Sparse regression code encoding and decoding method for reaching capacity region of MIMO multiple access channel

Abstract

The application discloses a sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability, which adopts a sparse regression code as a forward error correction code of a system. A random transformation matrix is introduced at an encoding end to perform encoding processing on a block sparse signal, so that an equivalent channel matrix is converted into a universal matrix, thereby ensuring decoding reliability of an MA-OAMP receiver under any channel matrix condition, and overcoming the dependence of a traditional AMP receiver on statistical characteristics of an observation matrix. Encoding of the sparse regression code is performed according to an optimal encoding criterion based on the MA-OAMP receiver, power distribution is reasonably performed on sparse blocks, and a time division technique is combined, so that approximation to the whole MIMO-MAC capacity domain is realized.

Description

Technical Field

[0001] This invention relates to the field of channel coding, and more particularly to a sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability. Background Technology

[0002] Channel capacity characterizes the fundamental limit of reliable information transmission and is an important theoretical benchmark for coding design. Over the past few decades, academia and industry have proposed various forward error correction codes that can approximate channel capacity on memoryless channels, such as Turbo codes, low-density parity-check (LDPC) codes, and Polar codes. Among them, LDPC codes and Polar codes have been widely adopted in 5G communication standards. Subsequently, sparse regressive codes, as a simple yet promising coding scheme, have entered the research field. Existing research shows that when using approximate message passing (AMP) algorithms and orthogonal or vector AMP (OAMP or VAMP) algorithms for decoding, sparse regressive codes can approximate the capacity of additive white Gaussian noise (AWGN) channels. However, similar to traditional coding schemes, existing sparse regressive code encoding and decoding systems are mainly geared towards memoryless channels such as point-to-point AWGN channels, Gaussian multiple access channels, and Gaussian broadcast channels. When applied to more complex linear AWGN channels in real-world communication scenarios, such as multipath channels or multiple-input multiple-output multiple-access channels (MIMO MAC), significant performance degradation often occurs.

[0003] To address the aforementioned issues, some scholars have proposed optimal coding criteria for AMP-type receivers. According to these criteria, AMP-type receivers can theoretically approximate the capacity or capacity range of a linear AWGN channel. However, these coding schemes are limited by the applicability conditions of AMP-type algorithms. Typically, AMP-type algorithms can only guarantee reliable decoding performance if the observation matrix follows the assumption of independent identically distributed (i.id) or possesses right-unitary invariance. However, channel matrices in practical communication systems generally do not meet these conditions. Therefore, applying AMP-type algorithms in real-world scenarios often requires introducing additional multi-carrier modulation to give the equivalent channel matrix the necessary special properties. Furthermore, although theoretical results show that multi-layer superposition coding can theoretically satisfy the requirements of the optimal coding criteria for AMP-type receivers, this scheme requires designing specific AWGN channel capacity reachable codes for each multi-layer structure in practical applications, and currently, there is a lack of feasible design examples. At the same time, the design of multi-layer AWGN channel capacity reachable codes often leads to high encoding and decoding complexity, thus limiting its engineering feasibility.

[0004] Therefore, the current technology has a drawback: most existing forward error correction coding schemes are designed for memoryless channels such as AWGN channels. When applied to complex linear AWGN channels such as multipath channels or multiple-input multiple-output multiple-access channels, they often fail to adequately match the channel characteristics, resulting in significant performance loss.

[0005] The optimal coding criteria proposed for linear AWGN channels based on AMP-type receivers are highly dependent on the statistical properties of the observation matrix. Such methods typically require the observation matrix to satisfy ideal conditions such as independent and identically distributed (IOD) or right-unitary invariance. However, channel matrices in real-world communication scenarios often lack these properties, significantly limiting the applicability of these coding criteria.

[0006] Within the existing theoretical framework, the optimal coding criterion based on AMP-type receivers has only achieved theoretical reachability guarantees under multi-layer superimposed coding structures. However, related research remains at the theoretical level, lacking concrete coding design examples that can be directly applied to engineering implementation. Furthermore, multi-layer superimposed coding requires the construction of multiple AWGN channel capacity reachable codes in practical design, potentially introducing excessively high encoding and decoding complexity, further limiting its practical application.

[0007] In conclusion, from both theoretical research and engineering implementation perspectives, designing forward error correction codes that can approximate the channel capacity or capacity domain of linear AWGNs remains a highly challenging research problem. This problem urgently requires a unified coding system that can adapt well to diverse channel conditions and effectively suppress potential inter-user interference in multi-user communication scenarios. Summary of the Invention

[0008] The purpose of this invention is to address the shortcomings of existing technologies by proposing a sparse regression code encoding and decoding method that is achievable in the capacity domain of a MIMO multiple access channel.

[0009] The objective of this invention is achieved through the following technical solution: a sparse regression code encoding and decoding method with MIMO multiple access channel capacity domain reachability, comprising:

[0010] The MIMO-MAC transceiver system using sparse regression codes as forward error correction codes performs channel initialization by selecting a point on the capacity domain dominance plane as the initial target rate point for each user.

[0011] Rate matching is performed by making the offset of the variance of the estimate at the nonlinear end of each user equal after being weighted by the random constraint parameters, and then iteratively modulating the random constraint parameters.

[0012] While ensuring error-free recovery, the coding criterion is to make the code rate approach the upper bound of the achievable rate. Random semi-unitary matrices are used to encode the block sparse signal. A lookup table of the user's linear SE input and output values ​​is constructed, and iterative power allocation is performed based on the coding results and the lookup table.

[0013] Furthermore, the channel initialization of the MIMO-MAC transceiver system using sparse regression codes as forward error correction codes specifically involves:

[0014]

[0015] in It is the signal received by the receiver from... The sum of the signals of each user after transmission through their respective channels and noise interference; It is the Gaussian channel noise vector of IID, with ; It comes from the first A sparse regression code for each user, encoded using a random transformation matrix. Representing the MIMO channel matrix corresponding to each user; For the number of received sequence symbols, For the first Number of transmitted sequence symbols per user Number of receiving antennas For the first Number of transmit antennas per user The number of transmitted sequence symbols for each pair of transmit and receive antennas;

[0016] Sparse regression codes By using the length of block sparse signal Using a random semi-unitary matrix Obtained through encoding.

