Space-frequency emission sequence design method for dual-function radar communication system

Abstract

The invention discloses a space-frequency emission sequence design method for a dual-function radar communication system, which comprises the following steps of: constructing an optimization problem of a space-frequency emission sequence by taking mutual information optimization of multiple communication users and simultaneous radar emission beam directional diagram control of multiple targets as target functions under multiple constraint conditions; wherein the constraint conditions comprise direction mismatch interference power constraint, radar emission vector constraint and power constraint; a communication emission vector set in the fixed # imgabs0 # solution optimization problem is converted into a first optimization sub-problem; solving a radar emission vector in the optimization problem by using a fixed # imgabs1 #, and converting the radar emission vector into a second optimization sub-problem; alternately solving the first optimization sub-problem and the second optimization sub-problem until a convergence condition is met, and determining a space-frequency transmission sequence; the design is effective in the radar function and the communication function of the spatial frequency domain.

Description

Technical Field

[0001] The present invention relates to the technical field of radar communication, and particularly to a method for designing an air-frequency transmission sequence for a dual-functional radar communication system. Background Art

[0002] With the rapid development of the Internet and wireless information transmission technologies, the number and utilization rate of wireless devices have exploded. Therefore, the demand for spectrum resources is increasing. Spectrum sharing strategies are crucial for solving the inevitable spectrum congestion problem in wireless communication systems. These strategies mainly focus on two main methods: The first method involves radar-communication coexistence, mainly considering that the radar system and the communication system operate independently in an actual scenario, and different frequency bands are allocated to the two systems by the spectrum regulatory agency to eliminate interference between them, aiming to reduce mutual interference and achieve coordinated spectrum sharing; this method emphasizes minimizing interference between the radar and the communication system and allowing them to operate in close proximity. The second method requires deploying a dual-functional radar communication (RadCom) system, which is a cutting-edge system that can effectively utilize the radio spectrum and reuse the same signal for radar and communication functions, that is, realizing radar and communication functions simultaneously using the same hardware platform, spectrum resources, and transmission waveform.

[0003] In recent years, due to the shortage of spectrum resources, by leveraging the existing network architecture and hardware, the dual-functional RadCom system can effectively alleviate the spectrum congestion problem and promote a series of innovative applications. However, there are still many challenges in the design of the dual-functional RadCom system in the prior art: (1) When designing the dual-functional radar communication system, the performance of the communication system or the radar system is often optimized separately, resulting in limited overall system performance and unable to achieve the optimal coexistence of radar and communication functions. Moreover, in practical applications, the uncertainty of the channel state information makes it easy for the performance of the radar and communication systems to decline simultaneously. (2) The related optimization formulas tend to exhibit non-convexity, so these optimization problems are considered NP-hard problems and it is difficult to find the global optimal solution. (3) The transmitter design is restricted by actual hardware limitations, including transmission power, similarity, detection probability, and constant modulus, which further increase the difficulty of system design. (4) In practical applications, there is often uncertainty in the channel state information of the dual-functional radar communication system. In the wireless channel, the actual propagation direction often does not match the assumed propagation direction, which may lead to the simultaneous decline of the performance of the radar and communication systems. (5) There is a lack of flexible control means for realizing multi-user communication and the optimal transmission beam pattern of the radar, making it difficult to meet the requirements of complex and changeable application scenarios.

[0004] In the related art, the literature "Research on Compromise Optimization Design Technology of Dual-Function Radar Communication Waveform, Nanjing University of Posts and Telecommunications, Hou Yuefeng" proposes to consider using constant modulus constraint as an evaluation criterion to design the dual-function radar communication waveform, to consider adding a precoding factor at the communication end to improve communication performance, and adding a constant modulus constraint at the radar end to reduce transmission distortion. At the same time, a weighting factor p is introduced to achieve the compromise optimization of communication and radar performance. Under the constant modulus constraint, a non-convex optimization problem of a quadratic equation with three variables is constructed, and a multi-variable alternating minimization solution framework is proposed to decompose the optimization problem, and the three sub-problems after decomposition are solved and discussed respectively, and finally the dual-function waveform after compromise optimization is obtained; this scheme explores waveform design from the system level, and proposes three ideas centered on radar / communication and collaborative design, respectively realizing radar functions through information embedding, using communication signals, or designing DFRC waveforms from scratch, focusing on exploring technical paths in different scenarios; the design centered on radar / communication can guarantee the main function, but there are problems such as limited communication rate or radar performance loss; collaborative design balances performance through methods such as Pareto optimization, but there are differences in applicability in different scenarios. Summary of the Invention

[0005] The technical problem to be solved by the present invention is how to optimize the overall system performance of dual-function radar communication, and improve the communication mutual information and the accuracy of the radar beam pattern.

