MIMO dual-functional radar communication joint robust transceiver design method

Abstract

The application discloses a MIMO dual-function radar communication joint robust transceiving design method, constructs a radar receiving signal model with amplitude and phase errors and a communication receiving signal model with channel estimation errors respectively, and deduces respective signal-to-interference-and-noise ratio expressions; constructs a non-convex optimization problem with radar signal-to-interference-and-noise ratio maximization as a target and communication signal-to-interference-and-noise ratio as a constraint, and is converted into a multiple fractional optimization problem through relaxation; adopts a D-AGP algorithm combining Dinkelbach transformation and alternating gradient projection, iteratively updates an auxiliary variable, iteratively alternately updates a precoding vector and a receiving beam forming vector in an inner layer until convergence, and generates a transmitting waveform according to the optimal precoding vector and outputs the receiving beam forming vector. The application simultaneously suppresses amplitude and phase errors and channel estimation errors, and improves radar detection capability and communication reliability of the system under non-ideal conditions.

Description

Technical Field

[0001] This invention relates to the field of radar and communication integration technology, and in particular to a robust joint transmit and receive design method for MIMO (Multi-Input Multi-Output) dual-function radar. Background Technology

[0002] Integrated radar-communication systems are a key technology for addressing spectrum resource constraints and achieving miniaturization and multi-functionality of equipment. In multi-input multi-output dual-function radar-communication systems, radar and communication functions share the same antenna array and transmitted waveform. In existing designs, one approach only optimizes the transmitted waveform or transmitted beamforming without considering receiver filtering, leading to a decrease in radar-to-interference-plus-noise ratio (SINR) and an increase in communication bit error rate. Another approach jointly designs the transmitted waveform / beamforming and the received filter, which can improve performance to some extent.

[0003] However, in practical systems, array amplitude and phase errors and CSI estimation errors are unavoidable. For example, amplitude and phase deviations between different array elements and suboptimal channel estimation can lead to received signal distortion and reduced beamforming gain in both the target and user directions, thus significantly degrading radar detection performance and communication quality. Current robust design research mainly focuses on pure radar or pure communication scenarios, and a few studies on DFRC systems only consider directional errors or only consider CSI estimation errors. There is still no robust transceiver design method that comprehensively considers both amplitude and phase errors and CSI estimation errors.

[0004] Therefore, there is an urgent need for a joint design method for MIMO DFRC systems that can simultaneously suppress the effects of amplitude and phase errors and CSI estimation errors. Summary of the Invention

[0005] This invention provides a robust MIMO dual-function radar communication joint transceiver design method, which solves the problem of poor system robustness caused by the failure to simultaneously consider amplitude and phase errors and channel estimation errors in the prior art, and achieves the effect of improving radar detection performance and communication reliability under non-ideal conditions.

[0006] This invention provides a robust joint transceiver design method for MIMO dual-function radar communication, comprising: A radar received signal model with amplitude and phase errors is constructed, and an expression for the radar received signal-to-interference-plus-noise ratio (SINR) is derived based on the radar received signal model. A communication received signal model with channel estimation errors is constructed, and an expression for the communication received SINR is derived based on the communication received signal model. With the radar received signal-to-interference-plus-noise ratio (SINR) expression as the optimization objective and the communication received SINR expression as the constraint, a primal non-convex optimization problem is constructed. The primal non-convex optimization problem is then subjected to convex relaxation and upper bound processing, transforming it into a multivariate fractional optimization problem. The D-AGP algorithm, which combines Dinkelbach transform and alternating gradient projection, is used to solve the multivariate fractional optimization problem. The auxiliary variables are updated by outer-layer iteration, and the radar precoding vector, communication precoding vector and received beamforming vector are updated by inner-layer iteration until convergence, so as to obtain the optimal radar precoding vector and the optimal communication precoding vector. The optimal transmit waveform is generated based on the optimal radar precoding vector and the optimal communication precoding vector, and the optimal receive beamforming vector is output.

[0007] In one possible implementation, the construction of a radar received signal model with amplitude and phase errors, and the derivation of the radar received signal-to-interference-plus-noise ratio (SINR) expression based on the radar received signal model, includes: The array amplitude and phase error is expressed as the sum of the nominal steering matrix and a norm-bounded error matrix to obtain the true steering matrix; wherein, the true steering matrix belongs to the set of uncertainties with the upper bound of the error norm as the radius; By replacing the nominal steering matrix with the real steering matrix, a radar received signal model with amplitude and phase errors is established, and the expression for the radar received signal with errors is obtained. At the receiving end, the radar received signal containing errors is weighted using the received beamforming vector to obtain the expression of the radar received signal after beamforming. Based on the expression of the radar received signal after beamforming, the expression for the radar received signal-to-interference-plus-noise ratio (SINR) is derived; wherein the expression for the radar received SINR is a quadratic form in which the numerator contains the received beamforming vector, the true steering matrix, and the transmitted waveform covariance matrix, and the denominator is the power of the interference term caused by the communication waveform to the radar and the sum of the quadratic forms of the received beamforming vector and the noise covariance matrix.