[0017] Furthermore, the step of selecting a point on the dominant surface of the capacity domain as the initial target rate point for each user specifically involves:

[0018] Given signal-to-noise ratio limit , The system channel noise power is arbitrarily selected at a point on the dominant surface of the capacity domain, which is constrained by the following constraints. As the target rate point:

[0019]

[0020] in Indicates the first number to be matched. The upper limit of the target rate for each user Representing the MIMO channel matrix corresponding to each user Represents the total number of users. The number of received sequence symbols.

[0021] Furthermore, the constraint that makes the weighted offset of the variance of the estimate at the nonlinear end for each user equal includes:

[0022] Randomly generate initialization parameters The user's variance satisfies the following constraints

[0023]

[0024] in Indicates the first The constraint parameters owned by each user. Indicates the first Variance of individual users.

[0025] Furthermore, the iterative modulation random constraint parameters are specifically as follows:

[0026] First, based on the initial constraint parameters Given user variance constraints, calculate the upper bound of the reachable rate for the u-th user.

[0027] Set the total error tolerance and the error tolerance for each user. The constraint parameters are updated in three stages:

[0028] The first phase of the update includes:

[0029] Calculate the upper bound of the achievable rate under the current constraint parameters. The superscript * indicates a parameter being updated;

[0030] like Proceed to the next update phase; otherwise, if Then the parameters Updated to: Conversely, if Then let Repeat this step after the update until... ;

[0031] The second phase of updates includes:

[0032] Calculate the upper bound of the achievable rate for all users under the current constraint parameters.

[0033] If at this time Then let the initial constraint parameters , ,like If it returns to the first update phase, it will proceed to the next update phase; otherwise, it will proceed to the next update phase.

[0034] like Then let and the second update phase;

[0035] The third phase of the update includes:

[0036] Calculate the upper bound of the achievable rate for all users under the updated initial constraint parameters.

[0037] if Then end the update and save. ;

[0038] Otherwise, return to the first phase of the update.

[0039] Furthermore, the formula for calculating the upper bound of the achievable rate among the iterative modulation random constraint parameters is as follows:

[0040]

[0041] in, The total length of the block sparse signal. For the size of the channel matrix,

[0042] , The inverse function of the MMSE function of the following Gaussian signal.

[0043]

[0044] For estimating the signal-to-noise ratio at the linear end, Estimating the variance for the nonlinear end;

[0045] For matrix R-transform, ; Let be the equivalent channel matrix for the u-th user. Represents the identity matrix;

[0046] To reduce matrix inverse With computational complexity, construct a block diagonal matrix:

[0047] For all users Solve the following equations.

[0048]

[0049] Make block sparse signal Number of sparse blocks and sparse block length ,Signal The total length is ;

[0050] Independent generation The random semi-unitary matrix of the n users, where the nth user's matrix is... The random semi-unitary matrix of each user is:

[0051]

[0052] in and They represent peacekeeping A 3D DFT matrix; The random sampling permutation matrix, Let iid be the random phase matrix. for Each independent random phase;

[0053] The receiving end receives the signal Multiply by the following demodulation matrix:

[0054]

[0055] remember Then the first The equivalent channel matrix for each user is:

[0056]

[0057] in All are diagonal matrices; matrices It is a row and column permutation matrix, its function is to transform the matrix Transform into a matrix ,in All are only in one dimension The small matrix; at this time the matrix

[0058]

[0059] It is a block diagonal matrix, where each sub-block is a matrix with dimension 1. The small matrix, after After row and column permutations, the computation of the inverse matrix is ​​reduced. The complexity.

[0060] Furthermore, when the system scale is extremely large, the power allocation specifically includes:

[0061] Initialize user Perform iterative power allocation

[0062] initialization ;No. Residual variance before the second phase transition , No. Residual power before the next phase transition

[0063] search Zhongyu index of the nearest value ;

[0064] turn up The index is value ;

[0065] calculate ,in It is a ratio set by humans. A quantity of even smaller magnitude; The length of the sparse block;

[0066] renew , ;

[0067] ,if Repeat the above iterative process. The number of sparse blocks; otherwise, save the number of blocks. Power allocation method for individual users ,make ,if Repeat the above iterative process; otherwise, the iteration ends and the output is cleared. .

[0068] Furthermore, when the system size is finite, a lookup table is constructed to minimize the block bit error rate for the sparse signal of the encoded block based on arbitrary signal-to-noise ratio and MMSE function values. The first lookup table is then established based on the linear SE function lookup table. A lookup table for nonlinear SE functions for each user;

[0069] The input is constructed as the optimization variables, the number of sparse blocks, the length of the sparse block, and the th sparse block. The fast lookup table of the block sparse signal MMSE function for each user and the first The objective function of a linear SE function lookup table for each user, the calculation process of the objective function includes:

[0070] Use a lookup table to find an approximate value for the fixed point and calculate the block error rate corresponding to that fixed point; output the calculated value for the first fixed point. Block error rate per user As a function When the optimization variable input is Output at time;

[0071] Use the MATLAB optimization function fmincon to call the objective function. Optimize it.

[0072] Furthermore, the establishment of the first lookup table based on the linear SE function... The lookup table for the nonlinear SE function for each user includes:

[0073] S3311, Regarding the first Linear SE function lookup table for each user Discrete set of linear SE output values The first in point Calculate the total Number ,in Represents the input power vector The One value;

[0074] S3312, in the The set of sampling points for the input values ​​of the MMSE function for a user block sparse signal Find with this Number closest Index of the number That is, ;

[0075] S3313, in the The discrete set of output values ​​for a user's fast lookup table Find the index as The number is... ;

[0076] S3314. Calculate when the input value is... At that time, the first The output value of the nonlinear SE function for each user ;

[0077] S3315 ,like If the condition is met, repeat steps S3311-S3315; otherwise, save the first step. The discrete point set of the output values ​​of the nonlinear SE function for a user And create a lookup table ,in Indicates the first The discrete point set of the input values ​​of the nonlinear SE function for the nth user, this set is related to the nth user's nonlinear SE function input value discrete point set, which is related to the nth user's nonlinear SE function input value discrete point set ... of the input value of the non The discrete point set of the input values ​​of the linear SE function for each user is completely identical.

