Turbo equalization method in low earth orbit satellite OTFS system

Abstract

The invention discloses a Turbo equalization method in a low earth orbit satellite OTFS system, and belongs to the technical field of wireless communication. The invention provides a Turbo equalization scheme based on an expectation-maximization-aided approximate orthogonal message passing (EMA-OAMP) algorithm, aiming at the problems of high detection complexity and poor detection performance of a traditional detector after a signal passes through a satellite-ground time-frequency doubly-selective channel, and provides a Turbo equalization scheme based on an expectation-maximization-aided approximate orthogonal message passing (EMA-OAMP) algorithm. The method comprises the following steps: firstly, converting a time-varying channel in a time delay-Doppler (DD) domain into a quasi-static sparse channel by using OTFS modulation; secondly, designing a detector based on an EMA-OAMP algorithm, efficiently identifying effective multipath components in a DD domain by using the OAMP algorithm, and introducing an EM module to dynamically obtain noise variance so as to improve signal detection performance; and finally, constructing a Turbo equalizer, cascading an EMA-OAMP detector and an LDPC decoder, and proposing an outer-layer dominant double-layer iteration termination strategy to realize collaborative optimization of symbol detection and decoding. According to the Turbo equalization scheme provided by the invention, the complexity is reduced, and the symbol detection performance is close to a maximum posterior probability algorithm.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology. Specifically, it relates to a Turbo equalization method in a low-Earth orbit satellite OTFS system. Background Technology

[0002] To achieve the vision of seamless 6G coverage, it is necessary to consider the integration of ground nodes and non-ground nodes to ultimately construct a converged network that meets the requirements of "air-space-sea-terrestrial" integration. LEO satellites, due to their advantages such as wide coverage, less susceptibility to extreme ground conditions, and shorter latency compared to NLEO satellites, are considered one of the most promising solutions for achieving "seamless connectivity" in the 6G era. However, the high-speed relative motion between LEO satellites and ground terminals can generate Doppler shifts of up to ±100kHz, while signal reflections from ground buildings can cause multipath interference. These factors collectively lead to time-frequency selective fading characteristics in the satellite-to-ground link channel, severely affecting the accurate reception of satellite signals by the ground receiver. To reduce the bit error rate of the received signal, the ground receiver typically needs to employ signal detection and equalization algorithms.

[0003] Traditional algorithms suffer from significant limitations in both signal detection and equalization. In signal detection, the maximum ratio combining algorithm (MRC) suffers from performance degradation due to its excessive sensitivity to noise and interference; the linear minimum mean square error (LMSE) algorithm requires precise channel matrix information and struggles to cope with the Doppler effect in high-speed, time-varying environments; and the approximate message passing algorithm amplifies noise in ill-conditioned satellite-to-ground channels, causing a sharp increase in bit error rate (BER) under low BER conditions. In equalization, traditional MMSE equalization not only suffers from an inherent error plateau but also has limited ability to suppress nonlinear interference such as phase noise. More seriously, the independent nature of the signal detection and decoding modules creates information silos, further amplifying the system's BER plateau and making it difficult to overcome overall performance bottlenecks.

[0004] A search revealed application CN117544456A, which discloses a Turbo equalization method, apparatus, device, and storage medium based on dual iteration. The method includes: combining LMMSE and EP algorithms to obtain a BEP equalizer; cascading the BEP equalizer and decoder to obtain a dual-iteration structure; prematurely terminating the iteration of the inner loop of the BEP equalizer using the convergence rate of the symbol probability and a preset convergence threshold; and prematurely terminating the iteration of the outer loop of the BEP equalizer and decoder using an auxiliary hard-decision iteration stopping criterion. Compared to traditional Turbo equalization schemes, this invention, based on a dual-iteration structure, applies an early termination iteration strategy to avoid unnecessary loops and iterations, significantly reducing complexity and computational load without sacrificing performance.

