Multi-slot MAMP receiver and coding method for MIMO multicarrier modulation system

Abstract

The invention discloses a multi-time slot MAMP receiver and coding method for an MIMO multicarrier modulation system, comprising a time domain linear estimation module gamma l (.) and a symbol domain nonlinear estimation module phi l (.), where l represents the number of iterations; the time domain linear estimation module adopts a matched filter to recover the received time domain signal to obtain an estimated value of the time domain signal; transforming the estimated value into a symbol domain through unitary transformation; and the symbol domain nonlinear estimation module calculates a log-likelihood ratio of each symbol and calculates an estimated value of each symbol through estimation of the symbol domain returned by the time domain linear estimation module. According to the method, the optimal MSE detection performance can be realized with extremely low complexity in a multi-time-slot transmission scene.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-carrier modulation systems, and particularly relates to a multi-slot MAMP receiver and coding method for a MIMO multi-carrier modulation system. Background Art

[0002] In terms of the detection algorithms of multi-carrier modulation systems, common linear detection algorithms, such as Linear Minimum Mean Square Error (LMMSE) and Zero Forcing (ZF) algorithms, have been widely applied to OFDM, OTFS, and AFDM systems. For example, for the OTFS system, a low-complexity iterative LMMSE detection algorithm was proposed in the paper "Low complexity Turbo SIC-MMSE detection for orthogonal time frequency space modulation". Although linear detection algorithms are simple to implement, they usually ignore the prior information inherent in the signals. In contrast, non-linear iterative detection algorithms can utilize the prior information of both the received signals and the signals to be estimated simultaneously, and achieve reliable signal recovery through iterative interference cancellation. For example, for the OTFS system, low-complexity Gaussian Message Passing (GMP) and Expectation Propagation (EP) algorithms have been successively proposed;

[0003] To further utilize the sparsity of the time-domain channel, the paper "Cross domain iterative detection for orthogonal time frequency space modulation" proposed a robust orthogonal approximate message passing algorithm (Cross Domain-Orthogonal Approximate Message Passing, CD-OAMP); for the interleaved frequency division multiplexing (Interleave Frequency Division Multiplexing, IFDM) system, the paper "Interleave frequency division multiplexing" proposed a low-complexity MSE-optimal memory approximate message passing algorithm (Cross Domain-Memory Approximate Message Passing, CD-MAMP) detection algorithm. However, CD-MAMP still has defects: it only considers the case of single-slot transmission, that is, the channel is invariant during data transmission, which cannot be fully guaranteed in actual communication systems.

[0004] Regarding the research on coded multi-carrier systems, under the assumption that the length of the coded word is equal to the dimension of the modulation matrix, the paper "Performance Analysis of Coded OTFS Systems over High-Mobility Channels" analyzed the upper bound of the performance of coded OTFS systems based on the conditional pairwise error probability (PEP) in 2021 and revealed the trade-off relationship between the coding gain and the diversity gain of coded OTFS systems; the paper "Error Performance of Coded AFDM Systems in Doubly Selective Channels" obtained the upper bound of its performance by studying the conditional PEP of coded AFDM systems in 2023 and gave the trade-off relationship between the coding gain and the diversity gain; the paper "Exploiting the Joint Sparsity for LDPC-Enhanced Delay-Doppler Multicarrier Modulation: A Parallel Belief Propagation-Based Approach" proposed a joint signal detection and decoding algorithm for coded multi-carrier systems based on low-density parity-check (LDPC) codes in 2024.

[0005] The above work is all based on the assumption that the length of the coded codeword is equal to the dimension of the modulation matrix. This assumption cannot be satisfied in most scenarios of actual communication systems because the amount of data transmitted in the actual system is too large, and it is still difficult to implement the modulation matrix of the corresponding dimension in hardware. It is necessary to segment the actual data before modulation. Therefore, the most important defect of the above work is that the assumption followed is difficult to implement in the actual system.

[0006] For the detection algorithms applied to multi-carrier systems mentioned above, the commonly used linear estimation algorithms usually ignore the prior information of the signal and are generally not optimal. For non-linear iterative algorithms: when there are a large number of short cycles in the factor graph constructed based on the transform domain channel matrix, the GMP algorithm has the possibility of divergence; the computational complexities of the EP algorithm and the CD-OAMP algorithm are very high, which limits their applications in large-scale systems; when the system scale is large, the CD-MAMP algorithm can guarantee the detection performance while reducing the computational complexity. However, all of the above algorithms only focus on the signal estimation and detection of uncoded systems and ignore the impact of coding constraints on signal detection. Therefore, they cannot accurately reflect the error-free recovery ability of the actual system. In addition, most of the existing detection algorithms are based on the assumption of an invariant channel. However, in actual high-mobility scenarios, the channel changes rapidly, resulting in the deterioration of the performance of existing detectors.

