A multi-node concurrent transmission signal superposition diversity method

Abstract

The present invention discloses a multi-node concurrent transmission signal superposition diversity method, comprising the following steps: S1, using a Turbo encoder to generate a Turbo code sequence; S2, applying phase perturbation to each Turbo code sequence; S3, performing non-orthogonal superposition in an air channel to form a complex baseband signal; S4, constructing an equivalent observation model; S5, modeling the transmission symbol matrix as a sparse matrix to obtain a symbol estimation matrix; S6, inputting the symbol estimation matrix into a Turbo decoder, performing iterative decoding using an improved Max-Log-MAP algorithm, and outputting a bit estimation sequence; S7, using a Zadoff-Chu preamble to complete initial phase estimation, and outputting an estimated phase sequence through a Kalman filter; S8, dynamically updating the equivalent observation model based on the estimated phase sequence to complete parallel computing and scheduling. The present invention integrates Turbo coding, sparse reconstruction, and phase perturbation modeling to achieve multi-node non-orthogonal concurrent transmission.

Description

Technical Field

[0001] The present invention relates to the technical field of communication and signal processing, and in particular to a multi-node concurrent transmission signal superposition diversity method. Background Art

[0002] With the rapid development of wireless communication systems and IoT applications, multi-node concurrent access and non-orthogonal transmission technologies have become key research directions for improving system capacity and spectrum utilization. Traditional orthogonal multiple access methods such as TDMA, FDMA, and OFDMA suffer from low resource allocation efficiency and high scheduling complexity in high-density connection scenarios. Therefore, non-orthogonal multiple access and sparse multiple access are emerging as candidate alternatives to orthogonal access. In such non-orthogonal systems, multiple users or nodes can transmit signals superimposed on the same time-frequency resources. The receiver must use a joint detection algorithm to recover the individual user signals. However, because the transmitted signals are indiscriminately superimposed over the air, the receiver faces extremely high interference cancellation complexity and challenges in reliable decoding.

[0003] Currently, multi-node concurrent transmission systems often use precoding, multi-user detection (MUD), or iterative detection decoding to mitigate non-orthogonal interference. Precoding schemes rely on global channel state information at the transmitter and are difficult to adapt to large-scale node scenarios. The computational complexity of MUD schemes increases exponentially with the number of nodes, and performance fluctuates significantly under conditions of strong interference or sparse connectivity. To improve decoding reliability and computational efficiency, some systems have introduced sparse modeling methods, treating multi-user transmitted signals as sparse matrices and achieving symbol reconstruction through compressed sensing, matching pursuit, and approximate message passing algorithms. While these methods have certain performance advantages in theory, in actual deployment, they suffer from limited recovery accuracy, accumulated reconstruction errors, and severe performance degradation when channel estimates are inaccurate.

[0004] On the other hand, to improve system robustness and diversity gain, some communication systems have introduced phase perturbation or spread spectrum modulation techniques, enhancing signal separation capabilities by introducing pseudo-random rotation sequences into the transmitted signal. However, most existing methods remain at the static perturbation level and fail to achieve a dynamically adjustable phase structure. Furthermore, the receiver relies on blind algorithms or pilot-assisted estimation to estimate perturbations, making it difficult to track phase drift under channel variations. This results in a significant mismatch between the received model and the actual signal, which in turn affects symbol detection and subsequent decoding performance.

[0005] In serial iterative structures like turbo decoding, the lack of joint modeling of signal structure and perturbation information makes it easy for overconfidence enhancement or transmission distortion to occur during the external information update process. This causes the bit error rate to plateau in the high signal-to-noise ratio range, limiting the upper limit of system performance. Although some studies have attempted to simplify the decoding process through Max-Log-MAP and introduce scaling factors to adjust confidence information, a complete end-to-end system design has not yet been established. In particular, there is a lack of effective coupling mechanisms between multiple submodules such as sparse reconstruction, turbo decoding, phase estimation, and model feedback.

[0006] Therefore, how to provide a multi-node concurrent transmission signal superposition diversity method is a problem that those skilled in the art urgently need to solve. Summary of the Invention

[0007] One purpose of the present invention is to propose a multi-node concurrent transmission signal superposition diversity method. The present invention integrates Turbo coding and an improved Max-Log-MAP decoding method, introduces Kasami code-driven phase perturbation and Zadoff-Chu preamble code auxiliary estimation, and combines sparse modeling with an approximate message passing algorithm to realize non-orthogonal concurrent superposition transmission of multi-node signals in the air, and dynamically constructs an updateable observation model at the receiving end. The method has the advantages of strong interference suppression, accurate symbol recovery, high decoding reliability, excellent computational efficiency and strong system scalability, and is suitable for large-scale intensive access scenarios.

[0008] A multi-node concurrent transmission signal superposition diversity method according to an embodiment of the present invention includes the following steps:

[0009] S1. Use the Turbo encoder to encode the original bit stream of each node and adjust it by puncturing according to the target bit rate to generate a Turbo code sequence;

[0010] S2. Applying phase perturbation to each Turbo coded sequence based on a pseudo-random sequence, where the phase perturbation is driven by a binary sequence consisting of Kasami codes, to generate a phase modulation sequence;

[0011] S3. Modulate and synthesize the Turbo coding sequence of each node with the phase modulation sequence, transmit synchronously by multiple nodes, and perform non-orthogonal superposition in the air channel to form a complex baseband signal;

[0012] S4. The receiving end constructs an equivalent observation model according to the complex baseband signal, where the equivalent observation model is represented as a received signal matrix consisting of the product of a channel response matrix, a phase disturbance matrix, and a transmitted symbol matrix, superimposed with a noise term;

[0013] S5. Modeling the transmission symbol matrix in the equivalent observation model as a sparse matrix, constructing an overcomplete dictionary, and performing sparse reconstruction using an approximate message passing algorithm to obtain a symbol estimation matrix;

[0014] S6. Input the symbol estimation matrix into a Turbo decoder, perform iterative decoding using an improved Max-Log-MAP algorithm, introduce a scaling factor to adjust the external information update process, and output a bit estimation sequence;

[0015] S7, using the Zadoff-Chu preamble to complete the initial phase estimation, using the bit estimation sequence as soft information input, and outputting the estimated phase sequence through the Kalman filter;

[0016] S8. Dynamically update the equivalent observation model based on the estimated phase sequence, and use a pipeline structure and AXI-Stream interface to complete parallel computing and scheduling.

