Cellular-free large-scale MIMO system multi-user joint decoding method based on model-driven deep learning

Abstract

The invention discloses a multi-user joint decoding method for a cellular-free large-scale MIMO system based on model-driven deep learning, and the method comprises the steps: building an optimization problem of a simulation combination matrix with maximization of the reachable rate of the cellular-free large-scale MIMO system as a target in a simulation part of data decoding; on the basis of a heuristic algorithm, an optimization target is simplified, an optimization problem is divided into a plurality of sub-problems, the single AP simulation precoding matrix optimization problem is solved one by one, and an optimal simulation combination matrix is obtained; a multi-user joint LDPC decoding algorithm is expanded to a cellular-free large-scale MIMO scene, multi-user joint LDPC decoding is realized based on an MIMO-LDPC-Net decoding network, an input layer of the MIMO-LDPC-Net decoding network generates an initial value as an input of a hidden layer, the hidden layer is formed by stacking modules composed of a first sub-layer, a second sub-layer and an MIMO detection layer, and the first sub-layer, the second sub-layer and the MIMO detection layer are stacked. The output layer generates a log-likelihood ratio of the variable node. Experiments show that compared with a traditional algorithm, the heuristic algorithm and the AI auxiliary joint decoding algorithm have a signal-to-noise ratio gain of 1dB.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of cell-free massive MIMO system communication, and particularly relates to a cell-free massive MIMO system multi-user joint decoding method based on model-driven deep learning. BACKGROUND

[0002] For the active detection and channel estimation problem in the passive random access protocol, the receiving end implements active device detection on the noisy observation signal, first identifies the code word set corresponding to the active terminal, and then carries out sparse channel parameter estimation in the angle domain based on the prior information. The passive random access protocol does not focus on the specific device sending information but only focuses on the code word set sent by the active device. The information bits sent by the active device are divided into a preamble sequence and a payload sequence: the preamble sequence is formed into a characteristic code word through codebook coding, and its reconstruction process can be converted into an active detection and channel estimation problem; the payload sequence is channel coded using an LDPC code, and its decoding performance directly depends on the code word set and channel state information obtained in the preamble stage. Although the existing literature has conducted in-depth research on the traditional decoding algorithm of LDPC, in the face of the multi-user MIMO interference channel characteristics in the large-scale machine type communication scenario, it is necessary to design an adaptive decoding algorithm to deal with the channel interference and other problems caused by the non-additive Gaussian channel.

[0003] In large-scale machine type communication, due to the uncertainty of active devices and the difficulty to obtain posterior probability in advance, the traditional MMSE receiver processing method involves complex matrix inversion, and the computational complexity is too high in the large-scale MIMO scenario. To solve this problem, one strategy is to combine the interference as noise with the message propagation algorithm, and propose a multi-user joint decoding algorithm, so as to reduce the computational complexity while realizing multi-user joint decoding. In the partially connected MIMO channel, the receiving end has both digital and analog combination matrices adjustable, although the existing research combines digital reception with multi-user joint decoding, it has not fully utilized the degree of freedom of the analog combination matrix, and the synergistic effect of analog and digital combination matrices can rival the spectral efficiency of the all-digital MIMO architecture, therefore, how to fully utilize the spatial degree of freedom of the analog combination matrix is crucial to improve the decoding error probability of the MIMO system. In addition, deep learning methods have shown significant advantages in improving the performance of LDPC decoding, for example, combining convolutional neural networks with message propagation algorithms can solve the LDPC decoding problem under colored noise and achieve better performance; by designing an LDPC decoding network through deep unfolding and introducing a self-checking mechanism, the learning process can be effectively accelerated to meet real-time requirements. SUMMARY

[0004] The application aims at providing a model-driven deep learning based multi-user joint decoding method for a cell-free massive MIMO system, aiming at the architecture characteristics of a partially connected MIMO system, designing a low-complexity analog beam combining matrix optimization method, and then designing a multi-user joint decoding method based on deep unfolding.

[0005] The technical scheme is as follows:

[0006] The model-driven deep learning based multi-user joint decoding method for the cell-free massive MIMO system comprises the following steps:

[0007] In the analog part of data decoding, an optimization problem of an analog combining matrix maximizing the achievable rate of the cell-free massive MIMO system is established; based on a heuristic algorithm, the optimization target is simplified, and the optimization problem is divided into a plurality of sub-problems, and a single-AP analog precoding matrix optimization problem is solved one by one to obtain an optimal analog combining matrix.

[0008] The multi-user joint LDPC decoding algorithm is extended to the cell-free massive MIMO scenario, and a MIMO-LDPC-Net decoding network is used to realize multi-user joint LDPC decoding, wherein an input layer of the MIMO-LDPC-Net decoding network generates an initial value as an input of a hidden layer, the hidden layer is stacked by a module composed of a first sub-layer, a second sub-layer and a MIMO detection layer, and an output layer generates a log-likelihood ratio of a variable node.

[0009] Further, the optimization problem of the analog combining matrix maximizing the achievable rate is expressed as:

[0010]

[0011] wherein the achievable rate is is a unit matrix, and p is an average transmission power, W RF,m is an analog combining matrix of the mth AP, is an i-th beam vector of the analog combining matrix of the mth AP, and N rf is a number of radio frequency links, is an additive white Gaussian noise variance, is a variance of a random variable in a channel vector of the active device k and the mth AP, and K a is a number of active devices, is a channel matrix.

