r(t), the continuous time-domain input-output relationship can be expressed as:

[0070]

[0071] Therefore, the input-output relationship in the time domain can be expressed as:

[0072] r = H·s + w (9)

[0073] in, With a mean of 0 and a variance of Gaussian white noise, It is a time-domain discrete channel matrix.

[0074]

[0075] in,

[0076] Due to the introduction of zero-padding (ZP) in the time domain, inter-block interference in the time domain is effectively avoided. Therefore, in the time domain, the input-output relationship in equation (9) is separated and can be processed independently, specifically expressed as follows:

[0077] r n =H n ·s n +w n ,n=0,...,N-1 (11)

[0078] in, And H nIt is the nth time-domain block channel matrix.

[0079] It is worth noting that, due to the Walsh-Hadamard extension, all N time-domain blocks have components equal to the information symbols of each delayed sequence domain.

[0080] S2: A block-time frequency single-tap equalizer is used to process the data output from the time-domain channel to obtain the time delay-time domain information symbol prediction value.

[0081] In static (or very low Doppler spread) wireless channels, assuming the time-domain channel matrix of each block is a cyclic matrix, it can be diagonalized in the frequency domain. For a given subcarrier and reference signal sequence, each frame can be transmitted using multiple channels, and each sub-block consists of corresponding channels. However, in mobile channels, due to the presence of time-varying channels, Doppler spread introduces interference between frequency-domain samples of each block, causing the time-domain channel matrix to no longer be cyclic. A frame will have good performance if it contains multiple subcarriers and the cross-correlation function values ​​between adjacent subcarriers are all greater than a given threshold. However, considering the short duration of each time-domain block relative to the entire frame, it can be assumed that the channels within each block are constant, but there are differences in the channels between blocks. The advantage of doing so is that it allows detection in each block using a single-tap MMSE equalizer, and then WHT is used to combine the block estimates.

[0082] Perform an M-point FFT operation on the received time-domain block to obtain the corresponding time-frequency block.

[0083]

[0084] Then, each time-frequency block can be subjected to MMSE equalization to obtain the information symbols of the frequency domain block:

[0085]

[0086] Where m = 0, ..., M-1, n = 0, ..., N-1, The AWGN noise variance for each time-domain block, and the frequency-domain channel coefficients, can be expressed by the following formula:

[0087]

[0088] Among them, F M This represents the transformation matrix used to perform an FFT operation on a time-domain signal. This represents the conjugate transpose of the transformation matrix used to perform FFT operations on a time-domain signal.

[0089] Perform an M-point IFFT operation on the information symbols of the frequency domain block to obtain the time delay-time domain information symbol estimate.

[0090]

[0091] S3: The estimated value of the time-delay-time domain information symbol is used as the initial estimate of the GS algorithm after being decided, and iterative detection is performed; the mean and variance are calculated based on the time-delay-time domain information symbols obtained from multiple iterations.

[0092] Dividing the entire frame into short blocks assumes that the channel remains constant over the duration (TTT) of each block. However, this assumption can lead to performance degradation in the case of high Doppler spread, especially for higher-order QAM symbols.

[0093] This invention employs the Matched Filtered Gauss-Seidel Message Passing (MF-GMP) algorithm to achieve equilibrium. First, the Gauss-Seidel (GS) method is used for a certain number of iterative estimations. Then, the estimated mean and variance are returned as soft information for the MP algorithm and used as the initial estimate. Next, the probability mass function, mean, and variance are calculated through the observation nodes and variable nodes, and the information is updated to perform iterative detection.

[0094] First, iterative detection is performed using the GS algorithm; then, the mean and variance are calculated based on the delay-time domain information symbols obtained from multiple iterations; specifically:

[0095] S31: The symbol vector of each time-domain block is determined to obtain the time-domain information symbol; the time-domain information symbol is subjected to matched filtering to obtain the time-domain input-output relationship.

