Cooperative distributed mamp signal recovery method for random multiplexing system

Abstract

The application discloses a kind of cooperation distributed MAMP signal recovery methods of random multiplexing system, this method is divided into inner iteration and outer iteration, inner iteration is each distributed node using local information to carry out local MAMP estimation, outer iteration is that center node collects the local estimation value of each distributed node after carrying out global optimal fusion to obtain global estimation value, and then feedback to each distributed node to carry out the next round of inner iteration.Local MAMP estimation uses cross-domain detection method with time domain channel sparsity, with very low complexity to carry out signal recovery.The application extends the local orthogonality of MAMP to global orthogonality, thereby proving that the local estimation value of each distributed node is subject to joint Gaussian distribution, and using the distribution, a global optimal fusion method is proposed, which outperforms Gaussian combining.The application is also applicable to channel correlation and noise correlation scenarios without additional preprocessing.

Description

Technical Field

[0001] This invention relates to the field of signal transmission, and more particularly to a cooperative distributed MAMP signal recovery method for a random multiplexing system. Background Technology

[0002] In highly mobile scenarios, such as high-speed trains, drones, and rapidly developing low Earth orbit satellite communication systems, the propagation environment of wireless signals is extremely complex and dynamically changing, posing a severe challenge to the stability and performance of communication systems. These scenarios share the common characteristic of extremely high relative speeds between transmitters and receivers, while the signal transmission path is affected by obstruction and reflection from the surrounding environment, causing the wireless channel to suffer from both multipath delay spread and significant Doppler shift. This dual effect, combined, forms a typical time-frequency dual-selective fading channel. Specifically, the difference in arrival time of signals along different paths caused by multipath effects results in frequency-selective fading and inter-symbol interference (ISI). Simultaneously, the Doppler shift caused by high-speed motion results in rapid temporal changes in the channel, leading to time-selective fading and inter-carrier interference (ICI). Time-frequency dual-selective fading presents a significant challenge to signal recovery; therefore, to ensure reliable and high-data-rate communication in highly mobile environments, system design must employ more advanced modulation and signal recovery techniques.

[0003] To overcome the challenges posed by time-frequency dual-selective fading in high-mobility scenarios, random multiplexing (RM) technology has been proposed as a promising solution. The core idea of ​​random multiplexing is to transform the original channel into a dense equivalent channel matrix using a random transformation (RT). This transformation mechanism ensures that the transmitted signal undergoes sufficient statistical fading by creating a dense channel matrix, which is crucial for overcoming deep fading and achieving reliable communication. Furthermore, the design of random multiplexing naturally imbues its equivalent channel matrix with right-unitary invariance. This key characteristic precisely satisfies the specific requirements of Approximate Message Passing (AMP) detectors for the channel matrix, enabling these advanced detectors to achieve maximum a posteriori (MAP) optimal performance. These combined characteristics make random multiplexing a powerful tool for addressing the complexity of high-mobility channels.

[0004] Driven by technological advancements and the demands of modern applications, a vast amount of high-dimensional datasets have been generated, often exceeding the processing capabilities of a single computer system. Therefore, distributed processing across multiple nodes has become an effective solution for handling computationally intensive tasks. Meanwhile, in the field of wireless communication, with the ever-increasing demands for data rates and coverage, centralized multiple-input multiple-output (MIMO) systems face performance bottlenecks, primarily limited by array aperture and channel spatial correlation. To overcome these limitations, a distributed antenna architecture has become an inevitable trend. Because antennas are distributed across different geographical locations, they experience more independent fading channels, significantly reducing spatial correlation between antennas and thus achieving greater diversity gain, effectively improving system reliability. Furthermore, the distributed deployment of antennas allows for more uniform signal coverage over a large area, effectively solving the coverage blind spots and edge effects inherent in centralized systems, greatly enhancing coverage performance. However, there is currently no distributed signal recovery method for stochastic multiplexing systems. Based on the advantages of the aforementioned distributed architecture, researching and designing cooperative distributed signal recovery methods for stochastic multiplexing systems has profound theoretical and practical significance. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a cooperative distributed MAMP signal recovery method for random multiplexing systems.

