A symbol-level sensing and communication integrated precoding method for random signals

Abstract

The application discloses a symbol-level sensing-integrated precoding for random signals, which comprises the following steps: (1) combining a data-dependent precoding structure to construct a transmitting signal model; (2) based on a constructive interference geometry structure, a double-layer default constraint model of a communication side is established, including a frame-level average default energy constraint and a single-symbol maximum default constraint; (3) using ELMMSE as a sensing performance index, a sensing side target function is constructed; (4) under a unified optimization framework, a hybrid iterative algorithm combining an outer projection gradient and an inner ADMM double-bounded relaxation projection is used to solve a precoding matrix, so that the communication and sensing performances are cooperatively optimized.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and particularly relates to a symbol-level integrated sensing precoding method for random signals. Background Technology

[0002] With the development of B5G / 6G wireless communication systems, BS (Base Station) is gradually evolving into intelligent nodes with communication and environmental awareness capabilities, namely ISAC (Interference-Induced Clustering) systems. In such systems, the transmitted signal simultaneously carries communication information and sensing functions, and its design directly determines the overall system performance. In MU-MISO communication systems, precoding techniques mainly rely on CSI (Concurrent Sequence Injection) to suppress multi-user interference. However, recent research has shown that interference is not always harmful; by rationally designing the transmitted signal, interference can be structurally superimposed at the receiver, thereby improving the decision margin of the received signal. This idea gave rise to CI (Interference Optimization) precoding technology, shifting precoding design from "interference suppression" to "interference utilization." Depending on the design paradigm, it can be divided into SLP (Segmented Logic Optimization) and BLP (Browser Logic Optimization), with BLP providing additional time dimension freedom through cross-slot joint optimization.

[0003] However, although CI precoding itself is based on instantaneous data symbols and has a natural data dependency, existing ISAC methods typically use deterministic signal covariance approximation in perception modeling. This means that the expected covariance in a statistical sense is replaced by the sample covariance within a finite number of frames. This type of method implicitly assumes that the transmitted signal can approximate its statistical characteristics through long-term averaging. However, in real-world systems, low latency constraints and finite frame length limitations make it difficult for the transmitted signal to meet the aforementioned long-frame averaging condition, leading to a significant deviation between the sample covariance and the true statistical covariance. Therefore, perception optimization methods based on deterministic covariance modeling cannot accurately reflect the actual perception performance driven by random signals. To address this issue, related research introduces ELMMSE as a perception performance metric to characterize the average estimation error driven by random signals. Simultaneously, ELMMSE explicitly depends on the instantaneous transmitted signal structure, tightly coupling the precoding design with the data symbols, thus leading to the DDP design framework. While this effectively measures system perception performance, it also significantly increases the complexity of communication constraint design.

[0004] On the communication side, CI precoding ensures demodulation reliability through decision region constraints. However, under the DDP framework, such constraints are more prone to infeasibility or excessive relaxation; especially in symbol-level precoding, the lack of temporal coordination makes it difficult to reconcile constraint violations between symbols, leading to performance degradation. In contrast, BLP can jointly optimize transmitted signals at the frame level, achieving cross-timeslot resource reallocation, thus providing the necessary degrees of freedom to simultaneously satisfy CI communication constraints and ELMMSE sensing objectives. However, existing methods have not yet effectively integrated these key elements. How to achieve the co-design of CI constraints and ELMMSE sensing objectives within the DDP structure, and improve communication and sensing performance under finite frame length conditions, remains a critical problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to address the above-mentioned problems by proposing a symbol-level integrated sensing precoding method for random signals. By introducing the ELMMSE sensing index within the DDP framework, the statistical characteristics of random signals are accurately characterized, thereby improving the modeling accuracy of sensing performance. Simultaneously, decision region constraints are constructed based on CI geometry, and combined with a BLP structure, transmitted signals are jointly designed across multiple time slots. This enables the system to dynamically adjust constraint violation behavior within a frame, achieving a synergistic improvement in communication reliability and sensing accuracy, while avoiding the performance bias problem introduced by deterministic covariance modeling in traditional methods. This effectively alleviates the performance degradation problem caused by constraint infeasibility or slack concentration in existing designs.

[0006] Technical Solution: To achieve the objectives of this invention, this invention proposes a symbol-level integrated syn-sensory precoding method for random signals, which includes the following steps:

[0007] Step 1: Construct a data-dependent transmission signal model based on the user modulation symbol matrix corresponding to the data frame to be transmitted by the base station.