[0007] In terms of the design of channel coding schemes, most of the existing coding scheme designs for multi-carrier modulation systems are limited to traditional point-to-point channels, which can only overcome channel noise and cannot overcome the inter-symbol interference caused by delay spread and Doppler frequency shift in high-mobility scenarios. In addition, most of the existing information-theoretic limit analyses for multi-carrier modulation systems are limited to ideal Gaussian signals or simple linear receivers, and do not deeply study the information-theoretic limits under the constraints of actual discrete input signals, resulting in the inability to effectively guide the design of transceivers in actual communication systems. Moreover, the performance analysis and coding scheme design of existing coded multi-carrier modulation systems both rely on the ideal assumption that the coding length is equal to the dimension of the modulation matrix, and it is difficult to be used to guide the design of actual coding and decoding schemes.

[0008] In terms of detection: The design of detection algorithms is all based on the assumption of transmission within a single time slot, ignoring the situation of signal transmission in multiple time slots and not fully considering the impact of coding and decoding on the actual system.

[0009] Coding: Most only consider Gaussian channels and design traditional point-to-point coding, which can only resist the influence of channel noise and cannot resist Doppler frequency shift and delay;

[0010] System limit performance: Most of the existing theoretical limit analyses are limited to the assumption of Gaussian signals, and there is still a lack of research on the system theoretical limits for arbitrary discrete inputs.

[0011] The combination of multi - carrier modulation and Multiple Input Multiple Output (MIMO) technology is crucial for the reliable transmission of wireless signals in complex environments and can significantly improve spectral efficiency. Existing research shows that in an uncoded doubly - selective channel, Orthogonal Time Frequency Space (OTFS) modulation and Affine Frequency Division Multiplexing (AFDM) have significant advantages over Orthogonal Frequency Division Multiplexing (OFDM). However, it is still uncertain whether these advantages can be extended to coded systems. Meanwhile, the analysis of the channel capacity limit of coded MIMO multi - carrier systems and the design of corresponding low - complexity and high - reliability receivers are still unclear. Summary of the Invention

[0012] To address the above - mentioned deficiencies of the prior art, the purpose of the present invention is to provide a multi - slot MAMP receiver and coding method for MIMO multi - carrier modulation systems, which considers the problem of multi - slot transmission. In an actual communication system, the transmission of a large amount of data leads to the fact that the transmitted data must pass through multiple time slots, and the corresponding channel will also change. Under multi - slot transmission, it can achieve the optimal detection of MSE with extremely low computational complexity and reach the information - theoretic limit performance.

[0013] To achieve the above purpose, the technical solution adopted by the present invention is:

[0014] A multi - slot MAMP receiver for a MIMO multi - carrier modulation system, including a time - domain linear estimation module and a non - linear estimation module in the symbol domain where represents the number of iterations;

[0015] The time - domain linear estimation module uses a matched filter to recover the received time - domain signal and obtain an estimated value of the time - domain signal;

[0016] Transform the estimated value to the symbol domain through unitary transformation;

[0017] The non - linear estimation module in the symbol domain calculates the log - likelihood ratio of each symbol and the estimated value of each symbol through the estimated value returned by the time - domain linear estimation module.

[0018] The MIMO multi-carrier modulation system is configured with J transmit antennas and U receive antennas. The transmitted signal passes through multiple time slots and experiences different channel fades. x j,t represents the signal transmitted by the J-th transmit antenna in the t-th time slot. Then, the time-domain received signal in the t-th time slot is expressed in the following form:

[0019] y t =H t x t +w t ,

[0020] where represents the signals transmitted by all antennas in the t-th time slot, represents the received signals of U receive antennas, represents the channel matrix, represents the channel additive white Gaussian noise.

[0021] Furthermore, the time-domain linear estimation module comprises memory-matching filters a serial-to-parallel conversion module, an orthogonality module, and a damping factor, represents the total number of time slots through which the transmitted signal passes;

[0022] The damping factor is used to ensure that the algorithm can converge and accelerate the convergence speed.