[0006] The objective of this invention is achieved through the following technical solution: a cooperative distributed MAMP signal recovery method for a random multiplexing system, comprising:

[0007] The transmitter modulates and randomly multiplexes the bit information, then transmits it to the receiver via an antenna.

[0008] The receiver consists of several distributed nodes. Each node performs an internal iterative calculation of the received signal using cross-domain MAMP detection to obtain a local estimate. The central node collects all the local estimates and performs an external iterative calculation to obtain a globally fused global estimate. The global estimate is then broadcast back to each distributed node as the initial value for the next round of internal iteration, thus initiating the next round of internal and external iterations. When the preset number of external iterations is reached, the nonlinear estimator in MAMP is used to process the global estimate to obtain the final estimated signal.

[0009] Furthermore, the random multiplexing at the transmitter end includes:

[0010] ;

[0011] in They are independent and identically distributed signal vectors. It is a random unitary matrix independent of the signal and channel. , It is a signal to be sent after random transformation. The equivalent channel experienced is represented as , It is a right-unitary invariant matrix.

[0012] Furthermore, the inner iterative calculation for cross-domain MAMP detection of the received signal includes:

[0013] The input is processed using a nonlinear estimator after a preset number of iterations to obtain signal estimates. The input includes global or local estimates. The global estimate is obtained through external iteration or initialization and serves as the initial input for the current iteration. The local estimate is the output of the previous iteration.

[0014] Damping estimation is performed after randomly transforming the signal estimate using a random unitary matrix.

[0015] The output value after damping estimation and the observation vector of the distributed nodes are input into the linear estimator. The output of the linear estimator is subjected to inverse random transformation to obtain the local estimate for the next inner iteration. After executing a preset number of iterations, the local estimate is output.

[0016] Furthermore, the calculation process of the linear estimator is as follows:

[0017] ,

[0018] ,

[0019] in, For the observation vectors of distributed nodes, This is an auxiliary state variable, initialized to 0. These are the weighting coefficients. , The scaling parameter is the output value after damping estimation. , , The variance of the input error for the linear estimator; , and They represent { The largest and smallest eigenvalues ​​of}, where and They represent the first The channel matrix of each distributed node and its conjugate transpose; The normalization coefficient is... These are the orthogonality coefficients.

[0020] Furthermore, the weighting coefficients Represented as

[0021] ,

[0022] in, ;

[0023] The orthogonality coefficients are... The error variance corresponding to the input of the linear estimator, and the intermediate parameters. , and The meaning of the formula is as follows:

[0024] ,

[0025] ,

[0026] ,

[0027] .

[0028] Furthermore, the normalization coefficient and orthogonality coefficients Represented as

[0029] ,

[0030] ;

[0031] Damping vector Represented as:

[0032] ,

[0033] ,

[0034] Representation matrix The inverse matrix.

[0035] Furthermore, the process of performing external iterations to obtain the globally estimated value after global fusion includes:

[0036] A linear fusion method is used to fuse the local estimates.

[0037] Construct a quadratic programming problem with the aim of minimizing the variance of the global estimate.

[0038] ;

[0039] in These are the fusion coefficients of the local estimated real values. Indicates taking the real part, The covariance matrix representing the errors between the local estimates of distributed nodes;

[0040] when When it is reversible, solving the problem yields:

[0041] ;

[0042] ;

[0043] ;

[0044] when When the matrix is ​​not invertible, its invertibility can be guaranteed by adding a small number of diagonal values.

[0045] Furthermore, the real part of the covariance matrix between the errors of the local estimates of the distributed nodes Obtained through approximate measurement methods:

[0046] ,

[0047]

[0048] in and These are the known variances of the outputs of the nonlinear estimator and the linear estimator, respectively.