[0012] Further, the optimization target is simplified as wherein

[0013] Furthermore, the single-AP analog precoding matrix optimization problem can be expressed as:

[0014]

[0015] in, For W RF,m The element in the nth row and rth column, Let m be the channel matrix of the m-th AP. W m It is additive white Gaussian noise.

[0016] Furthermore, the process of solving the simulated combination matrix using a heuristic algorithm is as follows: First, traverse from the first AP, and for the current AP pair... SVD decomposition is performed to obtain channel feature vectors, and beam vectors in the simulated combination matrix of the current AP are constructed based on these feature vectors. Subsequently, the optimal simulated combination matrix of the AP is generated through beam synthesis. Calculate Q again m Used to update the optimal simulation combination matrix for the next AP; repeat until the simulation combination matrices for all APs have been solved.

[0017] Furthermore, the neural network uses the received signal, interleaving mode, and channel matrix as input to generate messages from variable nodes to observation nodes, messages from check nodes to variable nodes, and messages from variable nodes to check nodes. In each hidden layer, the MIMO detection layer receives messages from the previous layer's variable nodes to observation nodes, messages from the check nodes to variable nodes, and the received signal to calculate messages from observation nodes to variable nodes and messages from variable nodes to observation nodes. The first sub-layer receives messages from the previous layer's variable nodes to check nodes to calculate messages from check nodes to variable nodes. The second sub-layer receives messages from the previous layer's observation nodes to variable nodes and messages from the check nodes to variable nodes to calculate messages from variable nodes to check nodes. The output layer generates log-likelihood ratio estimates for variable nodes through differentiable mappings. During training, the sigmoid function is used to smooth the output to maintain gradient differentiability, while during testing, it is converted to a sign function to achieve hard-decision output.

[0018] Furthermore, the first sub-layer implements message passing from the verification node to the variable node, enabling... Indicates the verification node c at layer l. kn Passed to variable node The news, Indicates the verification node c kn The update rule for the first sub-layer of the associated variable node set is as follows:

[0019]

[0020] in, Represents the variable node s at level l-1 kj Passed to the verification node c kn The message, sgn(·) represents the sign function, α (l) ,β (l) These represent the weight parameters and bias terms of the l-th layer of the neural network, respectively; the second sub-layer implements the message passing process from the variable node to the verification node, letting... Represents the l-th level variable node Passed to the verification node c kn The news, Represents the variable node Associated observation nodes Subscript set Represents variable nodes The neighboring nodes, the second-level update rule is:

[0021]

[0022] in, This represents the observation node output by the (l-1)th layer MIMO detection module. To variable node The news, Indicates the verification node c at layer l. kn′ Passed to variable node The message, γ (l) This represents the weight parameters of the second sub-layer.

[0023] Furthermore, the learnable parameters of the neural network are l max To determine the number of network layers, during actual training, the parameters {α} of the first layer are first... (1) ,β (1) ,γ (1) The training proceeds independently until convergence, then the parameters of the first layer are frozen and the parameters of the second layer are optimized separately. After the training of the base layers is completed, the parameters of the first two layers are jointly optimized through fine-tuning. This iterative process expands layer by layer to the lth... max Layers are formed to create a parameter learning paradigm that alternates between local and global approaches.

[0024] A computer system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the multi-user joint decoding method for a cellular-free massive MIMO system based on model-driven deep learning.

[0025] A computer program product comprising a computer program which, when executed by a processor, implements the steps of the model-driven deep learning based multi-user joint decoding method for a cell-free massive MIMO system.

[0026] Beneficial effects: The application proposes a heuristic analog combining matrix optimization method for the characteristics of the partially connected MIMO structure, extends the multi-user joint LDPC decoding algorithm to the partially connected MIMO scenario, and on this basis, expands the decoding algorithm into MIMO-LDPC-Net to solve the multi-user joint decoding problem under the MIMO channel. Experiments show that the MIMO-LDPC-Net algorithm is better than the multi-user joint LDPC decoding algorithm in the entire SNR range, and exhibits a performance gain of about 0.7 dB when the signal-to-noise ratio is greater than 13 dB. The heuristic algorithm + AI assisted joint decoding algorithm has a signal-to-noise ratio gain of 1 dB compared with the traditional algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 The method flowchart of the embodiment of the application is shown.

[0028] Figure 2 The schematic diagram of sparse interleaved multiple access is shown.

[0029] Figure 3 The LDPC decoding posterior probability factor graph is shown.

[0030] Figure 4 The MIMO-LDPC-Net network structure diagram is shown.

[0031] Figure 5 The error probability curve with signal-to-noise ratio is shown.

[0032] Figure 6 The heuristic algorithm error probability curve with signal-to-noise ratio is shown. DETAILED DESCRIPTION

[0033] The technical solutions of the application will be described in detail below with reference to the drawings and specific embodiments.