[0096] GS iteration is performed on the matched filter channel matrix block. The completed matrix input-output relationship after the time-domain symbol matched filtering operation in (9) can be written as:

[0097]

[0098] in, and

[0099] S32: Use the GS method to iteratively solve the least squares solution corresponding to the time-domain input-output relationship, and obtain the time delay-time domain information symbol for the current iteration.

[0100] The least-squares solution of the M-dimensional linear equation system in (16) is obtained iteratively using the GS method.

[0101]

[0102] Let D n and L n For a matched filter matrix Rn The matrix consists of diagonal and lower triangular elements. In each iteration, s is calculated. n The GS iterative method for estimating the value is given as follows:

[0103]

[0104] Where T n ∈C M×M It is the GS iteration matrix, a vector. It represents the estimate of the transmission time-domain sample of the nth block in the i-th iteration, i.e., the delay-time domain information symbol estimate.

[0105] S33: Perform hard decision on the least squares solution obtained through iterative solution to obtain the delayed sequence domain information symbol in each iteration process.

[0106] The delayed sequence field information symbol in the i-th iteration is represented as:

[0107]

[0108] in Furthermore, D(.) represents the decision function, which replaces all elements of the input with the nearest QAM symbol (measured by Euclidean distance).

[0109] S34: Relax and scale the delayed sequence domain information symbols to obtain new time-delay-time domain information symbols and use them as the initial values ​​in the next iteration process. Repeat steps S32 to S34 until the preset number of iterations is reached.

[0110] The hard decision estimate is transformed back to the time domain to update the time domain estimate to be used in the next iteration:

[0111]

[0112] Here, δ is a relaxation parameter used to improve the detector convergence of higher modulation schemes such as 64-QAM.

[0113] This invention requires a trade-off between the number of Gaussian GS iterations and the number of iterations. Too many iterations may cause the system to linger near local optima, while too few iterations may fail to provide sufficiently good initial values. Preferably, this invention uses Monte Carlo simulation to calculate the optimal number of iterations.

[0114] S4: Use the mean and variance as the initial estimates of the MP algorithm for iterative detection, and output the decision of the transmitted symbols that have reached the receiver after passing through the time domain channel.

[0115] Figure 4The diagram illustrates the connections and message passing between observation nodes and variable nodes, where circles represent variable nodes and squares represent observation nodes. In the MP algorithm, the mean and variance of the disturbance term are used as information sent from observation node y[d] to variable node x[c] to achieve information transmission. On the other hand, the corresponding probability mass function (pmf) is passed from symbol node x[c] to y[d], where d∈J(c).

[0116] S41: Initialize the probability mass function.

[0117]

[0118] S42: The observation node passes the mean and variance to the variable node.

[0119] This invention uses the estimated mean and estimated variance obtained after previous MMSE and GS iterations to replace the estimated mean and variance of the original MP iterative algorithm.

[0120] S43: The variable node updates the probability mass function using the current probability mass function, mean, and variance, and passes the new probability mass function to the observation node.

[0121] (pmf) vector It can be updated to:

[0122]

[0123] in, In the i-th iteration, the symbol a j The probability value, In the i-th iteration, the symbol a j The estimated value, The symbol 'a' represents the symbol passed from variable node c to observation node d in the (i-1)th iteration. j The posterior probability, Δ∈(0,1], is the damping factor used for improvement. It enhances performance by controlling the convergence rate, and:

[0124]

[0125] in,

[0126] S44: Calculate the convergence indicator and update the mean and variance.

[0127] The formula for calculating the convergence indicator is:

[0128]

[0129] Where, η (i)This represents the convergence indicator for the i-th iteration, where N represents the number of symbols in the system and M represents the number of subcarriers in the system. In the i-th iteration, the symbol a j For the probability value at position c, γ > 0 represents the threshold. The symbol set represents all possible symbols; I(·) represents an indicator function, which is specific if the independent variable... If the memory contains a true expression, then the specific value of this index function will be 1; otherwise, the result will be 0.