[0008] Step 2: Establish a two-layer default constraint model on the communication side. The two-layer default constraint model includes an average default energy constraint for controlling the overall default level at the frame level, and a single-symbol maximum default constraint for suppressing local extreme defaults.

[0009] Step 3: Using the expected weighted minimum mean square error (ELMMSE) as the sensing performance index, construct the objective function for the sensing side;

[0010] Step 4: Using the objective function constructed in Step 3 as the optimization objective and the double-layer violation constraint and transmit power limit constructed in Step 2 as constraints, construct a precoding optimization model, and solve the precoding matrix using a hybrid iterative algorithm combining the outer layer projection gradient and the inner layer alternating direction multiplier method (ADMM) with double bounded relaxation projection. This enables the coordinated optimization of communication and sensing performance.

[0011] Furthermore, in step 1, constructing the transmitted signal model includes:

[0012] Based on the data-dependent precoding structure, the transmitted signal is constructed as the product of the precoding matrix and the user modulation symbol matrix. , It is a precoding matrix based on modulation symbol matrix data correlation, wherein the base station is equipped with A transmit antenna provides services and performs sensing tasks for K single-antenna communication users. The data frame length is K, and the user modulation symbol matrix is... .

[0013] Furthermore, in step 2, establishing the two-layer default constraint model on the communication side includes:

[0014] Step 2.1, for the first The user in the first Each time slot, based on the received signal and target modulation symbols Phase alignment is performed to obtain the rotated received signal. ,in, Indicates the base station to the Downlink channel vectors for each user Indicates the first The transmit signal vector of each time slot, Indicates received noise. Indicates conjugate operation;

[0015] Step 2.2, for Modulation method, if the received signal after rotation is located at a point centered on the positive real axis and half an angle of... Within the judgment sector, the following conditions must be met:

[0016] ;

[0017] in, It indicates the modulation order. Indicates the first Communication decision margin parameters for each user and Let the real and imaginary parts of the complex number be represented respectively, and define the first... The user in the first The geometric mismatch function for each time slot is:

[0018] ;

[0019] when When this occurs, it indicates that the corresponding symbol satisfies the constructive disturbance constraint;

[0020] when When the symbol deviates from the target decision area, it indicates a geometrical breach on the communication side.

[0021] Step 2.3, in the above geometric mismatch function Building upon this foundation, to further characterize the degree to which communication constraints are satisfied, a nonnegative default quantity is introduced to measure the actual degree to which the received signal deviates from the target decision region. The first... The user in the first The default amount for each time slot is:

[0022] ;

[0023] Among them, when When, it means that the corresponding symbol satisfies the constructive disturbance constraint. ;when When this occurs, it indicates that the symbol deviates from the target decision region. Its numerical value reflects the degree of default;

[0024] Step 2.4: Construct frame-level average default energy constraints:

[0025] ;

[0026] in, Indicates the first Average default tolerance parameter for each user within a data frame;

[0027] Step 2.5: Construct the maximum default constraint for a single symbol:

[0028] ;

[0029] in, Indicates the first The maximum upper bound of single-symbol default for a single user.

[0030] Furthermore, in step 3, using ELMMSE as the perception performance index, constructing the perception-side objective function includes: constructing the perception-side objective function as a statistical average of random data symbols:

[0031] ;

[0032] in, Let represent the statistical correlation matrix of the sensing channel, i.e. , The TIR matrix to be estimated is... Here are the parameters related to the perceived signal-to-noise ratio, where... To perceive the standard deviation of noise, To sense the number of receiving antennas; Represents the statistical average of the signs of random data;

[0033] The aforementioned expectation-based optimization problem can be further decomposed into a conditional optimization subproblem for a given data frame realization, with a fixed user modulation symbol matrix. Transmit signal The corresponding single-frame perceptual target is written as: , which serves as the actual perception target used in the optimization process.

[0034] Furthermore, using the single-frame sensing target corresponding to ELMMSE on the sensing side as the optimization function, a two-layer violation constraint is introduced on the communication side, and considering the transmit power limit, the following unified optimization model is constructed:

[0035] ;

[0036] in, Let Frobenius norm be denoted, and P be the average transmit power per unit time slot.