[0006] The present invention solves the above technical problems through the following technical means:

[0007] A spatial-frequency transmit sequence design method for a dual-function radar communication system is proposed, including:

[0008] For a dual-function radar communication system, an optimization problem of the spatial-frequency transmit sequence is constructed with the mutual information optimization of multiple communication users and the control of the radar transmit beam pattern for multiple targets simultaneously as the objective function under multiple constraint conditions, where the constraint conditions include the direction mismatch interference power constraint of communication users, the radar transmit vector constraint, and the power constraint;

[0009] With a fixed Solve the communication transmit vector set in the optimization problem, and convert the optimization problem from a non-convex problem to a first optimization sub-problem, where m 0 represents the iteration index, represents the radar transmit vector at the m 0 -th iteration, and s t represents the radar transmit vector;

[0010] With a fixed Solve the radar transmit vector in the optimization problem, and convert the optimization problem from a non-convex problem to a second optimization sub-problem, where represents the m 0The communication transmit vector of the i-th iteration, s c,n represents the communication transmit vector;

[0011] Solve the first optimization sub-problem and the second optimization sub-problem alternately until the convergence condition is met, and determine the space-frequency transmit sequence. Both the first optimization sub-problem and the second optimization sub-problem are convex problems.

[0012] Furthermore, the optimization problem includes an objective function and constraint conditions, which are expressed by the formula:

[0013]

[0014]

[0015] where: γ 1 and γ 2 represent the weighting factors corresponding to the mutual information and the mean square error function respectively, which are mainly used to balance between the two objectives of maximizing the mutual information of the communication system and minimizing the beam pattern error of the radar system. By adjusting the values of γ 1 and γ 2 , the priorities of communication and radar functions can be flexibly balanced; ζ n and ζ k are the weighted sum framework parameters designed for multi-communication users in communication and multi-detection targets in radar respectively. ζ n is used to adjust the weights of different communication users in the mutual information calculation, and ζ k is used to adjust the weights of different radar detection targets in the beam pattern error calculation, so that the importance of different users and targets can be differentiated according to actual needs; MI n ({s c,n}, s t ) represents the mutual information of multiple communication users, which is a key indicator to measure the performance of the communication system. This indicator reflects the amount of information that the communication system can transmit under the given communication transmit vector s c,n and the radar transmit vector s t ; F R (β, {s c,n}, s t ) represents the mean square error between the designed beam pattern of the radar and the desired beam pattern, which is an important parameter to evaluate the performance of the radar system. β represents the scale factor used to adjust the amplitude of the desired beam pattern; Π i represents a matrix with all elements being 0 except the (i, i) element, represents the power of the radar transmit signal transmitted to the m-th spatial frequency band, represents the power of the communication user transmit signal to the n-th spatial frequency band, denotes a frequency - related response matrix, which describes the frequency - response characteristics at different frequency points q r1 and q r2 where the frequency - response characteristics are located, denotes an estimated frequency - related response matrix, denotes a spatial - angle - related response matrix, which describes the spatial - response characteristics corresponding to different spatial angles, denotes an estimated spatial - angle - related response matrix; η R,m and η c,n respectively denote the upper bounds of power corresponding to the radar function and the communication function. In the radar system, η R,m is used to limit the power of the radar - transmitted signal in the m - th spatial frequency band to ensure that the radar - transmitted power does not exceed the specified value; in the communication system, η c,n is used to limit the power of the communication - user - transmitted signal in the n - th spatial frequency band; s 0 denotes the radar - transmission vector when the detection signal is x 0 i.e., the reference vector; ξ denotes the similarity parameter, denotes the radar - transmission power parameter, representing the total power of the radar - transmitted signal, denotes the power of the communication - user - transmitted signal in the n - th spatial frequency band, ∥∥ 2 denotes the square of the Euclidean norm of a vector, which is used in the power - constraint condition to ensure that the power of the transmission vector meets the system requirements; denotes the convolution between two matrices, M, N, N t , D are respectively the number of radar - detection targets, the number of communication users, the number of transmitting units, and the coding length in the dual - function radar - communication system, (·) H denotes the Hermitian operator.