[0049] According to another aspect of the specification, a cooperative distributed MAMP signal recovery device for a random multiplexing system is also provided, including a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it implements the cooperative distributed MAMP signal recovery method for a random multiplexing system.

[0050] According to another aspect of the specification, a computer-readable storage medium is also provided, on which a program is stored, which, when executed by a processor, implements the cooperative distributed MAMP signal recovery method for a random multiplexing system.

[0051] The beneficial effects of this invention are: it exhibits strong anti-fading properties in high-mobility scenarios, and compared with existing technologies such as OFDM+MAMP, OTFS+MAMP, and AFDM+MAMP, the proposed RM+CD-MAMP has a lower bit error rate at the same signal-to-noise ratio. Furthermore, the proposed CD-MAMP reduces the computational load on a single processor while also reducing communication overhead. The inner iteration uses a low-complexity MAMP, further reducing complexity by leveraging the sparsity of the time-domain channel matrix. The outer iteration employs an optimal fusion method, which outperforms Gaussian combining and is also applicable to correlated channels and correlated noise scenarios, and it requires no preprocessing, thus exhibiting higher robustness. Attached Figure Description

[0052] Figure 1 This is a block diagram of a random multiplexing system.

[0053] Figure 2 This is a flowchart of the CD-MAMP signal recovery process.

[0054] Figure 3 This is a comparison diagram of the sparsity of time-domain channels and random transform-domain channels in high-mobility scenarios.

[0055] Figure 4 This is a performance comparison chart of CD-MAMP external iteration using the optimal fusion method and using Gaussian merging.

[0056] Figure 5 This is a performance comparison chart of the combined number of inner and outer iterations in CD-MAMP.

[0057] Figure 6 This is a performance comparison chart of RM+CD-MAMP, OFDM+MAMP, OTFS+MAMP, and AFDM+MAMP.

[0058] Figure 7 This is a schematic diagram of a cooperative distributed signal recovery device for a random multiplexing system provided in an embodiment of the present invention. Detailed Implementation

[0059] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0060] like Figure 1 As shown, the present invention provides a cooperative distributed MAMP signal recovery method for a random multiplexing system, the method comprising:

[0061] The transmitter modulates and randomly multiplexes the bit information, then transmits it to the receiver via an antenna.

[0062] In a communication transmitter, random multiplexing is defined by the following random transformation:

[0063] ,

[0064] in It is an independent and identically distributed (IID) signal vector. It is a random unitary matrix independent of the signal and channel. It is the signal to be transmitted after random transformation. (Send signal) The equivalent channel matrix experienced is represented as , Represents the original channel matrix. Equivalent channel matrix. It has the property of being right-unitary invariant, and its elements approximate the Haar distribution.

[0065] random unitary matrix It includes the IID matrix, the Haar distribution matrix, and the permutation-invariant matrix. The IID matrix and the Haar distribution matrix require highly complex methods for generation and storage, which is inconvenient for engineering implementation. The permutation-invariant matrix provides lower implementation complexity. The permutation-invariant matrix is ​​represented as... ,in For a uniform random permutation matrix, It is a deterministic unitary matrix. Typically... Structured transformation matrices with fast algorithmic properties are selected, such as Discrete Fourier Transform (DFT), Hadamard-Walsh Transform (HWT), and Interleaved Block Sparse Transform (IBST).

[0066] At the receiver, the received signal is discretized and vectorized.