[0037] Furthermore, in step 4, a hybrid iterative algorithm combining the outer layer projection gradient and the inner layer ADMM double bounded relaxation projection is used to solve the precoding matrix. The specific method is as follows:

[0038] For a given user modulation symbol matrix Data depends on precoding matrix Throughout the entire outer layer optimization process, the outer layer is treated as the optimization object. To simplify the symbolic representation, in steps (4.1) to (4.5), the outer layer is used as the optimization object. Recorded as ;in, Indicates the first The precoding matrix corresponding to the next outer iteration This represents the initial precoding matrix for the outer iteration. This represents the reference precoding matrix obtained by gradient update;

[0039] (4.1) Algorithm Initialization

[0040] For a given user modulation symbol matrix With data-dependent precoding matrix As the outer optimization variable, and its initial iteration value is denoted as... The initial precoding matrix is ​​a weighted combination of a zero-forcing precoding matrix and a random Gaussian matrix, expressed as:

[0041] ;

[0042] in, These are the preset weighting coefficients. ,in, This represents the matrix conjugate transpose operation. To follow a complex Gaussian distribution random matrix, The downlink channel matrix from base station to user; Perform a power projection operation to satisfy the total transmit power constraint, and use it as the initial point for subsequent optimization algorithms;

[0043] (4.2) Calculation and updating of gradient of outer sensing target

[0044] In the In the next outer iteration, based on the current precoding matrix Calculate the complex gradient of the single-frame sensing target function with respect to the precoding matrix. According to the matrix differentiation rule, the gradient expression is:

[0045] ;

[0046] in, The reference precoding matrix is ​​obtained by tentatively updating the autocorrelation matrix of the data symbols along the negative gradient direction. ,in, This is the current iteration step size;

[0047] (4.3) Inner layer ADMM double bounded relaxation constraint projection

[0048] To facilitate the projection of the reference matrix onto the feasible region that satisfies the two-level default constraints, auxiliary variables are introduced. and dual variables Among them, auxiliary variables This represents the ideal received signal matrix that satisfies the communication constraints. For the corresponding Lagrange multipliers, ADMM is used to alternately solve the constrained projection problem; the modulation symbol matrix is ​​fixed within each data frame. The subproblems are then updated as follows:

[0049] (4.3.1) Precoding matrix Nearest update

[0050] Building about The quadratic convex subproblem, with its derivative set to zero, expands to obtain the matrix equation:

[0051] ;

[0052] in, As ADMM penalty parameters, the above matrix equations are transformed into a system of linear equations using the Kronecker product property:

[0053] ;

[0054] in, This represents the matrix transpose operation. This represents the Kronecker product operation. This represents the vectorization operation of expanding a matrix into vectors column-wise. This is accomplished by solving the system of linear equations. Update;

[0055] (4.3.2) Auxiliary variables Update and double bounded relaxation cutoff

[0056] fixed Calculate intermediate variables ,in, Given the intermediate matrix of the received signal corresponding to the current iteration, based on the double bounded relaxation constraint, for... Calculate and correct the amount of default, and reconstruct the auxiliary variables based on the correction results. The specific steps are as follows:

[0057] (a) Phase alignment and original default calculation: For the first The user The signal of each time slot is multiplied by the conjugate target symbol. Perform rotation alignment to obtain the rotation domain signal. Define geometric deviation Extract the original default amount: ;

[0058] (b) Maximum Default Constraint Truncation for Single Symbol: Traverse all time slots within the data frame. If the geometric deviation of a certain time slot is greater than the preset upper bound of the maximum default for a single symbol... Then the deviation of that time slot will be forcibly truncated to ,Right now:

[0059] ;

[0060] (c) Frame-level average default energy constraint truncation: Calculate the first frame-level average default energy constraint truncation. The default energy of an individual user throughout the entire data frame ,like Then calculate the scaling factor. The final default amount is obtained by performing proportional scaling:

[0061] ;

[0062] otherwise, After the above processing, Simultaneously satisfying the single-symbol maximum default constraint and the frame-level average default constraint;

[0063] (d) Auxiliary variable reconstruction: Calculate the actual amount of deviation that needs to be corrected. Repair by pushing along the positive real axis within the rotation domain:

[0064] ;

[0065] Construct the rotation domain auxiliary variable matrix based on the above repair results. The corrected rotated domain signal is multiplied by the corresponding target sign to complete the inverse rotation, restoring it to the original signal domain, thus obtaining the updated auxiliary variable. ,in, This represents the received signal matrix after rotation domain correction. This represents the Hadamard element-wise product;

[0066] (4.3.3) Dual Update and Power Projection

[0067] Update dual variables:

[0068]

[0069] in, To update the step size factor in the dual operation, calculate the transmit power E corresponding to the current precoding matrix. ,like Then let To ensure that the total launch power constraint is met;