[0016] Furthermore, the mutual - information formula for multiple communication users is expressed as:

[0017]

[0018] In the formula: denotes the N - th interference - plus - noise covariance matrix, s c,j denotes the communication - transmission vector of user j, s c,i denotes the communication - transmission vector of user i, H n denotes the channel matrix of the n - th user, which describes the channel characteristics experienced by the communication signal during transmission, including information such as signal fading and delay, denotes the inverse matrix of the N - th interference - plus - noise covariance matrix; denotes the noise variance of the n - th communication user, reflecting the intensity of noise in the communication system, denotes ​The identity matrix in dimension represents the complex conjugate matrix of the communication transmit vector, represents the complex conjugate matrix of the channel matrix of user n, represents the defined symbol.

[0019] Furthermore, the formula for the mean square error between the radar design beam pattern and the desired beam pattern is expressed as:

[0020]

[0021] where: ω k represents the weighting parameter of the radar design beam in the k-th direction, represents the desired beam pattern, represents the complex conjugate matrix of the communication transmit vector, represents the autocorrelation matrix at the angle of and represents the complex conjugate matrix of the radar transmit vector, and K represents the dimension of beamforming.

[0022] Furthermore, the calculation formulas of the and are:

[0023]

[0024] where: q r1 , q r2 represent two different frequency points, represents the complex exponential related to the higher spatial angle, represents the complex exponential related to the lower spatial angle, [f m,u , f m,l represents the frequency band constraint, represents the spatial angle range, represents the higher spatial angle, represents the lower spatial angle, represents the complex exponential related to the higher frequency, represents the complex exponential related to the lower frequency.

[0025] Furthermore, the calculation formulas of the and are:

[0026]

[0027] where: q cn1 , q cn2 respectively represent two different frequency points, and respectively represent the higher spatial angle and the lower spatial angle, Denote the complex exponential related to the higher spatial angle, Denote the complex exponential related to the lower spatial angle, f n,u and f n,l respectively represent the higher frequency and the lower frequency, Denote the complex exponential related to the higher frequency, Denote the complex exponential related to the lower frequency.

[0028] Furthermore, the formula of the first optimization sub - problem is expressed as:

[0029]

[0030] Where: Denote the estimated transmit vector of the n - th communication user, Denote taking as the optimization variable to minimize the quadratic function γ 1 and γ 2 are weighting factors, representing the weights corresponding to the radar power and the communication power respectively. The weighting factor γ 1 and γ 2 are adjustable, and γ 1 +γ 2 = 1, Denote the radar performance matrix related to the n - th communication user, Denote the communication performance matrix related to the n - th communication user, ε n Denote the non - negative slack variable, ρ n Denote the penalty factor, I represents the identity matrix, Denote the estimated transmit vector of the j - th communication user, Denote the m 0 - th iteration's estimated value of the radar transmit vector, Denote the reference transmit vector, Denote the estimated channel matrix at the (i + 1)-th iteration, Denote the slack power constraint of the n - th communication user, Denote the complex conjugate transpose of the original transmit vector of the n - th communication user, Denote the complex conjugate transpose of the communication transmit vector at the (m 0 - 1)-th iteration, Denote the real - part operator.

[0031] Furthermore, the formula of the second optimization sub - problem is expressed as:

[0032]

[0033] Where: Denote the radar estimated transmit vector, Denote minimization, minimizing the quadratic function γ 1 and γ 2 are weighting factors, representing the weights corresponding to the radar power and the communication power respectively. The weighting factor γ 1 and γ 2 are adjustable, and γ 1 +γ 2 = 1, represents a matrix related to the performance of the radar system, represents a matrix related to the performance of the communication system, represents the estimated radar transmission vector, represents the estimated initial vector, represents a parameter that controls the penalty effect, represents a slack variable, represents the complex conjugate matrix of the estimated radar transmission vector, represents related to the frequency f m The function matrix is used to describe the correlation of the radar signal in the frequency domain. η R,m represents the upper limit of the interference caused by the radar transmission vector to the communication system at the m-th communication frequency, represents the m 0 The complex conjugate matrix of the estimated communication transmission vector at the (m - 1)-th iteration, represents the estimated channel matrix at the (i + 1)-th time, s t H represents the complex conjugate matrix of the radar transmission vector, represents the transmission power of the radar, represents the m 0 The complex conjugate matrix of the radar transmission vector at the (m - 1)-th iteration, represents the real part operator, represents the estimated radar transmission vector, represents a slack variable.

