Self-adaptive Gaussian message passing signal detection method for OTFS system

Abstract

The invention belongs to the technical field of wireless communication, and relates to a self-adaptive Gaussian message passing signal detection method for an OTFS system, which comprises the following steps: the system receives a signal transmitted by a channel, and initializes parameters of a GA-MP algorithm; executing the GA-MP algorithm on the to-be-estimated symbol of the current iteration round according to the received signal based on the parameters of the GA-MP algorithm of the current iteration round to obtain the posterior probability of the symbol; adjusting a damping factor in the parameter according to the posterior probability of the symbol to obtain a parameter of a next iteration round; s2, judging whether iteration is continued or not, if yes, obtaining a to-be-estimated symbol of a next iteration round, and returning to the step S2 to execute the next iteration on the symbol; otherwise, obtaining the final posterior probability of the sent signal; calculating an estimation result of the sent signal according to the final posterior probability, and performing post-processing optimization; according to the method, the damping factor is adaptively adjusted according to the posterior probability variation and the residual trend, and the convergence speed and the stability are effectively balanced.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology and relates to an adaptive Gaussian message passing signal detection method for OTFS systems. Background Technology

[0002] OTFS modulation technology has attracted widespread attention due to its excellent anti-Doppler performance in high-speed mobile scenarios. Gaussian approximation message passing (GA-MP) algorithm is an important low-complexity detection algorithm for OTFS system. However, the traditional GA-MP detection algorithm has the following limitations: (1) It usually adopts a fixed damping factor, which makes it difficult to balance convergence speed and stability in complex channel environments, and is prone to slow convergence or oscillation; (2) It adopts a fixed number of iterations, which results in invalid calculations after the algorithm converges early, or premature termination before sufficient convergence, causing waste of computing resources or performance loss; (3) Under low signal-to-noise ratio (SNR) or strong Doppler conditions, the posterior probability distribution of some symbols is flat (low confidence), which is prone to convergence to the wrong value and cause error propagation; (4) It independently detects strongly correlated symbol groups in the channel, ignoring the joint probability information between symbols, which affects the detection accuracy. Summary of the Invention

[0003] To address the aforementioned problems in the prior art, this invention employs an adaptive Gaussian message passing signal detection method for an OTFS system, comprising:

[0004] S1. The transmitter of the OTFS system sends a signal, and the receiver of the OTFS system receives the signal transmitted through the channel and initializes the parameters of the GA-MP algorithm. and the symbol of the transmitted signal to be estimated Among them, the GA-MP algorithm is a Gaussian approximation message passing algorithm;

[0005] S2. Based on the received signal, the parameters of the GA-MP algorithm for the current iteration round are... The symbol to be estimated for the transmitted signal in the current iteration round The message-passing steps of the GA-MP algorithm are executed to obtain the symbol to be estimated. The posterior probability and soft estimate;

[0006] S3. Based on the symbol to be estimated of the transmitted signal in the current iteration round. The posterior probability and soft estimate are used to adjust the parameters of the GA-MP algorithm in the current iteration round. The damping factor in the algorithm is used to obtain the parameters of the GA-MP algorithm for the next iteration. ;

[0007] S4. Determine whether to continue the iteration. If yes, obtain the symbol to be estimated for the transmitted signal in the next iteration round. Returning to step S2, the symbol to be estimated for the transmitted signal in the next iteration round. Perform the next iteration; otherwise, obtain the final posterior probability of the transmitted signal.

[0008] S5. Calculate the estimated result of the transmitted signal based on the final posterior probability of the transmitted signal; perform post-processing optimization on the estimated result of the transmitted signal to obtain the final estimated result of the transmitted signal.

[0009] Beneficial effects:

[0010] 1. This invention introduces a dynamic damping factor adjustment mechanism to adaptively adjust the damping factor based on the change in posterior probability and the residual trend, effectively balancing convergence speed and stability, reducing oscillations, and improving algorithm robustness. 2. This invention intelligently determines whether to terminate the iteration by setting gap threshold, confidence threshold, and symbol convergence rate threshold, avoiding invalid calculations, significantly reducing the number of iterations, and significantly reducing computational complexity. 3. This invention introduces a post-processing mechanism to specifically correct low-confidence symbols. By utilizing local and joint ML detection combined with an SNR-adaptive confidence threshold, an error rate performance gain of approximately 0.9 dB can be obtained in the medium-to-high SNR region (8-20 dB), effectively suppressing error propagation and improving overall detection accuracy. Attached Figure Description