[0023] The memory-matching filter is used for time-domain signal estimation. The input of the time-domain linear estimation module is multiplied by the conjugate transpose of the channel (H H ). "Memory" is reflected in that each output estimation value depends on the previous estimation values;

[0024] The serial-to-parallel conversion module is used to convert the received serial signal that has passed through multiple time slots into different time-slot parts through serial-to-parallel conversion;

[0025] The orthogonality module is used to eliminate the correlation between the input and output of the detection module. The outputs of time-domain detection and symbol-domain detection need to pass through the orthogonality module to eliminate the correlation with the input signal.

[0026] The damping factor is used to ensure that the algorithm can converge and accelerate the convergence speed.

[0027] Furthermore, the time-domain linear estimation module, based on the signals received in different time slots and the prior information of the transmitted signals updated by the non-linear end obtains the estimated value of the transmitted time-domain signal through the memory-matching filter, the serial-to-parallel conversion module, and the orthogonality module Among them, M is the total signal length, J represents the number of antennas, N represents the data length transmitted on one antenna within a time slot, and the iteration index starts from Start and initialize Estimate the signal Satisfy:

[0028]

[0029] Represents the signal of the input time-domain module in multiple time slots; Represents at the Combination of the estimated signals of all time slots during the Represents the estimated signal of the t-th time slot after serial-to-parallel conversion, while the input signal Is based on And the prior information of the transmitted signal updated at the non-linear end And obtained through a damping operation:

[0030]

[0031] Among them, Represents the damping vector of the linear weighted superposition of all estimated signals, Is a low-complexity memory matching filter based on the estimation results of previous iterations, and is expressed as follows:

[0032]

[0033] Is expressed as follows:

[0034]

[0035] Among them, Represents the estimated value, And Represents The maximum and minimum eigenvalues; the scaling coefficient Is to accelerate the convergence speed of the MS-CD-MAMP receiver, Is the theoretically optimal damping vector, And Represent the normalization coefficient and the orthogonalization coefficient respectively.

[0036] This variable represents the estimated signal obtained in each time slot. Since the signals in different time slots are processed in parallel, the serial-to-parallel conversion is to recombine all the Into a vector and then orthogonalize it with the input to obtain

[0037] The Inverse Uniform Transform (IUT) performs a cross-domain operation from the time domain to the symbol domain through the IUT, and the signal input to the non-linear detection module in the symbol domain and variance are calculated by the following formula:

[0038]

[0039] represents the identity matrix, and A represents the corresponding modulation matrix, that is, the transformation matrix of the unitary transform / inverse unitary transform.

[0040] The symbol domain non-linear estimation module includes a demodulator and an orthogonalization module, and the estimated signals of the two modules are iteratively updated through cross-domain operations;

[0041] For the input estimated signal, the demodulator calculates the estimated symbol by calculating the log-likelihood ratio of each symbol;

[0042] The orthogonalization module removes the correlation between the estimated signal output in the symbol domain and the input signal in the symbol domain.

[0043] The demodulator includes symbol-by-symbol MMSE demodulation operation and a posteriori probability (A-Posterior Probability, APP) decoding, and the output of the symbol domain non-linear estimation function is expressed as follows:

[0044]

[0045] where the parameter is a scalar determined by minimizing the mean square error, represents the orthogonalization parameter, in, the APP calculated for the k-th symbol of is expressed as follows:

[0046]

[0047] where χ ∈ S, and S represents the constraint constellation points of the transmitted symbols. After calculating the a posteriori estimate, the output variance of the symbol domain non-linear estimation module can be obtained accordingly :

[0048]

[0049] Inverse unitary transform: from the symbol domain to the time domain;

[0050] Unitary Transform: From Time Domain to Symbol Domain.

[0051] The unitary transform (Uniform Transform, UT) performs a cross-domain operation from the symbol domain to the time domain through UT;

[0052] The signal input to the linear detection module in the time domain and variance are calculated by the following formula:

[0053]

[0054] After one iteration, an input to the input time-domain linear estimation module is obtained again. Repeating this iterative process, the result of the last iteration will converge to the optimal MSE value, and this convergence value is used as the final output.