[0070] (4.4) Outer layer iterative convergence and output determination

[0071] Calculate the perceptual objective function value corresponding to the precoding matrix obtained by the inner ADMM projection, and compare it with the objective function value of the previous outer iteration. If the current objective function value is not greater than the objective function value of the previous iteration, accept the current update result and use it as the precoding matrix for the next outer iteration; otherwise, reduce the outer iteration step size according to a preset ratio and return to step (4.2) to perform gradient update again. Repeat the above process until the preset convergence condition is met, and output the final precoding matrix;

[0072] (4.5) Multiple random restart mechanism

[0073] To improve global optimization capabilities, random initial moments are regenerated. Repeat steps (4.1) to (4.4) multiple times; compare the perceptual objective function values ​​obtained from multiple solutions, and retain the precoding matrix that minimizes the objective function value and satisfies the double-layer default constraint as the final output result.

[0074] Through the above steps, the present invention achieves accurate solution of the precoding matrix, ensuring that sensing performance is optimized while meeting communication reliability requirements.

[0075] Beneficial effects: Compared with the prior art, the solution of the present invention has the following beneficial effects:

[0076] (1) Construct a two-layer control mechanism that combines a default quantity measurement method based on geometric mismatch with frame-level average default constraint and single-symbol maximum default constraint to suppress the concentrated distribution of default quantity in the time dimension, and appropriately expand the feasible domain while maintaining the controllability of the decision geometry structure, thereby improving the system's communication reliability and operational stability.

[0077] (2) Using ELMMSE as the objective function, the influence mechanism of random data signals on sensing performance is characterized from a statistical perspective. Under the condition of finite frame length, the average sensing error level of the system is accurately reflected, thereby improving the sensing accuracy.

[0078] (3) Under the unified optimization framework, the structural interference constraints on the communication side and the statistical performance indicators on the sensing side are integrated. The communication constraints are made flexible and adjustable by means of a two-layer default control mechanism. Under the premise of meeting the communication decision requirements, the signal design freedom is released, and the fine and controllable trade-off between communication performance and sensing performance is achieved. Attached Figure Description

[0079] Figure 1 Schematic diagram of the integrated communication and sensing system structure;

[0080] Figure 2 Flowchart of the integrated communication and sensing precoding method;

[0081] Figure 3 Comparison of bit error rate performance of different constructed interference precoding methods;

[0082] Figure 4 Curves showing the relationship between sensing performance and communication threshold under different constructed interference precoding methods. Detailed Implementation

[0083] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0084] like Figure 1 As shown, considering the MU-MISO ISAC system, the base station adopts the DDP framework and is equipped with... One transmitting antenna, for Each single-antenna user provides data transmission services and performs environmental sensing tasks. The system uses M-PSK modulation, with a data frame length of L. The sensing process is based on echo signals, and the base station is configured... Root receiving antenna.

[0085] like Figure 2 As shown, this invention proposes a symbol-level integrated synesthetic precoding method for random signals, which includes the following steps:

[0086] Step 1: Construct a data-dependent transmission signal model based on the user modulation symbol matrix corresponding to the data frame to be transmitted by the base station.

[0087] Step 2: Establish a two-layer default constraint model on the communication side. The two-layer default constraint model includes an average default energy constraint for controlling the overall default level at the frame level, and a single-symbol maximum default constraint for suppressing local extreme defaults.

[0088] Step 3: Using the expected weighted minimum mean square error (ELMMSE) as the sensing performance index, construct the objective function for the sensing side;

[0089] Step 4: Using the objective function constructed in Step 3 as the optimization objective and the double-layer violation constraint and transmit power limit constructed in Step 2 as constraints, construct a precoding optimization model, and solve the precoding matrix using a hybrid iterative algorithm combining the outer layer projection gradient and the inner layer alternating direction multiplier method (ADMM) with double bounded relaxation projection. This enables the coordinated optimization of communication and sensing performance.

[0090] Furthermore, in step 1, constructing the transmitted signal model includes:

[0091] Based on the data-dependent precoding structure, the transmitted signal is constructed as the product of the precoding matrix and the user modulation symbol matrix. , It is a precoding matrix based on modulation symbol matrix data correlation, wherein the base station is equipped with A transmit antenna provides services and performs sensing tasks for K single-antenna communication users. The data frame length is K, and the user modulation symbol matrix is... .