[0011] Figure 1 A flowchart of an adaptive Gaussian message passing signal detection method for an OTFS system provided in an embodiment of the present invention;

[0012] Figure 2 This is a modulation and demodulation framework diagram of an OTFS system provided in an embodiment of the present invention;

[0013] Figure 3 A low-Earth orbit satellite communication model diagram provided in an embodiment of the present invention;

[0014] Figure 4 A flowchart of the dynamic damping factor adjustment mechanism provided in this embodiment of the invention;

[0015] Figure 5 A flowchart of the iteration early stopping mechanism provided in this embodiment of the invention;

[0016] Figure 6 A flowchart illustrating the post-processing optimization mechanism provided in this embodiment of the invention;

[0017] Figure 7 This is a comparison chart of the bit error rates of the improved GA-MP algorithm and the original algorithm provided in this embodiment of the invention;

[0018] Figure 8A comparison chart of the number of iterations between the improved GA-MP algorithm and the original algorithm provided in this embodiment of the invention. Detailed Implementation

[0019] 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.

[0020] like Figure 1 As shown, this embodiment of the invention employs an adaptive Gaussian message passing signal detection method for an OTFS system, comprising:

[0021] S1. The OTFS system's transmitter sends a signal, and the OTFS system's receiver receives the transmitted signal after it has been transmitted through the channel, and initializes the parameters of the GA-MP algorithm. and the symbol of the transmitted signal to be estimated Among them, the GA-MP algorithm is a Gaussian approximation message passing algorithm;

[0022] The OTFS signal transmission model of the OTFS system is as follows: Figure 2 As shown, the specific process of signal transmission (modulation and demodulation) in the OTFS system is as follows:

[0023] S11. At the transmitting end, the transmitted symbols in the time-delay-Doppler domain... The two-dimensional transmitted symbol is obtained by placing it in a time-delay-Doppler domain grid. An inverse symplectic Fourier transform (ISFFT) is then performed on the two-dimensional transmitted symbol to the time-frequency domain, yielding the transmitted signal. ;

[0024] Specifically, sending symbols ;in, , The index of the matrix from which the symbols are sent is given, where N and M are the dimensions of the matrix's two dimensions. It is a modulated alphabet with Q elements; MN transmitted symbols are placed into one In the time-delay-Doppler domain grid, it is used as a two-dimensional transmitted symbol. The two-dimensional transmitted symbol in the time-delay-Doppler grid is then transformed into the time-frequency domain by ISFFT. The specific transformation expression is given by equation (1-1):

[0025] (1-1)

[0026] Where n=0,...,N-1, m=0,...,M-1.

[0027] S12. Transform the transmitted signal X[n,m] to the time domain using the Heisenberg transform, and then transmit the waveform pulse. The transmitted signal x(t) is obtained.

[0028] The specific transformation expression is given by equation (1-2):

[0029] (1-2)

[0030] in, denoted as the frequency interval between subcarriers, and T as the symbol period.

[0031] S13, Time Domain Signal The signal is transmitted via a wireless channel, and the receiving end receives the time-domain signal transmitted via the wireless channel. The received time-domain signal y(t) is transformed to the time-frequency domain by the Wigner Transform to obtain the received signal Y[n,m].

[0032] For the receiving end, the received time-domain signal y(t) is expressed as equation (1-3):

[0033] (1-3)

[0034] Among them, h( ) represents the channel impulse response. These represent time delay and Doppler frequency shift, respectively, with n(t) being the one-sided power spectral density. Complex Gaussian noise.

[0035] The time-domain received signal y(t) is transformed by Wigner to obtain the time-frequency domain signal Y[n,m], and the specific expression is given by equation (1-4):

[0036] (1-4)

[0037] (1-5)

[0038] In the formula, It is the received waveform pulse at the receiving end. This indicates the conjugate operation. These are the signal characteristics in the time-frequency domain.

[0039] S14. Transform the signal Y[n,m] using the Symptotic Finite Fourier Transform (SFFT) to obtain the time-delay-Doppler domain signal y(k,l).