[0034] Furthermore, the first optimization sub-problem and the second optimization sub-problem are alternately solved until the convergence condition is satisfied to determine the spatio-frequency transmission sequence, including:

[0035] Based on the ADMM algorithm, the first optimization sub-problem and the second optimization sub-problem are alternately solved until the convergence condition is satisfied, and the spatio-frequency transmission sequence is determined.

[0036] Furthermore, the weighting factors γ 1 and γ 2 are adjustable, and γ 1 +γ 2 = 1.

[0037] The advantages of the present invention are as follows:

[0038] (1) The present invention constructs an optimization problem of the space-frequency transmit sequence with the mutual information optimization of multiple communication users and the radar transmit beam pattern control of multiple objectives simultaneously under multiple constraint conditions as the objective function. It can comprehensively consider the performance requirements of the communication system and the radar system, and maximize the mutual information of multi-user communication and minimize the squared error between the designed beam pattern and the desired beam pattern by optimizing the transmit beam pattern and spectrum resource allocation, improving the communication mutual information and the accuracy of the radar beam pattern, while satisfying the hardware limitations and space-frequency power requirements of the system, and realizing the optimization of the overall system performance of the dual-functional radar communication.

[0039] (2) The present invention considers the uncertainty of the channel state information. By designing a robust optimization framework, it improves the performance stability of the system in a complex and changeable channel environment and ensures the robustness of the system-level performance.

[0040] (3) The design method proposed by the present invention can flexibly adjust the weighting factor according to actual requirements, realize the trade-off between multi-user communication and radar functions, and meet the requirements of different application scenarios.

[0041] (4) Based on the iterative algorithm of the double min-max framework, the present invention iteratively solves the constructed optimization problem, analyzes the convergence of the iterative algorithm, and verifies through numerical simulation that the proposed iterative algorithm has good convergence performance and can reach the optimal solution in a short time.

[0042] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present invention. Brief Description of the Drawings

[0043] Figure 1 is a schematic flow chart of a space-frequency transmit sequence design method for a dual-functional radar communication system proposed in an embodiment of the present invention;

[0044] Figure 2 is a schematic diagram of the analysis result of the convergence of the iterative algorithm in an embodiment of the present invention;

[0045] Figure 3 is a schematic diagram of the spectral distribution of the communication function in the space-frequency domain in an embodiment of the present invention;

[0046] Figure 4 is a schematic diagram of the spectral distribution of the radar function in the space-frequency domain in an embodiment of the present invention. Detailed Embodiments

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0048] As Figure 1 shown, an embodiment of the present invention proposes a spatial-frequency transmit sequence design method for a dual-functional radar communication system. The method includes the following steps:

[0049] S10. For a dual-functional radar communication system, an optimization problem of the spatial-frequency transmit sequence is constructed with the mutual information optimization of multiple communication users and the radar transmit beam pattern control of multiple objectives simultaneously as the objective function under multiple constraint conditions, where the constraint conditions include the direction mismatch interference power constraint of communication users, the radar transmit vector constraint, and the power constraint;

[0050] S20. With a fixed solve the communication transmit vector set in the optimization problem, and convert the optimization problem from a non-convex problem to a first optimization sub-problem, where m 0 represents the iteration index, represents the radar transmit vector at the m 0 -th iteration, and s t represents the radar transmit vector;

[0051] S30. With a fixed solve the radar transmit vector in the optimization problem, and convert the optimization problem from a non-convex problem to a second optimization sub-problem, where represents the communication transmit vector at the m 0 -th iteration, and s c,n represents the communication transmit vector;

[0052] S40. Alternately solve the first optimization sub-problem and the second optimization sub-problem until the convergence condition is satisfied to determine the spatial-frequency transmit sequence. Both the first optimization sub-problem and the second optimization sub-problem are convex problems.