[0017] Optionally, the S1 specifically includes:

[0018] S11. Configure a Turbo encoder for each node, where the Turbo encoder includes a first encoding branch, a second encoding branch, and an interleaver.

[0019] S12. Input the original bit stream to a first coding branch and an interleaver, wherein the first coding branch directly receives the original bit stream as input, and the interleaver permutes the original bit stream according to an interleaving rule. The interleaving rule adopts a block interleaving method, and fills the input bit stream by row according to a set row-column mapping relationship and then outputs it by column to form an interleaved bit stream;

[0020] S13: Input the interleaved bit stream to the second coding branch, and the first coding branch and the second coding branch respectively perform recursive convolution coding on the corresponding received bit streams, and output a first coding sequence and a second coding sequence;

[0021] S14, combining the original bit stream with the first coding sequence and the second coding sequence to form a Turbo coding output bit stream;

[0022] S15. Puncturing the Turbo coded output stream according to a redundancy requirement corresponding to a preset target code rate, deleting redundant bits, and generating a Turbo coded sequence.

[0023] Optionally, the S2 specifically includes:

[0024] S21. Generate a set of length for each node Kasami code sequence ,in Indicates the node number, represents a symbol index, wherein the Kasami code sequence is a periodic pseudo-random binary sequence;

[0025] S22, set the chip period and phase perturbation step size , where the chip period The duration of time corresponding to each code element and the phase perturbation step length is a constant value;

[0026] S23, each code element Map to the corresponding time interval , maintaining a constant phase perturbation value within the time interval ;

[0027] S24, construction node The continuous-time phase perturbation function of :

[0028] ;

[0029] in, Indicates at a point in time Previous node The instantaneous phase rotation applied, is the unit rectangular function, defined as The value is 1 when , otherwise it is 0, which is used to limit each disturbance value to be constant and valid within the chip period;

[0030] S25. Constructing a node based on the continuous-time phase disturbance function Complex exponential phase modulation function of:

[0031] ;

[0032] in, represents the complex exponential phase modulation function, Indicates at a point in time Previous node The phase modulation factor, represents an imaginary unit, satisfying , used to represent rotation operations in the complex plane;

[0033] S26. Output a phase modulation sequence of each node based on the complex exponential phase modulation function.

[0034] Optionally, the S3 specifically includes:

[0035] S31. Obtain a Turbo coding sequence and a corresponding phase modulation sequence of each node, and multiply each symbol of the Turbo coding sequence by a corresponding phase modulation factor in the phase modulation sequence to generate a phase modulation signal sequence;

[0036] S32, performing digital-to-analog conversion on the phase modulated signal sequence to convert it into an analog baseband signal for wireless transmission;

[0037] S33. Synchronize and control all nodes through a multi-node time synchronization mechanism, so that all nodes simultaneously transmit their respective analog baseband signals within a unified transmission time slot;

[0038] S34. In the air channel, the analog baseband signals transmitted by all nodes are superimposed in a non-orthogonal form at the receiving side to form a complex baseband signal.

[0039] Optionally, the S4 specifically includes:

[0040] S41, the receiving end receives the complex baseband signals transmitted synchronously by multiple nodes in real time, and discretizes them in time and space dimensions to form a receiving signal matrix , where each column corresponds to a symbol time slot and each row corresponds to the observation data of a receiving antenna channel;

[0041] S42, construct an equivalent observation model, and transform the received signal matrix Expressed as:

[0042] ;

[0043] in, represents the channel response matrix, with dimension , indicating that from Sending nodes to The complex channel gain of the receiving antennas; Represents the phase perturbation matrix, which is a one-dimensional The complex diagonal matrix, the diagonal elements are the phase modulation factors of each node at the corresponding time point; Represents the transmitted symbol matrix, with dimension , Indicates the total number of complex modulation symbols sent by each node in a time slot; Represents the noise matrix, which contains the complex white Gaussian noise component received by each channel.

[0044] Optionally, the S5 specifically includes:

[0045] S51. Modeling the transmission symbol matrix in the equivalent observation model as a sparse matrix, where the sparse matrix means that in any time slot, only no more than 10% of the total number of nodes are in an active state, that is, the corresponding symbol elements are non-zero, and the remaining symbol elements are zero;

[0046] S52, performing a product operation on the channel response matrix and the phase disturbance matrix to construct an overcomplete dictionary matrix required for sparse reconstruction, where the overcomplete dictionary matrix represents a complex linear mapping relationship from a transmitted symbol space to a received signal space;

[0047] S53. Establish the objective function of the sparse reconstruction problem:

[0048] ;

[0049] in, represents the L1 norm of the transmitted symbol matrix, Represents the minimize operation, represents the received signal matrix, represents the overcomplete dictionary matrix, represents the square of the L2 norm, Indicates the preset tolerance threshold;

[0050] S54, using an approximate message passing algorithm to iteratively solve the sparse reconstruction problem, specifically including: initializing a symbol estimation matrix and observation residuals, adjusting the symbol estimation in each iteration based on feedback from the observation residuals of the previous round, updating the posterior mean of each symbol element in combination with the noise variance and the Laplace sparsity prior, and terminating the iteration when the difference between the estimates of two consecutive iterations is less than a set difference threshold or the maximum number of iterations is reached;

[0051] S55. Output the symbol estimation matrix solved by the approximate message passing algorithm.