[0005] However, the above methods have the following shortcomings, and this method improves upon them. The comparative analysis is as follows: First, the above schemes use the LMMSE algorithm for linear detection, while this method uses the OAMP algorithm to equalize the estimation results after linear detection, resulting in higher detection accuracy. In addition, although the EP (Expectation Propagation) algorithm used in the above methods improves the equalization performance of higher-order constellations, the explicit matrix inversion in each iteration brings high computational complexity. This method introduces the EM algorithm, which does not require complex matrix operations during iteration and can accurately detect signals in complex channels. Finally, although the above methods terminate the inner and outer iterations early by setting a convergence threshold and a hard-decision iteration stopping criterion, the inner and outer convergence conditions still need to be met simultaneously to end the overall iteration process. This method proposes an outer-layer-dominated two-layer iteration termination strategy, which terminates the system iteration as soon as the outer iteration convergence condition is met, greatly reducing the iteration computational complexity while ensuring performance.

[0006] To address the aforementioned technical challenges, this invention proposes a Turbo equalization method for low-Earth orbit satellite OTFS systems. First, OTFS modulation technology is used to convert the biselective channel with fading and time-varying characteristics in the TF domain into a quasi-static sparse channel in the DD domain, thereby combating the adverse effects of Doppler shift and multipath effects. Second, to address the problem of poor detection performance due to the high sensitivity of traditional signal detection algorithms to noise and interference, an OAMP detector is used at the receiver. By combining a message passing framework with sparse prior characteristics, multipath components and noise are efficiently separated. Furthermore, an EM module is introduced to dynamically learn the system noise variance, improving signal detection accuracy. Finally, to address the poor dynamic adaptability and low information utilization efficiency of traditional equalization schemes, an iterative optimization scheme based on Turbo equalization is proposed. This scheme establishes a bidirectional information exchange mechanism between the EMA-OAMP detector and the LDPC decoder. The EMA-OAMP detector outputs the likelihood soft information of the symbols to the decoder, and the decoder feeds back the error-corrected prior information to the detector, forming a closed-loop optimization. Through this iterative process, the system's detection performance can gradually approach the optimal performance of the maximum a posteriori (MAP) algorithm. Summary of the Invention

[0007] This invention aims to solve the problems of the prior art mentioned above. A Turbo equalization method for low-Earth orbit satellite OTFS systems is proposed. The technical solution of this invention is as follows:

[0008] A Turbo equalization method in a low-Earth orbit satellite OTFS system includes the following steps:

[0009] S1: Design a signal detector based on the EMA-OAMP (Expectation Maximization-Assisted Orthogonal Approximation Message Passing) algorithm, perform linear and nonlinear estimation processing on the OTFS (Orthogonal Time-Frequency-Space) modulated signal, calculate the posterior mean and variance, and calculate the real-time noise variance through dynamic learning;

[0010] S2: Construct a Turbo equalizer, cascade the EMA-OAMP detector with the LDPC (low-density parity-check code) decoder, calculate the external log-likelihood ratio based on the posterior mean and variance output by the EMA-OAMP detector, and calculate the total probability of the estimated symbol after LDPC decoding and the updated mean and variance.

[0011] S3: Define the internal iteration relative error and the external iteration relative error, and propose an externally dominated two-layer iteration termination strategy for the constructed Turbo equalizer.

[0012] S4: Calculate the complexity of the EMA-OAMP detector and LDPC decoder, then calculate the overall complexity of the Turbo equalizer by combining the number of internal and external iterations, and compare and analyze it with the complexity of the maximum a posteriori probability (MAP) algorithm.

[0013] The advantages and beneficial effects of this invention are as follows:

[0014] This invention addresses the high complexity and high bit error rate of existing signal detection algorithms in satellite-to-ground time-frequency dual-selection channels by proposing a Turbo equalization method for LEO satellite OTFS systems. The main innovations of this invention are as follows: 1) It is the first time a Turbo dual-iteration structure based on a cascaded EMA-OAMP detector and LDPC decoder has been adopted in an LEO satellite downlink OTFS system. Compared with existing research, this invention overcomes the limitations of traditional OFDM modulation techniques and avoids the performance deficiencies of detection algorithms such as MMSE, bringing the system's bit error rate performance close to the optimal level of the MAP algorithm; 2) To address the performance degradation problem caused by the fixed noise variance assumption in existing algorithms, the EM algorithm is innovatively introduced into the OAMP detector, enabling real-time estimation and updating of noise parameters, effectively improving the system's robustness in dynamic channel environments; 3) A hierarchical iteration stopping mechanism is proposed. By jointly considering the convergence conditions of the EMA-OAMP internal iteration and the global iteration of the Turbo equalizer, a dual-layer iteration termination criterion dominated by the outer iteration is defined. This mechanism requires that as long as the outer iteration convergence condition is met, the system iteration will terminate even if the inner iteration has not yet converged, which greatly reduces the system complexity while ensuring detection performance.