[0130] The formulas for updating the mean and variance are as follows:

[0131]

[0132] in, In the i-th iteration, the symbol a j Statistical mean of the estimated values The symbol a represents the information passed from any intermediate node e to the observation node d in the (i-1)th iteration. j The posterior probability, a j Let H[d,e] represent the j-th symbol, H[d,e] represent the channel matrix, Q represent a constant normalized over all possible symbols, and I(d) represent the indicator function. In the i-th iteration, the symbol a j The statistical variance of the estimated value, σ 2 This represents the noise variance.

[0133] S45: If the current convergence indicator is greater than the convergence indicator of the previous iteration, then update the transmission symbol according to the current probability mass function.

[0134] If η (i) >η (i-1) Then update the transmission symbol:

[0135]

[0136] in, This represents the sign estimate at the c-th position. In the i-th iteration, the symbol a j The probability value at position c, It represents a symbol set that contains all possible symbols.

[0137] The algorithm updates the decisions related to the transmission symbols only if the current iteration provides a better evaluation than the previous one.

[0138] S46: Determine whether the convergence indicator meets the stopping criteria. If the convergence indicator meets the stopping criteria or the number of iterations reaches the maximum number of iterations, output the transmission symbol; otherwise, return to step S42.

[0139] The algorithm stops when at least one of the following conditions is met.

[0140] 1)η (i) =1.

[0141] 2)η (i) <η (i*) -ε, where i* is the iterative index from {1,…,(i-1)}, where η (i*) maximum.

[0142] 3) Reach the maximum number of iterations. Preferably, ε = 0.2 is chosen to ignore small fluctuations in η.

[0143] After iterative detection using the MP algorithm, the output is the decision value of the transmitted symbol from the transmitter to the receiver via the time-domain channel, i.e., the delay-time-domain information symbol estimate.

[0144] The Walsh-Hadamard transform is applied to the time-delay-time domain information symbol estimate to obtain the time-delay-sequence domain information symbol estimate.

[0145] Evaluation of the present invention:

[0146] This invention employs block-based MMSE for initial estimation to suppress inter-carrier interference and reduce the impact of Doppler shift on the signal. It also uses the GS algorithm, after a certain number of iterations, as initial values ​​for the MP algorithm to perform initial estimation, improving bit error rate performance. Furthermore, the computational efficiency of GS can effectively reduce the number of iterations in the MP algorithm, thereby reducing the overall computational load. The availability of this low-complexity detection method makes OTSM an attractive candidate for future wireless communication networks.

[0147] The message-passing-based block MMSE Gaussian-Seidel iterative equalization algorithm and existing iterative detection algorithms will be compared through simulation, and the simulation parameters in Table 1 will be used unless otherwise specified. As shown in Table 1, OTSM frames with N=32 and M=32 will be generated in the following simulations. The subcarrier spacing Δf is 15kHz, and the carrier frequency is 4GHz. The maximum delay spread (for integer taps) is set to 4(l max =4), approximately 4μs, therefore the maximum number of delay taps seen by the discrete receiver is L=4. The channel delay model is generated based on the standard EVA model in reference

[23] , with each point in the BER diagram sending 10 5 The frame signal, the channel Doppler frequency shift is achieved through Jakes' formula v i =vmax cos(θ i ) produced by v max For the maximum moving speed and θ i It is evenly distributed on [-π,π].

[0148] Table 1 Simulation Parameters

[0149]