[0052] Optionally, the S6 specifically includes:

[0053] S61, inputting the symbol estimation matrix as soft information into a Turbo decoder corresponding to each node, wherein the Turbo decoder includes a first decoding branch, a second decoding branch, and an interleaver, forming an iterative structure;

[0054] S62, in each iteration, the improved Max-Log-MAP algorithm is used to calculate the information bits The log-likelihood ratio The improved Max-Log-MAP algorithm is based on the forward recursive variable , backward recursive variables , branch metric function And the state transition path of receiving information constructs the metric difference:

[0055] ;

[0056] in, and Respectively represent the starting state and the ending state of the state transition;

[0057] S63, the branch metric function Indicates that at the symbol time From the starting state Transfer to the terminal state The log-likelihood measure of the corresponding path is:

[0058] ;

[0059] in, Indicates the The receiving symbol at the moment, Indicates that the input information bit is 、The path is Received The conditional probability of Represents the input information bit The prior probability of

[0060] S64. Introducing scaling factors while calculating external information , scale and correct the external information generated in each iteration;

[0061] S65: The extrinsic information generated by the first decoding branch is subjected to bit position rearrangement by the interleaver and then input into the second decoding branch. The second decoding branch uses the extrinsic information as a priori probability and performs path recursive operation and metric update in combination with the observation signal received by itself to obtain new extrinsic information. The new extrinsic information generated by the second decoding branch is transmitted back to the first decoding branch via the deinterleaver as a priori input for the next round of iteration. The two decoding branches alternately execute the new extrinsic information until the maximum number of iterations is reached or the change in the bit log-likelihood ratio between the previous and next rounds is less than a preset change threshold.

[0062] S66: Output the bit estimation sequence after the final iteration of the Turbo decoder as the restored original information bit stream.

[0063] Optionally, the S7 specifically includes:

[0064] S71. Embed a preamble consisting of a Zadoff-Chu sequence in a signal frame transmitted by each node to assist the receiving end in performing initial phase estimation.

[0065] S72. The receiving end extracts the Zadoff-Chu preamble from the received complex baseband signal and completes the initial phase offset estimation of each node based on the locally known sequence.

[0066] S73, using the bit estimation sequence as soft information input, and combining the phase evolution behavior of the received signal between multiple symbols to construct a dynamic observation data sequence;

[0067] S74. Based on the initial phase offset estimation of each node and the dynamic observation data sequence, a Kalman filter is used to perform recursive estimation of phase disturbance, and phase drift and carrier frequency offset are tracked in real time, and the estimated value is gradually corrected.

[0068] S75. Output the complete estimated phase sequence of each node.

[0069] Optionally, the S8 specifically includes:

[0070] S81. The receiving end obtains an estimated phase sequence corresponding to each node, where the estimated phase sequence represents a phase rotation change experienced by the node at each symbol time point.

[0071] S82, updating the phase perturbation matrix in the equivalent observation model according to the estimated phase sequence, replacing the diagonal elements corresponding to each node in the phase perturbation matrix with the phase modulation factors constructed according to the estimated phase sequence;

[0072] S83. Constructing a new equivalent observation model based on the updated phase perturbation matrix to describe the mapping relationship between the current received signal and the transmitted symbol;

[0073] S84, uses pipeline structure to improve data processing parallelism, and builds data transmission path through AXI-Stream interface to complete scheduling, and automatically updates equivalent observation model.

[0074] The beneficial effects of the present invention are:

[0075] (1) By introducing pseudo-random phase perturbations driven by Kasami codes into the signals transmitted by each node, differentiated modulation of non-orthogonal superposition at the physical layer is achieved, which improves the separability of signals when superimposed in the air and reduces the interference coupling between multiple nodes;

[0076] (2) The joint design of Turbo coding and Max-Log-MAP decoding, combined with the dynamic adjustment mechanism of soft information and scaling factors, effectively improves decoding convergence and error performance under low signal-to-noise ratio;

[0077] (3) Modeling the received symbols as sparse matrices, and performing low-complexity sparse reconstruction through an approximate message passing algorithm, thereby improving the accuracy of symbol estimation when some nodes are active and the channel conditions are complex;

[0078] (4) The Zadoff-Chu preamble and Kalman filter are introduced to realize the recursive estimation of phase disturbance and frequency offset compensation, thereby improving the receiver's adaptive ability to dynamic phase changes and enhancing the system robustness;

[0079] (5) Construct a dynamically updateable equivalent observation model, and combine the pipeline structure with the AXI-Stream interface to implement module-level parallel computing, optimize system throughput and deployability, and form multiple diversity gain mechanisms in the space, time, and modulation domains, which is suitable for large-scale distributed wireless communication scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0081] Figure 1 This is an overall flow chart of a multi-node concurrent transmission signal superposition diversity method proposed by the present invention;

[0082] Figure 2 This is a schematic diagram of the structure of a Turbo encoder for a multi-node concurrent transmission signal superposition diversity method proposed by the present invention;

[0083] Figure 3 This is a Max-Log-MAP decoding flow chart based on a Turbo decoder structure for a multi-node concurrent transmission signal superposition diversity method proposed by the present invention. DETAILED DESCRIPTION

[0084] The present invention will now be described in further detail with reference to the accompanying drawings, which are simplified schematic diagrams that illustrate the basic structure of the present invention in a schematic manner.