[0008] In one possible implementation, the step of constructing a communication received signal model with channel estimation error and deriving a communication received signal-to-interference-plus-noise ratio (SINR) expression based on the communication received signal model includes: The channel state information estimation error is represented as the sum of the nominal channel vector and a norm-bounded error vector to obtain the true channel vector; wherein, the true channel vector belongs to the set of uncertainties with the upper bound of the error norm as the radius; By replacing the nominal channel vector with the real channel vector, a communication received signal model with channel estimation error is established, resulting in an expression for the communication received signal containing the error. Based on the error-containing communication received signal expression, the communication received signal-to-interference-plus-noise ratio (SINR) expression is derived; wherein, the numerator of the communication received SINR expression is the power of the desired communication waveform, and the denominator is the sum of the interference term power and noise power composed of the communication precoding vector, the real channel vector, and the radar precoding vector.

[0009] In one possible implementation, the step of constructing the primordial non-convex optimization problem with the radar received signal-to-interference-plus-noise ratio (SINR) expression as the optimization objective and the communication received SINR expression as the constraint condition includes: Using the radar received signal-to-interference-plus-noise ratio (SINR) expression as the optimization objective function, and the communication received SINR expression as the interference power constraint at the communication receiver, along with the total energy constraint of the transmit precoding vector and the energy constraint of the receive beamforming vector, we construct the original non-convex optimization problem. The interference power constraint at the communication receiver is: the power of the interference term in the communication receiver signal-to-interference-plus-noise ratio expression is less than a preset threshold; wherein, the interference term includes: radar precoding vector and communication precoding vector; The total energy constraint of the transmit precoding vector is: the squared L2 norm of the radar precoding vector and the communication precoding vector are both equal to 1; The energy constraint of the receiving beamforming vector is: the square of the second norm of the receiving beamforming vector is equal to 1; The original non-convex optimization problem aims to maximize the radar receive signal-to-interference-plus-noise ratio (SINR), and is constrained by the interference power constraint of the communication receiver, the total energy constraint of the transmit precoding vector, and the energy constraint of the receive beamforming vector.

[0010] In one possible implementation, the process of performing convex relaxation and upper bound on the original non-convex optimization problem to transform it into a multivariate fractional optimization problem includes: The total energy constraint of the transmit precoding vector and the energy constraint of the receive beamforming vector are relaxed from equality constraints to inequality constraints, resulting in the relaxed energy constraint conditions. The interference power constraint at the communication receiver is scaled down using the triangle inequality and the Cauchy-Schwarz inequality to obtain a deterministic communication interference constraint expression. The inner product result in the communication interference constraint expression is made real by phase rotation to obtain the relaxed communication interference constraint. By taking upper bounds for both the numerator and denominator in the radar received signal-to-interference-plus-noise ratio (SINR) expression, we obtain the upper bound expression for the radar received SINR. This transforms the original non-convex optimization problem into a multivariate fractional optimization problem with the upper bound expression for the radar received SINR as the objective function and the relaxed energy constraint and the relaxed communication interference constraint as the constraint conditions.

[0011] In one possible implementation, the D-AGP algorithm, which combines Dinkelbach transform and alternating gradient projection, is used to solve the multivariate fractional optimization problem. This involves iteratively updating auxiliary variables in the outer layer and alternately updating the radar precoding vector, communication precoding vector, and received beamforming vector in the inner layer until convergence, yielding the optimal radar precoding vector and optimal communication precoding vector. This includes: Outer iteration: Auxiliary variables are introduced, and the multivariate fractional optimization problem is transformed into a subtractive form based on the Dinkelbach transform. At the end of each outer iteration, the auxiliary variables are updated according to the current radar precoding vector, communication precoding vector, and received beamforming vector. Inner iteration: Within each outer iteration, two of the three variables are fixed, and the radar precoding vector, communication precoding vector and received beamforming vector are updated alternately in sequence. The update of each variable adopts the gradient projection method, and the non-convex terms in the objective function are expanded by first-order Taylor to obtain a convex approximation. Repeat the outer iteration and the inner iteration until the change of the auxiliary variable is less than a preset threshold or the maximum number of outer iterations is reached, to obtain the optimal radar precoding vector and the optimal communication precoding vector.

[0012] In one possible implementation, the outer iteration includes: Initialize the auxiliary variables to zero or any value; In the k-th outer iteration, the current radar precoding vector, communication precoding vector, and receiver beamforming vector are substituted into the subtractive optimization problem. The auxiliary variable is fixed as the updated value of the previous iteration. The subtractive optimization problem is solved to obtain the new radar precoding vector, communication precoding vector, and receiver beamforming vector. Calculate a new auxiliary variable, which is equal to the numerator of the current radar received signal-to-interference-plus-noise ratio expression divided by the denominator; Determine whether the absolute value of the difference between the new auxiliary variable and the auxiliary variable of the previous iteration is less than a preset threshold: if it is less than the preset threshold, terminate the outer iteration; otherwise, continue to the next outer iteration.