[0034] As shown in Figure 1 The model-driven deep learning based multi-user joint decoding method for a cell-free massive MIMO system disclosed by the embodiment of the application mainly includes the following steps:

[0035] In the analog part of data decoding, an optimization problem of analog combining matrix maximizing the achievable rate of the cell-free massive MIMO system is established; based on a heuristic algorithm, the optimization target is simplified, and the optimization problem is divided into a plurality of sub-problems, and a single AP analog precoding matrix optimization problem is solved one by one to obtain the optimal analog combining matrix;

[0036] The multi-user joint LDPC decoding algorithm is extended to a large-scale MIMO scenario without cells, and multi-user joint LDPC decoding is implemented based on a MIMO-LDPC-Net decoding network, wherein an input layer of the MIMO-LDPC-Net decoding network generates initial values as inputs of a hidden layer, the hidden layer is stacked by a module composed of a first sub-layer, a second sub-layer and a MIMO detection layer, and an output layer generates log-likelihood ratios of variable nodes.

[0037] The detailed steps of the embodiments of the application are exemplarily described below in combination with a specific system model.

[0038] I. System model

[0039] The embodiment establishes a data transmission model of active devices, for the convenience of symbol description, the embodiment only considers a single carrier case, and data of different carriers can be processed respectively. Let v k ∈{0,1} B denote a binary message sequence sent by an active device k, B is the length of the sent information bits, and an encoding function The binary sequence of the active device is encoded into a sent code word, L is the total pilot length, and the received signal obtained by the mth AP can be represented as:

[0040]

[0041] wherein m = 1, 2,..., M ap , M ap is the number of APs, κ a is a set of active devices, h k,m is a channel vector of the active device k and the mth AP, W RF,m is an analog combining matrix of the mth AP, is a noise matrix.

[0042] The received signals of all APs are aggregated to obtain:

[0043]

[0044] wherein In passive random access, the receiving end needs to process the received signal to generate an estimate of the binary message sequence It is noted that passive random access does not need to identify the active device sending the message, but only needs to identify the sent code word. We evaluate the performance of data decoding by using the false alarm rate and the false detection rate:

[0045]

[0046] We use an LDPC encoding-based passive random access protocol, and the overall encoding process is as follows: Figure 2As shown. The device's binary message will be divided into two parts, respectively by the codebook. Encode using both L and LDPC codes, L p Let N and N be the pilot length and codebook size of the CS (Compressed Sensing) stage, respectively. Let Indicates v k The front B p The device k selects the i-th bit from codebook A. k Each code word, we will Treat i as an integer k The binary representation of, i.e. During the CS phase, the active device maps the message sequence into codewords based on the codebook, and the received signal obtained by the CPU is:

[0047]

[0048] Z p For Gaussian white noise, Γ=(γ nk ) N×K ∈{0,1} N×K Represents a binary selection matrix. In passive random access, the total number of devices does not affect the result. Define Φ = diag(φ1, φ2, ..., φ N )and in The received signal in the CS phase can be represented as:

[0049]

[0050] LDPC codes are a class of linear block codes based on sparse parity-check matrices, first proposed by Robert G. Gallager in 1962. Due to their performance approaching the Shannon limit and their efficient iterative decoding algorithm, LDPC codes have become a core error-correcting coding technique in modern communication systems. An LDPC code can be completely determined by a generator matrix G and a parity-check matrix H, allowing... Indicates the remaining B of device k d A binary message, the LDPC encoded codeword is: LDPC-encoded codewords are modulated and converted into symbol sequences that can be transmitted over the channel. To enhance the sparsity of the signal, we employ a sparse expansion strategy, considering the symbol sequence... Fill in:

[0051]

[0052] Where L d This is the pilot length for the decoding stage. Next, we will... Reorder, let indicates the interleaving pattern is i k a random interleaver with interleaving pattern , and the final coded sequence is obtained by interleaving and concatenating the code words from the CS stage

[0053] The received signals from the CS encoding stage and the LDPC encoding stage are

[0054]

[0055] Hybrid precoding is a key technology in millimeter wave massive MIMO systems, aiming to balance system performance and hardware complexity. Due to the serious path loss in the millimeter wave frequency band, a large-scale antenna array is needed for compensation, but full-digital precoding requires each antenna to be connected to a radio frequency chain, which is costly. Hybrid precoding combines analog precoding and digital precoding, reducing the number of radio frequency chains while maintaining performance close to full-digital precoding. Hybrid precoding algorithms usually have high computational complexity, and in the configuration of large-scale MIMO scene passive random access protocol, the number of antennas and active devices may cause the system's delay requirement to be difficult to meet. When performing multi-user joint decoding, the embodiment considers optimizing the analog combining matrix separately, and uses a multi-user joint decoding algorithm framework to realize the joint processing of MIMO detection and LDPC decoding. Next, the optimization problem of the analog combining matrix will be established. The channel estimation of the active device is equivalent to MMSE estimation, and the true value is equal to the estimated value plus Gaussian white noise. Let denote the channel vector of the active device k and the mth AP, Δh k,m is a random variable independent of and follows a complex Gaussian distribution with zero mean and variance Let s k denote the data symbol sent by the active device k at a certain time slot, and the received signal of the mth AP is:

[0056]

[0057] where ρ is the average transmit power, is an additive Gaussian white noise with zero mean and variance . Assuming that all signal processing processes are carried out on the CPU side, aggregating all AP received signals can be obtained:

[0058]

[0059] Let Expression (11) can be rewritten as:

[0060]

[0061] where Assume Then Expression (12) is the final received signal at the receiving end, which we equivalently model as a single-user MIMO channel. The achievable rate R of the massive MIMO system is given by

[0062]

[0063] where We design the analog combining matrix W to maximize the achievable rate R RF The optimization problem can be formulated as

[0064]

[0065] where is the i-th beam vector of the analog combining matrix of the m-th AP, and N rf is the number of RF chains. Due to the constant modulus constraint of the analog precoding matrix, the phase adjustability of each array element is limited, which leads to the non-convexity of the optimization problem P in mathematics, and traditional convex optimization tools cannot be directly applied. Especially in massive MIMO systems, as the antenna size increases, the complexity of problem solving also increases significantly. Next, we will combine the characteristics of massive MIMO to approximate the original problem and obtain a heuristic algorithm for the analog combining matrix.

[0066] II. Heuristic optimization algorithm

[0067] The following gives the design of the analog combining matrix optimization algorithm under the massive MIMO system. In the massive MIMO system, when the number of antennas is sufficiently large, we have Therefore The objective function can be further simplified as The original optimization problem can be approximated as

[0068]

[0069] where Although the original problem has been sufficiently simplified in form, the number of antennas involved in the massive MIMO system is extremely large, and when the problem size is large, direct solution still faces high computational complexity. Therefore, based on the following theorem, the original problem is decomposed into several sub-problems of similar type, and the computational complexity is effectively reduced by solving them one by one.

[0070] Theorem: In a massive MIMO system with M apThe total achievable sum rate in a large-scale MIMO system with K APs The achievable sum rate for the mth AP.

[0071]

[0072] where is the channel matrix of the mth AP, where K a denotes the number of active users and:

[0073]

[0074] According to the theorem, the original optimization problem of precoding matrix can be decomposed into M ap single-AP analog precoding matrix optimization problems which are solved one by one:

[0075]

[0076] where is the element in the nth row and rth column of W RF,m . Let u mr denote the eigenvector corresponding to the rth largest singular value of the matrix , the optimal solution of the above problem is: The eigenvalues and eigenvectors of a matrix are usually solved by SVD decomposition, and the computational complexity is M an is the number of antennas of each AP. The time complexity of the direct solution of the original problem P' is as high as The embodiment decomposes the original problem into M ap sub-problems which are solved iteratively, and the computational complexity of each sub-problem is reduced to Through this divide-and-conquer strategy, the overall time complexity is reduced from to , achieving a complexity reduction of two orders of magnitude.

[0077]

[0078] As can be seen from expression (16), the optimal analog combining matrix not only depends on the channel matrix of the mth AP, but also depends on the channel matrices of the first m-1 APs. The optimal analog combining matrix depends on the channel state information of all APs The AP node does not perform signal processing locally, and under the system architecture based on CPU centralized processing, algorithm 1 shows the heuristic optimization solving process of the analog combining matrix. First, starting from the first AP, the SVD is executed for the current AP to obtain the channel eigenvector (steps 2-5), and the beam vectors in the analog combining matrix of the current AP are constructed based on the eigenvector; then the optimal analog combining matrix of the AP is generated through beam synthesis (Step 7); steps 8-9 calculate Q m for updating the optimal analog combining matrix of the next AP; repeat the above steps until the analog combining matrix of all APs is solved.

[0079] III. Multi-user joint decoding algorithm

[0080] In order to further improve the decoding performance of multi-user scene under the partial connection MIMO channel, the following will be based on the heuristic algorithm of the analog combining matrix, and will focus on designing a joint LDPC decoding algorithm suitable for multi-user scene. This decoding algorithm will make full use of the design results of the analog combining matrix, so as to realize more efficient and reliable data recovery. Although the traditional LDPC decoding algorithm based on message passing mechanism can approach the Shannon limit performance in the additive white Gaussian noise channel, its direct extension is difficult to adapt to the special transmission characteristics of the partial connection MIMO channel. Therefore, based on the proposed multi-user joint LDPC decoding framework, this embodiment fuses model-driven deep learning technology to construct a neural network algorithm with channel adaptation capability. This scheme expands the traditional iterative algorithm into a deep neural network structure, while maintaining the theoretical advantages of the message passing mechanism, and introduces trainable decoding parameters to adapt to the multi-user interference characteristics under the partial connection MIMO channel.

[0081] (1) LDPC decoding algorithm based on message propagation

[0082] After completing the active user detection and channel estimation phase to obtain key parameters such as interleaving mode and channel matrix, the receiving end enters the LDPC decoding phase to reconstruct the original information bits of the transmitting end from the received signal. LDPC decoding algorithm is divided into hard decoding and soft decoding, and the soft decoding algorithm based on message propagation calculates the posterior probability of information bits, and iteratively transmits posterior probability information between variable nodes and check nodes, which can theoretically approach the Shannon capacity limit. The passive random access protocol under large-scale machine type communication requires high computational complexity for MIMO detection, and the traditional method of first performing linear processing to recover the transmitted symbols and then performing data decoding needs to bear high computational cost. We jointly process the MIMO detection process and the LDPC decoding process based on message propagation, and consider the received data in the LDPC phase:

[0083] The task of the LDPC decoder is to recover the information sequence sent by the active devices based on the received signal Y d , the interleaving pattern and the channel matrix . The interleaving pattern i k and the channel matrix h k are one-to-one corresponding, which can be found from the received data expression k and the codeword sequence are also one-to-one corresponding. In the sending process, the information sequence v k of the active device k is divided into the preamble sequence and the payload sequence . The interleaving pattern is determined by the preamble sequence , the codeword sequence is determined by the payload sequence , and the interleaving pattern i k and the codeword sequence are one-to-one corresponding in the decoding process. The complete information sequence sent by the active device can be correctly reconstructed. Figure 3 For the factor graph form of expression (19), the entire factor graph is composed of variable nodes {s kl}, check nodes {c kn}, observed nodes {y ml} and edges connecting the nodes. The upper half is the Tanner graph representation of all active devices, and the connection relationship of the Tanner graph of each device is completely determined by the check matrix. For the kth device, if the element c ln = 1, it means that there is an edge between the variable node s kl and the check node c kn . The connection relationship in the lower half is determined by expression (21), and there is an interleaver between the variable node and the observed node of each active device. The purpose of interleaving is to reduce the impact of burst errors in the transmission process, and interleaving only changes the arrangement relationship of the variable node without affecting the message propagation process. It is noted that the coded codeword has undergone zero padding before interleaving, and the number of variable nodes and observed nodes of each active device is not necessarily equal. It can be seen from the factor graph that the message propagation process is divided into four steps: first, the observed node message flows to the variable node, second, the variable node message flows to the observed node, then the variable node message flows to the check node, and finally the check node message flows to the variable node. Assuming that the system uses BPSK modulation, the messages transmitted by each node are defined as follows:

[0084] · represents the message transmitted by the variable node s to the check node c kn ;

[0085] · represents the message transmitted by the check node c kn to the variable node the message passed to the variable node

[0086] · denotes the observation node the message passed to the variable node the message passed to the variable node

[0087] · denotes the variable node the message passed to the observation node the message passed to the observation node

[0088] Considering the message passing from the observation node to the variable node , in the multi-user channel, there are not only Gaussian noise but also interference signals from other users, we adopt the strategy of regarding interference as noise to deal with it, regarding the multi-user interference as equivalent noise, the received signal expression of the observation node

[0089]

[0090] where denote the index of the variable node associated with the observation node , respectively, denotes the Gaussian white noise with mean zero and variance . According to the central limit theorem, when the number of active devices is sufficiently large, the multi-user interference can be approximated as a Gaussian random variable with mean and variance

[0091]

[0092] For the BPSK system, the posterior mean and variance of the element

[0093]

[0094] denotes the log-likelihood ratio under the condition that the observation node is known, which can be expressed as

[0095]

[0096] denotes the probability of the variable node under the condition that the observation node is known, the new needs to collect the messages of the check nodes associated with the variable node and other observation nodes, which can be expressed as

[0097] ​​

[0098] represents the set of observation nodes associated with variable node The subscript set is used for the message passing between variable nodes and check nodes. For the message passing, we adopt the log-domain message propagation algorithm:

[0099]

[0100] where represents the set of variable nodes associated with check node c kn After the message passing converges, the log-likelihood ratio of variable node can be represented as:

[0101]

[0102] When the log-likelihood ratio is greater than 0, the information bit is decoded as 1, otherwise 0. The algorithm terminates when the iteration reaches the maximum number or all codewords are successfully detected.

[0103] Interleaving pattern and channel matrix The error in the active device estimation can degrade the performance of the detection algorithm. We can verify the correctness of the active device estimation by exploiting the characteristics of the LDPC code. Let denote the signal reconstructed by the decoding algorithm for device k, if then device k is an active device, otherwise, device k is misidentified as an active device or the decoding is incorrect. We use SIC to enhance the performance of the multi-user LDPC decoding, let and denote the correct codeword and active devices obtained by the multi-user LDPC decoding algorithm, and denote all the correctly detected codewords and active devices satisfying the constraints, respectively. To reduce the multi-user interference, we cancel the correctly detected codewords from the received signal:

[0104] and are initialized as empty sets. When the received signal Y d , interleaving pattern and channel matrix are given, the LDPC decoding algorithm outputs the verified codeword and active devices The currently detected codeword and active devices are added to ​and interfered signal for input of next round LDPC decoding algorithm, the algorithm repeats constantly until or Algorithm 2 shows the whole process of multi-user joint LDPC decoding, the algorithm takes the received signal Y d , interleaving pattern and channel estimation as input, steps 6-12 correspond to the multi-user decoding process based on message passing, steps 13-14 eliminate the correctly detected codeword from the received signal, the eliminated signal is taken as the input of the next round of multi-user joint LDPC decoding, the algorithm repeats the above steps until there is no new codeword.

[0105] The passive random access protocol detects the information bit sequence sent by the active device, but does not identify the specific active device. The information bits of the active device k in the sending process are divided into two parts, the preamble sequence and the payload sequence , and the complete sending information needs to be correctly spliced from the bit sequences in and . Each corresponds to a unique interleaving pattern and channel matrix, while the interleaving pattern is uniquely determined by . Using the corresponding relationship of the interleaving pattern, the two separated information sequences can be correctly spliced.