[0085] refer to Figure 1-Figure 3 A multi-node concurrent transmission signal superposition diversity method comprises the following steps:

[0086] S1. Use the Turbo encoder to encode the original bit stream of each node and adjust it by puncturing according to the target bit rate to generate a Turbo code sequence;

[0087] S2. Applying phase perturbation to each Turbo coded sequence based on a pseudo-random sequence, where the phase perturbation is driven by a binary sequence consisting of Kasami codes, to generate a phase modulation sequence;

[0088] S3. Modulate and synthesize the Turbo coding sequence of each node with the phase modulation sequence, transmit synchronously by multiple nodes, and perform non-orthogonal superposition in the air channel to form a complex baseband signal;

[0089] S4. The receiving end constructs an equivalent observation model according to the complex baseband signal, where the equivalent observation model is represented as a received signal matrix consisting of the product of a channel response matrix, a phase disturbance matrix, and a transmitted symbol matrix, superimposed with a noise term;

[0090] S5. Modeling the transmission symbol matrix in the equivalent observation model as a sparse matrix, constructing an overcomplete dictionary, and performing sparse reconstruction using an approximate message passing algorithm to obtain a symbol estimation matrix;

[0091] S6. Input the symbol estimation matrix into a Turbo decoder, perform iterative decoding using an improved Max-Log-MAP algorithm, introduce a scaling factor to adjust the external information update process, and output a bit estimation sequence;

[0092] S7, using the Zadoff-Chu preamble to complete the initial phase estimation, using the bit estimation sequence as soft information input, and outputting the estimated phase sequence through the Kalman filter;

[0093] S8. Dynamically update the equivalent observation model based on the estimated phase sequence, and use a pipeline structure and AXI-Stream interface to complete parallel computing and scheduling.

[0094] This method builds an end-to-end multi-node concurrent transmission and reception decoding system, integrating Turbo coding, phase perturbation, sparse modeling, and dynamic observation update techniques to achieve reliable separation and restoration of multi-node data in a non-orthogonal overlay environment. The soft-information-driven Turbo iterative structure and Kalman filter perturbation estimation enhance the system's adaptability to dynamic channel conditions such as phase variation and frequency offset. The overall architecture is highly parallelizable and deployable, making it suitable for scenarios such as the Internet of Things and large-scale access, with excellent robustness and high channel capacity utilization.

[0095] In this embodiment, S1 specifically includes:

[0096] S11. Configure a Turbo encoder for each node, where the Turbo encoder includes a first encoding branch, a second encoding branch, and an interleaver.

[0097] S12. Input the original bit stream to a first coding branch and an interleaver, wherein the first coding branch directly receives the original bit stream as input, and the interleaver permutes the original bit stream according to an interleaving rule. The interleaving rule adopts a block interleaving method, and fills the input bit stream by row according to a set row-column mapping relationship and then outputs it by column to form an interleaved bit stream;

[0098] S13: Input the interleaved bit stream to the second coding branch, and the first coding branch and the second coding branch respectively perform recursive convolution coding on the corresponding received bit streams, and output a first coding sequence and a second coding sequence;

[0099] S14, combining the original bit stream with the first coding sequence and the second coding sequence to form a Turbo coding output bit stream;

[0100] S15. Puncturing the Turbo coded output stream according to a redundancy requirement corresponding to a preset target bit rate, deleting redundant bits, and generating a Turbo coded sequence.

[0101] The turbo coding structure, consisting of two recursive convolutional encoders and an interleaver, effectively improves the coding redundancy and structural symmetry of the original information. The introduction of a block interleaver breaks up inter-bit correlation, enhancing robustness against burst errors. This structure offers excellent soft information traceability and decomposability during iterative decoding, providing stable redundancy support for the receiver's recovery process, effectively reducing the bit error rate and enhancing channel coding gain.

[0102] In this embodiment, S2 specifically includes:

[0103] S21. Generate a set of length for each node Kasami code sequence ,in Indicates the node number, represents a symbol index, wherein the Kasami code sequence is a periodic pseudo-random binary sequence;

[0104] S22, set the chip period and phase perturbation step size , where the chip period The duration of time corresponding to each code element and the phase perturbation step length is a constant value;

[0105] S23, each code element Map to the corresponding time interval , maintaining a constant phase perturbation value within the time interval ;

[0106] S24, construction node The continuous-time phase perturbation function of :

[0107] ;

[0108] in, Indicates at a point in time Previous node The instantaneous phase rotation applied, is the unit rectangular function, defined as The value is 1 when , otherwise it is 0, which is used to limit each disturbance value to be constant and valid within the chip period;

[0109] S25. Constructing a node based on the continuous-time phase disturbance function Complex exponential phase modulation function of:

[0110] ;

[0111] in, represents the complex exponential phase modulation function, Indicates at a point in time Previous node The phase modulation factor, represents an imaginary unit, satisfying , used to represent rotation operations in the complex plane;

[0112] S26. Output a phase modulation sequence of each node based on the complex exponential phase modulation function.

[0113] The phase perturbation mechanism uses a binary pseudo-random sequence driven by Kasami codes, combined with a continuous-time perturbation function and complex exponential modulation, to uniquely identify each node under co-frequency transmission conditions, thereby improving signal differentiation. Constant-step phase perturbation forms a time-consistent modulation sequence, creating an a priori foundation for interference suppression and decoding separation at the receiver, enhancing the multi-node system's anti-interference and non-orthogonal decoupling capabilities.