[0013] In one possible implementation, the inner iteration includes: In each outer iteration, the following alternating update loop is executed: Step 1: Fix the communication precoding vector and the received beamforming vector, and construct a subproblem about the radar precoding vector using the radar precoding vector as a variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the radar precoding vector using the gradient projection method, and project the updated radar precoding vector onto the feasible region defined by the total transmit energy constraint and the communication interference constraint. Step 2: Fix the radar precoding vector and the received beamforming vector, and construct a subproblem about the communication precoding vector using the communication precoding vector as a variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the communication precoding vector using the gradient projection method, and project the updated communication precoding vector onto the feasible region defined by the total transmit energy constraint and the communication interference constraint. Step 3: Fix the radar precoding vector and the communication precoding vector, and construct a subproblem about the received beamforming vector using the received beamforming vector as a variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the received beamforming vector using the gradient projection method, and project the updated received beamforming vector onto the feasible region defined by the received energy constraint. Repeat steps one through three until the change in the objective function is less than the preset inner iteration threshold or the maximum number of inner iterations is reached.

[0014] In one possible implementation, generating the optimal transmit waveform based on the optimal radar precoding vector and the optimal communication precoding vector, and outputting the optimal receive beamforming vector, includes: Extract the optimal radar precoding vector, optimal communication precoding vector, and optimal receiver beamforming vector from the converged D-AGP algorithm; Multiply the optimal radar precoding vector by the desired radar waveform to obtain the radar transmission component; Multiply the optimal communication precoding vector by the desired communication waveform to obtain the communication transmission component; The radar transmission component is added to the communication transmission component to generate the optimal transmission waveform; Output the optimal transmit waveform and the optimal receive beamforming vector.

[0015] One or more technical solutions provided in this invention have at least the following technical effects or advantages: This invention simultaneously considers array amplitude and phase errors and CSI estimation errors, significantly improving the robustness of MIMO DFRC systems under non-ideal conditions. The proposed D-AGP algorithm transforms the non-convex fractional optimization problem into an alternating gradient projection iteration, with each update step possessing a closed-form solution, controllable computational complexity, and proven convergence. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the steps of a robust joint transceiver design method for MIMO dual-function radar communication provided in an embodiment of the present invention. Figure 2 The radar waveform diagram received by the MIMO DFRC system provided in the embodiments of the present invention and the prior art methods; Figure 3 Communication waveform diagrams of the method of the present invention and existing methods provided in the embodiments of the present invention; Figure 4 The transmit beam pattern and receive beam pattern formed by the method of the present invention and existing methods are provided in the embodiments of the present invention; Figure 5 A diagram showing the variation of the main lobe received SINR of the radar compared to existing methods, provided for embodiments of the present invention; Figure 6 The graph provided in this embodiment compares the bit error rate of the present invention with the signal-to-noise ratio (SNR) of the present invention and existing methods. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0018] This invention provides a robust joint transceiver design method for MIMO dual-function radar communication, see [link to relevant documentation]. Figure 1 The process includes the following steps S101 to S104.

[0019] S101, Construct a radar received signal model with amplitude and phase errors, and derive the radar received signal-to-interference-plus-noise ratio (SINR) expression based on the radar received signal model; Construct a communication received signal model with channel estimation errors, and derive the communication received SINR expression based on the communication received signal model. Specifically, in step S101, a radar received signal model with amplitude and phase errors is constructed, and the radar received signal-to-interference-plus-noise ratio expression is derived based on the radar received signal model, including the following steps S101.1.1 to S101.1.4.

[0020] S101.1.1, the array amplitude and phase error is expressed as the sum of the nominal steering matrix and a norm-bounded error matrix to obtain the true steering matrix; where the true steering matrix belongs to the set of uncertainties with the upper bound of the error norm as the radius; S101.1.2, replace the nominal steering matrix with the real steering matrix to establish a radar received signal model with amplitude and phase errors, and obtain the radar received signal expression with errors; S101.1.3, at the receiving end, the received beamforming vector is used to weight the radar received signal containing errors to obtain the expression of the radar received signal after beamforming; S101.1.4 Based on the expression of the radar received signal after beamforming, the expression of the radar received signal-to-interference-plus-noise ratio is derived; where the radar received signal-to-interference-plus-noise ratio expression is a quadratic form in the numerator containing the received beamforming vector, the true steering matrix and the transmitted waveform covariance matrix, and the denominator is the power of the interference term caused by the communication waveform to the radar and the sum of the quadratic forms of the received beamforming vector and the noise covariance matrix.