[0092] Furthermore, in step 2, establishing the two-layer default constraint model on the communication side includes:

[0093] Step 2.1, for the first The user in the first Each time slot, based on the received signal and target modulation symbols Phase alignment is performed to obtain the rotated received signal. ,in, Indicates the base station to the Downlink channel vectors for each user Indicates the first The transmit signal vector of each time slot, Indicates received noise. Indicates conjugate operation;

[0094] Step 2.2, for Modulation method, if the received signal after rotation is located at a point centered on the positive real axis and half an angle of... Within the judgment sector, the following conditions must be met:

[0095] ;

[0096] in, It indicates the modulation order. Indicates the first Communication decision margin parameters for each user and Let the real and imaginary parts of the complex number be represented respectively, and define the first... The user in the first The geometric mismatch function for each time slot is:

[0097] ;

[0098] when When this occurs, it indicates that the corresponding symbol satisfies the constructive disturbance constraint;

[0099] when When the symbol deviates from the target decision area, it indicates a geometrical breach on the communication side.

[0100] Step 2.3, in the above geometric mismatch function Building upon this foundation, to further characterize the degree to which communication constraints are satisfied, a nonnegative default quantity is introduced to measure the actual degree to which the received signal deviates from the target decision region. The first... The user in the first The default amount for each time slot is:

[0101] ;

[0102] Among them, when When, it means that the corresponding symbol satisfies the constructive disturbance constraint. ;when When this occurs, it indicates that the symbol deviates from the target decision region. Its numerical value reflects the degree of default;

[0103] Step 2.4: Construct frame-level average default energy constraints:

[0104] ;

[0105] in, Indicates the first Average default tolerance parameter for each user within a data frame;

[0106] Step 2.5: Construct the maximum default constraint for a single symbol:

[0107] ;

[0108] in, Indicates the first The maximum upper bound of single-symbol default for a single user.

[0109] Furthermore, in step 3, using ELMMSE as the perception performance index, constructing the perception-side objective function includes: constructing the perception-side objective function as a statistical average of random data symbols:

[0110] ;

[0111] in, Let represent the statistical correlation matrix of the sensing channel, i.e. , The TIR matrix to be estimated is... Here are the parameters related to the perceived signal-to-noise ratio, where... To perceive the standard deviation of noise, To sense the number of receiving antennas; Represents the statistical average of the signs of random data;

[0112] The aforementioned expectation-based optimization problem can be further decomposed into a conditional optimization subproblem for a given data frame realization, with a fixed user modulation symbol matrix. Transmit signal The corresponding single-frame perceptual target is written as: , which serves as the actual perception target used in the optimization process.

[0113] Furthermore, using the single-frame sensing target corresponding to ELMMSE on the sensing side as the optimization function, a two-layer violation constraint is introduced on the communication side, and considering the transmit power limit, the following unified optimization model is constructed:

[0114] ;

[0115] in, Let Frobenius norm be denoted, and P be the average transmit power per unit time slot.

[0116] Furthermore, in step 4, a hybrid iterative algorithm combining the outer layer projection gradient and the inner layer ADMM double bounded relaxation projection is used to solve the precoding matrix. The specific method is as follows:

[0117] For a given user modulation symbol matrix Data depends on precoding matrix Throughout the entire outer layer optimization process, the outer layer is treated as the optimization object. To simplify the symbolic representation, in steps (4.1) to (4.5), the outer layer is used as the optimization object. Recorded as ;in, Indicates the first The precoding matrix corresponding to the next outer iteration This represents the initial precoding matrix for the outer iteration. This represents the reference precoding matrix obtained by gradient update;

[0118] (4.1) Algorithm Initialization

[0119] For a given user modulation symbol matrix With data-dependent precoding matrix As the outer optimization variable, and its initial iteration value is denoted as... The initial precoding matrix is ​​a weighted combination of a zero-forcing precoding matrix and a random Gaussian matrix, expressed as:

[0120] ;

[0121] in, These are the preset weighting coefficients. ,in, This represents the matrix conjugate transpose operation. To follow a complex Gaussian distribution random matrix, The downlink channel matrix from base station to user; Perform a power projection operation to satisfy the total transmit power constraint, and use it as the initial point for subsequent optimization algorithms;

[0122] (4.2) Calculation and updating of gradient of outer sensing target

[0123] In the In the next outer iteration, based on the current precoding matrix Calculate the complex gradient of the single-frame sensing target function with respect to the precoding matrix. According to the matrix differentiation rule, the gradient expression is:

[0124] ;

[0125] in, The reference precoding matrix is ​​obtained by tentatively updating the autocorrelation matrix of the data symbols along the negative gradient direction. ,in, This is the current iteration step size;