[0040] Y[n,m] is transformed into the time-delay-Doppler domain by SFFT to obtain the signal y(k,l), whose transformation expression is given by equation (1-6):

[0041]

[0042] (1-6)

[0043] in, For the time-delay-Doppler domain complex Gaussian noise, The sampled version of the channel impulse response function is expressed by equation (1-7):

[0044] (1-7)

[0045] In one embodiment, for a low-Earth orbit satellite mobile communication scenario, the positional relationship between the satellite and the ground communication terminal is as follows: Figure 3 As shown. The Doppler effect is caused by the relative motion between the transmitting and receiving ends, mainly manifested in two parts: Doppler frequency shift and Doppler spread. The frequency broadening caused by the superposition of Doppler frequency shift and multipath effect is called Doppler spread. The Doppler frequency shift depends on the relative speed and position of the satellite and the ground terminal. The maximum Doppler frequency shift... The calculation formula is equation (1-8):

[0046] (1-8)

[0047] In the formula: v is the relative velocity, and c is the speed of light. For carrier frequency, The elevation angle between the satellite and the ground equipment.

[0048] Maximum Doppler Shift The Doppler frequency shift and its rate of change in low-Earth orbit (LEO) satellite communications are directly proportional to the carrier frequency and relative velocity. These factors primarily depend on the relative velocity of the space or airborne platform, the speed of the user equipment, and the carrier frequency. Since both the satellite and the user equipment move relative to the Earth, their effects on the Doppler frequency shift can be geometrically superimposed. Therefore, the Doppler frequency shift in LEO satellite communications is... This can be expressed as equation (1-9):

[0049] (1-9)

[0050] In the formula, Let θ be the terminal's moving speed, and ɵ be the angle between the user equipment's moving direction and the satellite projection plane. The frequency shift caused by the high-speed motion of a low-orbit satellite is expressed by equation (1-10):

[0051] (1-10)

[0052] In the formula, Represents the Earth's radius. Indicates the satellite's altitude above the ground. This indicates the satellite's moving speed.

[0053] The parameters of the GA-MP algorithm include: symbol posterior mean, symbol posterior variance, damping factor, step size, etc. All symbols of the transmitted signal are used as initialization parameters to be estimated. .

[0054] S2. Based on the received signal, the parameters of the GA-MP algorithm for the current iteration round are... The symbol to be estimated for the transmitted signal in the current iteration round The message-passing steps of the GA-MP algorithm are executed to obtain the symbol to be estimated. The posterior probability and soft estimate; the posterior probability includes the posterior mean and posterior variance;

[0055] The message passing steps of the GA-MP algorithm are the steps of each iteration of the GA-MP algorithm. The GA-MP algorithm is an existing signal detection algorithm, which has been recorded in many papers, such as the journal paper "Gaussian Approximate Message Passing Detection of Orthogonal Time Frequency Space Modulation" published by Luping Xiang, Yusha Liu, Lie-Liang Yang, etc. The posterior probability is calculated according to formula (22) in the paper, and the soft estimate is the mean of the Gaussian approximate message, which is calculated according to formula (26) in the paper.

[0056] S3. Based on the symbol to be estimated of the transmitted signal in the current iteration round. The posterior probability and soft estimate are used to adjust the parameters of the GA-MP algorithm in the current iteration round. The damping factor in the algorithm is used to obtain the parameters of the GA-MP algorithm for the next iteration. ;

[0057] The flowchart of the dynamic damping factor adjustment mechanism of the present invention is as follows: Figure 4 As shown, the underlying assumption of this mechanism is that the change in posterior probability is strongly correlated with the convergence speed. The core idea is to monitor the change in the posterior probability distribution in real time and use it as the basis for adjusting the damping factor.

[0058] Specifically, the dynamic damping factor adjustment mechanism adjusts the parameters of the GA-MP algorithm in the current iteration t. The damping factors include:

[0059] S31. Based on the posterior probability of the symbol to be estimated in the current iteration t and the previous iteration t-1. Calculate the change in posterior probability ;

[0060] The change in the posterior probability distribution directly reflects the current convergence state of the algorithm: a large change indicates that the algorithm is still in the fast convergence phase, requiring a larger damping factor to accelerate convergence; a small change indicates that the algorithm is entering the convergence stationary phase, requiring a smaller damping factor to improve estimation accuracy. By dynamically adjusting the damping factor, a balance can be achieved between convergence speed and stability, thereby optimizing the overall performance of the GA-MP detection algorithm. The definition of the change in posterior probability is as follows:

[0061]

[0062] in, and Let represent the posterior mean and posterior variance of the k-th symbol of the transmitted signal at iteration round t, respectively.

[0063] S32. Soft estimate of the symbol to be estimated based on the received signal y, the channel matrix H, and the current iteration round t. Calculate the step size for the damping factor;

[0064] To ensure that the adjustment step size of the damping factor varies with the actual convergence process, a dynamic step size is adopted. The step size for calculating the damping factor includes: calculating the residual for the current iteration based on the received signal, the channel matrix, and the soft estimate of the symbol to be estimated in the current iteration t. Obtain the residual from the previous iteration. Based on the residual of the current iteration round The residual from the previous iteration Calculate the rate of change of residuals According to the residual rate of change Calculate the step size for the damping factor.