[0114] In this embodiment, S3 specifically includes:

[0115] S31. Obtain a Turbo coding sequence and a corresponding phase modulation sequence of each node, and multiply each symbol of the Turbo coding sequence by a corresponding phase modulation factor in the phase modulation sequence to generate a phase modulation signal sequence;

[0116] S32, performing digital-to-analog conversion on the phase modulated signal sequence to convert it into an analog baseband signal for wireless transmission;

[0117] S33. Synchronize and control all nodes through a multi-node time synchronization mechanism, so that all nodes simultaneously transmit their respective analog baseband signals within a unified transmission time slot;

[0118] S34. In the air channel, the analog baseband signals transmitted by all nodes are superimposed in a non-orthogonal form at the receiving side to form a complex baseband signal.

[0119] On the transmitter side, the signal's physical layer modulation mapping is achieved by multiplying the turbo-coded symbols with the phase modulation factor. This is then combined with digital-to-analog conversion to generate an analog baseband signal. A multi-node time synchronization mechanism ensures signal consistency on the transmitter side, creating a stable non-orthogonal overlay structure over the air. This approach enables multi-user concurrency without the need for frequency or code division, improving system spectrum efficiency and reducing scheduling complexity.

[0120] In this embodiment, the S4 specifically includes:

[0121] S41, the receiving end receives the complex baseband signals transmitted synchronously by multiple nodes in real time, and discretizes them in time and space dimensions to form a receiving signal matrix , where each column corresponds to a symbol time slot and each row corresponds to the observation data of a receiving antenna channel;

[0122] S42, construct an equivalent observation model, and transform the received signal matrix Expressed as:

[0123] ;

[0124] in, represents the channel response matrix, with dimension , indicating that from Sending nodes to The complex channel gain of the receiving antennas; Represents the phase perturbation matrix, which is a one-dimensional The complex diagonal matrix, the diagonal elements are the phase modulation factors of each node at the corresponding time point; Represents the transmitted symbol matrix, with dimension , Indicates the total number of complex modulation symbols sent by each node in a time slot; Represents the noise matrix, which contains the complex white Gaussian noise component received by each channel.

[0125] The equivalent observation model represents the received signal matrix as consisting of the product of the channel response matrix, the phase perturbation matrix, and the transmitted symbol matrix, plus a noise term. This enables unified, abstract modeling of the actual channel and modulation mechanism. The equivalent observation model is discretizable, scalable, and computable, providing high-fidelity input conditions for sparse reconstruction and decoding. Furthermore, the matrix format is compatible with multi-antenna receiving structures and possesses inherent spatial diversity capabilities.

[0126] In this embodiment, the S5 specifically includes:

[0127] S51. Modeling the transmission symbol matrix in the equivalent observation model as a sparse matrix, where the sparse matrix means that in any time slot, only no more than 10% of the total number of nodes are in an active state, that is, the corresponding symbol elements are non-zero, and the remaining symbol elements are zero;

[0128] S52, performing a product operation on the channel response matrix and the phase disturbance matrix to construct an overcomplete dictionary matrix required for sparse reconstruction, where the overcomplete dictionary matrix represents a complex linear mapping relationship from a transmitted symbol space to a received signal space;

[0129] S53. Establish the objective function of the sparse reconstruction problem:

[0130] ;

[0131] in, represents the L1 norm of the transmitted symbol matrix, Represents a minimize operation, represents the received signal matrix, represents the overcomplete dictionary matrix, represents the square of the L2 norm, Indicates the preset tolerance threshold;

[0132] S54, using an approximate message passing algorithm to iteratively solve the sparse reconstruction problem, specifically including: initializing a symbol estimation matrix and observation residuals, adjusting the symbol estimation in each iteration based on feedback from the observation residuals of the previous round, updating the posterior mean of each symbol element in combination with the noise variance and the Laplace sparsity prior, and terminating the iteration when the difference between the estimates of two consecutive iterations is less than a set difference threshold or the maximum number of iterations is reached;

[0133] S55. Output the symbol estimation matrix solved by the approximate message passing algorithm.

[0134] By implementing sparse modeling of the transmitted symbol matrix, introducing an overcomplete dictionary and a sparse reconstruction framework, the computational dimensionality of decoding is significantly reduced. The approximate message passing algorithm boasts low complexity, fast convergence, and robustness, making it suitable for dense access scenarios with extremely low node activity. High reconstruction accuracy and a clear iteration termination mechanism avoid the risk of model oscillation and misestimation, ensuring effective input for subsequent turbo decoding.

[0135] In this embodiment, S6 specifically includes:

[0136] S61, inputting the symbol estimation matrix as soft information into a Turbo decoder corresponding to each node, wherein the Turbo decoder includes a first decoding branch, a second decoding branch, and an interleaver, forming an iterative structure;

[0137] S62, in each iteration, the improved Max-Log-MAP algorithm is used to calculate the information bits The log-likelihood ratio The improved Max-Log-MAP algorithm is based on the forward recursive variable , backward recursive variables , branch metric function And the state transition path of receiving information constructs the metric difference:

[0138] ;

[0139] in, and Respectively represent the starting state and the ending state of the state transition;

[0140] S63, the branch metric function Indicates that at the symbol time From the starting state Transfer to the terminal state The log-likelihood measure of the corresponding path is:

[0141] ;

[0142] in, Indicates the The receiving symbol at the moment, Indicates that the input information bit is 、The path is Received The conditional probability of Represents the input information bit The prior probability of

[0143] S64. Introducing scaling factors while calculating external information , scale and correct the external information generated in each iteration;

[0144] S65: The extrinsic information generated by the first decoding branch is subjected to bit position rearrangement by the interleaver and then input into the second decoding branch. The second decoding branch uses the extrinsic information as a priori probability and performs path recursive operation and metric update in combination with the observation signal received by itself to obtain new extrinsic information. The new extrinsic information generated by the second decoding branch is transmitted back to the first decoding branch via the deinterleaver as a priori input for the next round of iteration. The two decoding branches alternately execute the new extrinsic information until the maximum number of iterations is reached or the change in the bit log-likelihood ratio between the previous and next rounds is less than a preset change threshold.