[0078] Furthermore, the step of using a lookup table to find an approximate fixed point and calculating the block error rate corresponding to that fixed point includes...

[0079] Searching for the first The discrete point set of the output values ​​of the nonlinear SE function for a user and the The discrete point set of the output values ​​of the linear SE function for each user index of the closest value ,Right now ;

[0080] Calculate when the fixed point is At that time, the first Block error rate per user

[0081] ,in For variables that follow a standard normal distribution, The cumulative function of the standard normal distribution is given by: .

[0082] The beneficial effects of this invention are:

[0083] This invention employs sparse regression codes as the forward error correction codes for the system. A random transformation matrix is ​​introduced at the encoding end to encode the block sparse signal, transforming the equivalent channel matrix into a universal matrix. This ensures the decoding reliability of the MA-OAMP receiver under arbitrary channel matrix conditions, overcoming the dependence of traditional AMP-type receivers on the statistical properties of the observation matrix.

[0084] Sparse regression codes are encoded based on the optimal coding criteria of the MA-OAMP receiver. By allocating power reasonably to the sparse blocks, the entire MIMO-MAC capacity domain can be approximated. Attached Figure Description

[0085] Figure 1 This invention describes a MIMO-MAC transceiver system that uses sparse regression codes as forward error correction codes.

[0086] Figure 2 This is the upper bound of the user rate in the MIMO-MAC transceiver system of this invention;

[0087] Figure 3 The optimal coding criterion based on the MA-OAMP receiver upon which the embodiments of the present invention depend;

[0088] Figure 4 The piecewise phase transition characteristics of the block sparse signal under asymptotic conditions are the basis of the embodiments of the present invention.

[0089] Figure 5 This invention provides a performance comparison of various coding techniques in a single-user AWGN channel, as shown in the embodiments of the present invention.

[0090] Figure 6 This invention provides a performance comparison of various coding techniques in a single-user MIMO channel, as shown in the embodiments of the present invention.

[0091] Figure 7 This invention provides a performance comparison of various coding techniques in a dual-user MIMO channel, as presented in the embodiments of the present invention. Detailed Implementation

[0092] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0093] like Figure 1 As shown, consider a containing A MIMO-MAC transceiver system with a single user and using sparse regression codes as forward error correction codes:

[0094]

[0095] in It is the signal received by the receiver from... The sum of the signals of each user after transmission through their respective channels and noise interference; It is the Gaussian channel noise vector of IID, with ; It comes from the first A sparse regression code for each user, encoded using a random transformation matrix. Representing the The MIMO channel matrix corresponding to each user. For the number of received sequence symbols, For the first Number of transmitted sequence symbols per user Number of receiving antennas For the first Number of transmit antennas per user This represents the number of transmission sequence symbols for each pair of transmit and receive antennas.

[0096] Specifically,

[0097] Sparse regression codes By using a length of block sparse signal Using a random semi-unitary matrix Obtained by encoding, satisfying

[0098]

[0099] in It is by A length of Block sparse signal composed of independent sparse blocks (i.e., block sparse signal) length satisfy ),satisfy

[0100]

[0101] Among them, the first Each sparse block contains only one non-zero symbol, and the magnitude of this non-zero symbol is... The sparse signal block satisfies the average power constraint.

[0102]

[0103] random semiunitary matrix The equivalent channel matrix needs to be made A universal class matrix that satisfies the following conditions:

[0104] It is spectrally convergent and possesses a bounded spectral norm, satisfying... .

[0105] For any fixed constant and constants ,have

[0106]

[0107] in This represents the largest element in the matrix.

[0108] Theoretically, only unitary matrices randomly selected from the entire feasible region are strictly optimal; however, experimental results show that most randomly generated unitary matrices are good modulation matrices. Therefore, easily implemented random unitary matrices can be chosen, such as permutation-invariant matrices that can be implemented using fast algorithms. ,in This is a partial sampling permutation matrix. For dimension Transform matrices that can be implemented using fast transform algorithms, such as Discrete Cosine Transform (DCT), Discrete Fourier Transform (DFT), and Hadamard Walsh Transform (HWT), etc. Let iid be the random phase matrix, where for Each independent random phase.

[0109] If for any ,matrix If the empirical spectral distributions all converge to a compactly supported distribution, then the capacity domain of the above MIMO-MAC can be expressed as:

[0110]

[0111] in Indicates the first The achievable rate of error-free decoding for individual users This represents the system signal-to-noise ratio. The corresponding system and capacity are also shown. satisfy

[0112]

[0113] At the same time, assuming Represents a sequence The In which arrangement can the capacity domain of the above MIMO-MAC be determined? endpoints satisfy

[0114]

[0115] Subscript Corresponding to the arrangement The first in Each element.

[0116] The MA-OAMP algorithm is an extension of the classic OAMP / VAMP algorithm in multiple access scenarios, and is suitable for signal detection in the aforementioned MIMO-MAC. For simplicity, subsequent discussions will focus on the first... For one user, the signal estimation method is completely consistent for the remaining users. Assume that... ( As the first Initial estimates for each user, Given the initial variance, the MA-OAMP algorithm iterates as follows:

[0117]

[0118] in: and They are the first Estimates of the linear and nonlinear ends in the next iteration; and They are the first The estimated signal-to-noise ratio of the linear end and the estimated variance of the nonlinear end in the next iteration; For the first Posterior estimator in the next iteration; For the first Orthogonal parameters of the linear end in the next iteration; Just a signal With an input signal-to-noise ratio of The minimum mean square error (MMSE) function at that time. , recorded as Then, in the iterative process described and The state evolution (SE) iterative equation can be accurately predicted.

[0119]

[0120] Since the MMSE function of many signals does not have a closed-form expression, the above... The posterior estimation of variance is usually used as an approximation, i.e.