[0065] The residual rate of change and the residual are defined as follows:

[0066]

[0067]

[0068] The above formula is used in residual calculation. This soft estimate is used to approximate... This hard-line ruling was issued because... It will not be calculated during the iteration process and will only be obtained after the iteration stops. The soft estimate value will be updated in each iteration's message passing step. Therefore, when calculating the residual during the iteration process, it is necessary to use this soft estimate value to replace . The specific step size adjustment strategy is as follows:

[0069]

[0070] where a > 1, b < 1, c < b are adjustment coefficients for controlling different strategies respectively, and are the upper and lower limits of the step size adjustment value respectively, are the incremental step size and the decremental step size respectively, , are the maximum threshold, intermediate threshold, and minimum threshold of the residual change rate respectively;

[0071] When the residual change rate is greater than the highest threshold, it indicates that the residual is rapidly decreasing at this time, indicating that the current direction is correct, and the step size can be increased; when the residual change rate is less than the intermediate threshold, the residual is slowly decreasing and approaching the convergence region, and the step size needs to be reduced to avoid oscillation; when the residual change rate is less than the lowest threshold, it indicates that the residual is rising at this time, and the step size should be greatly reduced to prevent the algorithm from falling into a local optimum. This mechanism adjusts the step size in real time according to the convergence state and sets the upper and lower limits to prevent the step size from getting out of control, accelerating the algorithm convergence and fine-tuning the later adjustment.

[0072] S33. Set the threshold of the posterior probability change amount, and the threshold is set to [0.01, 0.1]. Judge whether the posterior probability change amount is greater than the posterior probability change amount threshold. If so, increase the damping factor of the current iteration round t according to the step size of the damping factor to obtain the damping factor of the next iteration round t + 1 ; otherwise, reduce the damping factor of the current iteration round t according to the step size of the damping factor to obtain the damping factor of the next iteration round t + 1 .

[0073] The specific adjustment formula is as follows:

[0074]

[0075] where the incremental and decremental step sizes of the damping factor , are to prevent the algorithm from being unstable due to the damping factor being too large or too small, and set the upper and lower limits of the damping factor and . If If the value is greater than the threshold, it indicates that the algorithm is still in the fast convergence phase. In this case, the damping factor can be increased to accelerate convergence. If... If the value is less than or equal to the threshold, it indicates that the algorithm has entered the convergent and stable phase. At this point, a smaller damping factor is needed to improve the accuracy of the estimation.

[0076] S4. Determine whether to continue the iteration. If yes, obtain the symbol to be estimated for the transmitted signal in the next iteration round. Returning to step S2, the symbol to be estimated for the transmitted signal in the next iteration round. Perform the next iteration; otherwise, obtain the final posterior probability of the transmitted signal.

[0077] This invention proposes a dual-threshold convergence monitoring mechanism, referencing the convergence rate of traditional message passing algorithms. By dynamically tracking the convergence trajectory of the symbolic posterior probability, it achieves adaptive allocation of computing resources. The dual thresholds are the confidence threshold and the gap threshold.

[0078] like Figure 5 As shown, determining whether to continue the iteration includes:

[0079] Set the gap threshold and symbol convergence rate threshold, based on the number of symbols to be estimated in the current iteration t of the transmitted signal. The posterior probability is used to calculate the sign convergence rate of the current iteration t. and its change ; Obtain the sign convergence rate of the previous iteration. ;

[0080] The sign convergence rate is shown below:

[0081]

[0082] in, The symbol to be estimated for the transmitted signal in the current iteration round t The quantity, when At the time of its establishment, Otherwise, it is 0. The symbol to be estimated The posterior probability of the l-th modulation symbol in symbol k.

[0083] Simultaneously define the change in convergence rate. :

[0084]

[0085] When calculating the symbolic convergence rate, record the posterior probability and algebra of the iteration with the best symbolic convergence rate to facilitate subsequent state backtracking.