[0145] S66: Output the bit estimation sequence after the final iteration of the Turbo decoder as the restored original information bit stream.

[0146] The improved Max-Log-MAP algorithm implements a dual-branch alternating iterative structure within the Turbo decoder. Soft information is transferred between branches via an interleaver and deinterleaver, continuously optimizing the prior probability estimate. A scaling factor is introduced to control the update intensity, preventing oversaturation of confidence information and improving decoding stability. The overall structure converges to the optimal solution within a limited number of iterations, significantly improving the system's information recovery capabilities in weak channel conditions.

[0147] In this embodiment, the S7 specifically includes:

[0148] S71. Embed a preamble consisting of a Zadoff-Chu sequence in a signal frame transmitted by each node to assist the receiving end in performing initial phase estimation.

[0149] S72. The receiving end extracts the Zadoff-Chu preamble from the received complex baseband signal and completes the initial phase offset estimation of each node based on the locally known sequence.

[0150] S73, using the bit estimation sequence as soft information input, and combining the phase evolution behavior of the received signal between multiple symbols to construct a dynamic observation data sequence;

[0151] S74. Based on the initial phase offset estimation of each node and the dynamic observation data sequence, a Kalman filter is used to perform recursive estimation of phase disturbance, and phase drift and carrier frequency offset are tracked in real time, and the estimated value is gradually corrected.

[0152] S75. Output the complete estimated phase sequence of each node.

[0153] The excellent autocorrelation properties of the Zadoff-Chu preamble are utilized to achieve precise initial phase estimation. Combining bit soft information with the received signal state, and recursively updating through Kalman filtering, this approach accurately tracks phase perturbations and frequency offset variations in the node's transmitted signal. This estimation structure exhibits excellent responsiveness in dynamic environments, providing a reliable foundation for updating the equivalent observation model and enhancing the robustness of the entire decoding chain.

[0154] In this embodiment, the S8 specifically includes:

[0155] S81. The receiving end obtains an estimated phase sequence corresponding to each node, where the estimated phase sequence represents a phase rotation change experienced by the node at each symbol time point.

[0156] S82, updating the phase perturbation matrix in the equivalent observation model according to the estimated phase sequence, replacing the diagonal elements corresponding to each node in the phase perturbation matrix with the phase modulation factors constructed according to the estimated phase sequence;

[0157] S83. Constructing a new equivalent observation model based on the updated phase perturbation matrix to describe the mapping relationship between the current received signal and the transmitted symbol;

[0158] S84, uses pipeline structure to improve data processing parallelism, and builds data transmission path through AXI-Stream interface to complete scheduling, and automatically updates equivalent observation model.

[0159] Based on the estimated phase sequence, the phase perturbation matrix in the equivalent observation model is updated in real time to construct an equivalent receive channel mapping that reflects the current state. A pipelined architecture and AXI-Stream interface support high-concurrency computing, improving system throughput and execution efficiency. The model update mechanism is modular and scalable, providing efficient decoupling and decoding capabilities for large-scale node environments, and has great potential for engineering implementation.

[0160] Example 1:

[0161] To verify the feasibility of this invention, we applied it to a simulated multi-node communication platform to construct a representative wireless transmission scenario. This platform, comprising multiple heterogeneous transmitting nodes and multi-antenna receiving terminals, simulated a temporary deployment without fixed base stations, addressing real-world communication challenges in urban environments with high interference and frequent dynamic channel changes.

[0162] In the test scenario, in disaster emergency response, unmanned combat networks, and / or edge computing environments, multiple terminal devices need to upload key data to the central node at the same time. In this scenario, the traditional orthogonal multiple access method is difficult to adapt to scenarios with high concurrency and tight resources. The spectrum utilization rate is low and the synchronization accuracy requirements are high, resulting in increased bit error rate and frequent system bottlenecks. To this end, the present invention designs a multi-node synchronous transmission mechanism, introduces Turbo coding to enhance redundancy, and realizes node signal decorrelation through phase perturbation driven by Kasami code. The sparse modeling and message passing algorithm are combined to realize the joint recovery of multi-node signals at the receiving end.

[0163] In simulation tests, each node encodes the bit stream using an independent Turbo encoder, superimposes phase perturbations driven by Kasami codes, and transmits the bit stream. The receiver constructs an equivalent observation model, employs a sparse reconstruction algorithm to estimate the symbol matrix, and then performs Turbo decoding using an improved Max-Log-MAP algorithm. Kalman filtering accurately performs phase tracking and frequency offset compensation. The entire processing flow is deployed on a programmable platform, utilizing a pipelined architecture and AXI-Stream bus architecture for parallel processing and efficient data throughput.

[0164] Five consecutive rounds of testing revealed that, with a fixed number of eight nodes, the channel SNR ranged from 6.5dB to 14.5dB, demonstrating excellent system robustness. The number of turbo decoding iterations was controlled between 4 and 7, with an average bit error rate ranging from a minimum of 0.867% to a maximum of 1.550%, significantly outperforming traditional non-orthogonal communication schemes. Symbol recovery accuracy remained between 97.13% and 99.20%, with an average frequency offset compensation error below 0.05 rad, demonstrating that the Kalman filter effectively suppresses phase distortion caused by multipath and frequency offset. Furthermore, the system's total decoding delay was kept to 1622 milliseconds, meeting low-latency communication requirements.

[0165] Table 1 Summary of test results of multi-node Turbo decoding scheme

[0166]

[0167] The test results in Table 1 above fully demonstrate that the method proposed in the present invention can achieve highly reliable non-orthogonal signal recovery in a multi-node asynchronous environment, and has excellent error suppression capability and decoding efficiency. It effectively supplements and upgrades the traditional multiple access communication mode and has strong application and promotion value.