[0121]

[0122] The MIMO-MAC capacity domain reachable sparse regression code coding technique based on MA-OAMP receiver provided by this invention uses independent random semi-unitary matrices to compress and encode the block sparse signal, thereby obtaining a sparse regression code that can be decoded using an MA-OAMP receiver. Furthermore, under the guidance of the optimal coding scheme based on MA-OAMP receiver, by appropriately allocating power to the block sparse signal, the user rate group can approximate the entire MIMO-MAC capacity domain.

[0123] Compared to existing sparse regression codes for encoding and decoding memoryless AWGN channels, this invention is applicable to complex linear AWGN channels in real-world communication scenarios, and has a wider range of applications.

[0124] Example 1 described below is a capacity-domain achievable power allocation scheme assuming an infinitely large system size. The implementation of Example 1 is as follows: the sparse block length of the block sparse signal is extremely long (…). The number of sparse blocks is extremely large ( And the size of the channel matrix is ​​extremely large. ).

[0125] Example 1:

[0126] S1, Channel Initialization

[0127] S11, Assuming the system has... Each user has 1 independent user, and each user has 100 transmit antennas. The number of receiving antennas is The number of sequence symbols transmitted between each pair of transmit and receive antennas is .

[0128] S12. Assume that for each pair of transmit and receive antennas, the signal is transmitted in blocks on a static multipath channel, and each sub-block has... Each subcarrier has a guard interval between blocks. A cyclic prefix (CP) is added at the transmitter, and the CP is removed at the receiver. The transmitter and receiver use a root-raised cosine filter for pulse shaping and matched filtering. The transmitter pulse interval and the receiver symbol sampling interval are both [missing information]. Then the first The channel matrix of each user satisfies

[0129]

[0130] The channel matrix corresponding to each pair of transceiver antennas satisfy It is by Sub-block It was made by piecing together pieces diagonally, so And each sub-block satisfies

[0131]

[0132] in

[0133] The parameters involved in the above channel model are:

[0134]

[0135] in It is the number of channel taps; It is a fuzzy function of the root-raised cosine function. It is a root-raised cosine function. This is the roll-off factor; The first one set by humans Receiver power gain for each user The first one set by humans Random phase of each path, The first in the 5G-3GPP standard Normalized amplitude coefficients for each path; The first in the 5G-3GPP standard Normalized delay of each path, The latency scaling factor is set manually.

[0136] S2, Rate Matching

[0137] S21, Given the signal-to-noise ratio limit Choose any point on the dominant surface of the capacity domain, which is defined by the following constraints. As the target rate point:

[0138]

[0139] in Indicates the first number to be matched. The upper limit of the target rate for each user; Represents the identity matrix.

[0140] S22, For all users Solve the following equations.

[0141]

[0142] Make block sparse signal Number of sparse blocks and sparse block length .Signal The total length is .

[0143] S23. Construct a block diagonal matrix to reduce the computational complexity of matrix inversion.

[0144] S231, Independent Generation The random semi-unitary matrix of the n users, where the nth user's matrix is... The random semi-unitary matrix of each user is:

[0145]

[0146] in and They represent peacekeeping A 3D DFT matrix; The random sampling permutation matrix, Let iid be the random phase matrix. for Each independent random phase.

[0147] S232, Assuming the receiver receives the signal... Multiply by the following demodulation matrix

[0148]

[0149] remember Then the first The equivalent channel matrix for each user is:

[0150]

[0151] in Both are diagonal matrices because this is because the channel matrix generated in S1 It has a block Toplitz loop structure; matrix It is a row and column permutation matrix, its function is to transform the matrix Transform into a matrix ,in All are only in one dimension The small matrix. At this time, the matrix...

[0152]

[0153] It is a block diagonal matrix, where each sub-block is a matrix with dimension 1. A small matrix. Therefore, after... After row and column permutations, the computation of the inverse matrix can be reduced. The complexity.

[0154] S24. Randomly generate initialization parameters And assume that the user variance satisfies the following user variance constraint.

[0155]

[0156] in Indicates the first The constraint parameters owned by each user. Indicates the first Variance for each user. For all users calculate

[0157]

[0158] in Given constraint parameters Given the aforementioned user variance constraints, the first... The upper limit of the achievable rate for each user; , The inverse function of the MMSE function of the following Gaussian signal.

[0159]

[0160] For matrix R-transform, The variance Satisfying constraints

[0161]

[0162] save .

[0163] like Figure 2 As shown, when it is known hour, Corresponding to the area in green in the graph, the red line represents the VTF function. The blue line represents the MMSE function of the Gaussian signal. .

[0164] S25, Initialization Set the total error tolerance ,initialization ,in Indicates the first Constraint parameter matching values ​​for each user.

[0165] S251, Considering the first Individual users, set error tolerance ,calculate

[0166]

[0167] in Given constraint parameters In the case of the first The upper limit of the achievable rate for each user; , For matrix R-transform, The variance Satisfying constraints

[0168]

[0169] if Enter S252;

[0170] Otherwise, if Then the parameters Updated to: Conversely, if Then let Then repeat S251 until... .

[0171] S252, under the constraints

[0172]

[0173] Under the premise that, for all users calculate

[0174]

[0175] in , For matrix R-transform, The variance Satisfying constraints

[0176]

[0177] save .

[0178] If at this time Then let , .like Then repeat S251-S252; otherwise proceed to S253.

[0179] Otherwise, then let And repeat S252.

[0180] S253, under the constraints

[0181]

[0182] Under the premise that, for all users calculate

[0183]

[0184] in , For matrix R-transform, The variance Satisfying constraints

[0185]

[0186] save .

[0187] if Then S25 ends and is saved. ;

[0188] Otherwise, repeat S251-S253.

[0189] S3, Sparse Regressive Code Encoding

[0190] S31, Initialization Establish a linear SE function lookup table

[0191] S311, in the interval Perform sufficient discrete sampling on the sample and save the obtained sample number. A set of sampling points for the linear SE input value of a user .

[0192] S312, For point sets Each point in In all Satisfying the following constraints

[0193]

[0194] Calculate the first under the premise The first point in the discrete set of linear SE output values ​​of the nth user sampling points

[0195]

[0196] in Save the first Discrete set of linear SE output values ​​for a user

[0197]

[0198] This established users Linear SE function lookup table .