[0015] The EMA-OAMP Turbo equalization scheme proposed in this invention effectively solves the shortcomings of existing methods in terms of computational complexity and bit error rate performance through the above-mentioned technical innovations, providing an efficient and reliable signal detection solution for the LEO satellite OTFS system. Attached Figure Description

[0016] Figure 1 This is a network model diagram constructed according to a preferred embodiment of the present invention;

[0017] Figure 2 This is a flowchart of a Turbo equalization method in a low-orbit satellite OTFS system as described in this invention;

[0018] Figure 3 This is a flowchart of the overall communication process of a Turbo equalization method in a low-orbit satellite OTFS system constructed according to a preferred embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0020] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0021] A Turbo equalization method for a low-Earth orbit (LEO) satellite OTFS system. Considering the Doppler frequency shift and multipath effects present in the downlink of LEO satellites, the EMA-OAMP detection algorithm is used to enhance the system's resistance to Doppler and multipath interference. Subsequently, the detector is combined with an LDPC decoder to further reduce the receiver's bit error rate. The specific steps are as follows:

[0022] Step 1: The generated input bitstream is encoded, interleaved, and mapped before being modulated using OTFS. The modulated signal is then transmitted to the ground receiver via an NTN-TDL-D simulated time-frequency dual-selection channel. At the ground receiver, the satellite-transmitted signal is demodulated using OTFS, and the demodulated received signal matrix and channel matrix are used as known parameters in subsequent calculations of EMA-OAMP.

[0023] The second step: The EMA-OAMP detector first performs preliminary detection of the received signal through the LE module, and then uses the NLE module to equalize and optimize the output of the LE to suppress residual interference. Next, the noise variance is estimated and updated in real time through the EM module to improve the detector's environmental adaptability. Finally, the LLR is calculated based on the posterior mean and posterior variance and passed as extrinsic information to the LDPC decoder for iterative decoding.

[0024] Step 3: The extrinsic information output by the detector is demapped and deinterleaved, and then fed into the LEPC decoder as prior information. If, under the convergence condition of the EMA-OAMP algorithm, the difference between the extrinsic information before and after decoding is less than a given threshold, the Turbo iteration process is terminated, and the final LLR is directly output as the detection result. Otherwise, the decoded extrinsic information is re-interleaved and re-mapped, and fed back to the EMA-OAMP detector for the next global iteration.

[0025] Step 4: Conduct a complexity comparison analysis between the proposed Turbo equalizer and the theoretical MAP detection algorithm to demonstrate that the proposed Turbo equalizer has the advantage of lower complexity while maintaining similar performance.

[0026] The main symbols and parameters involved in this invention and their meanings are listed in Table 1.

[0027] Table 1. Main Symbols, Parameters, and Their Meanings

[0028]

[0029] Preferably, in the first step, the NTN-TDL model simultaneously considers the Doppler shift caused by both ground receiver motion and satellite motion. Its principle is to describe channel characteristics through changes in signal amplitude. Assuming each tap represents a combination of paths with the same time delay, the generalized stationary uncorrelated scattering model considers signals with different time delays to be uncorrelated at the receiver. Therefore, the fading of different taps can be changed to mimic multipath channel transmission. The NTN-TDL channel model is divided into four types: NTN-TDL-A and NTN-TDL-B are suitable for non-line-of-sight propagation conditions, while NTN-TDL-C and NTN-TDL-D are suitable for line-of-sight propagation conditions. In low-Earth orbit satellite downlink communication, line-of-sight propagation conditions are relatively ideal, and the ground terminal's observation elevation angle is less than 45°, meeting the applicability conditions of NTN-TDL-D. NTN-TDL-C is suitable for GEO / MEO scenarios with elevation angles >45°. Considering all factors, NTN-TDL-D is selected as the channel model.

[0030] The Doppler shift caused by satellite motion depends on parameters such as satellite speed, orbit, elevation angle, and carrier frequency, and its basic formula is shown below.