[0106]

[0107] (2) AI-assisted multi-user joint LDPC decoding algorithm

[0108] In the previous section, we derived the multi-user joint LDPC decoding algorithm based on message passing. The message passing of variable nodes and check nodes is based on the message passing algorithm in the logarithmic domain, which involves a large number of tangent function and inverse tangent function operations. The hardware that can calculate the tangent function has high cost and high implementation complexity. In practice, the simplified sum algorithm or offset sum algorithm is more commonly used, which simplifies the tangent function operation at the cost of part of the performance. Model-driven deep learning provides a new choice for implementing LDPC decoding algorithms with low complexity and high performance. It can learn optimized parameters from a small amount of data sets to improve network performance. In the following, we use model-driven deep learning to enhance the performance of the LDPC decoding algorithm based on message passing.

[0109] All devices share the same parity-check matrix, and the message update process from variable nodes to parity nodes follows the same Tanner graph structure. The LDPC decoding network designed for a single user device possesses cross-device transfer capabilities. The core of the model-driven deep learning-based decoding network construction method lies in establishing a mapping relationship between the iterative algorithm and the neural network layers, thereby compensating for various errors caused by approximation in the iterative algorithm. Compared to the complex hyperbolic function operations inherent in logarithmic message propagation algorithms, the minimum-sum decoding algorithm significantly reduces computational complexity while maintaining suboptimal decoding performance through linear approximation of the parity node update rule. The iterative process of this algorithm can be deconstructed into three feature stages: forward message passing from variable nodes to parity nodes; backward message passing from parity nodes to variable nodes; and log-likelihood ratio output based on soft-decision information. We map the minimum-sum decoding algorithm to an l max The neural network consists of layers, each modeled as a neural layer with two learnable parameters. The first sub-layer implements message passing from the verification node to the variable node, allowing... This represents the first-level verification node c. kn Passed to variable node The message, the first sub-layer update rule is:

[0110]

[0111] Where sgn(·) represents the sign function, α (l) ,β (l) These represent the weight parameters and bias terms of the first layer of the neural network, respectively. The second sub-layer implements the message passing process from the variable node to the verification node. Represents the first-level variable node Passed to the verification node c kn The message, the second sub-layer update rule is:

[0112]

[0113] Where γ (l) This represents the weight parameters of the second sub-layer. This hierarchical mapping mechanism not only preserves the physical interpretability of the minimum-sum algorithm, but more importantly, achieves global optimization of the decoding parameters through the backpropagation algorithm. Note the calculation... Messages from the observation node to the verification node are required. We map the message passing process between the variable node and the observation node to the MIMO detection module. For the stability of the algorithm, the MIMO detection module does not introduce additional learnable parameters. Let... This indicates the observation node output by the first-layer MIMO detection module. To the variable node The news, This represents the variable node output by the first-layer MIMO detection module. to the observation nodes . The update rule of the MIMO detection module is given by the multi-user joint LDPC decoding algorithm:

[0114] At the last layer of the network, we compute the log-likelihood ratios of the variable nodes, and define the output layer of the network as:

[0115]

[0116] σ(·) denotes the activation function. The information recovery problem of the neural network can be modeled as an N-dimensional binary classification optimization problem, where each dimension corresponds to a binary bit in the original information bit sequence. The step characteristic of the hard decision output will cause the neural network to lose gradient information during backpropagation, which severely restricts the training effect of the model. In the training phase, we use the sigmoid function:

[0117] This function has two significant advantages: first, its continuous and derivable S-shaped curve provides a stable gradient flow for backpropagation, effectively avoiding the gradient vanishing phenomenon during training; second, the output value can be interpreted as the posterior probability of the bit value, and this soft decision characteristic enables the network to retain the reliability information required for channel decoding. In the testing phase, we use the sign function to generate the bit sequence:

[0118] This differentiated processing strategy in the training and testing phases ensures the numerical stability of the training process while meeting the physical layer requirement of determining the bit output for the communication system.

[0119] Figure 4 The MIMO-LDPC-Net decoding network structure proposed in this embodiment is shown, which is divided into input layer, hidden layer and output layer. The input layer generates initial values as the input of the hidden layer, the hidden layer is stacked by the modules composed of the first sub-layer, the second sub-layer and the MIMO detection layer, and the output layer generates the log-likelihood ratio of the variable node. The learnable parameters of the network are The neural network generates d and and the channel matrix as inputs and In each hidden layer, the MIMO detection layer receives the messages from the previous layer and the received signal Y d to calculate the messages from the observation nodes to the variable nodes Variable node Message to check node First sub-layer receives message of previous layer Calculate check node c kn Message to variable node Second sub-layer receives message of previous layer And Calculate variable node Message to check node c kn The output layer generates the log-likelihood ratio estimate value of the variable node through the differentiable mapping, the sigmoid function is used to smooth the output in the training stage to keep the gradient derivable, and the sign function is converted in the test stage to realize the hard decision output.