[0199] S313, ,like Then repeat S311-S312; otherwise proceed to S32.

[0200] S32, Initialization Perform iterative power allocation

[0201] S321, Initialization Initialize the first Residual variance before the second phase transition , No. Residual power before the next phase transition .

[0202] S322, Search Zhongyu index of the nearest value .

[0203] S323, found The index is value .

[0204] S324, Calculation ,in It is a ratio set by humans. Smaller quantities, even smaller in scale.

[0205] S325, Update , .

[0206] S326, ,if Repeat S322-S325; otherwise, save the first... Power allocation method for individual users And enter S327.

[0207] S327, ,if Repeat steps S321-S326; otherwise, end the iteration and output the result. .

[0208] like Figure 4 As shown, when the first The power allocation method for the user's block sparse signal is as follows: At that time, its MMSE function exhibits the segmented phase transition characteristics shown by the blue line in the figure.

[0209] At the same time, such as Figure 3As shown, the MMSE function of a block sparse signal resembles the black line in the figure, approximating the VTF function. With Gaussian MMSE function The smaller of the two is therefore able to satisfy the optimal coding criterion based on the MA-OAMP receiver.

[0210] Based on an embodiment of a capacity-domain achievable power allocation scheme assuming an infinitely large system size, the technical principles include:

[0211] When the system channel noise power is At that time, the first The upper bound of the achievable error-free recovery rate per user per received symbol is as follows: (i.e., there is) ) represents

[0212]

[0213] in :

[0214] The inverse function of the following Gaussian signal MMSE function

[0215]

[0216] For matrix The R-transform, also known as the variational transfer function (VTF) of MA-OAMP, is where... .

[0217] Assuming the variance of all users It can be determined by a hidden variable. Characterized by these variances forming a vector The following constraints must be met: 1) ;2) For any , ,Right now element-wise greater than or equal to ;3) For any , ,Right now The sum of all elements is strictly greater than In particular, the constraints that are repeatedly used in the embodiments. It is a special constraint that satisfies this constraint.

[0218] According to the MMSE theorem for rate, when the first The MMSE function for the block sparse signal of a user is: At that time, the first The average code rate per user per received symbol is

[0219]

[0220] in Indicates the first The inverse function of the block sparse signal MMSE function for each user. Therefore, combined with the first... Upper limit of achievable speed for individual users The integral expression is given by [the expression] to ensure error-free recovery while approximating the upper bound of the achievable rate. For any [the condition]... The MMSE function of the signal should satisfy

[0221]

[0222] That is

[0223]

[0224] Encoding according to the above optimal coding criteria can approximate the endpoints of the capacity domain; combining it with time-division techniques can approximate the entire dominant surface of the capacity domain, and thus the entire capacity domain. Theoretical research shows that under asymptotic conditions ( ), No. The MMSE function of a user's block sparse signal in the interval It exhibits piecewise Gaussian phase transition characteristics:

[0225]

[0226] Among them: belonging to the first The power of the 0th sparse block for a user is defined as ;No. The user experienced the first The residual power before the next phase transition is .

[0227] Based on this, when the sparse block length of the sparse signal... and the number of sparse blocks When both approaches infinity, the block sparse signal can be iteratively power-allocated as follows.

[0228] Step 1: Initialization .

[0229] Step 2: Initialization , .

[0230] Step 3: Solve the following fixed-point equation.

[0231]

[0232] in MMSE function for Gaussian signals.

[0233] Step 4: Calculation

[0234]

[0235] in It is orders of magnitude lower than Positive numbers.

[0236] Step 5: ,if Repeat Step 3-Step 4; otherwise, proceed to Step 6.

[0237] Step 6: ,if Repeat Step 2-Step 5; otherwise, the iteration ends.

[0238] Since the VTF and MMSE functions of MA-OAMP do not directly reflect the MA-OAMP decoding process, an SE form equivalent to the above-mentioned optimal coding criterion is proposed to better control the decoding performance of the system in practical applications.

[0239]

[0240] in Indicates the first SE function for each user's nonlinear terminal, Indicates the first SE function for each user's linear end, For the first The inverse function of the linear SE function for individual users. Based on the phase transition properties of the MMSE function for block sparse signals, its nonlinear SE function is in the interval... The above exhibits the following piecewise phase transition properties.

[0241]

[0242] Therefore, the above iterative power allocation can be transformed into a form based on the nonlinear SE function, and the specific steps are as follows:

[0243] Step 1: Initialization .

[0244] Step 2: Initialization , , .

[0245] Step 3: Calculation

[0246]

[0247] in For the linear side, use the SE function.

[0248] Step 4: ,if If not, repeat Step 3; otherwise, proceed to Step 5.

[0249] Step 5: ,if Repeat Step 2-Step 4; otherwise, the iteration ends.

[0250] Example 2 described below is a capacity-domain achievable power allocation scheme assuming a finite system size. The implementation of Example 2 is as follows: due to the limited resources of the actual system, the sparse block length and number of sparse blocks in the block-sparse signal are both very limited. Furthermore, the size of the channel matrix is ​​also quite limited. .

[0251] Example 2:

[0252] S1, Channel initialization, is exactly the same as in Example 1, so it is omitted.

[0253] S2, rate matching, is exactly the same as in Example 1, so it is omitted.

[0254] S3, Sparse Regressive Code Encoding

[0255] S31, the steps are exactly the same as in Example 1, so they are omitted. However, it should be noted that in calculating S312: At this value ,in This indicates that the target noise power (the reciprocal of the target signal-to-noise ratio) needs to be optimized and needs to be set manually. (Example 1 when running S312:) In This represents system noise, which is the reciprocal of the signal-to-noise ratio limit.

[0256] S32, Initialization , establish the first Fast lookup table for block sparse signaling MMSE function for individual users

[0257] S321, in Select a suitable and sufficiently large interval, perform a sufficient number of discrete samples within that interval, and save the result. The set of sampling points for the input values ​​of the MMSE function for a user block sparse signal .