[0021] For example, suppose the MIMO DFRC system is composed of The system consists of a uniform linear array of antennas, with an antenna spacing of half a wavelength. The transmitted waveform is represented as follows: (1) in, , These are radar and communication precoding vectors, respectively. , These are the desired radar waveform and communication waveform, respectively, satisfying... , .

[0022] The received signal of a MIMO DFRC system can be expressed as: (2) in, Indicates the direction of the target. Represents the transmit and receive steering matrices. This represents the additive white Gaussian noise matrix.

[0023] In the receiver of a MIMO DFRC system, the beamformed received signal can be represented as: (3) in, This represents the received beamforming vector.

[0024] Considering amplitude and phase errors, the expression for the radar received signal containing these errors is: (4) in, Belongs to the set of uncertainties Let be the upper bound of the error norm. Then the expression for the radar received signal after beamforming is: (5) The radar received signal-to-interference-plus-noise ratio (SINR) can then be expressed as: (6) Specifically, in step S101, a communication received signal model with channel estimation error is constructed, and the communication received signal-to-interference-plus-noise ratio expression is derived based on the communication received signal model, including the following steps S101.2.1 to S101.2.3.

[0025] S101.2.1, the channel state information estimation error is expressed as the sum of the nominal channel vector and a norm-bounded error vector to obtain the true channel vector; where the true channel vector belongs to the set of uncertainties with the upper bound of the error norm as the radius; S101.2.2, replace the nominal channel vector with the real channel vector to establish a communication received signal model with channel estimation error, and obtain the expression of the communication received signal with error; S101.2.3, Based on the expression for the received communication signal with error, derive the expression for the received signal-to-interference-plus-noise ratio (SINR); where the numerator of the SINR expression is the power of the desired communication waveform, and the denominator is the sum of the power of the interference term and the noise power, which are composed of the communication precoding vector, the real channel vector, and the radar precoding vector.

[0026] For example, the received signal of a downlink user can be represented as: (7) in, It is the communication channel vector from the transmitter to the user. It is an additive white Gaussian noise vector.

[0027] Considering the CSI estimation error, the true channel vector is: (8) in, Belongs to the set of uncertainties The upper bound of the error norm and The expression for the received communication signal containing errors is: (9) The signal-to-interference-plus-noise ratio (SINR) of the received signal can be expressed as: (10) S102, with the maximization of the radar received signal-to-interference-plus-noise ratio expression as the optimization objective and the communication received signal-to-interference-plus-noise ratio expression as the constraint, construct the original non-convex optimization problem, and perform convex relaxation and upper bound processing on the original non-convex optimization problem to transform it into a multivariate fractional optimization problem. Specifically, in step S102, the original non-convex optimization problem is constructed with the radar received signal-to-interference-plus-noise ratio expression as the optimization objective and the communication received signal-to-interference-plus-noise ratio expression as the constraint condition, including the following steps S1021 to S1025.

[0028] S1021, taking the radar received signal-to-interference-plus-noise ratio expression as the optimization objective function, the communication received signal-to-interference-plus-noise ratio expression as the communication receiver interference power constraint, and adding the transmit precoding vector total energy constraint and the receive beamforming vector energy constraint, constitutes the original non-convex optimization problem; S1022, The interference power constraint at the communication receiver is: the power of the interference term in the communication receiver signal-to-interference-plus-noise ratio expression is less than a preset threshold; wherein, the interference term includes: radar precoding vector and communication precoding vector; S1023, the total energy constraint of the transmit precoding vector is: the square of the second norm of the radar precoding vector and the communication precoding vector is equal to 1; S1024, The energy constraint of the receiving beamforming vector is: the square of the second norm of the receiving beamforming vector is equal to 1; S1025, the original non-convex optimization problem aims to maximize the radar receiver signal-to-interference-plus-noise ratio, and is constrained by the interference power constraint at the communication receiver, the total energy constraint of the transmit precoding vector, and the energy constraint of the receive beamforming vector.

[0029] For example, with maximizing the radar received signal-to-interference-plus-noise ratio as the optimization objective and communication interference constraints and transmit and receive energy constraints as conditions, a joint robust optimization problem is constructed: (11a) (11b) (11c) (11d)

[0030] Specifically, in step S102, the original non-convex optimization problem is subjected to convex relaxation and upper bound processing, transforming it into a multivariate fractional optimization problem, including: (1) Relax the total energy constraint of the transmit precoding vector and the energy constraint of the receive beamforming vector from equality constraints to inequality constraints to obtain the relaxed energy constraint conditions. (2) The interference power constraint of the communication receiver is scaled down using the triangle inequality and the Cauchy-Schwarz inequality to obtain a deterministic communication interference constraint expression. The inner product result in the communication interference constraint expression is made real by phase rotation to obtain the relaxed communication interference constraint. (3) Take the upper bounds of the numerator and denominator in the radar received signal-to-interference-plus-noise ratio expression to obtain the upper bound expression of the radar received signal-to-interference-plus-noise ratio. The original non-convex optimization problem is transformed into a multivariate fractional optimization problem with the upper bound expression of the radar received signal-to-interference-plus-noise ratio as the objective function and the relaxed energy constraint and the relaxed communication interference constraint as the constraint conditions.