[0053] It should be noted that in this embodiment, through system modeling and analysis of the dual-functional radar communication system, a joint framework for the dual functions of the radar and communication systems is derived. An optimization problem is constructed to maximize the mutual information of multi-user communication and minimize the mean square error between the designed beam pattern and the desired beam pattern by optimizing the transmit beam pattern and spectrum resource allocation under multiple constraints. The optimization problem is iteratively solved, and through alternating iteration and constraint conditions, the collaborative optimization of multiple objectives is achieved. The spatio-frequency transmit sequence can comprehensively consider the performance requirements of the communication system and the radar system, improve the communication mutual information and the accuracy of the radar beam pattern, and at the same time meet the hardware limitations and spatio-frequency power requirements of the system, realizing the optimization of the overall performance of the dual-functional radar communication system.

[0054] Generally speaking, this embodiment focuses on the compromise optimization design of the dual-functional radar communication waveform. Aiming at the waveform distortion caused by the oversaturation of the radar amplifier and the communication performance loss caused by the too low sidelobe of the constant envelope waveform, a multi-variable non-convex optimization model is constructed by introducing the constant modulus / peak-to-average power ratio constraint and the precoding factor, and the alternating minimization framework and the particle swarm algorithm are used for iterative solution to achieve the dynamic balance of radar and communication performance. The transmission distortion is reduced by the constant modulus constraint, so that the communication bit error rate and the radar beam sidelobe ratio reach an acceptable range; the waveform design based on the peak-to-average power ratio constraint significantly improves the communication rate while ensuring the radar performance, approaching the ideal waveform effect.

[0055] As a further technical solution, before the step S10: for the dual-functional radar communication system, an optimization problem of the spatio-frequency transmit sequence is constructed with the mutual information optimization of multiple communication users and the radar transmit beam pattern control of multiple targets as the objective function under multiple constraints. First, a system modeling and analysis of the dual-functional radar communication system is carried out, and the specific process is as follows:

[0056] Consider that the dual-functional radar communication system includes a dual-functional radar communication base station, multiple communication users, and a radar detection target. The dual-functional radar communication base station is equipped with N t antennas, that is, transmit units, and they are located in a Uniform Linear Array (ULA). The RadCom system provides communication services for N communication users, that is, N receiving units, and detects a single radar target by transmitting the dual-functional radar communication waveform, where the coding length of the communication data can be expressed as D.

[0057] (1) For the radar function, consider M point targets with directions of , represents the spatial angle of the l-th target, which is used to determine the radar beam pointing and the target position, and L represents the number of targets detected by the radar, which is used to define the total number of targets to be considered in the optimization problem; then the received signal of the target It can be modeled as:

[0058]

[0059] Wherein, is the steering matrix of the m-th target transceiver. The communication transmit vector and symbol can be written in a form corresponding to the radar expression, that is, the transmit vector of the n-th communication user and the information symbol x n , the radar transmit vector is represented by , the information symbol is x n , represents the space composed of all N t D-dimensional complex column vectors, each element is a complex number, and the form of the vector in the space is The symbol representing the mathematical expectation is used to describe the average value of a random variable; z i is the radar interference, is the radar noise, ~ means following a certain distribution, represents the complex normal distribution (Complex Normal Distribution), that is, the extension of the real normal distribution in the complex number domain. For an N-dimensional complex random vector z~CN(μ,Σ), where: μ is an N-dimensional complex vector representing the mean vector of the complex random vector, that is Σ is an N×N covariance matrix, which describes the correlation between the components of the complex random vector; in , the mean vector is μ = 0 (here 0 is an N t D-dimensional zero vector), indicating that the mean of the radar noise is zero, represents the power of the noise. In the complex normal distribution, for a zero-mean complex random vector, the elements on the diagonal of its covariance matrix reflect the power of each component. Since the covariance matrix is it shows that each component of the radar noise has the same power represents N t D×N t D identity matrix. The identity matrix is a square matrix with all elements on the main diagonal equal to 1 and all other elements equal to 0, and its form is: The covariance matrix is which means that the components of the radar noise z R,n are uncorrelated with each other and have the same power That is to say, the radar noise is a zero-mean, uncorrelated and equal-power complex Gaussian noise.

[0060] (2) For the n-th communication user, the received signal of the user z c,nIt can be modeled as:

[0061]

[0062] Where, is the nth user channel, and are multi - user interference and radar signal interference respectively, s c,i is the transmit vector of the ith user, x i is the symbol sent by the ith communication user, is the Hermitian matrix of H n ; is the nth user noise, represents the noise power at the receiver of the nth communication user, represents N t D×N t dimensional identity matrix.