[0086] Based on the sign convergence rate of the current iteration round t Determine if convergence has occurred (i.e., determine if the symbol convergence rate of the current iteration t is equal to 1). If yes, stop the iteration and send the signal to the symbol to be estimated in the current iteration t. The posterior probability is used as the sign to be estimated. Final posterior probability Otherwise, determine the change in the sign convergence rate of the current iteration t. Is it less than the gap threshold and the sign convergence rate of the previous iteration? If the symbol convergence rate is higher than the threshold, stop the iteration and proceed with the estimation of the symbol of the transmitted signal in the current iteration round t. The posterior probability is used for state backtracking, and the posterior probability obtained after backtracking is used as the symbol to be estimated in the current iteration t. Final posterior probability Otherwise, continue iterating.

[0087] The sign convergence threshold should be set to different values ​​under different conditions. Optionally, the threshold range is 0.9 to 0.98.

[0088] When the sign convergence rate equals 1, the algorithm can be considered to have fully converged. Continuing to iterate would waste computational resources, so iteration stops at this point. The change in the convergence rate... If the convergence rate is less than the gap threshold and the convergence rate of the previous generation is already higher than the set threshold, it means that the current iteration is proceeding in the opposite direction of convergence. If the convergence rate of the previous generation is acceptable, continuing the iteration will not have a significant effect, and may even make the algorithm converge worse. Therefore, the iteration should be stopped at this time.

[0089] State backtracking uses the posterior probability with the best convergence rate from the previous iterations.

[0090] Obtain the symbol to be estimated for the transmitted signal in the next iteration round. This includes: setting a confidence threshold, and estimating the sign to be estimated. Mid-maximum posterior probability Symbols with a confidence level greater than the confidence threshold are classified as high-confidence symbols, while the remaining symbols are classified as low-confidence symbols. Low-confidence symbols are then used as the symbols to be estimated in the next iteration. The posterior probability of the high-confidence symbol in the current iteration is used as the final posterior probability of the high-confidence symbol. The high-confidence symbol will not be recalculated in subsequent iterations, thus saving computational resources.

[0091] S5. Calculate the estimated result of the transmitted signal based on the final posterior probability of the transmitted signal. The estimation results of the transmitted signal are post-processed and optimized to obtain the final estimation result of the transmitted signal; among which, Let S be the estimated result for symbol k, and S be the total number of symbols.

[0092] Post-processing optimizations include:

[0093] Step 1: Determine each symbol in the transmitted signal as a low-confidence symbol or a high-confidence symbol based on the posterior probability and channel conditions;

[0094] The following are considered as low-confidence or high-confidence symbols:

[0095] The final posterior probability of symbol k Obtain the maximum posterior probability of symbol k. With the second largest posterior probability Calculate the maximum posterior probability for each symbol k. With the second largest posterior probability confidence interval : ;

[0096] Consider using an adaptive threshold decision method, where channel conditions are considered as a factor influencing the threshold, and the threshold is calculated and determined based on the channel conditions. , The specific formula is as follows:

[0097]

[0098]

[0099] in, , , , These are two judgment thresholds. , Adjustment coefficient, These are the current signal-to-noise ratio and the signal-to-noise ratio reference point, respectively. Adaptive threshold adjustment relaxes the decision criteria when the SNR is low and tightens them when the SNR is high, thus avoiding overprocessing.

[0100] Maximum posterior probability Less than the judgment threshold And confidence interval Less than the judgment threshold The symbol is used as a low-confidence symbol, that is, the decision condition for a low-confidence symbol is... The remaining symbols are treated as high-confidence symbols.

[0101] Step 2: Combine the low-confidence symbols of the same element in the received signal y to obtain multiple groups of strongly correlated symbols;

[0102] The elements in the received signal y are connected to multiple transmitted symbols through the channel matrix H, forming the "observation constraints" for message transmission.

[0103] Step 3: Perform joint maximum likelihood re-detection on the strongly correlated symbol group, and perform local maximum likelihood re-detection on the remaining low-confidence symbols to obtain the re-detection estimation results for all low-confidence symbols;

[0104] The purpose of local maximum likelihood re-detection is to correct individual low-confidence symbols. Local maximum likelihood re-detection for low-confidence symbols k includes:

[0105] From the global observation equation model ( Extract the local observation equation model from the low-confidence symbol k, and extract the index set of observation equations (factor nodes) connected by the low-confidence symbol k based on the local observation equation model. The formula is shown below:

[0106]

[0107] in, The factor graph connection indicator matrix is ​​used for the local observation equation model. When the nth observation equation is connected to the kth symbol... The value is 1 if it is 1, otherwise it is 0.