[0055] A coding method for a multi-slot MAMP receiver for a MIMO multi-carrier modulation system includes the following steps;

[0056] The time-domain linear detection module uses memory-matched filtering and utilizes the covariance matrix of state evolution to evaluate the asymptotic performance of the multi-slot cross-domain MAMP receiver (MS-CD-MAMP receiver), that is:

[0057]

[0058] Through the covariance calculated between the time-domain linear estimation module and the symbol-domain non-linear estimation module, that is, γ SE (·) and are represented by the MSE function of, that is:

[0059]

[0060] As the number of iterations increases, the iterative covariance matrix becomes high-dimensional and complex, making it difficult to directly analyze. According to the fixed-point consistency of the MS-CD-MAMP algorithm and the MS-CD-OAMP algorithm, the MSE transfer function of the MS-CD-OAMP algorithm can be equivalently transformed into a single-input single-output form similar to MS-CD-OAMP. For the same APP decoder By combining orthogonal, cross-domain, and damping operations into the time-domain linear estimation module, an equivalent MS-CD-MAMP receiver is obtained;

[0061] At this time, the linear and non-linear ends of the MS-CD-MAMP receiver are represented in the following form:

[0062]

[0063] Based on the above formula, the detection curve of the MS-CD-MAMP receiver is obtained. Further, based on the I-MMSE theorem, the maximum achievable rate of the MS-CD-MAMP receiver can be calculated. Then, the corresponding decoding curve is designed to fit the detection curve, and the parameters of the LDPC code are designed according to the transition relationship of the decoding curve.

[0064] The multi-slot MAMP receiver is applicable to multi-carrier modulation with any unitary matrix as the modulation matrix, such as OFDM, OTFS, AFDM, or IFDM.

[0065] The multi-slot MAMP receiver is also applicable to single-antenna and multi-antenna scenarios.

[0066] Advantages of the present invention:

[0067] The present invention considers the problem of multi-slot transmission. In an actual communication system, the transmission of a large amount of data causes the transmitted data to necessarily pass through multiple time slots, and the corresponding channel will also change. Under multi-slot transmission, MSE-optimal detection can be achieved with extremely low complexity.

[0068] The MS-CD-MAMP receiver proposed by the present invention has a significant advantage in terms of computational complexity.

[0069] The present invention compares the bit error rate performance of LDPC codes optimized based on the optimal coding principle and traditional point-to-point designed coding schemes in multi-carrier modulation systems such as OTFS / AFDM / OFDM. Compared with the traditional point-to-point coding scheme, the optimal coding scheme given by the present invention has a significant gain. Description of the Drawings

[0070] Figure 1 Schematic diagram of the coded multi-carrier system

[0071] Figure 2 Frame of the MS-CD-MAMP receiver

[0072] Figure 3 Frame of the equivalent MS-CD-MAMAP receiver

[0073] Figure 4 VSE of the equivalent MS-CD-MAMP receiver

[0074] Figure 5 VSE transfer curve of the MS-CD-MAMP receiver

[0075] Figure 6 Bit error rate performance of MS-CD-MAMP and MS-CD-OAMP receivers under the MS-CD-MAMP and MS-CD-OAMP receiver schemes designed based on the optimized coding scheme, point-to-point regular LDPC code, and irregular LDPC code Detailed Embodiments

[0076] The present invention will be further described in detail below with reference to the accompanying drawings.

[0077] The combination of multi-carrier modulation and multiple-input multiple-output (MIMO) technology is the key to reliable wireless signal transmission in complex environments, which can significantly improve the spectrum utilization rate. However, the information-theoretic limit analysis for coded MIMO multi-carrier systems and the corresponding low-complexity and high-reliability receiver design are still unclear. Therefore, the present invention proposes an MS-CD-MAMP receiver and analyzes its information-theoretic limit and optimal coding scheme in multi-carrier MIMO systems.

[0078] The present invention proposes a low-complexity and high-reliability MS-CD-MAMP (Multi-Slot-Cross-Domain-Memory-Approximate-Message-Passing) receiver for coded MIMO multi-carrier modulation systems, and analyzes its information-theoretic limit and optimal coding criterion for coded MIMO multi-carrier modulation systems.

[0079] As Figure 1 shown, the coded MIMO multi-carrier modulation system model:

[0080] Consider a coded MIMO multi-carrier modulation system with J transmit antennas and U receive antennas. Since a large amount of data needs to be transmitted, the transmitted signal usually goes through multiple time slots and experiences different channel fades. x j,t represents the signal transmitted by the Jth transmit antenna in the tth time slot. Then, the time-domain received signal in the tth time slot is expressed in the following form:

[0081] y t = H t x t + w t ,

[0082] where represents the signals transmitted by all antennas in the tth time slot, represents the received signals of U receive antennas, represents the channel matrix, represents the channel additive white Gaussian noise.