[0031] For example, the transmit and receive energy constraints (11d) are convexly relaxed to inequalities: (12) By using the triangle inequality and the Cauchy-Schwarz inequality, the communication interference constraints (11b) and (11c) are relaxed, and the inner product is made real by phase rotation: (13) (14) Taking an upper bound on the objective function (11a), we obtain the relaxed multivariate fractional optimization problem: (15) S103 uses the D-AGP algorithm, which combines Dinkelbach transform and alternating gradient projection, to solve the multivariate fractional optimization problem. It updates the auxiliary variables through outer iteration and alternately updates the radar precoding vector, communication precoding vector and receiving beamforming vector through inner iteration until convergence, thus obtaining the optimal radar precoding vector and the optimal communication precoding vector. Specifically, in step S103, the D-AGP algorithm, which combines Dinkelbach transform and alternating gradient projection, is used to solve the multivariate fractional optimization problem. The auxiliary variables are updated through outer iteration, and the radar precoding vector, communication precoding vector and received beamforming vector are updated alternately through inner iteration until convergence is achieved, thus obtaining the optimal radar precoding vector and the optimal communication precoding vector. This includes the following steps S1031 to S1033.

[0032] S1031, Outer Iteration: Introduce auxiliary variables and transform the multivariate fractional optimization problem into a subtractive form based on the Dinkelbach transform. At the end of each outer iteration, update the auxiliary variables according to the current radar precoding vector, communication precoding vector and received beamforming vector. Here, the outer iteration includes: (1) Initialize the auxiliary variables to zero or any value; (2) In the kth outer iteration, the current radar precoding vector, communication precoding vector and receiving beamforming vector are substituted into the subtractive optimization problem, the auxiliary variable is fixed as the updated value of the previous iteration, and the subtractive optimization problem is solved to obtain the new radar precoding vector, communication precoding vector and receiving beamforming vector. (3) Calculate the new auxiliary variable, which is equal to the numerator of the current radar received signal-to-interference-plus-noise ratio expression divided by the denominator; (4) Determine whether the absolute value of the difference between the new auxiliary variable and the auxiliary variable of the previous iteration is less than the preset threshold: if it is less than the preset threshold, terminate the outer iteration; otherwise, continue to the next outer iteration.

[0033] S1032, Inner Iteration: In each outer iteration, two of the three variables are fixed, and the radar precoding vector, communication precoding vector and receiving beamforming vector are updated alternately in sequence. The update of each variable adopts the gradient projection method, and the non-convex terms in the objective function are expanded by first-order Taylor to obtain a convex approximation. Here, the inner iteration includes: In each outer iteration, the following alternating update loop is executed: Step 1: Fix the communication precoding vector and the received beamforming vector, and construct a subproblem about the radar precoding vector using the radar precoding vector as the variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the radar precoding vector using the gradient projection method, and project the updated radar precoding vector onto the feasible region defined by the total transmit energy constraint and the communication interference constraint. Step 2: Fix the radar precoding vector and the received beamforming vector, and construct a subproblem about the communication precoding vector using the communication precoding vector as a variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the communication precoding vector using the gradient projection method, and project the updated communication precoding vector onto the feasible region defined by the total transmit energy constraint and the communication interference constraint. Step 3: Fix the radar precoding vector and the communication precoding vector, and construct a subproblem about the received beamforming vector using the received beamforming vector as a variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the received beamforming vector using the gradient projection method, and project the updated received beamforming vector onto the feasible region defined by the received energy constraint. Repeat steps one through three until the change in the objective function is less than the preset inner iteration threshold or the maximum number of inner iterations is reached.

[0034] S1033, repeat the outer and inner iterations until the change of the auxiliary variable is less than the preset threshold or the maximum number of outer iterations is reached, to obtain the optimal radar precoding vector and the optimal communication precoding vector.

[0035] For example, firstly, based on the Dinkelbach transform, the multivariate fractional optimization problem (15) is transformed into: (16) in, ; Auxiliary variables In the In the next iteration, it is updated to: (17) The precoding vector and the received beamforming vector are then updated iteratively using the alternating gradient projection method.

[0036] (1) Update .

[0037] For the The outer iteration and the first Within the first iteration, fixed and , The update can be obtained by solving the following optimization problem: (18) make , .

[0038] To ensure convexity, a first-order Taylor expansion is performed on the negative quadratic term in the objective function (18), and the optimization problem (18) can be relaxed as follows: (19) in, and: .