[0126] (4.3) Inner layer ADMM double bounded relaxation constraint projection

[0127] To facilitate the projection of the reference matrix onto the feasible region that satisfies the two-level default constraints, auxiliary variables are introduced. and dual variables Among them, auxiliary variables This represents the ideal received signal matrix that satisfies the communication constraints. For the corresponding Lagrange multipliers, ADMM is used to alternately solve the constrained projection problem; the modulation symbol matrix is ​​fixed within each data frame. The subproblems are then updated as follows:

[0128] (4.3.1) Precoding matrix Nearest update

[0129] Building about The quadratic convex subproblem, with its derivative set to zero, expands to obtain the matrix equation:

[0130] ;

[0131] in, As ADMM penalty parameters, the above matrix equations are transformed into a system of linear equations using the Kronecker product property:

[0132] ;

[0133] in, This represents the matrix transpose operation. This represents the Kronecker product operation. This represents the vectorization operation of expanding a matrix into vectors column-wise. This is accomplished by solving the system of linear equations. Update;

[0134] (4.3.2) Auxiliary variables Update and double bounded relaxation cutoff

[0135] fixed Calculate intermediate variables ,in, Given the intermediate matrix of the received signal corresponding to the current iteration, based on the double bounded relaxation constraint, for... Calculate and correct the amount of default, and reconstruct the auxiliary variables based on the correction results. The specific steps are as follows:

[0136] (a) Phase alignment and original default calculation: For the first The user The signal of each time slot is multiplied by the conjugate target symbol. Perform rotation alignment to obtain the rotation domain signal. Define geometric deviation Extract the original default amount: ;

[0137] (b) Maximum Default Constraint Truncation for Single Symbol: Traverse all time slots within the data frame. If the geometric deviation of a certain time slot is greater than the preset upper bound of the maximum default for a single symbol... Then the deviation of that time slot will be forcibly truncated to ,Right now:

[0138] ;

[0139] (c) Frame-level average default energy constraint truncation: Calculate the first frame-level average default energy constraint truncation. The default energy of an individual user throughout the entire data frame ,like Then calculate the scaling factor. The final default amount is obtained by performing proportional scaling:

[0140] ;

[0141] otherwise, After the above processing, Simultaneously satisfying the single-symbol maximum default constraint and the frame-level average default constraint;

[0142] (d) Auxiliary variable reconstruction: Calculate the actual amount of deviation that needs to be corrected. Repair by pushing along the positive real axis within the rotation domain:

[0143] ;

[0144] Construct the rotation domain auxiliary variable matrix based on the above repair results. The corrected rotated domain signal is multiplied by the corresponding target sign to complete the inverse rotation, restoring it to the original signal domain, thus obtaining the updated auxiliary variable. ,in, This represents the received signal matrix after rotation domain correction. This represents the Hadamard element-wise product;

[0145] (4.3.3) Dual Update and Power Projection

[0146] Update dual variables:

[0147] ;

[0148] in, To update the step size factor in the dual operation, calculate the transmit power E corresponding to the current precoding matrix. ,like Then let To ensure that the total launch power constraint is met;

[0149] (4.4) Outer layer iterative convergence and output determination

[0150] Calculate the perceptual objective function value corresponding to the precoding matrix obtained by the inner ADMM projection, and compare it with the objective function value of the previous outer iteration. If the current objective function value is not greater than the objective function value of the previous iteration, accept the current update result and use it as the precoding matrix for the next outer iteration; otherwise, reduce the outer iteration step size according to a preset ratio and return to step (4.2) to perform gradient update again. Repeat the above process until the preset convergence condition is met, and output the final precoding matrix;

[0151] (4.5) Multiple random restart mechanism

[0152] To improve global optimization capabilities, random initial moments are regenerated. Repeat steps (4.1) to (4.4) multiple times; compare the perceptual objective function values ​​obtained from multiple solutions, and retain the precoding matrix that minimizes the objective function value and satisfies the double-layer default constraint as the final output result.

Claims

1. A symbol-level synesthetic integrated precoding method for random signals, characterized in that, The method includes the following steps: Step 1: Construct a data-dependent transmission signal model based on the user modulation symbol matrix corresponding to the data frame to be transmitted by the base station. Step 2: Establish a two-layer default constraint model on the communication side. The two-layer default constraint model includes an average default energy constraint for controlling the overall default level at the frame level, and a single-symbol maximum default constraint for suppressing local extreme defaults. Step 3: Using the expected weighted minimum mean square error (ELMMSE) as the sensing performance index, construct the objective function for the sensing side; Step 4: Using the objective function constructed in Step 3 as the optimization objective and the double-layer violation constraint and transmit power limit constructed in Step 2 as constraints, construct a precoding optimization model, and solve the precoding matrix using a hybrid iterative algorithm combining the outer layer projection gradient and the inner layer alternating direction multiplier method (ADMM) with double bounded relaxation projection. This enables the coordinated optimization of communication and sensing performance.