[0168] This embodiment significantly improves transmission reliability and decoding performance in non-orthogonal superposition environments by constructing a multi-node concurrent signal superposition diversity scheme based on turbo coding and sparse reconstruction. Experimental results show that under test conditions with eight nodes and a low-to-medium average channel SNR, the proposed scheme achieves symbol recovery accuracy exceeding 97% while maintaining a low bit error rate (BER as low as 0.86%), effectively compensating for performance degradation caused by frequency offset and phase perturbations. Furthermore, by introducing the soft information alternation mechanism and phase estimation feedback in the Max-Log-MAP decoding structure, the proposed scheme can achieve converged and stable bit estimation results within a limited number of iterations, meeting the low latency and high robustness requirements of practical communication systems. This embodiment fully demonstrates the diversity effect in multi-node coordinated transmission. By combining the strong error correction capabilities of turbo coding with the decoupling advantages of sparse modeling, it constructs a highly scalable and computationally efficient receive processing flow.

[0169] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A multi-node concurrent transmission signal superposition diversity method, characterized in that: The steps include: S1. Use the Turbo encoder to encode the original bit stream of each node and adjust it by puncturing according to the target bit rate to generate a Turbo code sequence; S2. Applying phase perturbation to each Turbo coded sequence based on a pseudo-random sequence, wherein the phase perturbation is driven by a binary sequence consisting of Kasami codes, and combining a continuous-time phase perturbation function with a complex exponential phase modulation function to generate a phase modulation sequence; S3. Modulate and synthesize the Turbo coding sequence of each node with the phase modulation sequence, transmit synchronously by multiple nodes, and perform non-orthogonal superposition in the air channel to form a complex baseband signal; S4. The receiving end constructs an equivalent observation model according to the complex baseband signal, where the equivalent observation model is represented as a received signal matrix consisting of the product of a channel response matrix, a phase disturbance matrix, and a transmitted symbol matrix, superimposed with a noise term; S5. Modeling the transmission symbol matrix in the equivalent observation model as a sparse matrix, constructing an overcomplete dictionary, and performing sparse reconstruction using an approximate message passing algorithm to obtain a symbol estimation matrix; S6. Input the symbol estimation matrix into a Turbo decoder, perform iterative decoding using an improved Max-Log-MAP algorithm, introduce a scaling factor to adjust the external information update process, and output a bit estimation sequence; The improved Max-Log-MAP algorithm is based on the forward recursive variable , backward recursive variables , branch metric function And the state transition path of receiving information constructs the metric difference: ； in, and Respectively represent the starting state and the ending state of the state transition; The branch metric function Indicates that at the symbol time From the starting state Transfer to the terminal state The log-likelihood measure of the corresponding path is: ； in, Indicates the The receiving symbol at the moment, Indicates that the input information bit is 、The path is Received The conditional probability of Represents the input information bit The prior probability of S7, using the Zadoff-Chu preamble to complete the initial phase estimation, using the bit estimation sequence as soft information input, and outputting the estimated phase sequence through the Kalman filter; S8. Dynamically update the equivalent observation model based on the estimated phase sequence, and use a pipeline structure and AXI-Stream interface to complete parallel computing and scheduling.

2. The multi-node concurrent transmission signal superposition diversity method according to claim 1, characterized in that: Said S1 specifically includes: S11. Configure a Turbo encoder for each node, where the Turbo encoder includes a first encoding branch, a second encoding branch, and an interleaver. S12. Input the original bit stream to a first coding branch and an interleaver, wherein the first coding branch directly receives the original bit stream as input, and the interleaver permutes the original bit stream according to an interleaving rule. The interleaving rule adopts a block interleaving method, and fills the input bit stream by row according to a set row-column mapping relationship and then outputs it by column to form an interleaved bit stream; S13: Input the interleaved bit stream to the second coding branch, and the first coding branch and the second coding branch respectively perform recursive convolution coding on the corresponding received bit streams, and output a first coding sequence and a second coding sequence; S14, combining the original bit stream with the first coding sequence and the second coding sequence to form a Turbo coding output bit stream; S15. Puncturing the Turbo coded output stream according to a redundancy requirement corresponding to a preset target bit rate, deleting redundant bits, and generating a Turbo coded sequence.

3. The multi-node concurrent transmission signal superposition diversity method according to claim 1, characterized in that: The S2 specifically includes: S21. Generate a set of length for each node Kasami code sequence ,in Indicates the node number, represents a symbol index, wherein the Kasami code sequence is a periodic pseudo-random binary sequence; S22, set the chip period and phase perturbation step size , where the chip period The duration of time corresponding to each code element and the phase perturbation step length is a constant value; S23, each code element Map to the corresponding time interval , maintaining a constant phase perturbation value within the time interval ; S24, construction node The continuous-time phase perturbation function of : ； in, Indicates at a point in time Previous node The instantaneous phase rotation applied, is the unit rectangular function, defined as The value is 1 when , otherwise it is 0, which is used to limit each disturbance value to be constant and valid within the chip period; S25. Constructing a node based on the continuous-time phase disturbance function Complex exponential phase modulation function of: ； in, represents the complex exponential phase modulation function, Indicates at a point in time Previous node The phase modulation factor, represents an imaginary unit, satisfying , used to represent rotation operations in the complex plane; S26. Output a phase modulation sequence of each node based on the complex exponential phase modulation function.