[0039] To solve the unconstrained optimization problem (19), the gradient projection method is used: (20) in, Let be the step size parameter, and the gradient vector be: (twenty one) Projected to The closed-form solution is: (twenty two) in, The Lagrange multiplier is given by the unique negative root of the quartic equation.

[0040] Projected to The optimal solution is: (twenty three) (2) Update .

[0041] For the The outer iteration and the first Within the first iteration, fixed and , The update can be obtained by solving the following optimization problem: (twenty four) make , .

[0042] Problem (24) can be rewritten as: (25) in: and .

[0043] To solve the unconstrained optimization problem (25), the gradient projection method is used: (26) in, Let be the step size parameter, and the gradient vector be: (27) Projected to The closed-form solution is: (28) in The Lagrange multiplier is given by the unique positive root of the quartic equation.

[0044] Projected to The optimal solution is: (29) (3) Update .

[0045] when and When fixed, the first The outer iteration and the first In the next iteration The update can be obtained by solving the following optimization problem: (30) make .

[0046] To ensure convexity, a first-order Taylor expansion is performed on the negative quadratic term in the objective function (30), and the optimization problem (30) can be relaxed as follows: (31) in:

[0047] For problem (31), gradient projection is used for updating: (32) in, Let be the step size parameter, and the gradient vector be: (33) Projected to The optimal solution is: (34) Iterate until the change in the objective function is less than the threshold. Or it may reach the maximum number of inner iterations.

[0048] S104 generates the optimal transmit waveform based on the optimal radar precoding vector and the optimal communication precoding vector, and outputs the optimal receive beamforming vector.

[0049] Specifically, in step S104, the optimal transmit waveform is generated based on the optimal radar precoding vector and the optimal communication precoding vector, and the optimal receive beamforming vector is output, including the following steps S1041 to S1045.

[0050] S1041, extract the optimal radar precoding vector, optimal communication precoding vector and optimal receiver beamforming vector from the converged D-AGP algorithm; S1042, multiply the optimal radar precoding vector with the desired radar waveform to obtain the radar transmission component; S1043, multiply the optimal communication precoding vector with the desired communication waveform to obtain the communication transmission component; S1044 adds the radar transmission component to the communication transmission component to generate the optimal transmission waveform; S1045 outputs the optimal transmit waveform and the optimal receive beamforming vector.

[0051] For example, iterating outwards to auxiliary variables Change less than threshold The optimal precoding vector is obtained when the maximum number of outer iterations is reached. , and optimal receive beamforming vector This leads to the generation of the optimal transmission waveform: (35) In a specific simulation embodiment provided by the invention: 1. Simulation conditions: The simulation of this invention was performed in the MATLAB software environment.

[0052] 2. Simulation content: The MIMO DFRC system employs a 16-element uniform linear array with an element spacing of half a wavelength. The target direction is set as... User orientation set to The desired radar waveform is a linear frequency modulated signal with a time-bandwidth product of 64 and a transmit power of [value missing]. The desired communication waveform is a QPSK signal with a bandwidth of [missing information]. The transmission power is The system signal-to-noise ratio is set to... The amplitude error between different units follows... arrive The uniform distribution, the phase error between different units follows arrive The uniform distribution of the CSI estimation error. The magnitude of the CSI estimation error follows a constant. arrive The uniform distribution of the CSI estimation error follows a phase that obeys the equation. arrive The uniform distribution. The internal iteration threshold is set to... The external iteration threshold is set to The number of Monte Carlo experiments was 500.

[0053] Four performance metrics are defined: received waveform error, transmit gain loss and received power, average received SINR in the radar main lobe and communication bit error rate. The performance of the proposed joint robust transmit waveform and receive beamforming (JR-TWRB) design method is evaluated by comparing it with the transmit energy (TE) constraint method and the joint transmit-receive beamforming (JT-RB) method.

[0054] 3. Simulation effect analysis: Figure 2 and Figure 3 These are the radar waveforms received by the MIMO DFRC system and the communication waveforms received by the user under different methods. The waveform obtained by the method of this invention is closest to the desired waveform, and the average relative error of the radar is... The average relative error of communication is The values ​​are all much smaller than those of the comparison method.

[0055] Figure 4 The transmit and receive beam patterns are generated using different methods. The method of this invention has the highest gain in the main lobe direction. The radar transmit gain loss is calculated. Communication transmission gain loss Radar receiving power All indicators are superior to the TE and JT-RB methods.

[0056] Figure 5 The variation of the radar main lobe received SINR under different methods is shown. The average received SINR of the radar main lobe using the method of this invention is... It is higher than the comparison method.

[0057] Figure 6The graphs show the variation of communication bit error rate with signal-to-noise ratio under different methods. The method of this invention has the lowest communication bit error rate and exhibits performance very similar to the desired QPSK waveform.