[0067] ,

[0068] in It is the received observation vector. It is the time-domain channel matrix. It is the equivalent channel matrix. It is additive white Gaussian noise (AWGN). Indicates the noise variance. It is the identity matrix. For... For a distributed system consisting of n distributed nodes, the nth The observation vectors received by the distributed nodes are

[0069] ,

[0070] in Indicates the first The length of each distributed node is The observation vector, , Indicates the first Equivalent channel matrix of distributed nodes It is the first An AWGN with multiple distributed nodes. Centralized signal recovery methods require each distributed node to collect all observation vectors { } and equivalent channel matrix { The data is transmitted to a central node for centralized processing. This results in significant communication overhead and latency. This invention proposes a signal recovery method consisting of local computation via inner iteration and global processing via outer iteration to reduce communication overhead. Figure 2 As shown. Specifically, each distributed node utilizes local information { The local estimate is obtained by performing MAMP computation. The central node gathers all { Global fusion is performed to obtain the global estimate. Then The broadcast feedback is sent to each distributed node as the initial value for the next round of iteration.

[0071] CD-MAMP consists of an inner-iteration cross-domain MAMP detection and an outer-iteration optimal fusion.

[0072] (1) Intra-domain MAMP: This invention utilizes the sparsity of the time-domain channel and employs a cross-domain MAMP detection method to reduce complexity. Cross-domain MAMP includes a linear estimator (LE). And a nonlinear estimator (NLE) and random transformation modules, such as Figure 2 The local estimation module is shown in the diagram. Each distributed node performs cross-domain MAMP detection locally, with the first... Taking a distributed node as an example, let and They represent { The largest and smallest eigenvalues ​​of}, where and They represent the first The channel matrix of each distributed node and its conjugate transpose. Define intermediate variable parameters. , It is a variable scalar. , , Represents the identity matrix.

[0073] Cross-domain MAMP: Intra-iterative index from arrive Initialize parameters and linearly estimate intermediate variables Damping vector Linear estimation results ,

[0074] NLE: ,

[0075] RT: ,

[0076] Damping: ,

[0077] MLE: ,

[0078] ,

[0079] IRT:

[0080] in, It is an orthogonal nonlinear estimator function. This invention defines the input and output errors of the linear estimator, and the corresponding error variance, as follows:

[0081] , ,

[0082] , .

[0083] Similarly, the input and output errors of the nonlinear estimator and the corresponding error variance are expressed as follows:

[0084] , .

[0085] , .

[0086] Scaling parameters After optimization, it is , This invention defines characteristic coefficients.

[0087]

[0088] To simplify the formula expression, the iteration index value is constrained. , Define simplified variables

[0089]

[0090] ,

[0091] ,

[0092] Optimized weight coefficients Represented as

[0093] ,

[0094] in

[0095]

[0096] Normalization coefficient and orthogonality coefficients To represent as

[0097] ,

[0098] .

[0099] Damping vector It can be represented as

[0100] ,

[0101] ,

[0102] Representation matrix The inverse matrix.

[0103] go through The local estimate output of the next iteration is And the variance is All local estimates are transmitted to the central node for global optimal fusion. Orthogonal parameters and the orthogonal nonlinear estimation function The local estimation error is guaranteed to satisfy the following orthogonality constraints.

[0104] ,

[0105] ,

[0106] ,

[0107] ,

[0108] The extended Stein's lemma can be used to generalize local orthogonality constraints to global orthogonality constraints. Under global orthogonality constraints, the local estimation error matrix... The elements in each column are IID (Individual Identifier), and the elements in the same row are jointly Gaussian distributed. This is the local estimate. Error The two are joint Gaussians.

[0109] (2) External iteration (global optimal fusion): External iteration is to combine the local estimates of the internal iteration of each distributed node. Using global fusion function A global optimal merging process is performed to obtain the final global estimate. This is based on the fact that all local estimates are for the same signal. The estimation, and possessing joint Gaussian properties, is presented using a linear fusion method in this invention. The external iterative index is used for the... For example, the local estimate This is represented as The fused global estimate Represented as

[0110] ,

[0111] The fusion coefficients are real numbers that satisfy... Global estimate variance Represented as

[0112] ,

[0113] in This indicates an error in the local estimates of the distributed nodes. The covariance matrix between them. This invention aims to minimize the variance of the global estimate. To construct a quadratic programming problem for the purpose of

[0114]

[0115] because The fusion coefficients are real numbers, therefore , To denote the real part, the above quadratic programming problem can be rewritten as:

[0116] .