[0063] Furthermore, and are the channel matrices corresponding to the target and the users, which can be described by physical propagation,

[0064]

[0065] In the formula, α m and are complex gains, a t (·) and a r (·) are the transmit steering vector and receive steering vector of the target respectively, v r,n (·) is the nth receive steering vector, (·) T and (·) H represent the transpose operator and Hermitian operator respectively. Considering the angular parameters and are uncorrelated uniformly distributed random variables, obeying and are the actual directions, while Δ m and Δ n represent the corresponding direction mismatches, i.e., direction uncertainties. p n represents the channel path index of the nth user, used to identify the specific path in the multipath components, P n represents the number of channel paths of the nth user, used to define the complexity of the channel model, I D represents the D×D identity matrix, used to construct the multi - dimensional channel response matrix, represents the tensor product, used to combine the identity matrix and the direction vector, supporting spatio - frequency joint modeling.

[0066] In this example, by means of modeling analysis, the performance indicators, constraints and problem characteristics of radar and communication are quantified, providing a clear objective (maximizing communication mutual information + minimizing radar beam error), strict constraints (spatial-frequency power, direction mismatch, power limitation) and a solution method (convex decomposition + ADMM) for the subsequent optimization problem. These conclusions not only solve the collaborative design problem of the dual-functional system, but also provide theoretical support for resource allocation, interference management and hardware adaptation in practical engineering.

[0067] As a further preferred technical solution, based on the above modeling analysis of the dual-functional radar communication system, a joint framework for the dual functions of the radar and communication systems is derived. The process of constructing the optimization problem of the spatial-frequency transmission sequence includes:

[0068] (1) For a multi-user communication system, the figure of merit is the user mutual information MI n ({s c,n},s t ) and can be defined as:

[0069]

[0070] where represents the covariance matrix of the Nth interference plus noise,

[0071] (2) For the radar, mathematically speaking, it is the transmitted beam pattern power in a specific direction which can be calculated as:

[0072]

[0073] where represents a matrix related to the spatial angle and is defined by . Among them, I D is the D×D-dimensional identity matrix, represents the Kronecker product (tensor product), is the transmitted steering vector of the target, is 's complex conjugate transpose matrix. Comprehensively considering the characteristics of the identity matrix and the transmitted steering vector at the angle , it reflects the signal propagation and radiation characteristics of the radar in the direction of this angle. represents the spatial angle.

[0074] Furthermore, in order to ensure the robustness of the system-level performance, the uncertainty of the prior knowledge of the channel propagation direction must be considered. Correspondingly, considering the basic component of the radar is the difference between the designed transmitted and desired beam patterns pointing to the target direction, denoted as F R (β,{sc,n ,s t ) can be expressed as:

[0075]

[0076] where ω k is the weighting parameter in the k-th direction, β and represent the scale factor and the desired beam pattern, F R () represents a quantization index of the difference between the beam pattern transmitted by the radar design and the desired beam pattern, represents the spatial angle related to the k-th direction associated matrix.

[0077] (3) Here, the constraints of the uncertain detection region and the exclusive operating frequency band of two function systems are considered

[0078] Specifically, the power of the radar transmitted signal transmitted to the q-th spatial frequency band can be expressed as:

[0079]

[0080] where represents the radar vector transmitted by the n-th antenna, i.e., s t = vec(S t ), vec(·) represents the vectorization operator, represents the set of N t × D-dimensional matrices in the complex domain, f R represents the operating frequency range of the radar, represents the vector or matrix related to the spatial angle associated, e(f m ) represents the vector or matrix related to the frequency f m associated, represents the complex conjugate transpose of the vector s t , represents the complex conjugate transpose of the matrix m associated with the frequency f , represents the matrix related to the spatial angle associated.

[0081] And there is:

[0082]

[0083] In the formula, q r1 , q rw represent two different frequency points, represents the complex exponential related to the higher spatial angle, Represents a complex exponential related to a lower spatial angle, [f m,u , f m,l represents a frequency band constraint, represents a spatial angle range, represents a higher spatial angle, represents a lower spatial angle, represents a complex exponential related to a higher frequency, represents a complex exponential related to a higher frequency.