[0058] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this invention can be used in numerous general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, mobile communication terminals, multiprocessor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0059] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A robust joint transceiver design method for MIMO dual-function radar communication, characterized in that, include: A radar received signal model with amplitude and phase errors is constructed, and an expression for the radar received signal-to-interference-plus-noise ratio (SINR) is derived based on the radar received signal model. A communication received signal model with channel estimation errors is constructed, and an expression for the communication received SINR is derived based on the communication received signal model. With the radar received signal-to-interference-plus-noise ratio (SINR) expression as the optimization objective and the communication received SINR expression as the constraint, a primal non-convex optimization problem is constructed. The primal non-convex optimization problem is then subjected to convex relaxation and upper bound processing, transforming it into a multivariate fractional optimization problem. The D-AGP algorithm, which combines Dinkelbach transform and alternating gradient projection, is used to solve the multivariate fractional optimization problem. The auxiliary variables are updated by outer-layer iteration, and the radar precoding vector, communication precoding vector and received beamforming vector are updated by inner-layer iteration until convergence, so as to obtain the optimal radar precoding vector and the optimal communication precoding vector. The optimal transmit waveform is generated based on the optimal radar precoding vector and the optimal communication precoding vector, and the optimal receive beamforming vector is output.

2. The MIMO dual-function radar communication joint robust transceiver design method according to claim 1, characterized in that, The construction of a radar received signal model with amplitude and phase errors, and the derivation of the radar received signal-to-interference-plus-noise ratio (SINR) expression based on the radar received signal model, includes: The array amplitude and phase error is expressed as the sum of the nominal steering matrix and a norm-bounded error matrix to obtain the true steering matrix; wherein, the true steering matrix belongs to the set of uncertainties with the upper bound of the error norm as the radius; By replacing the nominal steering matrix with the real steering matrix, a radar received signal model with amplitude and phase errors is established, and the expression for the radar received signal with errors is obtained. At the receiving end, the radar received signal containing errors is weighted using the receiving beamforming vector to obtain the expression of the radar received signal after beamforming. Based on the expression of the radar received signal after beamforming, the expression for the radar received signal-to-interference-plus-noise ratio (SINR) is derived; wherein the expression for the radar received SINR is a quadratic form in which the numerator contains the received beamforming vector, the true steering matrix, and the transmitted waveform covariance matrix, and the denominator is the power of the interference term caused by the communication waveform to the radar and the sum of the quadratic forms of the received beamforming vector and the noise covariance matrix.

3. The robust MIMO dual-function radar communication joint transceiver design method according to claim 1, characterized in that, The construction of a communication received signal model with channel estimation error, and the derivation of the communication received signal-to-interference-plus-noise ratio (SINR) expression based on the communication received signal model, includes: The channel state information estimation error is represented as the sum of the nominal channel vector and a norm-bounded error vector to obtain the true channel vector; wherein, the true channel vector belongs to the set of uncertainties with the upper bound of the error norm as the radius; By replacing the nominal channel vector with the real channel vector, a communication received signal model with channel estimation error is established, and the expression for the communication received signal with error is obtained. Based on the error-containing communication received signal expression, the communication received signal-to-interference-plus-noise ratio (SINR) expression is derived; wherein, the numerator of the communication received SINR expression is the power of the desired communication waveform, and the denominator is the sum of the interference term power and noise power composed of the communication precoding vector, the real channel vector, and the radar precoding vector.

4. The robust MIMO dual-function radar communication joint transceiver design method according to claim 1, characterized in that, The process of constructing the primal non-convex optimization problem, with the radar received signal-to-interference-plus-noise ratio (SINR) expression as the optimization objective and the communication received SINR expression as the constraint, includes: Using the radar received signal-to-interference-plus-noise ratio (SINR) expression as the optimization objective function, and the communication received SINR expression as the interference power constraint at the communication receiver, along with the total energy constraint of the transmit precoding vector and the energy constraint of the receive beamforming vector, we construct the original non-convex optimization problem. The interference power constraint at the communication receiver is: the power of the interference term in the communication receiver signal-to-interference-plus-noise ratio expression is less than a preset threshold; wherein, the interference term includes: radar precoding vector and communication precoding vector; The total energy constraint of the transmit precoding vector is: the squared L2 norm of the radar precoding vector and the communication precoding vector are both equal to 1; The energy constraint of the receiving beamforming vector is: the square of the second norm of the receiving beamforming vector is equal to 1; The original non-convex optimization problem aims to maximize the radar receive signal-to-interference-plus-noise ratio (SINR), and is constrained by the interference power constraint of the communication receiver, the total energy constraint of the transmit precoding vector, and the energy constraint of the receive beamforming vector.