[0031]

[0032] Where α model R is the satellite elevation angle, R is the Earth's radius, and h is the satellite altitude. The NTN-TDL-D model under line-of-sight conditions is chosen to model the LEO satellite downlink; the channel response expression is:

[0033]

[0034] Where P is the number of channel paths, a n α n τ n and ε m These are the complex gain, delay, angle of arrival, and maximum Doppler shift of the Doppler spacing on the nth path, respectively. Based on the above information, the DD domain channel impulse response is shown below.

[0035]

[0036] In the formula, P represents the total number of multipaths, and h p ,τ p ,ν p These represent the channel gain, time delay, and Doppler offset corresponding to the P-th path, respectively. Among them l p and k p Representing integer delay taps and Doppler taps respectively, κ p This represents the fractional Doppler exponent. Based on these parameters, the effective channel matrix in the time domain of the OTFS system is:

[0037]

[0038] Where Π is the interleaving matrix (positive cyclic shift), representing the effect of delay, and its specific expression is as follows:

[0039]

[0040] This means that each path generates an l p Step cycle time offset, This reflects the Doppler frequency offset characteristics of the channel, where Δ = diag[ω] 0 ,ω 1 ,…,ω MN-1 Simulate the Doppler effect. Let M be a complex exponential basis, describing the phase change in the DD domain. In traditional broadband systems, M is large enough to satisfy l. p Approximate normalization to integers. When N is sufficiently large, the fractional Doppler values ​​can be rounded to integers. Furthermore, to ensure ICI resistance, the CP length should be greater than the maximum delay. The effective channel matrix in the DD domain is then obtained as follows:

[0041]

[0042] The component of the Pth element in the effective channel matrix of the DD domain caused by the Pth path is as follows:

[0043]

[0044] Where a is the DD domain resource cell index at the sending end, and b is the DD domain resource cell index at the receiving end, satisfying 0 ≤ a, b ≤ MN-1. a =a / M represents the discrete Doppler frequency shift corresponding to the transmission resource cell a, l a =ak a M represents the discrete delay corresponding to the transmission resource cell a, l p Let [·] represent the discrete time delay of the P-th path. M This indicates taking the modulo operation with respect to M, ensuring that the index cycles through [0, M-1]. When l... a <l p This indicates that multipath propagation introduces additional time delay differences, requiring the use of a more complex phase term k. a M compensates for this difference, ensuring the phase continuity of the signal in the DD domain; when l a ≥l p Only the weighted sum of path Doppler and delay difference is retained; if b does not satisfy the calculation result of "delay difference cycle + Doppler difference cycle", it means that there is no energy transmission of the p-th path from the transmitting resource cell a to the receiving resource cell b, and the channel gain is 0. For the p-th path, each transmitting resource cell will only map to one receiving resource cell, satisfying b = [l a -l p ] M +M[k a -k p ] N ,therefore Each row and column contains only one non-zero element, thus H DD It is a sparse matrix, with only p non-zero elements in each row and column.

[0045] Preferably, in the second step, the AMP algorithm's linear iteration process includes an "onsager" term to eliminate the correlation between the channel matrix and the estimation result during the iteration process. OAMP adds a divergence-free constraint to the nonlinear estimation to replace the "onsager" term. Simultaneously, in the linear estimation, a decorrelation matrix is ​​used to generalize the original AMP channel matrix so that it is no longer limited to matched filtering. The following three quasi-decorrelation matrices are defined:

[0046] 1) Matched Filter (MF):

[0047]

[0048] 2) False Inverse (PINV):

[0049]

[0050] 3) Linear minimum mean square error (LMMSE):

[0051]

[0052] Matched filters have the lowest computational complexity, requiring only the conjugate transpose, and can maximize SNR, but they do not consider interference and multipath effects. They are suitable for channel matrices H. DD Orthogonal or approximately orthogonal columns exhibit near-optimal performance at high SNR. Pseudo-inverse passes through. H was completely eliminated DD While improving correlation, LMMSE amplifies noise and increases complexity due to the need for matrix inversion. It is suitable for channels with full column rank and small condition numbers (to avoid inversion instability) and performs well in ideal or pilot-assisted channels, but is unstable in ill-conditioned matrices with strong correlation. LMMSE strikes a balance between noise suppression and interference cancellation, minimizing MSE, and is suitable for low to medium SNR or non-ideal channels with strong correlation. LMMSE adaptively adjusts decorrelation strength through noise variance, achieving a complexity comparable to pseudo-inversion but with greater robustness. In the DD domain of OTFS, the channel matrix typically exhibits block sparsity; using MF or PINV may ignore multipath interference, leading to performance degradation. LMMSE simplifies inversion by utilizing sparsity, making it more suitable for OTFS systems.