[0117] when When it is reversible, solving the problem yields:

[0118] ,

[0119] ,

[0120] .

[0121] when In cases of irreversibility, this invention ensures matrix invertibility in engineering practice by adding a small number of diagonal values. After obtaining the global estimate, it is broadcast to each distributed node, and the first... The global estimate is obtained in the next outer iteration. As the initial value for the next iteration of each distributed node. Initiate the next round of inner and outer iterations, such as Figure 2 As shown.

[0122] Approximate measurement: It is worth noting that, Indicates a local estimation error Covariance moments between . It is the signal to be estimated, therefore the theoretical derivation This cannot be achieved. The present invention provides a method for approximate measurement to obtain... Approximate value.

[0123] ,

[0124]

[0125] in and These are the known variances of the outputs of the nonlinear estimator and the linear estimator, respectively.

[0126] The Gaussian merging of traditional inventions is represented as

[0127] ; .

[0128] Traditional Gaussian merging assumes that the merged components are independent and does not consider correlations; this is a special case of the present invention when the components are independent. Therefore, the optimal fusion method of the present invention theoretically outperforms traditional Gaussian merging.

[0129] Specifically, the parameters used in this embodiment are as follows:

[0130] 1. Implementation of the transmitter

[0131] The following describes a specific implementation of a multi-carrier random multiplexing system transmitter, using MATLAB for software simulation. Figure 1 The diagram shows a single configuration with baseband parameters set as follows: subcarrier spacing 15kHz, number of subcarriers N=400, ideal bandwidth 6MHz, and carrier frequency 4GHz. Random multiplexing uses a permutation-invariant matrix. ,in It is a random permutation matrix. As a discrete Fourier matrix, the signal after QPSK or 16QAM modulation can be directly used in the implementation process. Performing a Discrete Fourier Transform has a complexity of O(n log n). The signal transmitted by this transmitter is .

[0132] 2. Multipath Fading Channel Setup

[0133] In high-mobility scenarios, this invention selects a dual-selective channel model for modeling, and its time-delay Doppler response is expressed as follows:

[0134]

[0135] Indicates the transmission path, Indicates path gain. Indicates path delay. Indicates path Doppler frequency shift, This represents the Dirac function. The basic parameters for setting the channel are: number of multipath paths. The power spectrum of these 5 paths is [1 0.18 0.17 0.15 0.12], the maximum delay is 1.5 microseconds, the relative speed is 300 km / h, the transmit and receive filters are root-raised cosine filters with roll-off coefficients, and the sampling rate is the same as the ideal bandwidth, i.e., 6MHz. Finally, the channel is discretized and vectorized to obtain the time-domain channel matrix. .

[0136] 3. Implementation of the receiver (signal recovery)

[0137] In the simulation, after the transmitter and channel settings are completed, the receiver receives the time-domain signal. , This represents AWGN. The received time-domain signal is analyzed using a CD-MAMP detector. Perform signal detection and set the number of distributed nodes. Number of inner iterations Number of outer iterations The CD-MAMP detection process is performed as follows:

[0138] initialization, , , , , , , , , ,

[0139] External iteration execution by = 1 to :

[0140] ① All distributed nodes Independent execution of cross-domain MAMP with internal iterations, the internal iterations are executed by = 1 to :

[0141] NLE: ,

[0142] RT: ,

[0143] Damping: ,

[0144] MLE: ,

[0145] ,

[0146] IRT: ,

[0147] The specific expressions for each parameter are given in “(1) Intra-iteration (Cross-domain MAMP)” above, and the distributed nodes execute. The local estimate is output during the next iteration. .