5. The robust MIMO dual-function radar communication joint transceiver design method according to claim 1, characterized in that, The process of performing convex relaxation and upper bound processing on the original non-convex optimization problem to transform it into a multivariate fractional optimization problem includes: The total energy constraint of the transmit precoding vector and the energy constraint of the receive beamforming vector are relaxed from equality constraints to inequality constraints, resulting in the relaxed energy constraint conditions. The interference power constraint at the communication receiver is scaled down using the triangle inequality and the Cauchy-Schwarz inequality to obtain a deterministic communication interference constraint expression. The inner product result in the communication interference constraint expression is made real by phase rotation to obtain the relaxed communication interference constraint. By taking upper bounds for both the numerator and denominator in the radar received signal-to-interference-plus-noise ratio (SINR) expression, we obtain the upper bound expression for the radar received SINR. This transforms the original non-convex optimization problem into a multivariate fractional optimization problem with the upper bound expression for the radar received SINR as the objective function and the relaxed energy constraint and the relaxed communication interference constraint as the constraint conditions.

6. The robust MIMO dual-function radar communication joint transceiver design method according to claim 1, characterized in that, The D-AGP algorithm, which combines Dinkelbach transform and alternating gradient projection, is used to solve the multivariate fractional optimization problem. This is achieved by iteratively updating auxiliary variables in the outer layer and alternately updating the radar precoding vector, communication precoding vector, and received beamforming vector in the inner layer until convergence, yielding the optimal radar precoding vector and optimal communication precoding vector. This includes: Outer iteration: Auxiliary variables are introduced, and the multivariate fractional optimization problem is transformed into a subtractive form based on the Dinkelbach transform. At the end of each outer iteration, the auxiliary variables are updated according to the current radar precoding vector, communication precoding vector, and received beamforming vector. Inner iteration: Within each outer iteration, two of the three variables are fixed, and the radar precoding vector, communication precoding vector and received beamforming vector are updated alternately in sequence. The update of each variable adopts the gradient projection method, and the non-convex terms in the objective function are expanded by first-order Taylor to obtain a convex approximation. Repeat the outer iteration and the inner iteration until the change of the auxiliary variable is less than a preset threshold or the maximum number of outer iterations is reached, to obtain the optimal radar precoding vector and the optimal communication precoding vector.

7. The MIMO dual-function radar communication joint robust transceiver design method according to claim 6, characterized in that, The outer iteration includes: Initialize the auxiliary variables to zero or any value; In the k-th outer iteration, the current radar precoding vector, communication precoding vector, and receiver beamforming vector are substituted into the subtractive optimization problem. The auxiliary variable is fixed as the updated value of the previous iteration. The subtractive optimization problem is solved to obtain the new radar precoding vector, communication precoding vector, and receiver beamforming vector. Calculate a new auxiliary variable, which is equal to the numerator of the current radar received signal-to-interference-plus-noise ratio expression divided by the denominator; Determine whether the absolute value of the difference between the new auxiliary variable and the auxiliary variable of the previous iteration is less than a preset threshold: if it is less than the preset threshold, terminate the outer iteration; otherwise, continue to the next outer iteration.

8. The MIMO dual-function radar communication joint robust transceiver design method according to claim 6, characterized in that, The inner iteration includes: In each outer iteration, the following alternating update loop is executed: Step 1: Fix the communication precoding vector and the received beamforming vector, and construct a subproblem about the radar precoding vector using the radar precoding vector as a variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the radar precoding vector using the gradient projection method, and project the updated radar precoding vector onto the feasible region defined by the total transmit energy constraint and the communication interference constraint. Step 2: Fix the radar precoding vector and the received beamforming vector, and construct a subproblem about the communication precoding vector using the communication precoding vector as a variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the communication precoding vector using the gradient projection method, and project the updated communication precoding vector onto the feasible region defined by the total transmit energy constraint and the communication interference constraint. Step 3: Fix the radar precoding vector and the communication precoding vector, and construct a subproblem about the received beamforming vector using the received beamforming vector as a variable; perform a first-order Taylor expansion on the negative quadratic term in the subproblem to obtain a convex approximation, update the received beamforming vector using the gradient projection method, and project the updated received beamforming vector onto the feasible region defined by the received energy constraint. Repeat steps one through three until the change in the objective function is less than the preset inner iteration threshold or the maximum number of inner iterations is reached.

9. The robust MIMO dual-function radar communication joint transceiver design method according to claim 1, characterized in that, The step of generating the optimal transmit waveform based on the optimal radar precoding vector and the optimal communication precoding vector, and outputting the optimal receive beamforming vector, includes: Extract the optimal radar precoding vector, optimal communication precoding vector, and optimal receiver beamforming vector from the converged D-AGP algorithm; Multiply the optimal radar precoding vector by the desired radar waveform to obtain the radar transmission component; Multiply the optimal communication precoding vector by the desired communication waveform to obtain the communication transmission component; The radar transmission component is added to the communication transmission component to generate the optimal transmission waveform; Output the optimal transmit waveform and the optimal receive beamforming vector.

Images