[0053] Preferably, in the fourth step, the complexity of the MAP detection algorithm is first analyzed, and then the complexity of the proposed Turbo equalizer is analyzed and compared with that of the MAP detection algorithm, showing that, under similar performance conditions, the complexity of the proposed Turbo equalizer is much lower than that of the MAP detection algorithm.

[0054] 1) Complexity of MAP algorithm

[0055] MAP detection is theoretically the optimal signal detection method, but its complexity increases exponentially with system size in OTFS systems. MAP detection requires traversing all possible combinations of transmitted symbols and selecting the sequence with the highest posterior probability (for simplicity, the DD field indices will not be highlighted in the following formulas):

[0056]

[0057] Where |S| represents the modulation order of the modulation symbol table S, and MN is the total number of symbols in the OTFS frame, so there are a total of |S| MN-1 One possibility. A single symbol x a MAP detection can be viewed as excluding x a External |S| MN-1 The marginal posterior probability mass function is calculated from the possible x, i.e.:

[0058]

[0059] According to Bayes' theorem, the above formula can be expressed in the following form.

[0060]

[0061] Treating both noise and signal as random variables with iid distributions, we can obtain

[0062]

[0063] Since fractional Doppler shift is not considered, H DD Each row or column in the array contains only P elements. H... DD The set of real column indices for the non-zero elements in row b and the set of real row indices for the non-zero elements in column a are respectively represented as follows: Formula (43) can be further expressed as:

[0064]

[0065] Where, x [b] This indicates that C is satisfied. b The vector consists of P x's indices in the middle column. Combining this with the formula above, we can see the final... The expression is shown below.

[0066]

[0067] Even with OTFS modulation technology, H DD Despite its sparsity property, the MAP detection algorithm still achieves a time complexity of O(|S|). P(P-I)MN ).

[0068] 2) The complexity of the proposed Turbo equalizer

[0069] The total complexity of the Turbo equalizer consists of nested outer and inner iterations. Considering M is the number of subcarriers and N is the number of time slots, the complexity of the LDPC decoder is O(E·I). LDPC ), where E represents the check variable (usually 3 times the code length), I LDPC This represents the number of decoding iterations. The EM is primarily responsible for residual power calculation and exponential smoothing, with a complexity of O(MN). The complexity of the EM-OAMP detector is O(PMN·I). OAMP Here, P represents the channel sparsity. Therefore, the overall complexity of the Turbo equalizer is O(I0). Turbo ·[I OAMP ·SMN+EI LDPC ]). Among them, I Turbo This indicates the number of Turbo's outer iterations.

[0070] 3) Comparison of the complexity of MAP detector and Turbo equalizer

[0071] The parameter is set as follows: ITurbo =5, I LDPC =5, I OAMP With P=3, M=64, N=32, code length 2048, and using 64QAM for symbol mapping, the total complexity of the EMA-OAMP detector is approximately 5 × 3 × 5 × 2048 ≈ 1.5 × 10⁻⁶. 5 The complexity of the LDPC decoder is approximately 5 × 5 × 6144 ≈ 1.5 × 10⁻⁶ times per frame; 5 Therefore, the complexity of the entire Turbo equalizer is approximately 3 × 10⁻⁶ times per frame. 5 The time complexity is 64 times per frame. However, if the MAP detection algorithm is used, the overall complexity will reach 64. 5×4×64×32 Even with full utilization of the sparsity of the channel matrix, the complexity still far exceeds that of the proposed Turbo equalization scheme.

[0072] The model involved in this invention is as follows:

[0073] Network Model

[0074] The primary application of this invention is the downlink of LEO satellite communication, such as... Figure 1 As shown, when LEO satellites transmit messages to ground users, the high-speed relative motion between the satellite and the ground receiver causes a Doppler shift that disrupts the orthogonality between subcarriers. Simultaneously, reflections of the satellite's transmitted signals from other ground structures create scattering paths, causing multipath interference to the ground receiver. Therefore, the LEO satellite downlink channel is a time-frequency dual-selection channel that simultaneously incorporates Doppler shift and multipath effects, posing a challenge to the ground receiver in correctly receiving information transmitted by the satellite.

[0075] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions.