[0148] The in-round iteration loop ends.

[0149] ② The central node collects all local estimates { , , , Perform global fusion.

[0150] , , , ,

[0151] ,

[0152] Where the covariance matrix The approximate measurement method is obtained according to "(2) External Iteration (Global Optimal Fusion)" above. Finally, the global estimate is... The broadcast feedback is sent to each distributed node as the initial value for the next round of iteration. .

[0153] The outer iteration loop ends.

[0154] The final estimated value is output as follows. .

[0155] 4. Complexity Analysis

[0156] The following is a complexity analysis of CD-MAMP. The computational complexity of each distributed node mainly comes from LE (Leadership), NLE (Non-Leadership), and random transformations. For LE, all calculations consist of matrix multiplication of vectors, with a complexity of O(n log n). Because this invention employs a cross-domain detection method, LE is performed in a banded, sparse time-domain channel. If the time-domain channel matrix... Each line has If there are 1 non-zero element, then the LE complexity is further reduced to 1. As for NLE, the complexity of symbol-by-symbol MMSE estimation is... The random transformation in this invention uses the discrete Fourier transform form with a complexity of O(n). The number of inner iterations is The number of outer iterations is Therefore, the complexity of a single distributed node is... The central node needs The computation time to calculate the approximate covariance matrix is ​​O(n log n). Regarding communication overhead, each distributed node needs to transmit its local estimate to the central node in each external iteration. The central node then performs global fusion and feeds back the estimate as the initial value. The total overhead is... The number of inner iterations affects the number of outer iterations; when the inner iterations are sufficient... It converges in just two outer iterations, as shown below. Figure 6 As shown.

[0157] CD-MAMP has broad application prospects in distributed signal recovery. The local computation plus global fusion approach adopted in this invention eliminates the need for each distributed node to transmit all local information to the central node for centralized processing; instead, it transmits local estimates, reducing communication overhead. Furthermore, this invention employs a cross-domain detection method during local estimation, placing the complex linear estimation within a strip-sparse time-domain channel, further reducing computational complexity. At the central node, this invention provides a globally optimal fusion method, aiming to minimize the variance of the fused global estimate, considering the correlation between the local estimates of each distributed node, and designing the optimal fusion coefficients. This invention also designs an approximate measurement method to calculate the covariance matrix, cleverly avoiding the involvement of unknown signals. The theoretical covariance derivation. The optimal fusion method provided by this invention fully considers the correlation between the components and performs better than the Gaussian merging method based on the independence assumption, such as... Figure 4 As shown.

[0158] Corresponding to the aforementioned embodiment of a CD-MAMP signal recovery method for a random multiplexing system, the present invention also provides an embodiment of a CD-MAMP signal recovery device for a random multiplexing system.

[0159] See Figure 7 The present invention provides a CD-MAMP signal recovery device for a random multiplexing system, comprising a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement a CD-MAMP signal recovery method for a random multiplexing system as described in the above embodiment.

[0160] The embodiment of the CD-MAMP signal recovery device for a random multiplexing system provided by this invention can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device reading the corresponding computer program instructions from non-volatile memory into memory and executing them. From a hardware perspective, such as... Figure 7The diagram shown is a hardware structure diagram of any device with data processing capabilities, where the CD-MAMP signal recovery device of the random multiplexing system provided by the present invention is located. Except for... Figure 7 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0161] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0162] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0163] This invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements a CD-MAMP signal recovery method for a random multiplexing system as described in the above embodiments.

[0164] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device of any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units and external storage devices of any data processing device. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0165] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the CD-MAMP signal recovery method for a random multiplexing system.