[0108] Obtain the observation equation index set from the received signal y. The corresponding elements yield the local received signal vector of symbol k. The formula is shown below:

[0109]

[0110] Extract the index set from the complete channel matrix H The corresponding row yields the channel matrix for symbol k. The formula is shown below:

[0111]

[0112] Based on the local received signal vector of symbol k and channel matrix Calculate the residual vector of symbol k ;

[0113]

[0114] in, The residual signal after interference cancellation. Channel matrix for symbol k The j-th column in Let j be the estimated value of all symbols except for symbol k.

[0115] Generate a constellation point candidate set for symbol k Candidate set Typically, it is the complete constellation set A (such as 4-QAM, 16-QAM, etc.) or a subset thereof, with the subset selecting neighboring constellation points based on the initial estimation results of symbol k;

[0116] Based on the residual vector of symbol k Channel matrix and constellation point candidate set Construct the optimization objective function for symbol k; the formula is shown below:

[0117]

[0118]

[0119] in, It is the k-th column in the channel matrix of symbol k. Let i be the i-th constellation point in the candidate set. Point for constellation Distance metric.

[0120] Solving the objective function yields the re-detection estimation results for the low-confidence symbol k. .

[0121] When multiple low-confidence symbols are connected to the same element in the received signal y, it is inappropriate to treat this group of low-confidence symbols as strongly correlated symbols and perform individual maximum likelihood re-detection. Therefore, joint maximum likelihood symbol detection should be performed on this group of symbols. Joint maximum likelihood re-detection of strongly correlated symbol groups includes:

[0122] For symbol groups The received signal model is:

[0123]

[0124] in, Symbol group in received signal y The corresponding signal, Symbol group in the complete channel matrix H The corresponding sub-channel matrix, Symbol group in the transmitted signal The corresponding transmission vector, symbol group External interference For symbol group The set of factor node (observation equation) indexes, The set of indices in the complete channel matrix H and the submatrix corresponding to the symbol j, Symbol group in the transmitted signal The estimation results of the sign j outside z g This is channel noise.

[0125] Calculate strongly correlated symbol groups based on the received signal model. Residual signal after interference cancellation The formula is shown below:

[0126]

[0127] Generate strongly correlated symbol groups Joint candidate constellation space ;in, It is the modulation constellation set A. It is a symbol group Size, express The Cartesian product of all possible combinations of symbols;

[0128] According to the strongly correlated symbol group residual signal Channel matrix and joint candidate constellation space Constructing strongly correlated symbol groups The optimization objective function is shown in the following formula;

[0129]

[0130]

[0131] in, For joint candidate constellation space Candidate vectors in.

[0132] Solving the objective function yields a set of strongly correlated symbols. Re-detection estimation results .

[0133] The flowchart of the entire post-processing optimization mechanism is as follows: Figure 6 As shown. After completing all the above steps, the final detected symbol sequence is output.

[0134] The simulation uses the NTN-TDL channel model specified in 3GPP TR 38.811, with the LEO satellite altitude at 1500km, the terminal moving speed at 500km / h, and the modulation scheme at 4QAM.

[0135] Figure 7The results show the bit error rate (BER) of different algorithms at different signal-to-noise ratios (SNRs). The improved GA-MP algorithm and the GA-MP algorithm both outperform the MMSE, MP, and ZF algorithms. Compared to the original algorithm, the improved algorithm exhibits a deterioration in BER at low SNRs. For example, in the 0–6 dB range, at the same BER level (based on BER=0.17), the improved algorithm requires approximately an additional 0.35 dB SNR to achieve the performance of the original algorithm. This phenomenon is mainly caused by the following mechanism characteristics:

[0136] 1. At low SNR, channel noise dominates system errors, leading to drastic fluctuations in the posterior probability distribution. In this case, the dynamic damping factor tends to maintain a large value, which, while accelerating convergence, excessively smooths the iterative updates, weakening the algorithm's ability to explore the real signal path, effectively reducing the algorithm's gain.

[0137] 2. Noise interference causes a slow increase in symbol confidence and significant fluctuations in the convergence rate. The iteration stopping mechanism may continue iterating before the backtracking threshold is reached, or it may misjudge convergence due to random fluctuations and prematurely output a suboptimal solution.

[0138] 3. The core of the post-processing mechanism is to correct low-confidence symbols through local / joint machine learning (ML) detection. Its effectiveness depends on two key conditions: the residual signal must contain a sufficient signal-to-interference-plus-noise ratio (SINR); and there must be a distinguishable Euclidean distance between candidate symbols and true symbols. At low SNR, these conditions are violated, leading to an increased correction failure rate. At low SNR, the proportion of low-confidence symbols increases significantly, and the Euclidean distance between their true symbols and interference signals is close. In this case, local ML detection suffers from insufficient residual SNR, resulting in a higher probability of incorrect correction; joint ML detection suffers from an exponential increase in the candidate space, but in practice, it is strictly limited to avoid a dramatic increase in computational overhead and to prevent weakening the joint optimization effect.