[0083] As Figure 2 shown, the MS-CD-MAMP receiver: For the coded MIMO multi-carrier modulation system, Figure 2 The framework of the MS-CD-MAMP receiver proposed by the present invention is given:

[0084] The MS-CD-MAMP receiver includes a time-domain linear estimation module and a non-linear estimation module in the symbol domain wherein represents the number of iterations; Time-domain linear estimation module: A matched filter is adopted to recover the received time-domain signal, that is, to obtain the estimated value of the time-domain signal;

[0085] After obtaining the estimated value of the time-domain signal, it is transformed to the symbol domain through unitary transformation and then the symbol domain is estimated;

[0086] Symbol-domain non-linear estimation module: Through the estimated value returned by the linear estimation module, calculate the log-likelihood ratio of each symbol and calculate the estimated value of each symbol. Time-domain linear estimation module contains memory matched filters serial-to-parallel conversion module, orthogonalization module, and damping operation, represents all the time slots that the transmitted signal has passed through; Memory matched filter: Used for time-domain signal estimation, multiply the input of the time-domain linear estimation module by the conjugate transpose of the channel (H H ), and the "memory" is reflected in that the estimated value of each output depends on the previous estimated value;

[0087] Serial-to-parallel conversion: Since the received serial signal passes through multiple time slots, serial-to-parallel conversion is required to distinguish the parts of the signal passing through different time slots;

[0088] Orthogonalization module: To eliminate the correlation between the output estimated value and the input;

[0089] The symbol-domain non-linear estimation module consists of a demodulator and an orthogonalization module, and the estimated signals of the two modules are iteratively updated through cross-domain operations. Demodulator: Calculate the estimated symbol by calculating the log-likelihood ratio of each symbol;

[0090] Orthogonalization module: Remove the correlation between the input signal and the output signal.

[0091] Next, each module will be further introduced.

[0092] 1. Time-domain signal detection: The time-domain linear estimation module is based on the signals received within different time slots and the prior information of the transmitted signal updated by the non-linear end to estimate the transmitted time-domain signal through the memory matched filter, serial-to-parallel conversion, and orthogonalization module where M is the total length of the signal, is the number of time slots, J represents the number of antennas, N represents the data length transmitted on one antenna within a time slot, and the iteration index starts from Start and initialize Estimate the signal Satisfy:

[0093]

[0094] Among them, Represents the combination of estimated signals for all time slots in the th iteration, Represents the estimated signal in the t-th time slot after serial-to-parallel conversion, and the input signal Is based on The prior information of the transmitted signal updated by the non-linear end And obtained through a damping operation:

[0095]

[0096] Among them, Indicates the damping vector of the linear weighted superposition of all estimated signals, which can theoretically ensure accelerating the convergence speed of the MAMP algorithm, Is a low-complexity memory matching filter based on the estimated results of previous iterations, expressed as follows:

[0097]

[0098] Expressed as follows:

[0099]

[0100] Among them, Represents the estimated value, And Indicates The maximum and minimum eigenvalues; correspondingly, the scaling coefficient Is to accelerate the convergence speed of the MAMP receiver, Is the theoretically optimal damping vector, And Represent the normalization coefficient and the orthogonalization coefficient respectively.

[0101] 2. Inverse Uniform Transform (IUT): Perform a cross-domain operation from the time domain to the symbol domain through IUT,

[0102] The signal input to the non-linear detection module in the symbol domain And the variance Are calculated by the following formula:

[0103]

[0104] denotes the identity matrix, and A denotes the corresponding modulation matrix, i.e., the transformation matrix of the unitary transform / inverse unitary transform;

[0105] 3. Symbol-domain non-linear estimation module: Symbol non-linear estimation function includes a demodulator and an orthogonalization module;

[0106] wherein the demodulator includes symbol-by-symbol MMSE demodulation operation and a posteriori probability (A-Posterior Probability, APP) decoding, and the output of the symbol non-linear estimation function is expressed as follows:

[0107]

[0108] where the parameter is a scalar determined by minimizing the mean square error, denotes the orthogonalization parameter, in, the APP calculated for the k-th symbol of is expressed as follows:

[0109]

[0110] where χ ∈ S, and S represents the constellation points of the transmitted symbols. After calculating the a posteriori estimate, the output variance of the symbol-domain non-linear estimation module can be obtained accordingly :

[0111]

[0112] Inverse unitary transform: From the symbol domain to the time domain;

[0113] Unitary transform: From the time domain to the symbol domain;

[0114] 4. Unitary transform (Uniform Transform, UT): Perform cross-domain operations from the symbol domain to the time domain through UT;

[0115] The signal input to the linear detection module in the time domain and variance are calculated by the following formula:

[0116]

[0117] After one iteration, an input to the input time-domain linear estimation module is obtained again. The iterative process is repeated, and the result of the last iteration will converge to the optimal MMSE value. This convergence value is then used as the final output.

[0118] The encoding method of the MS-CD-MAMP receiver includes the following steps;

[0119] In the time-domain linear detection module, memory-matched filtering is adopted, and the covariance matrix of state evolution is used to evaluate the asymptotic performance of the MS-CD-MAMP receiver, that is:

[0120]

[0121] According to the orthogonality and independent and identically distributed characteristics, the asymptotic MSE performance of the MS-CD-MAMP algorithm is determined by the covariance calculated between the time-domain linear estimation module and the symbol-domain nonlinear estimation module, namely γ SE (·) and The MSE function of is represented as:

[0122]

[0123] It can be seen from the above formula that as the number of iterations increases, the iterative covariance matrix becomes high-dimensional, making the analysis complex. Next, it is necessary to transform it so that the MSE transfer function is equivalent to a single-input single-output form similar to MS-CD-OAMP, thereby simplifying the achievable rate analysis of the MS-CD-MAMP algorithm.

[0124] According to the fixed-point consistency of the MS-CD-MAMP algorithm and the MS-CD-OAMP algorithm, for the same APP decoder the multi-dimensional SE of MS-CD-MAMP can converge to the same SE fixed point as the SISO SE of the MS-CD-OAMP algorithm. By incorporating orthogonal, cross-domain, and damping operations into the time-domain linear estimation module, an equivalent MS-CD-MAMP receiver can be obtained. Figure 3 The block diagram of the equivalent MS-CD-MAMP receiver is given.

[0125] At this time, the linear and nonlinear ends of the MS-CD-MAMP receiver are represented in the following form:

[0126]

[0127] To further simplify the theoretical analysis of MS-CD-MAMP, variational SE will be introduced below to analyze the maximum achievable rate of the MS-CD-MAMP receiver:

[0128] Define represent the input signal-to-interference-ratio (SINR) and the output mean squared error (MSE), Figure 4 The variational SE of the equivalent MS-CD-MAMP receiver is given as follows. The specific calculation expression is as follows:

[0129]

[0130] where represents the MSE function of the LMMSE estimator in the MS-CD-OAMP algorithm, represents the inverse of it, represents an additive white Gaussian noise vector independent of s, represents the coding constraint.

[0131] It should be noted that although the VSE cannot accurately characterize the MSE performance of the system, since it can converge to the same fixed point as the SE, it can be used to analyze the achievable rate of the receiver and guide the design of the optimal coding scheme.

[0132] Figure 5 The transfer curve of the VSE is given. Since coding will necessarily bring gain, therefore, in Figure 5 the demodulation transfer curve should be the upper bound of the decoding transfer curve i.e.,

[0133]

[0134] Assume that there is a unique fixed point between and Then, in order to achieve error-free decoding, a decoding channel should exist between and

[0135]

[0136] Therefore, the upper bound of the decoding curve is obtained as:

[0137]

[0138] Based on the I-MMSE theorem, the achievable rate of the MS-CD-MAMP receiver with a fixed decoding transfer function is calculated as:

[0139]

[0140]

[0141] Based on the above analysis and derivation, it can be determined that when this occurs, the MS-CD-MAMP receiver can reach the maximum achievable rate.

[0142] Therefore, the optimal coding principle of the MS-CD-MAMP receiver can be obtained:

[0143] That is, using the decoding transfer curve as the constraint condition and maximizing the code rate as the optimization objective to design the parameters of the encoder, an optimal coding scheme is obtained.