[0076] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0077] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0078] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A Turbo equalization method in a low-Earth orbit satellite OTFS system, characterized in that, Includes the following steps: S1: Design a signal detector based on the EMA-OAMP expectation-maximization assisted orthogonal approximation message passing algorithm, perform linear and nonlinear estimation processing on the signal after OTFS orthogonal time-frequency conditioning, calculate the posterior mean and variance, and calculate the real-time noise variance through dynamic learning; S2: Construct a Turbo equalizer, cascade the EMA-OAMP detector with the LDPC low-density parity-check decoder, calculate the external log-likelihood ratio based on the posterior mean and variance output by the EMA-OAMP detector, and calculate the total probability of the estimated symbol after LDPC decoding and the updated mean and variance. S3: Define the internal iteration relative error and the external iteration relative error, and propose an externally dominated two-layer iteration termination strategy for the constructed Turbo equalizer. S4: Calculate the complexity of the EMA-OAMP detector and LDPC decoder, then calculate the overall complexity of the Turbo equalizer by combining the number of internal and external iterations, and compare and analyze it with the complexity of the maximum a posteriori probability (MAP) algorithm.

2. The Turbo equalization method in a low-Earth orbit satellite OTFS system according to claim 1, characterized in that, Step S1 involves designing a detector based on the EMA-OAMP algorithm to detect and process the signal modulated by OTFS and dynamically estimate the system noise variance. The specific process is as follows: Define the bitstream signal generated by the satellite transmitter as b = {b1, b2, ..., b} B After LDPC encoding, the encoded vector c = {c1, c2, ..., c} is obtained. K After interleaving, we get d = {d1, d2, ..., d} K }, which is then mapped to the symbol sequence x. d ={x1,x2,…,x X }, and the symbol sequence x d Rearranged into an M×N dimension DD time-delay Doppler domain signal matrix X DD ; For the signal matrix X in the DD domain DD To perform OTFS modulation, the inverse symplectic finite Fourier transform is first performed to obtain the signal matrix in the TF domain; Among them, F M This indicates performing an M-point Fourier transform in the time delay dimension. This indicates an N-point inverse Fourier transform in the Doppler dimension; when the subcarrier spacing is Δf and the time interval is T, the duration and bandwidth of the entire transmitted signal matrix are NT and MΔf, respectively; subsequently, X... TF Perform a Heisenberg transformation and add a pulse-shaped waveform matrix G with a duration of [0, T). tx Obtain a time-domain signal matrix suitable for channel transmission; After the time-domain signal passes through the NTN-TDL-D non-terrestrial network tapped delay line-D simulated time-domain effective channel, the time-domain signal received by the ground receiver is: y T (t)=∫∫h(τ,ν)e j2πν(t-τ) x T (t-τ)dτdν+z T (t) (3) Where z T (t) represents additive white Gaussian noise in the time domain, τ and ν represent the time delay and Doppler symbol, respectively, h(τ,ν) represents the channel impulse response in the D-domain, and x T (t-τ) represents the time-domain signal transmission vector with a time delay of τ, and finally the expression of the received vector after OTFS demodulation is obtained; Among them, I M H represents an identity matrix of dimension M×M. DD The channel matrix in the DD domain, z DD Represents the noise vector in the DD domain, x DD Represents the signal vector in the DD domain; Based on OAMP, an EM expectation-maximization module is added to improve signal detection accuracy by dynamically learning the system noise variance. This improves the signal detection accuracy after OTFS demodulation. DD and H DD The data is fed into the EMA-OAMP detector for linear estimation (LE) and nonlinear estimation (NLE), as shown in the following expressions: AND:r t =you t-1 +W t (y DD -H DD you t-1 ) (5) Where t represents the number of iterations, r t U represents the linear estimation result of the t-th iteration. t-1 W represents the result of the (t-1)th iteration nonlinear estimation. t Let u represent the decorrelation matrix for the t-th iteration. t+1 This represents the result of the (t+1)th iteration nonlinear estimation. Let R = x be an arbitrary component of the Lipzig continuous function in the t-th iteration. DD +τ t z DD Indicates that y DD =H DD x DD +z DD The hybrid model in the middle is decoupled for signal x DD AWGN observations, η t Represents a nonlinear decorrelation function that satisfies C t It is an arbitrary constant; LE can eliminate interference caused by multipath interference and Doppler shift. In the NLE step... This is a compensation for the "noise statistical characteristics." Subtracting this term weakens the influence of Gaussian noise and improves the estimation accuracy. Formula (6) can be further simplified to in γ is used to adjust the scaling ratio of NLE output. t Let P(u) represent the posterior variance in the t-th iteration. By iterating through these two estimators, the posterior probability P(u) is obtained. t+1 |y DD H DD It is decomposed into a series of Reduce the complexity of this step; the error recursion (ER) corresponding to LE and NLE is: ER-LE:h t =r t -x=B t q t-1 +W t n (7) ER-NLE:q t+1 =u t+1 -x=η t (h t +x)-x (8) Among them, B t =I MN -W t H DD Let W represent the linear transformation matrix for error propagation in the t-th iteration. t B represents the decorrelation matrix for the t-th iteration; t q t-1 Indicates the previous NLE error q t-1 After linear transformation B t Propagation error, W t n represents the noise after linear transformation W t The introduced error; the MSE corresponding to LE and NLE are respectively: Where h t+1 Let q represent the LE error recursion in the (t+1)th iteration. t+1 Let σ represent the NLE error recursion in the (t+1)th iteration. 2 This represents the noise variance after the EM module has learned it. Further empirical estimation of the NLE estimation error: The final posterior mean μ t and posterior variance γ t The calculation formulas are as follows: s k =[s k,1 ,s k,2 [0,0],[0,1],[1,0][1,1],k=1,2,3,4 represent complex symbols modulated using QPSK, and the corresponding modulation constellation set is... The EM algorithm dynamically corrects noise parameters by maximizing the likelihood function, ensuring that the error orthogonality constraint is always satisfied in each iteration.