2. The symbol-level synesthetic integrated precoding method for random signals according to claim 1, characterized in that, In step 1, constructing the transmitted signal model includes: Based on the data-dependent precoding structure, the transmitted signal is constructed as the product of the precoding matrix and the user modulation symbol matrix. , It is a precoding matrix based on modulation symbol matrix data correlation, wherein the base station is equipped with A transmit antenna provides services and performs sensing tasks for K single-antenna communication users. The data frame length is K, and the user modulation symbol matrix is... .

3. The symbol-level synesthetic integrated precoding method for random signals according to claim 2, characterized in that, Step 2, establishing the two-layer default constraint model on the communication side, includes: Step 2.1, for the first The user in the first Each time slot, based on the received signal and target modulation symbols Phase alignment is performed to obtain the rotated received signal. ,in, Indicates the base station to the Downlink channel vectors for each user Indicates the first The transmit signal vector of each time slot, Indicates received noise. Indicates conjugate operation; Step 2.2, for Modulation method, if the received signal after rotation is located at a point centered on the positive real axis and half an angle of... Within the judgment sector, the following conditions must be met: ； in, It indicates the modulation order. Indicates the first Communication decision margin parameters for each user and Let the real and imaginary parts of the complex number be represented respectively, and define the first... The user in the first The geometric mismatch function for each time slot is: ； when When this occurs, it indicates that the corresponding symbol satisfies the constructive disturbance constraint; when When the symbol deviates from the target decision area, it indicates a geometrical breach on the communication side. Step 2.3, in the above geometric mismatch function Building upon this foundation, to further characterize the degree to which communication constraints are satisfied, a nonnegative default quantity is introduced to measure the actual degree to which the received signal deviates from the target decision region. The first... The user in the first The default amount for each time slot is: ； Among them, when When, it means that the corresponding symbol satisfies the constructive disturbance constraint. ;when When this occurs, it indicates that the symbol deviates from the target decision region. Its numerical value reflects the degree of default; Step 2.4: Construct frame-level average default energy constraints: ； in, Indicates the first Average default tolerance parameter for each user within a data frame; Step 2.5: Construct the maximum default constraint for a single symbol: ； in, Indicates the first The maximum upper bound of single-symbol default for a single user.

4. The symbol-level synesthetic integrated precoding method for random signals according to claim 3, characterized in that, In step 3, ELMMSE is used as the perception performance index, and the objective function for the perception side is constructed as follows: The objective function on the sensing side is constructed as a statistical average of the random data symbols: ； in, Let represent the statistical correlation matrix of the sensing channel, i.e. , The TIR matrix to be estimated is... Here are the parameters related to the perceived signal-to-noise ratio, where... To perceive the standard deviation of noise, To sense the number of receiving antennas; Represents the statistical average of the signs of random data; The aforementioned expectation-based optimization problem can be further decomposed into a conditional optimization subproblem for a given data frame realization, with a fixed user modulation symbol matrix. Transmit signal The corresponding single-frame perceptual target is written as: , which serves as the actual perception target used in the optimization process.

5. The symbol-level synesthetic integrated precoding method for random signals according to claim 4, characterized in that, Using the single-frame sensing target corresponding to ELMMSE on the sensing side as the optimization function, a two-layer violation constraint is introduced on the communication side, and considering the transmit power limit, the following unified optimization model is constructed: ； in, Let Frobenius norm be denoted, and P be the average transmit power per unit time slot.