[0144] Figure 6 Figures 1 and 2 in [reference] compare the BER under different paths, showing the BER performance of the MS-CD-MAMP algorithm in an 8×4 MIMO system with the optimized coding scheme, when the number of paths is {2, 5} and the antenna correlation is 0.6. The BER is 10 -5 obtains a gain of approximately 4 dB, indicating that the MS-CD-MAMP algorithm can make full use of multipath diversity.

[0145] Figure 6 In [reference], Figures 3, 4, and 5 compare the BER under different numbers of time slots, showing the BER of the MS-CD-MAMP algorithm in 8×8 and 4×4 MIMO systems with the optimized coding scheme when the number of time slots is {1, 5, 25}. When the number of time slots is 5 and 1, there is a performance loss of approximately 0.2 - 0.5 dB and 0.6 - 0.8 dB compared to when the number of time slots is 25. However, compared to when the number of time slots is 25, there is still a performance gain with the traditional point-to-point regular LDPC code and irregular LDPC code coding schemes. This illustrates the importance of designing an optimized coding scheme in a MIMO multi-carrier system.

[0146] Figure 6 Figure 6 in [reference] compares the BER at different speeds, showing the BER of the MS-CD-MAMP algorithm in 8×8 and 4×4 MIMO systems with the optimized coding scheme when the moving speed is {0, 300, 500} km / h. The BER performance at different speeds is 0.5 - 1 dB away from the theoretical limit, indicating that the optimized codeword can still exhibit robustness at different speeds.

[0147] Compared with the most advanced receivers in the existing MIMO multi-carrier modulation systems, including GMP, CD-OAMP, DD-OAMP, DD-MAMP, and LMMSE, the MS-CD-MAMP receiver proposed in the present invention has a significant advantage in terms of computational complexity.

[0148] Table 1: Comparison of the complexities of different receivers

[0149]

[0150] where H eff,t represents the equivalent channel matrix for all users to send data in the \(t\) -th time slot, represents H eff,t the number of non - zero elements in each row, represents B eff,t the number of non - zero elements in each row, represents the number of iterations, represents the maximum number of channel taps.

Claims

1. A multi-time-slot MAMP receiver for a MIMO multi-carrier modulation system, characterized in that including a time-domain linear estimation module γ l (·) and a symbol-domain nonlinear estimation module φ l (·), where l represents the number of iterations; The time-domain linear estimation module uses a matched filter to recover the received time-domain signal of the MIMO multi-carrier modulation system, obtaining an estimated value of the time-domain signal; Transform the estimated value to the symbol domain through unitary transformation; The symbol-domain non-linear estimation module calculates the log-likelihood ratio of each symbol and the estimated value of each symbol through the estimated signal returned by the time-domain linear estimation module.

2. The multi-slot MAMP receiver for a MIMO multi-carrier modulation system according to claim 1, wherein The MIMO multi-carrier modulation system is configured with J transmit antennas and U receive antennas. The transmitted signal passes through multiple time slots and experiences different channel fades. x j,t represents the signal transmitted by the Jth transmit antenna in the tth time slot. Then, the time-domain received signal in the tth time slot is expressed in the following form: y t = H t x t + w t , wherein represents the signals transmitted by all antennas within the \(t\)-th time slot, represents the received signals of \(U\) receiving antennas, represents the channel matrix, represents the channel additive white Gaussian noise.

3. The multi-time-slot MAMP receiver for the MIMO multi-carrier modulation system according to claim 1, wherein The time-domain linear estimation module γ l (·) includes memory-matching filters a serial-to-parallel conversion module, an orthogonalization module, and a damping factor, indicating all the time slots through which the transmitted signal passes; The memory - matched filter is used for time - domain signal estimation, multiplying the input of the time - domain linear estimation module by the conjugate transpose of the channel (H H ), the serial - to - parallel conversion module is used to distinguish different time slots and then send them to the memory - matched filter for separate detection. The orthogonalization module is used to eliminate the correlation between the input and output of the detection module, and then through the serial - to - parallel conversion module, the estimation result is converted into a serial form and sent to the symbol - domain detection module; the damping factor is used to ensure that the algorithm can converge and accelerate the convergence speed.