3. The Turbo equalization method in a low-Earth orbit satellite OTFS system according to claim 2, characterized in that, The EM algorithm consists of an E-step and an M-step, which are specifically implemented in OAMP as follows: First, calculate the current estimated noise variance using the E-step. log-likelihood expectation This represents the noise variance after the nth symbol EM module has learned it; Then, the noise variance is updated by maximizing the expected likelihood through M steps. In OAMP, the closed-form solution is the formula provided by the user, as shown below; EM steps are adjusted in real time. This adapts the linear estimator of OAMP to the current channel state.

4. The Turbo equalization method in a low-Earth orbit satellite OTFS system according to claim 3, characterized in that, Step S2 constructs a Turbo equalizer by cascading the EMA-OAMP detector and the LDPC decoder. The EMA-OAMP detector outputs extrinsic information to the LDPC decoder, and the extrinsic information corrected by the LDPC decoder is then fed back to the EMA-OAMP detector. Specifically, this includes calculating the external log-likelihood ratio, calculating the total symbol probability, and updating the mean and variance. To obtain full-channel diversity gain, the receiver needs to calculate the gain of each bit relative to the entire received sequence y. DD The posterior probability P(d) n,j |y DD ), where d n =[d n,1 ,d n,2 ] is relative to the symbol x n Interleaved bits; estimated symbols by computation To estimate P(d) using the posterior probability n,j |y DD ): in, Represents the nth modulation symbol x n The estimated value, d n,j Represents the nth modulation symbol x n The j-th bit in the corresponding interleaved bits, Indicates the sign estimate Under the condition, bit d n,j The posterior probability of taking b, Π j′:j′≠j P(d n,j′ ) represents the bits d for all j′≠j. n,j′ The product of prior probabilities This indicates that in the bit vector d n Under the condition, the symbolic estimate The conditional probability function; The first term in the above equation is the external log-likelihood ratio. The first term represents the difference between the posterior and prior information, i.e., the information extracted from the equalizer that is irrelevant to the current bit. In the OAMP algorithm, this can be seen as passing on the "new discovery of the current node" to other nodes to avoid information reuse. The second term is defined as the prior information output by the decoder. This indicates that "initial assumptions" are provided for the current iteration, and the two should remain strictly independent. For ease of calculation... Assumption It follows a Gaussian distribution, i.e. in, To estimate the error The mean, For e n,k The variance. Directly calculate the external message. and It's rather complex; we define the prior distribution of the transmitted symbol sequence as a complex Gaussian distribution. The prior mean here This indicates that the LLR output from the LDPC decoder in the (i-1)th Turbo iteration is obtained through a nonlinear transformation. n They are approximately independent, and the estimated posterior distribution can be expressed as: Similarly, the posterior mean μ here n By fusing observation data and prior information p(x) n The Bayesian estimate obtained has an estimation error compared to... Significantly reduced, This represents the external log-likelihood ratio, where the ratio is... middle The solution for the term can be written in the following form: Where, x n The external variance and mean are as follows: Substitution The expression can be obtained as follows: If quadrature phase shift keying (QPSK) with Gray mapping is used, then x n The external LLRs of the two code points carried can be represented as: The result Deinterleaving is performed to obtain the decoding prior external This information is passed to the decoder as prior information; after decoding, the decoder outputs the decoded a posteriori external information. The encoded posterior externality is obtained through interleaving operations. Considering the definition of LLR, the final estimated total probability P(x) of the symbol is obtained. n =s k The expression for ) is shown below; Where sgn(.) represents the symbol function, and tanh(.) is the hyperbolic tangent function, which converts the decoded external LLR into probabilistic information of the symbol, satisfying... The updated mean and variance can be expressed as follows: The updated mean and variance will then be used as prior information to feed into the EMA-OAMP detector to generate new posterior information, thereby providing the optimal estimate of the mean and variance of the variables.