[0258] S322, For point sets Each point in Conduct numerous Monte Carlo simulation experiments to obtain the result when the input value is... At that time, the first Approximate value of the output of the fast lookup table of the sparse signal MMSE function for each user block ,Right now ,in satisfy

[0259]

[0260] Save the first The discrete set of output values ​​for a user's fast lookup table

[0261] Thus, the first Fast lookup table for block sparse signaling MMSE function for individual users .

[0262] S323, ,like Then repeat S321-S322; otherwise proceed to S33.

[0263] S33. Constructing an optimization function ,in Represents the input power vector. Indicates the first The number of sparse blocks per user Indicates the first The length of the sparse block for each user Indicates the number generated in S32 A user's block sparse signal MMSE function fast lookup table Indicates the number generated in S31 A linear SE function lookup table for each user.

[0264] S331, Initialization , establish the first Lookup table for nonlinear SE functions for individual users

[0265] S3311, Regarding the first Linear SE function lookup table for each user Discrete set of linear SE output values The first in point Calculate the total Number ,in Represents the input power vector The Values.

[0266] S3312, in the The set of sampling points for the input values ​​of the MMSE function for a user block sparse signal Find with this Number closest Index of the number That is, .

[0267] S3313, in the Quick Lookup Table for Individual Users The discrete point set of the output values Find the index as The number is... .

[0268] S3314. Calculate when the input value is... At that time, the first The output value of the nonlinear SE function for each user .

[0269] S3315 ,like If the condition is met, repeat steps S3311-S3315; otherwise, save the first step. The discrete point set of the output values ​​of the nonlinear SE function for a user And create a lookup table ,in Indicates the first The discrete point set of the input values ​​of the nonlinear SE function for the nth user, this set is related to the nth user's nonlinear SE function input value discrete point set, which is related to the nth user's nonlinear SE function input value discrete point set ... of the input value of the non The discrete point set of the input values ​​of the linear SE function for each user is completely identical.

[0270] S332. Use a lookup table to find an approximate value for the fixed point and calculate the block error rate corresponding to the fixed point.

[0271] S3321, Searching for the first The discrete point set of the output values ​​of the nonlinear SE function for a user and the The discrete point set of the output values ​​of the linear SE function for each user index of the closest value ,Right now ;

[0272] S3322, Calculate when the fixed point is At that time, the first Block error rate per user

[0273] ,in For variables that follow a standard normal distribution, The cumulative function of the standard normal distribution is given by: .

[0274] S333, Output the calculated result of the first... Block error rate per user As a function When the optimization variable input is The output at that time.

[0275] S34, Initialization Optimize power allocation.

[0276] S341, Human selection of the first The initial iteration point (initial power allocation vector) for each user is: , The length should be The MATLAB optimization function fmincon is used to call the objective function in S36. Optimization was performed, and the optimization result was obtained as follows:

[0277]

[0278] in This refers to an anonymous function that uses the first input position as the optimization variable and the other input positions as input constants. Indicates the initial optimization point as ;con1 refers to the first constraint con2 refers to the second constraint. ,in Optimization variables The One element, Refer to variables The length.

[0279] MATLAB's fmincon function uses an optimization algorithm to iterate and gradually find the objective function. Minimum optimal solution Therefore, only the initial point of the iteration needs to be specified. The `fmincon` function will then update the input automatically during the iteration process. It's important to note that the actual `fmincon` function requires other parameters, but these are mostly manually adjusted; for simplicity, their specification is omitted here.

[0280] S342, .like If the result is satisfactory, repeat step S341; otherwise, output the optimization result. .

[0281] Based on an embodiment of a capacity-domain achievable power allocation scheme assuming a finite system size, the technical principles include:

[0282] The iterative power allocation in Example 1 is strictly achievable within the capacity domain only when the length and number of sparse blocks and the system size are extremely large. However, the size of the transmitted signal and the channel matrix in a real system is unlikely to be infinite. Therefore, the power allocation needs to be optimized to achieve better decoding performance in practical communication systems. The actual decoding performance of a user can be determined by the first iteration of MA-OAMP convergence. Fixed point of the decoder for a single user The signal-to-noise ratio and the power allocation method of the block sparse signal are determined. This can be obtained by solving the following SE fixed-point equation.

[0283]

[0284] For the sake of simplicity, Recorded as So when the input signal-to-noise ratio is obtained... After that, the system's first Section Error Rate (SER) per user It can be obtained from the following formula

[0285]

[0286] in For variables that follow a standard normal distribution, The cumulative function of the standard normal distribution is given by:

[0287]

[0288] Therefore, the optimal system is the first The decoding performance for a single user is equivalent to minimizing SER. This is then transformed into solving the following constrained optimization problem.

[0289]

[0290] It should be noted that, due to the first The non-linear SE function for each user Since it lacks a closed-form expression, the following solution to the SE fixed-point equation...

[0291]

[0292] Need to be established in advance The lookup table is as follows: First, through a sufficient number of Monte Carlo experiments, the following... Fast lookup table for block sparse signaling MMSE function for individual users

[0293]

[0294] in Is The first sample obtained by sampling within a manually set interval The set of sampled points for the input values ​​of the MMSE function for sparse signals in a user block. satisfy

[0295]

[0296] For variables that follow a standard normal distribution, the expected value is... The calculation is for all The above lookup table can be used to quickly obtain the signal-to-noise ratio. At that time, the first MMSE function for block sparse signals of individual users Output value

[0297]

[0298] Therefore, for any signal-to-noise ratio Its corresponding MMSE function value The above lookup table can be used for quick estimation: for any In the set Find and closest value Then the MMSE function value is

[0299] in For set Chinese index The corresponding value. Further, a lookup table for the SE function at the non-linear end can be obtained.

[0300]

[0301] Furthermore, because the actual system does not satisfy the asymptotic condition ( To achieve error-free recovery, the actual operating signal-to-noise ratio (SNR) of the system should be slightly higher than the SNR limit. Here, the SNR limit refers to the theoretical SNR corresponding to a given system and rate upper bound (i.e., system and capacity). Taking an AWGN channel as an example, given the system and capacity... bit / sym, then the signal-to-noise ratio limit of the system is dB.