[0150] according to Figure 5 The results show that, under high signal-to-noise ratio (SNR) conditions and with different equalization algorithms, the proposed algorithm significantly improves bit error rate performance compared to traditional GS and MP algorithms. Furthermore, the iterative detection algorithm based on a block-domain single-tap equalizer also demonstrates a significant improvement in bit error rate performance compared to the single-tap equalizer iterative detection algorithm. This is mainly because the proposed algorithm significantly improves bit error rate performance compared to traditional GS and MP algorithms by improving initial estimation, effectively handling complex interference factors, reducing complexity and iteration count, and designing a better equalizer. Under high SNR conditions, these improvements fully leverage the algorithm's advantages and improve the overall system performance. This means that in high SNR environments, the proposed algorithm can more effectively equalize and detect signals, thereby achieving better bit error rate performance. In contrast, traditional single-tap frequency domain equalization combined with GS iterative algorithm, time-domain block equalization combined with GS iterative algorithm, single-tap frequency domain equalization combined with MP iterative algorithm, and time-domain block equalization combined with MP iterative algorithm may perform poorly under these conditions. Figure 5 The results show that the proposed algorithm achieves better performance under high signal-to-noise ratio conditions, which indicates that the algorithm has a good performance advantage in OTSM systems.

[0151] according to Figure 6 The comparison results show that under high signal-to-noise ratio conditions and different modulation schemes, the proposed algorithm is still applicable to different modulation schemes, and the iterative detection algorithm based on the block frequency domain single-tap equalizer still has a significant improvement in bit error rate performance compared to the single-tap equalizer iterative detection algorithm. In summary... Figure 6 The results show that the proposed algorithm can achieve better performance under different modulation methods and high signal-to-noise ratio conditions, which indicates that the algorithm has good applicability in OTSM systems.

[0152] To more intuitively evaluate the performance under different user mobility rates and signal-to-noise ratios, we conducted a three-dimensional in-depth analysis of the GS algorithm, the MP algorithm, and the algorithm proposed in this invention, such as... Figure 7 As shown in the figure. Figure (a) is a 3D view of user speed, signal-to-noise ratio, and algorithm; Figures (b), (c), and (d) are 3D views from different angles for clearer observation. Figure 7As can be seen, with the increase of speed and signal-to-noise ratio, the proposed algorithm has a better performance advantage than the traditional GS and MP algorithms. Therefore, the proposed algorithm can well meet the requirements of future wireless mobile communication systems.

[0153] In summary, this invention first employs block-by-block MMSE detection in the time-frequency domain to accurately recover and demodulate the signal, suppressing inter-carrier interference and reducing the impact of Doppler shift on the signal. Then, a Gaussian-Seidel (GS) method with matched filtering is used for a certain number of iterations as an initial estimate. Next, Bayesian networks and Markov random fields are used between observation nodes and variable nodes to capture direct and indirect dependencies between variables, and information is updated for iterative detection. The computational efficiency of the GS iterative method effectively reduces the number of message passing (MP) iterations while providing a better initial estimate, thereby reducing the overall computational load and improving bit error rate performance. Simulation experiments show that the equalizer significantly improves bit error rate performance under different speeds, systems, and modulation schemes, especially performing excellently in high-speed mobile environments. This innovative research is of great significance for improving the performance of OTSM systems, providing a more reliable and high-quality signal processing solution for wireless communication systems in practical applications. The excellent performance of the proposed algorithm in high-speed mobile conditions is of great significance for applications in mobile communications and vehicle-to-everything (V2X) networks, laying a solid foundation for providing high-quality communication services.