5. The Turbo equalization method in a low-Earth orbit satellite OTFS system according to claim 1, characterized in that, Step S3 defines the internal iteration relative error and the external iteration relative error, and proposes an externally dominated two-layer iteration termination strategy for the constructed Turbo equalizer, specifically including: The core of the designed Turbo equalizer is to iterate over external information between the detector and decoder. Within the EMA-OAMP detector, there are also iterations between the LE module and the NLE module, and between the NLE module and the EM module. Therefore, stopping conditions need to be set hierarchically to control the t-th iteration of the EMA-OAMP detector. inner The estimate of the second inner iteration is expressed as t inner The estimate after -1 inner iterations is expressed as Define the internal iteration relative error: The internal iteration error threshold is denoted as δ. inner When ∈ inner ≤δ inner When the signal estimation of the detector is considered sufficiently stable, iteration can be stopped even if the number of iterations has not reached the maximum value, because continuing iteration contributes very little to improving accuracy; when the number of iterations has reached the set maximum number of iterations, even if ∈ inner >δ inner The internal iteration process also stops; after the internal iteration stops, soft information is output to the LDPC decoder. The core of Turbo iteration is the convergence of soft information, allowing the Turbo equalizer to achieve its t-th iteration. outer The external information output by the next iteration decoder and detector are respectively and Define the external iteration relative error: Set the outer iteration threshold to 10 times the inner iteration threshold, i.e., δ outer ≈10·δ inner When ∈ outer ≤δ outer This indicates that the external information no longer changes significantly, and the Turbo iteration converges; additionally, if the external iteration reaches the set maximum number of iterations, ∈ still exists. outer >δ outer In order to reduce complexity, the entire system iteration process will also be terminated.

6. The Turbo equalization method in a low-Earth orbit satellite OTFS system according to claim 5, characterized in that, When the inner iteration stopping condition is met first, the inner iteration ends, but the outer iteration continues until the outer iteration stopping condition is met, and the system converges. When the outer iteration stopping condition is met first, the outer iteration stops, the inner iteration terminates directly, and the system converges. When the inner iteration converges but the outer iteration does not converge due to excessively high LDPC code rate or burst noise in the channel, the system will terminate the inner iteration. The Turbo equalizer further optimizes the signal estimation based on this stable soft information through cyclic processing of interleaving, mapping, and decoding until the outer convergence condition is met. Conversely, if the outer iteration has converged but the inner iteration has not, the entire iteration process is terminated directly. The Turbo equalizer adopts this outer-dominated dual-layer termination condition strategy. When the iteration process meets the termination condition, the system uses the extrinsic information output by the last EMA-OAMP detector as prior information input to the LDPC decoder. The LDPC decoder uses external information exchange between variable nodes and check nodes to make the detection performance of the Turbo equalizer monotonically increase with the number of iterations, and the final bit error rate performance of the system can approach the theoretically optimal MAP detector.

7. A storage medium that internally stores a computer program, characterized in that, When the computer program is read by the processor, step S6 executes the Turbo equalization method in the low-orbit satellite OTFS system as described in any one of claims 1 to 6.

Images