[0302] like Figure 5 The figure shows the decoding performance in a single-user AWGN channel. System parameters are as follows: number of blocks. 32; Number of subcarriers per block 256; bandwidth per block 40 MHz; carrier frequency 4 GHz; maximum latency is 1 Signal-to-noise ratio limit: 7 dB; When using the optimized power allocation strategy (Example 2), the target signal-to-noise ratio is set to: 9dB. Target rate upper bound: = 2.585 bits / sym. Code length is 8192. The sparse block length and number of blocks in the block sparse signal are... (1937, 1937). To compare the decoding performance with current advanced encoding and decoding schemes, this paper selects the LDPC code in the 5G-3GPP standard as the benchmark scheme. The code rate of the underlying LDPC code is... With a code length of 32768 bits / sym and 0.646 bits / sym, after 16-QAM modulation, a sequence of length 8192 is obtained, resulting in an improvement in spectral efficiency. In the figure, the blue line represents the decoding performance of the sparse regression code obtained using the iterative power allocation strategy (Example 1); the red line represents the decoding performance of the sparse regression code obtained using the optimized power allocation strategy (Example 2); the black line represents the decoding performance of the sparse regression code obtained using the average power allocation strategy; the magenta line represents the decoding performance of the sparse regression code obtained using the exponential power allocation strategy in existing literature; and the green line represents the performance result of the 5G-3GPP standard LDPC code after one linear minimum mean square error (LMMSE) equalization and 100 iterations of belief propagation (BP) decoding.

[0303] like Figure 6 The figure shows the decoding performance in a single-user MIMO channel. System parameters are as follows: number of transmit antennas... 2. Number of receiving antennas 2; Number of blocks 32; Number of subcarriers per block 256; bandwidth per block 40 MHz; carrier frequency 4 GHz; maximum latency is 1 Signal-to-noise ratio limit: 7 dB; When using the optimized power allocation strategy (Example 2), the target signal-to-noise ratio is set to: 9 dB. Target rate upper limit: = 2.262 bits / sym. Code length is 8192. The sparse block length and number of blocks in the block sparse signal are... (1723, 1723). To compare the decoding performance with current advanced encoding and decoding schemes, this paper selects the LDPC code in the 5G-3GPP standard as the benchmark scheme. The code rate of the underlying LDPC code is... With a code length of 32768 bits and a bit length of 0.5655 bits / sym, after 16-QAM modulation, a sequence of length 8192 is obtained, resulting in an improvement in spectral efficiency. In the figure, the blue line represents the decoding performance of the sparse regression code obtained using the iterative power allocation strategy (Example 1); the red line represents the decoding performance of the sparse regression code obtained using the optimized power allocation strategy (Example 2); the black line represents the decoding performance of the sparse regression code obtained using the average power allocation strategy; the magenta line represents the decoding performance of the sparse regression code obtained using the exponential power allocation strategy in existing literature; and the green line represents the performance result of the 5G-3GPP standard LDPC code after one linear minimum mean square error (LMMSE) equalization and 100 iterations of belief propagation (BP) decoding.

[0304] like Figure 7 The figure shows the decoding performance in a two-user MIMO channel. The system parameters are as follows: number of transmit antennas... 2. Number of receiving antennas 2; Number of blocks 32; Number of subcarriers per block 256; bandwidth per block 40 MHz; carrier frequency 4 GHz; maximum latency is 1 Signal-to-noise ratio limit: 10 dB; When employing the optimized power allocation strategy (Example 2), the optimized target signal-to-noise ratios for the two users are set as follows: 11.5 dB, 12.5 dB. Target rate upper bound group: =(2.352,1.177) bits / sym. The code length for both users is 8192. The sparse block lengths and number of sparse blocks for the two users' block sparse signals are respectively... (1783, 1783), (971,971). To compare the decoding performance with current advanced encoding and decoding schemes, this paper selects the LDPC code in the 5G-3GPP standard as the benchmark scheme. The code rate of the underlying LDPC code is divided into... (0.5880, 0.5884) bits / sym, with code lengths of (32768, 16384), are modulated by 16-QAM to obtain sequences of length 8192, resulting in an improvement in spectral efficiency. In the figure, the blue line represents the decoding performance of the sparse regression code obtained using the iterative power allocation strategy (Example 1); the red line represents the decoding performance of the sparse regression code obtained using the optimized power allocation strategy (Example 2); the black line represents the decoding performance of the sparse regression code obtained using the average power allocation strategy; the magenta line represents the decoding performance of the sparse regression code obtained using the exponential power allocation strategy in existing literature; and the green line represents the performance result of the 5G-3GPP standard LDPC code after one linear minimum mean square error (LMMSE) equalization and 100 iterations of belief propagation (BP) decoding.

[0305] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0306] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this application. This application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability, characterized in that, include: The MIMO-MAC transceiver system using sparse regression codes as forward error correction codes performs channel initialization by selecting a point on the capacity domain dominance plane as the initial target rate point for each user. Rate matching is performed by making the offset of the variance of the estimate at the nonlinear end of each user equal after being weighted by the random constraint parameters, and then iteratively modulating the random constraint parameters. While ensuring error-free recovery, the coding criterion is to make the code rate approach the upper bound of the achievable rate. Random semi-unitary matrices are used to encode the block sparse signal. A lookup table of the user's linear SE input and output values ​​is constructed, and iterative power allocation is performed based on the coding results and the lookup table.

2. The sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability as described in claim 1, characterized in that, The channel initialization of the MIMO-MAC transceiver system using sparse regression codes as forward error correction codes specifically involves: in It is the signal received by the receiver from... The sum of the signals of each user after transmission through their respective channels and noise interference; It is the Gaussian channel noise vector of IID, with ; It comes from the first A sparse regression code for each user, encoded using a random transformation matrix. Representing the MIMO channel matrix corresponding to each user; For the number of received sequence symbols, For the first Number of transmitted sequence symbols per user Number of receiving antennas For the first Number of transmit antennas per user The number of transmitted sequence symbols for each pair of transmit and receive antennas; Sparse regression codes By using the length of block sparse signal Using a random semi-unitary matrix Obtained through encoding.