[0154] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An iterative MMSE equalization method for an OTSM system in a high-speed mobile environment, characterized in that, Includes the following steps: S1: Construct an OTSM system model, which includes a transmitter, a time-domain channel, and a receiver; S2: A block-time frequency single-tap equalizer is used to process the data output from the time-domain channel to obtain the time delay-time domain information symbol prediction value; S3: The time-delay-time domain information symbol prediction value is used as the initial estimate for the GS algorithm after being decided, and is then used for iterative detection; The mean and variance are calculated based on the time-delay-time domain information symbol estimates obtained from multiple iterations. The process of iterative detection using the GS algorithm includes: S31: The symbol vector of each time-domain block is determined to obtain the time-domain information symbol; the time-domain information symbol is subjected to matched filtering to obtain the time-domain input-output relationship; S32: Use the GS algorithm to iteratively solve the least squares solution corresponding to the time-domain input-output relationship, and obtain the time delay-time-domain information symbol estimate for the current iteration; S33: Perform hard decision on the least squares solution obtained through iterative solution to obtain the delayed sequence field information symbol in each iteration process; S34: Relax and scale the delayed sequence domain information symbols to obtain new time-delay-time domain information symbols and use them as the initial values ​​in the next iteration process. Repeat steps S32 to S34 until the preset number of iterations is reached. S4: Iterative detection is performed using the mean and variance as initial estimates for the MP algorithm, outputting the decision of the transmitted symbols arriving at the receiver after passing through the time-domain channel. The process of iterative detection using the mean and variance as initial estimates for the MP algorithm includes: S41: Initialize the probability mass function; S42: The observation node passes the mean and variance to the variable node; S43: The variable node updates the probability mass function using the current probability mass function, mean, and variance, and passes the new probability mass function to the observation node; S44: Calculate the convergence indicator and update the mean and variance; S45: If the current convergence indicator is greater than the convergence indicator of the previous iteration, then update the transmission symbol according to the current probability mass function; S46: Determine whether the convergence indicator meets the stopping criteria. If the convergence indicator meets the stopping criteria or the number of iterations reaches the maximum number of iterations, output the transmission symbol; otherwise, return to step S42.

2. The MMSE iterative equalization method for an OTSM system in a high-speed mobile environment according to claim 1, characterized in that, The process of processing the time-domain channel output data using a block-based time-frequency single-tap equalizer includes: The time-domain vector output from the time-domain channel is divided into N time-domain blocks, and each block is subjected to an M-point FFT to obtain N frequency-domain blocks. MMSE equalization is performed on each frequency domain block to obtain information symbols for multiple frequency domain blocks; Perform an M-point IFFT on the information symbols of each frequency domain block to obtain the time delay-time domain information symbol estimate.

3. The MMSE iterative equalization method for an OTSM system in a high-speed mobile environment according to claim 1, characterized in that, The formula for updating the probability mass function is: in, The symbol a represents the information passed from variable node c to observation node d in the i-th iteration. j The posterior probability, Δ represents the damping factor, a j Represents the j-th symbol. The symbol a represents the information passed from variable node c to observation node d in the i-th iteration. j The estimated value, The symbol 'a' represents the symbol passed from variable node c to observation node d in the (i-1)th iteration. j The posterior probability.

4. The MMSE iterative equalization method for an OTSM system in a high-speed mobile environment according to claim 1, characterized in that, The formula for calculating the convergence indicator is: Where, η (i) This represents the convergence indicator for the i-th iteration, where N represents the number of symbols in the system, M represents the number of subcarriers in the system, and a j Represents the j-th symbol. In the i-th iteration, the symbol a j At position c, the probability value is represented by γ, which indicates the threshold. I represents the symbol set, and I(·) represents the indicator function.

5. The MMSE iterative equalization method for an OTSM system in a high-speed mobile environment according to claim 1, characterized in that, The formulas for updating the mean and variance are as follows: in, In the i-th iteration, the symbol a j Statistical mean of the estimated values The symbol a represents the information passed from any intermediate node e to the observation node d in the (i-1)th iteration. j The posterior probability, a j Let H[d,e] represent the j-th symbol, H[d,e] represent the channel matrix, Q represent a constant normalized over all possible symbols, and I(d) represent the indicator function. In the i-th iteration, the symbol a j The statistical variance of the estimated value, σ 2 This represents the noise variance.

6. The MMSE iterative equalization method for an OTSM system in a high-speed mobile environment according to claim 1, characterized in that, The formula for updating the transmission symbol is: in, This represents the sign estimate at the c-th position. In the i-th iteration, the symbol a j At position c, the probability value a j Represents the j-th symbol. Represents a set of symbols.

7. The MMSE iterative equalization method for an OTSM system in a high-speed mobile environment according to claim 1, characterized in that, The stopping criterion is that the convergence indicator is 1 or the following condition is met: Where, η (i) This indicates the convergence indicator for the i-th iteration. ε represents the maximum convergence indicator, and ε represents a small constant.

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