[0120] In the training process, the cross-entropy loss function is used to evaluate the error between the network output and the true value, for the estimated value of the network output And the true value v k , the cross-entropy loss is defined as:

[0121]

[0122] Where is the soft estimate value of the i-th information bit, v k (i) is the information bit transmitted in the i-th transmission. In specific training, we consider a l max layer decoding network, first train the parameters {alpha (1) , beta (1) , gamma (1)} of the first layer independently until convergence, then freeze the parameters of the layer and optimize the parameters of the second layer alone; after completing the basic layer training, the parameters of the first two layers are optimized through joint fine-tuning This iterative process is extended to the l max layer by layer, forming a "local-global" alternating parameter learning paradigm. In particular, each layer of the network is initialized to inherit the multi-user joint LDPC decoding algorithm, which is equivalent to the original LDPC decoding algorithm when optimizing the hyperparameters, and the network has a good initial value, providing a benchmark guarantee for the performance gain of deep learning. The network has only a small number of learnable parameters, requires a small data set and has a short training time. Compared with the traditional sum algorithm which uses a greedy algorithm to obtain the weight and bias term, the network algorithm proposed in the present application has more learning ability for each layer to allocate learnable parameters, and learning parameters based on back propagation is beneficial to learning the features in the data set to compensate for the performance loss caused by simplification.

[0123] ​​​The proposed AI-assisted multi-user joint LDPC decoding algorithm is systematically simulated and verified below. The key parameters such as the number of device information bits, the number of iterations of the AI-assisted algorithm, and the LDPC code rate are shown in Table 1. The hyperparameter configuration for network training: the sample sizes of the training set, validation set, and test set are 10,000, 1,000, and 3,000, respectively, the batch size is set to 64, the initial learning rate is 0.001, and the fine-tuning is performed using the staged weight decay strategy (the decay factors are 1, 0.5, and 0.1, respectively). The performance evaluation is based on the proposed P md , P fa As evaluation indicators, we will analyze the various parameters of the system next.

[0124] We first evaluate the performance of the proposed MIMO-LDPC-Net decoding network. To simplify the analysis process, no additional zero padding and interleaving operations are introduced in the experimental design, i.e., no interleaving and deinterleaving processing is required between the variable nodes and the observation nodes. To eliminate the coupling effect of active user detection and channel estimation on decoding performance, this embodiment uses real channel matrices in both training and testing stages, and assumes that the number of active devices is known. Figure 5 The comparison curves of error probability versus signal-to-noise ratio are shown. The experimental results show that the multi-user joint LDPC decoding algorithm, MIMO-LDPC-Net, and the algorithm combined with SIC all show an accelerated downward trend in error probability as the signal-to-noise ratio improves, and the improvement in signal-to-noise ratio condition significantly improves the detection performance. The MIMO-LDPC-Net algorithm is superior to the multi-user joint LDPC decoding algorithm in the entire SNR range, and exhibits a performance gain of about 0.7 dB when the signal-to-noise ratio is greater than 13 dB. It is worth noting that although the SIC technology can effectively suppress multi-user interference and improve performance in the low signal-to-noise ratio region by checking the matrix code word correctness, its performance gain tends to saturate in the high signal-to-noise ratio region.

[0125] Table 1: Sparse interleaved multiple access parameter configuration

[0126]

[0127] Figure 6The error probability performance curves of three algorithms with the change of signal-to-noise ratio are compared: 1) the benchmark scheme of using the random phase analog combining matrix; 2) the heuristic algorithm + multi-user joint LDPC decoding algorithm; 3) the heuristic algorithm + MIMO-LDPC-Net decoding network. The experimental results show that the error probability of the three algorithms decreases significantly with the increase of SNR, among which the heuristic algorithm + AI assisted joint decoding algorithm shows the optimal performance, and can realize a performance gain of up to 1dB compared with other schemes. It is worth noting that simply using the heuristic algorithm can optimize the analog combining matrix to improve the channel capacity and significantly reduce the error probability, and the gain amplitude is greater than the AI trained neural network when the signal-to-noise ratio is greater than 13dB. This phenomenon shows that optimizing the analog combining matrix at the system design level may have a greater contribution to performance improvement than the pure data-driven AI training strategy, especially in the channel capacity limited scenario.

[0128] The embodiment of the present application also discloses a computer system, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, and the computer program realizes the steps of the model-driven deep learning based multi-user joint decoding method of the cell-free massive MIMO system when executed by the processor.

[0129] The embodiment of the present application also discloses a computer program product, comprising a computer program, and the computer program realizes the steps of the model-driven deep learning based multi-user joint decoding method of the cell-free massive MIMO system when executed by the processor.

[0130] The program code for implementing the method of the present application can be written in any combination of one or more programming languages. The program code can be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the program code, when executed by the processor or controller, causes the steps of the method of the present application to be implemented. The program code can be executed entirely on a machine, partially on a machine, partially on a machine as a separate software package and partially on a remote machine or server. The present application does not detail the known technology of those skilled in the art.