3. The sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability according to claim 1, characterized in that, The specific steps for selecting a point as the initial target rate point for each user on the dominant surface of the capacity domain are as follows: Given signal-to-noise ratio limit , The system channel noise power is arbitrarily selected at a point on the dominant surface of the capacity domain, which is constrained by the following constraints. As the target rate point: in Indicates the first number to be matched. The upper limit of the target rate for each user Representing the MIMO channel matrix corresponding to each user Represents the total number of users. The number of received sequence symbols.

4. The sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability according to claim 1, characterized in that, The constraint that makes the offset of the estimate variance of each user on the nonlinear end equal after being weighted by the random constraint parameters specifically includes: Randomly generate initialization parameters The user's variance satisfies the following constraints in Indicates the first The constraint parameters owned by each user. Indicates the first Variance of individual users.

5. The sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability according to claim 4, characterized in that, The specific iterative modulation random constraint parameters are: First, based on the initial constraint parameters Given user variance constraints, calculate the upper bound of the reachable rate for the u-th user. Set the total error tolerance and the error tolerance for each user. The constraint parameters are updated in three stages: The first phase of the update includes: Calculate the upper bound of the achievable rate under the current constraint parameters. The superscript * indicates a parameter being updated; like Proceed to the next update phase; otherwise, if Then the parameters Updated to: Conversely, if Then let Repeat this step after the update until... ; The second phase of updates includes: Calculate the upper bound of the achievable rate for all users under the current constraint parameters. If at this time Then let the initial constraint parameters , ,like If it returns to the first update phase, it will proceed to the next update phase; otherwise, it will proceed to the next update phase. like Then let and the second update phase; The third phase of the update includes: Calculate the upper bound of the achievable rate for all users under the updated initial constraint parameters. if Then end the update and save. ; Otherwise, return to the first phase of the update.

6. The sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability according to claim 5, characterized in that, The formula for calculating the upper bound of the achievable rate among the iterative modulation random constraint parameters is as follows: in, The total length of the block sparse signal. For the size of the channel matrix, , The inverse function of the MMSE function of the following Gaussian signal. For estimating the signal-to-noise ratio at the linear end, Estimating the variance for the nonlinear end; For matrix R-transform, ; Let be the equivalent channel matrix for the u-th user. Represents the identity matrix; To reduce matrix inverse With computational complexity, construct a block diagonal matrix: For all users Solve the following equations. Make block sparse signal Number of sparse blocks and sparse block length ,Signal The total length is ; Independent generation The random semi-unitary matrix of the n users, where the nth user's matrix is... The random semi-unitary matrix of each user is: in and They represent peacekeeping A 3D DFT matrix; The random sampling permutation matrix, Let iid be the random phase matrix. for Each independent random phase; The receiving end receives the signal Multiply by the following demodulation matrix: remember Then the first The equivalent channel matrix for each user is: in All are diagonal matrices; matrices It is a row and column permutation matrix, its function is to transform the matrix Transform into a matrix ,in All are only in one dimension The small matrix; at this time the matrix It is a block diagonal matrix, where each sub-block is a matrix with dimension 1. The small matrix, after After row and column permutations, the computation of the inverse matrix is ​​reduced. The complexity.

7. The sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability according to claim 1, characterized in that, When the system is extremely large, the power allocation specifically includes: Initialize user Perform iterative power allocation initialization ;No. Residual variance before the second phase transition , No. Residual power before the next phase transition search Zhongyu index of the nearest value ; turn up The index is value ; calculate ,in It is a ratio set by humans. A quantity of even smaller magnitude; The length of the sparse block; renew , ; ,if Repeat the above iterative process. The number of sparse blocks; otherwise, save the number of blocks. Power allocation method for individual users ,make ,if Repeat the above iterative process; otherwise, the iteration ends and the output is cleared. .

8. The sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability according to claim 1, characterized in that, When the system size is finite, a lookup table is constructed to minimize the block bit error rate for the sparse signal of the encoded block based on arbitrary signal-to-noise ratio and MMSE function values. The first lookup table is then established based on the linear SE function lookup table. A lookup table for nonlinear SE functions for each user; The input is constructed as the optimization variables, the number of sparse blocks, the length of the sparse block, and the th sparse block. The fast lookup table of the block sparse signal MMSE function for each user and the first The objective function of a linear SE function lookup table for each user, the calculation process of the objective function includes: Use a lookup table to find an approximate value for the fixed point and calculate the block error rate corresponding to that fixed point; output the calculated value for the first fixed point. Block error rate per user As a function When the optimization variable input is Output at time; Use the MATLAB optimization function fmincon to call the objective function. Optimize it.

9. A sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability according to claim 8, characterized in that, The first step is to establish a lookup table based on the linear SE function. The lookup table for the nonlinear SE function for each user includes: S3311, Regarding the first Linear SE function lookup table for each user Discrete set of linear SE output values The first in point Calculate the total Number ,in Represents the input power vector The One value; S3312, in the The set of sampling points for the input values ​​of the MMSE function for a user block sparse signal Find with this Number closest Index of the number That is, ; S3313, in the The discrete set of output values ​​for a user's fast lookup table Find the index as The number is... ; S3314. Calculate when the input value is... At that time, the first The output value of the nonlinear SE function for each user ; S3315 ,like If the condition is met, repeat steps S3311-S3315; otherwise, save the first step. The discrete point set of the output values ​​of the nonlinear SE function for a user And create a lookup table ,in Indicates the first The discrete point set of the input values ​​of the nonlinear SE function for the nth user, this set is related to the nth user's nonlinear SE function input value discrete point set, which is related to the nth user's nonlinear SE function input value discrete point set ... of the input value of the non The discrete point set of the input values ​​of the linear SE function for each user is completely identical.

10. A sparse regression code encoding and decoding method for MIMO multiple access channel capacity domain reachability according to claim 8, characterized in that, The step of finding an approximate value of a fixed point using a lookup table and calculating the block error rate corresponding to that fixed point includes... Searching for the first The discrete point set of the output values ​​of the nonlinear SE function for a user and the The discrete point set of the output values ​​of the linear SE function for each user index of the closest value ,Right now ; Calculate when the fixed point is At that time, the first Block error rate per user ,in For variables that follow a standard normal distribution, The cumulative function of the standard normal distribution is given by: .

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