6. The symbol-level synesthetic integrated precoding method for random signals according to claim 5, characterized in that, In step 4, a hybrid iterative algorithm combining the outer projection gradient and the inner ADMM double bounded relaxation projection is used to solve the precoding matrix. The specific method is as follows: For a given user modulation symbol matrix Data depends on precoding matrix Throughout the entire outer layer optimization process, the outer layer is treated as the optimization object. To simplify the symbolic representation, in steps (4.1) to (4.5), the outer layer is used as the optimization object. Recorded as ;in, Indicates the first The precoding matrix corresponding to the next outer iteration This represents the initial precoding matrix for the outer iteration. This represents the reference precoding matrix obtained by gradient update; (4.1) Algorithm Initialization For a given user modulation symbol matrix With data-dependent precoding matrix As the outer optimization variable, and its initial iteration value is denoted as... The initial precoding matrix is ​​a weighted combination of a zero-forcing precoding matrix and a random Gaussian matrix, expressed as: ； in, These are the preset weighting coefficients. ,in, This represents the matrix conjugate transpose operation. To follow a complex Gaussian distribution random matrix, The downlink channel matrix from base station to user; Perform a power projection operation to satisfy the total transmit power constraint, and use it as the initial point for subsequent optimization algorithms; (4.2) Calculation and updating of gradient of outer sensing target In the In the next outer iteration, based on the current precoding matrix Calculate the complex gradient of the single-frame sensing target function with respect to the precoding matrix. According to the matrix differentiation rule, the gradient expression is: ； in, The reference precoding matrix is ​​obtained by tentatively updating the autocorrelation matrix of the data symbols along the negative gradient direction. ,in, This is the current iteration step size; (4.3) Inner layer ADMM double bounded relaxation constraint projection To facilitate the projection of the reference matrix onto the feasible region that satisfies the two-level default constraints, auxiliary variables are introduced. and dual variables Among them, auxiliary variables This represents the ideal received signal matrix that satisfies the communication constraints. For the corresponding Lagrange multipliers, ADMM is used to alternately solve the constrained projection problem; the modulation symbol matrix is ​​fixed within each data frame. The subproblems are then updated as follows: (4.3.1) Precoding matrix Nearest update Building about The quadratic convex subproblem, with its derivative set to zero, expands to obtain the matrix equation: ； in, As ADMM penalty parameters, the above matrix equations are transformed into a system of linear equations using the Kronecker product property: ； in, This represents the matrix transpose operation. This represents the Kronecker product operation. This represents the vectorization operation of expanding a matrix into vectors column-wise. This is accomplished by solving the system of linear equations. Update; (4.3.2) Auxiliary variables Update and double bounded relaxation cutoff fixed Calculate intermediate variables ,in, Given the intermediate matrix of the received signal corresponding to the current iteration, based on the double bounded relaxation constraint, for... Calculate and correct the amount of default, and reconstruct the auxiliary variables based on the correction results. The specific steps are as follows: (a) Phase alignment and original default calculation: For the first The user The signal of each time slot is multiplied by the conjugate target symbol. Perform rotation alignment to obtain the rotation domain signal. Define geometric deviation Extract the original default amount: ; (b) Maximum Default Constraint Truncation for Single Symbol: Traverse all time slots within the data frame. If the geometric deviation of a certain time slot is greater than the preset upper bound of the maximum default for a single symbol... Then the deviation of that time slot will be forcibly truncated to ,Right now: ； (c) Frame-level average default energy constraint truncation: Calculate the first frame-level average default energy constraint truncation. The default energy of an individual user throughout the entire data frame ,like Then calculate the scaling factor. The final default amount is obtained by performing proportional scaling: ； otherwise, After the above processing, Simultaneously satisfying the single-symbol maximum default constraint and the frame-level average default constraint; (d) Auxiliary variable reconstruction: Calculate the actual amount of deviation that needs to be corrected. Repair by pushing along the positive real axis within the rotation domain: ； Construct the rotation domain auxiliary variable matrix based on the above repair results. The corrected rotated domain signal is multiplied by the corresponding target sign to complete the inverse rotation, restoring it to the original signal domain, thus obtaining the updated auxiliary variable. ,in, This represents the received signal matrix after rotation domain correction. This represents the Hadamard element-wise product; (4.3.3) Dual Update and Power Projection Update dual variables: in, To update the step size factor in the dual operation, calculate the transmit power E corresponding to the current precoding matrix. ,like Then let To ensure that the total launch power constraint is met; (4.4) Outer layer iterative convergence and output determination Calculate the perceptual objective function value corresponding to the precoding matrix obtained by the inner ADMM projection, and compare it with the objective function value of the previous outer iteration. If the current objective function value is not greater than the objective function value of the previous iteration, accept the current update result and use it as the precoding matrix for the next outer iteration; otherwise, reduce the outer iteration step size according to a preset ratio and return to step (4.2) to perform gradient update again. Repeat the above process until the preset convergence condition is met, and output the final precoding matrix; (4.5) Multiple random restart mechanism To improve global optimization capabilities, random initial moments are regenerated. Repeat steps (4.1) to (4.4) multiple times; compare the perceptual objective function values ​​obtained from multiple solutions, and retain the precoding matrix that minimizes the objective function value and satisfies the double-layer default constraint as the final output result.

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