[0139] However, the improved algorithm proposed in this invention shows a significant performance improvement over the original algorithm at medium to high signal-to-noise ratios (SNR). At the same BER level (based on BER=0.00015), the improved algorithm improves the SNR by approximately 0.9 dB. If the SNR discrete points are uniformly distributed, with 0–6 dB considered low SNR and 8–20 dB considered high SNR, the improved algorithm still shows performance improvement over the original algorithm, with an SNR improvement of approximately 0.5 dB. This indicates that the post-processing mechanism of the improved algorithm can still reduce the bit error rate overall.

[0140] Figure 8The results show the bit error rate (BER) changes of the improved algorithm and the original algorithm under different maximum iteration counts. During simulation, the SNR was set to 22 dB, and the modulation scheme was 4-QAM. The algorithm converged when the BER stabilized. The results show that, compared to the original algorithm, the improved GA-MP algorithm reduces the number of iterations from 11 to approximately 9, and the average number of iterations is reduced by about 18%, indicating that the dynamic adjustment mechanism of the damping factor and the early stopping mechanism of the iterations accelerate convergence.

[0141] 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 adaptive Gaussian message passing signal detection method for an OTFS system, characterized in that, include: S1. The transmitter of the OTFS system sends a signal, and the receiver of the OTFS system receives the signal transmitted through the channel and initializes the parameters of the GA-MP algorithm. and the symbol of the transmitted signal to be estimated Among them, the GA-MP algorithm is a Gaussian approximation message passing algorithm; S2. Based on the received signal, the parameters of the GA-MP algorithm for the current iteration round are... The symbol to be estimated for the transmitted signal in the current iteration round The message-passing steps of the GA-MP algorithm are executed to obtain the symbol to be estimated. The posterior probability and soft estimate; S3. Based on the symbol to be estimated of the transmitted signal in the current iteration round. The posterior probability and soft estimate are used to adjust the parameters of the GA-MP algorithm in the current iteration round. The damping factor in the algorithm is used to obtain the parameters of the GA-MP algorithm for the next iteration. ; S4. Determine whether to continue the iteration. If yes, obtain the symbol to be estimated for the transmitted signal in the next iteration round. Returning to step S2, the symbol to be estimated for the transmitted signal in the next iteration round. Perform the next iteration; otherwise, obtain the final posterior probability of the transmitted signal. S5. Calculate the estimated result of the transmitted signal based on the final posterior probability of the transmitted signal; perform post-processing optimization on the estimated result of the transmitted signal to obtain the final estimated result of the transmitted signal.

2. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 1, characterized in that, Adjusting the parameters of the GA-MP algorithm in the current iteration round t The damping factors include: The change in posterior probability is calculated based on the posterior probability of the symbol to be estimated in the current iteration t and the previous iteration t-1. The step size of the damping factor is calculated based on the received signal, the channel matrix, and the soft estimate of the symbol to be estimated in the current iteration round t. Set a threshold for the change in posterior probability. Determine whether the change in posterior probability is greater than the threshold. If it is, increase the damping factor of the current iteration t according to the step size of the damping factor to obtain the damping factor of the next iteration t+1. Otherwise, decrease the damping factor of the current iteration t according to the step size of the damping factor to obtain the damping factor of the next iteration t+1.

3. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 2, characterized in that, The step size for calculating the damping factor includes: calculating the residual for the current iteration t based on the received signal, the channel matrix, and the soft estimate of the symbol to be estimated in the current iteration t; obtaining the residual for the previous iteration t-1; and calculating the rate of change of the residual based on the residual for the current iteration t and the residual for the previous iteration t-1. According to the residual rate of change The step size for calculating the damping factor is given by the following formula: Where a, b, and c are adjustment coefficients. and These are the upper and lower limits of the step size adjustment value, respectively. These are the increment step size and the decrement step size, respectively. , These are the maximum threshold, intermediate threshold, and minimum threshold for the residual rate of change, respectively.

4. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 1, characterized in that, Determining whether to continue iteration includes: Set the gap threshold and symbol convergence rate threshold, based on the number of symbols to be estimated in the current iteration t of the transmitted signal. The posterior probability is used to calculate the sign convergence rate of the current iteration t. and its change ; Obtain the sign convergence rate of the previous iteration. ; Based on the sign convergence rate of the current iteration round t Determine if convergence has occurred. If convergence has occurred, stop the iteration and send the signal to be estimated for the symbol in the current iteration t. The posterior probability is used as the sign to be estimated. The final posterior probability; otherwise, determine the change in the sign convergence rate of the current iteration t. Is it less than the gap threshold and the sign convergence rate of the previous iteration? If the symbol convergence rate is higher than the threshold, stop the iteration and proceed with the estimation of the symbol of the transmitted signal in the current iteration round t. The posterior probability is used for state backtracking, and the posterior probability obtained after backtracking is used as the symbol to be estimated. The final posterior probability; otherwise, continue iterating.

5. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 4, characterized in that, Calculate the symbolic convergence rate and its change include: in, The symbol to be estimated in the current iteration round t of the transmitted signal Quantity, The symbol to be estimated The posterior probability of the l-th modulation symbol in symbol k.

6. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 1, characterized in that, Obtain the symbol to be estimated for the transmitted signal in the next iteration round. This includes: setting a confidence threshold, and estimating the sign to be estimated. Mid-maximum posterior probability Symbols with a confidence level greater than the confidence threshold are classified as high-confidence symbols, while the remaining symbols are classified as low-confidence symbols. Low-confidence symbols are then used as the symbols to be estimated in the next iteration. The posterior probability of the high-confidence symbol in the current iteration round is taken as the final posterior probability of the high-confidence symbol; where, The symbol to be estimated The posterior probability of the l-th modulation symbol in symbol k.

7. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 1, characterized in that, Post-processing optimization of the estimated results of the transmitted signal includes: Based on the posterior probability and channel conditions, each symbol in the transmitted signal is determined to be a low-confidence symbol or a high-confidence symbol; By combining low-confidence symbols that share the same element in the received signal y, multiple groups of strongly correlated symbols are obtained. Joint maximum likelihood re-detection is performed on the strongly correlated symbol group, and local maximum likelihood re-detection is performed on the remaining low-confidence symbols to obtain the re-detection estimation results for all low-confidence symbols.

8. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 7, characterized in that, Determining whether each symbol in the transmitted signal is a low-confidence symbol includes: The final posterior probability of symbol k Obtain the maximum posterior probability of symbol k. With the second largest posterior probability Calculate the maximum posterior probability for each symbol k. With the second largest posterior probability confidence interval Calculate the threshold based on channel conditions , ; Maximum posterior probability Less than the judgment threshold And confidence interval Less than the judgment threshold The symbol is used as the low confidence symbol, and the rest of the symbols are used as the high confidence symbols.

9. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 7, characterized in that, Local maximum likelihood re-detection of low-confidence symbol k includes: Obtain the local observation equation model for the low-confidence symbol k, and extract the observation equation index set connected by the low-confidence symbol k based on the local observation equation model. ; Obtain the observation equation index set from the received signal y. The corresponding elements yield the local received signal vector of symbol k. ; Extract the index set from the complete channel matrix H The corresponding row yields the channel matrix for symbol k. ; Based on the local received signal vector of symbol k and channel matrix Calculate the residual vector of symbol k ;in, Channel matrix for symbol k The j-th column in The symbol estimation result for symbol j; Generate a constellation point candidate set for symbol k According to the residual vector of symbol k Channel matrix and constellation point candidate set Construct the optimization objective function for symbol k: ;in, Channel matrix for symbol k The k-th column in; Solving the objective function yields the re-detection estimation results for the low-confidence symbol k. .

10. The adaptive Gaussian message passing signal detection method for an OTFS system according to claim 7, characterized in that, Joint maximum likelihood re-detection of strongly correlated symbol groups includes: Constructing strongly correlated symbol groups Received signal model: in, Symbol group in received signal y The corresponding signal, Symbol group in the complete channel matrix H The corresponding sub-channel matrix, Symbol group in the transmitted signal The corresponding transmission vector, For symbol group External interference For symbol group The set of observation equation indices The set of indices in the complete channel matrix H and the submatrix corresponding to the symbol j, Symbol group in the transmitted signal The estimation results of the sign j outside z g Channel noise; Calculate strongly correlated symbol groups based on the received signal model. residual signal ; Generate strongly correlated symbol groups Joint candidate constellation space According to the strongly correlated symbol group residual signal Channel matrix and joint candidate constellation space Construct the optimization objective function: ;in, For joint candidate constellation space Candidate vectors in; Solving the objective function yields a set of strongly correlated symbols. Re-detection estimation results .

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