4. The multi-time slot MAMP receiver for a MIMO multi-carrier modulation system according to claim 3, wherein The time-domain linear estimation module is based on the signals received in different time slots and the prior information of the transmitted signals updated by the non-linear end to estimate the transmitted time-domain signals through a memory matching filter, a serial-parallel conversion module, and an orthogonalization module where M is the total length of the signal, J represents the number of antennas, N represents the length of the data transmitted on one antenna in one time slot, the iteration index starts from l = 1, and the initialization estimated signal satisfies: Represents the signal of the input time-domain module within multiple time slots; Represents the combination of the estimated signals of all time slots at the l-th iteration, Represents the estimated signal of the t-th time slot after serial-to-parallel conversion, while the input signal is based on and the prior information of the transmitted signal updated by the non-linear end and obtained through a damping operation: Among them, is a damping vector representing the linearly weighted superposition of all estimated signals, is a low-complexity memory matching filter based on the estimation results of previous iterations, expressed as follows: It is expressed as follows: Among them, represents the estimated value, and denotes the maximum and minimum eigenvalues; the scaling coefficient is for accelerating the convergence rate of the MAMP receiver, is the theoretically optimal damping vector, and represent the normalization coefficient and the orthogonalization coefficient respectively; Represents the estimated signal obtained in each time slot.

5. The multi-slot MAMP receiver for a MIMO multi-carrier modulation system according to claim 1, characterized in that, The symbol domain non-linear estimation module includes a demodulator and an orthogonalization module, and the estimated signals of the two modules are iteratively updated through cross-domain operations; The demodulator first performs time-domain detection. After obtaining the estimated signal in the time domain, it performs inverse unitary transformation to transform the time-domain signal to the symbol domain, and calculates the estimated symbol by calculating the log-likelihood ratio of each symbol; The orthogonalization module removes the correlation between the estimated signal output in the symbol domain and the input signal in the symbol domain.

6. The multi-slot MAMP receiver for a MIMO multi-carrier modulation system according to claim 5, characterized in that, The inverse unitary transform performs a cross-domain operation from the time domain to the symbol domain through the IUT, and the signal input to the non-linear detection module in the symbol domain and variance are calculated by the following formula: denotes the identity matrix, and A denotes the corresponding modulation matrix, that is, the transformation matrix of the unitary transformation / inverse unitary transformation.

7. The multi-time slot MAMP receiver for a MIMO multi-carrier modulation system according to claim 6, characterized in that, The demodulator includes symbol-by-symbol MMSE demodulation operations and posterior probability decoding, and the output of the symbol non-linear estimation function is expressed as follows: where the parameter is a scalar determined by minimizing the mean square error, represents the orthogonality parameter, in the APP calculated for the k-th symbol of where χ ∈ S, S represents the constellation points of the transmitted symbols, and the output variance of the symbol-domain non-linear estimation module is obtained after calculating the posterior estimate 8. The multi-slot MAMP receiver for a MIMO multi-carrier modulation system according to claim 6, characterized in that, The unitary transformation performs a cross-domain operation from the symbol domain to the time domain through UT; The signal input to the linear detection module in the time domain Sum of variances Is calculated by the following formula: After one iteration, an input to the input time-domain linear estimation module is obtained. Repeat this iterative process, and the result of the last iteration will converge to the optimal MMSE value. This convergence value is used as the final output.

9. Coding method for multi - time - slot MAMP receiver for MIMO multi - carrier modulation system, characterized in that, Including the following steps; The time-domain linear detection module uses memory matched filtering and uses the covariance matrix of state evolution to evaluate the asymptotic performance of the multi-slot cross-domain MAMP receiver, that is: The covariance calculated between the time-domain linear estimation module and the symbol-domain non-linear estimation module, i.e., γ SE (·) and represented by the MSE function of, i.e.: The MSE transfer function is equivalent to a single-input single-output form similar to MS-CD-OAMP for the same APP decoder By combining orthogonal, cross-domain, and damping operations into the time-domain linear estimation module, an equivalent MS-CD-MAMP receiver is obtained; At this time, the linear and non-linear ends of the MS-CD-MAMP receiver are expressed in the following form: Based on the above formula, obtain the detection curve of the MS-CD-MAMP receiver; calculate the maximum achievable rate of the MS-CD-MAMP receiver based on the I-MMSE theorem, then design the corresponding decoding curve to fit the detection curve, and then design the parameters of the LDPC code according to the transition relationship of the decoding curve.

10. The multi-slot MAMP receiver according to any one of claims 1-8, characterized in that The multi-slot MAMP receiver is applicable to multi-carrier modulation with any unitary matrix as the modulation matrix; the multi-slot MAMP receiver is also applicable to single-antenna and multi-antenna.

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