[0166] 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 examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0167] 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 cooperative distributed MAMP signal recovery method for a random multiplexing system, characterized in that, include: The transmitter modulates and randomly multiplexes the bit information, then transmits it to the receiver via an antenna. The receiver consists of several distributed nodes. Each node performs an internal iterative calculation of the received signal using cross-domain MAMP detection to obtain a local estimate. The central node collects all the local estimates and performs an external iterative calculation to obtain a globally fused global estimate. The global estimate is then broadcast back to each distributed node as the initial value for the next round of internal iteration, thus initiating the next round of internal and external iterations. When the preset number of external iterations is reached, the nonlinear estimator in MAMP is used to process the global estimate to obtain the final estimated signal.

2. The cooperative distributed MAMP signal recovery method for a random multiplexing system according to claim 1, characterized in that, The random multiplexing at the transmitter end includes: ； in They are independent and identically distributed signal vectors. It is a random unitary matrix independent of the signal and channel. , It is a signal to be sent after random transformation. The equivalent channel experienced is represented as , It is a right-unitary invariant matrix.

3. The cooperative distributed MAMP signal recovery method for a random multiplexing system according to claim 1, characterized in that, The inner iterative calculation for cross-domain MAMP detection of the received signal includes: The input is processed using a nonlinear estimator after a preset number of iterations to obtain signal estimates. The input includes global or local estimates. The global estimate is obtained through external iteration or initialization and serves as the initial input for the current iteration. The local estimate is the output of the previous iteration. Damping estimation is performed after randomly transforming the signal estimate using a random unitary matrix. The output value after damping estimation and the observation vector of the distributed nodes are input into the linear estimator. The output of the linear estimator is subjected to inverse random transformation to obtain the local estimate for the next inner iteration. After executing a preset number of iterations, the local estimate is output.

4. The cooperative distributed MAMP signal recovery method for a random multiplexing system according to claim 3, characterized in that, The calculation process of the linear estimator is as follows: ， ， in, For the observation vectors of distributed nodes, This is an auxiliary state variable, initialized to 0. These are the weighting coefficients. , The scaling parameter is the output value after damping estimation. , , The variance of the input error for the linear estimator; , and They represent { The largest and smallest eigenvalues ​​of}, where and They represent the first The channel matrix of each distributed node and its conjugate transpose; The normalization coefficient is... These are the orthogonality coefficients.

5. The cooperative distributed MAMP signal recovery method for a random multiplexing system according to claim 4, characterized in that, The weighting coefficient Represented as ， in, ; The orthogonality coefficients are... The error variance corresponding to the input of the linear estimator, and the intermediate parameters. , and The meaning of the formula is as follows: ， ， ， 。 6. The cooperative distributed MAMP signal recovery method for a random multiplexing system according to claim 5, characterized in that, The normalization coefficient and orthogonality coefficients Represented as ， ； Damping vector Represented as: ， ， Representation matrix The inverse matrix.

7. The cooperative distributed MAMP signal recovery method for a random multiplexing system according to claim 1, characterized in that, The global estimate obtained by performing external iteration calculations includes: A linear fusion method is used to fuse the local estimates. Construct a quadratic programming problem with the aim of minimizing the variance of the global estimate. ； in These are the fusion coefficients of the local estimated real values. Indicates taking the real part, The covariance matrix representing the errors between the local estimates of distributed nodes; when When it is reversible, solving the problem yields: ； ； ； when When the matrix is ​​not invertible, its invertibility can be guaranteed by adding a small number of diagonal values.

8. The cooperative distributed MAMP signal recovery method for a random multiplexing system according to claim 7, characterized in that, The real part of the covariance matrix between the errors of the local estimates of the distributed nodes Obtained through approximate measurement methods: ， in and These are the known variances of the outputs of the nonlinear estimator and the linear estimator, respectively.

9. A cooperative distributed MAMP signal recovery device for a random multiplexing system, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements a cooperative distributed MAMP signal recovery method for a random multiplexing system as described in any one of claims 1-8.

10. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements a cooperative distributed MAMP signal recovery method for a random multiplexing system as described in any one of claims 1-8.

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