4. The multi-node concurrent transmission signal superposition diversity method according to claim 1, characterized in that: The S3 specifically includes: S31. Obtain a Turbo coding sequence and a corresponding phase modulation sequence of each node, and multiply each symbol of the Turbo coding sequence by a corresponding phase modulation factor in the phase modulation sequence to generate a phase modulation signal sequence; S32, performing digital-to-analog conversion on the phase modulated signal sequence to convert it into an analog baseband signal for wireless transmission; S33. Synchronize and control all nodes through a multi-node time synchronization mechanism, so that all nodes simultaneously transmit their respective analog baseband signals within a unified transmission time slot; S34. In the air channel, the analog baseband signals transmitted by all nodes are superimposed in a non-orthogonal form at the receiving side to form a complex baseband signal.

5. The multi-node concurrent transmission signal superposition diversity method according to claim 1, characterized in that: The S4 specifically includes: S41, the receiving end receives the complex baseband signals transmitted synchronously by multiple nodes in real time, and discretizes them in time and space dimensions to form a receiving signal matrix , where each column corresponds to a symbol time slot and each row corresponds to the observation data of a receiving antenna channel; S42, construct an equivalent observation model, and transform the received signal matrix Expressed as: ； in, represents the channel response matrix, with dimension , indicating that from Sending nodes to The complex channel gain of the receiving antennas; Represents the phase perturbation matrix, which is a one-dimensional The complex diagonal matrix, the diagonal elements are the phase modulation factors of each node at the corresponding time point; Represents the transmitted symbol matrix, with dimension , Indicates the total number of complex modulation symbols sent by each node in a time slot; Represents the noise matrix, which contains the complex white Gaussian noise component received by each channel.

6. The multi-node concurrent transmission signal superposition diversity method according to claim 1, characterized in that: The S5 specifically includes: S51. Modeling the transmission symbol matrix in the equivalent observation model as a sparse matrix, where the sparse matrix means that in any time slot, only no more than 10% of the total number of nodes are in an active state, that is, the corresponding symbol elements are non-zero, and the remaining symbol elements are zero; S52, performing a product operation on the channel response matrix and the phase disturbance matrix to construct an overcomplete dictionary matrix required for sparse reconstruction, where the overcomplete dictionary matrix represents a complex linear mapping relationship from a transmitted symbol space to a received signal space; S53. Establish the objective function of the sparse reconstruction problem: ； in, represents the L1 norm of the transmitted symbol matrix, Represents a minimize operation, represents the received signal matrix, represents the overcomplete dictionary matrix, represents the square of the L2 norm, Indicates the preset tolerance threshold; S54, using an approximate message passing algorithm to iteratively solve the sparse reconstruction problem, specifically including: initializing a symbol estimation matrix and observation residuals, adjusting the symbol estimation in each iteration based on feedback from the observation residuals of the previous round, updating the posterior mean of each symbol element in combination with the noise variance and the Laplace sparsity prior, and terminating the iteration when the difference between the estimates of two consecutive iterations is less than a set difference threshold or the maximum number of iterations is reached; S55. Output the symbol estimation matrix solved by the approximate message passing algorithm.

7. The multi-node concurrent transmission signal superposition diversity method according to claim 1, characterized in that: The S6 specifically includes: S61, inputting the symbol estimation matrix as soft information into a Turbo decoder corresponding to each node, wherein the Turbo decoder includes a first decoding branch, a second decoding branch, and an interleaver, forming an iterative structure; S62, in each iteration, the improved Max-Log-MAP algorithm is used to calculate the information bits The log-likelihood ratio ; S63. Introducing a scaling factor while calculating external information , scale and correct the external information generated in each iteration; S64: The extrinsic information generated by the first decoding branch is subjected to bit position rearrangement by the interleaver and then input into the second decoding branch. The second decoding branch uses the extrinsic information as a priori probability and performs path recursive operation and metric update in combination with the observation signal received by itself to obtain new extrinsic information. The new extrinsic information generated by the second decoding branch is transmitted back to the first decoding branch via the deinterleaver as a priori input for the next round of iteration. The two decoding branches alternately execute the new extrinsic information until the maximum number of iterations is reached or the change in the bit log-likelihood ratio between the previous and next rounds is less than a preset change threshold. S65 . Output the bit estimation sequence after the final iteration of the Turbo decoder as the restored original information bit stream.

8. The multi-node concurrent transmission signal superposition diversity method according to claim 1, characterized in that: The S7 specifically includes: S71. Embed a preamble consisting of a Zadoff-Chu sequence in a signal frame transmitted by each node to assist the receiving end in performing initial phase estimation. S72. The receiving end extracts the Zadoff-Chu preamble from the received complex baseband signal and completes the initial phase offset estimation of each node based on the locally known sequence. S73, using the bit estimation sequence as soft information input, and combining the phase evolution behavior of the received signal between multiple symbols to construct a dynamic observation data sequence; S74. Based on the initial phase offset estimation of each node and the dynamic observation data sequence, a Kalman filter is used to perform recursive estimation of phase disturbance, and phase drift and carrier frequency offset are tracked in real time, and the estimated value is gradually corrected. S75. Output the complete estimated phase sequence of each node.

9. The multi-node concurrent transmission signal superposition diversity method according to claim 1, characterized in that: The S8 specifically includes: S81. The receiving end obtains an estimated phase sequence corresponding to each node, where the estimated phase sequence represents a phase rotation change experienced by the node at each symbol time point. S82, updating the phase perturbation matrix in the equivalent observation model according to the estimated phase sequence, replacing the diagonal elements corresponding to each node in the phase perturbation matrix with the phase modulation factors constructed according to the estimated phase sequence; S83. Constructing a new equivalent observation model based on the updated phase perturbation matrix to describe the mapping relationship between the current received signal and the transmitted symbol; S84, uses pipeline structure to improve data processing parallelism, and builds data transmission path through AXI-Stream interface to complete scheduling, and automatically updates equivalent observation model.

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