Claims

1. A multi-user joint decoding method for cellular-free massive MIMO systems based on model-driven deep learning, characterized in that, Includes the following steps: In the simulation part of data decoding, an optimization problem of the simulation combination matrix is ​​established with the objective of maximizing the achievable rate of the non-cellular massive MIMO system. Based on a heuristic algorithm, the optimization objective is simplified and the optimization problem is decomposed into multiple subproblems. The single AP simulation precoding matrix optimization problem is solved one by one to obtain the optimal simulation combination matrix. The multi-user joint LDPC decoding algorithm is extended to the non-cellular large-scale MIMO scenario. Multi-user joint LDPC decoding is realized based on the MIMO-LDPC-Net decoding network. The input layer of the MIMO-LDPC-Net decoding network generates initial values ​​as input to the hidden layer. The hidden layer is composed of stacked modules consisting of the first sub-layer, the second sub-layer, and the MIMO detection layer. The output layer generates the log-likelihood ratio of the variable nodes.

2. The multi-user joint decoding method for cellular-free massive MIMO systems based on model-driven deep learning according to claim 1, characterized in that, The optimization problem of maximizing the achievable rate of the simulated combination matrix is ​​expressed as: Among them, the achievable rate For an identity array, ρ is the average transmit power, and W is the transmit power. RF,m Let m be the simulated combination matrix of the m-th AP. Let N be the i-th beam vector of the simulated combination matrix of the m-th AP. rf This refers to the number of radio frequency links. Variance of additive white Gaussian noise Let K be the variance of the random variables in the channel vector of active device k and the m-th AP. a The number of active devices. This is the channel matrix.

3. The multi-user joint decoding method for cellular-free massive MIMO systems based on model-driven deep learning according to claim 2, characterized in that, The optimization objective is simplified to in 4. The multi-user joint decoding method for cellular-free massive MIMO systems based on model-driven deep learning according to claim 3, characterized in that, The single-AP analog precoding matrix optimization problem is expressed as: in, For W RF,m The element in the nth row and rth column, Let m be the channel matrix of the m-th AP. It is additive white Gaussian noise.

5. The multi-user joint decoding method for cellular-free massive MIMO systems based on model-driven deep learning according to claim 4, characterized in that, The process of solving the simulated combination matrix using a heuristic algorithm is as follows: First, traverse from the first AP, and for the current AP pair... SVD decomposition is performed to obtain channel feature vectors, and beam vectors in the simulated combination matrix of the current AP are constructed based on these feature vectors. Subsequently, the optimal simulated combination matrix of the AP is generated through beam synthesis. Calculate Q again m Used to update the optimal simulation combination matrix for the next AP; repeat until the simulation combination matrices for all APs have been solved.

6. The multi-user joint decoding method for cellular-free massive MIMO systems based on model-driven deep learning according to claim 1, characterized in that, The neural network takes the received signal, interleaving mode, and channel matrix as input to generate messages from the variable node to the observation node, messages from the check node to the variable node, and messages from the variable node to the check node. In each hidden layer, the MIMO detection layer receives messages from the variable node to the observation node, messages from the check node to the variable node, and received signals from the previous layer to calculate messages from the observation node to the variable node and messages from the variable node to the observation node. The first sub-layer receives messages from the variable nodes of the previous layer and passes them to the verification nodes, then calculates the messages from the verification nodes to the variable nodes. The second sub-layer receives messages from the observation nodes and verification nodes of the previous layer and passes them to the variable nodes, then calculates the messages from the variable nodes to the verification nodes. The output layer generates log-likelihood ratio estimates for the variable nodes through differentiable mappings. During the training phase, the sigmoid function is used to smooth the output to maintain gradient differentiability, while during the testing phase, it is converted to a sign function to achieve hard decision output.

7. The multi-user joint decoding method for cellular-free massive MIMO systems based on model-driven deep learning according to claim 6, characterized in that, The first sub-layer implements message passing from the verification node to the variable node, making Indicates the verification node c at layer l. kn Passed to variable node The news, Indicates the verification node c kn The update rule for the first sub-layer of the associated variable node set is as follows: in, Represents the variable node s at level l-1 kj Passed to the verification node c kn The message, sgn(·) represents the sign function, α (l) ,β (l) These represent the weight parameters and bias terms of the l-th layer of the neural network, respectively; the second sub-layer implements the message passing process from the variable node to the verification node, letting... Represents the l-th level variable node Passed to the verification node c kn The news, Represents the variable node Associated observation nodes Subscript set Represents variable nodes The neighboring nodes, the second-level update rule is: in, This represents the observation node output by the (l-1)th layer MIMO detection module. To variable node The news, Indicates the verification node c at layer l. kn′ Passed to variable node The message, γ (l) This represents the weight parameters of the second sub-layer.

8. The multi-user joint decoding method for cellular-free massive MIMO systems based on model-driven deep learning according to claim 7, characterized in that, The learnable parameters of a neural network are l max To determine the number of network layers, during actual training, the parameters {α} of the first layer are first... (1) ,β (1) ,γ (1) The training proceeds independently until convergence, then the parameters of the first layer are frozen and the parameters of the second layer are optimized separately. After the training of the base layers is completed, the parameters of the first two layers are jointly optimized through fine-tuning. This iterative process expands layer by layer to the lth... max Layers are formed to create a parameter learning paradigm that alternates between local and global approaches.

9. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed by the processor, it implements the steps of the multi-user joint decoding method for non-cellular massive MIMO systems based on model-driven deep learning as described in any one of claims 1-8.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the multi-user joint decoding method for non-cellular massive MIMO systems based on model-driven deep learning as described in any one of claims 1-8.

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