[0084] Specifically, for a communication user, the spatial frequency band power is given by Equation (9):

[0085]

[0086] where, represents the communication vector transmitted by the nth antenna, s c,n = vec(S c,n ), f C represents the operating frequency range of the communication user, represents the spatial angle of the communication user (such as the direction of the coverage area), represents the communication signal direction vector related to the spatial angle , represents the communication signal frequency response vector related to the frequency f n , represents the complex conjugate transpose of the nth communication user's transmission vector, represents the complex conjugate transpose of the frequency-related matrix of the communication signal, represents the spatial angle-related matrix of the communication signal, Tr(·) represents the trace of the matrix.

[0087] And there is:

[0088]

[0089] where, f n,u (f n,l ) and are the higher (lower) frequency and spatial angle respectively, [f n,u , f n,l is the communication frequency band constraint, is the spatial range corresponding to the communication frequency band; q cn1 , q cn2 represent two different frequency points respectively, represents the complex exponential term corresponding to the higher spatial angle, represents the complex exponential term corresponding to the lower spatial angle, represents the complex exponential term corresponding to the higher frequency, Represents the complex exponential term corresponding to the lower frequency.

[0090] Therefore, determining the multiple constraint conditions includes: 1) Direction mismatch interference power constraint: The direction mismatch interference power constraints of N users and the spatial frequency band power constraint of the radar transmission signal where {η C,n} and {η R,m} respectively represent the upper bounds of the power corresponding to the communication and radar functions. 2) The radar transmission vector satisfies some ideal characteristics in the reference vector s 0 , and the radar transmission vector constraint is where ξ is the similarity parameter, and π i represents a matrix with all factors being 0 except for the elements of (i, i). 3) Power constraints and represent the power occurrence parameters, represents the transmission power parameter of the nth communication user.

[0091] Finally, aiming at the optimization of the mutual information MI of multiple communication users and the control of the radar transmission beam pattern for multiple targets simultaneously, the system is designed, and the optimization problem is determined as:

[0092]

[0093] where γ 1 and γ 2 are the weighting factors, representing the weights corresponding to the mutual information and the squared error function respectively. The weighting factors γ 1 and γ 2 are adjustable, and γ 1 +γ 2 =1. The weighted sum framework is developed for multiple communication users and multiple radar targets by using the parameters ζ n and ζ k respectively.

[0094] This scheme constructs a non-convex optimization problem by jointly optimizing the space-frequency transmission sequences of the radar and communication, comprehensively considering their mutual interference, channel direction uncertainty, power constraints, performance indicators, and radar signal stability, and realizes the efficient cooperation of the dual-functional system: 1) By jointly designing the transmission vector and beamforming, the communication capacity and radar detection accuracy are balanced; 2) Relaxation variables and penalty factors are introduced to cope with channel fluctuations and enhance robustness; 3) The space-frequency constraint effectively suppresses the cross-system interference; 4) The power allocation realizes the efficient utilization of resources; 5) The similarity constraint ensures the stability of the radar beam. This scheme significantly improves the overall performance and anti-interference ability of the system under hardware limitations.

[0095] Considering the non-convexity of the objective function (11a) and the constraints (11d) and (11e) in the optimization problem shown in formula (11), for non-convex multivariable optimization, an effective optimization process, namely the iterative process of DMM-ADMM (Distributed Alternating Direction Method of Multipliers), will be derived next.

[0096] First, it is necessary to prove that the optimization problem shown in formula (11) constructed in this embodiment can be converted into a convex proposition. The process is as follows:

[0097] (1) {s c,n} Optimization: In the first stage, with fixed Solve the set {s c,m} where m 0 represents the iteration index, then there is:

[0098]

[0099] Proposition 1: Problem (12) can be transformed into:

[0100]

[0101] The proof process is as follows:

[0102] First, for the expression about s c,n , define:

[0103]

[0104]

[0105] Then there is:

[0106]

[0107] Among them, is the maximum eigenvalue of D n , D n is the matrix defined above, I is the identity matrix, is the estimated signal at the (m 0 -1)th iteration.

[0108] Combined with the expression ∥∥s c,n ∥∥ 2 = P C,n , The quadratic function can be constructed as:

[0109]

[0110] In the formula, represents the maximum eigenvalue of and n denotes the estimated D

[0111] Among them, moreover, there is:

[0112]

[0113] Then, the positive semi - definite framework of

[0114] Secondly, for it can be rewritten as:

[0115]

[0116] In the formula, denotes the N r,n × D - dimensional identity matrix, R Cin represents the input capacity, represents the constraint rate with respect to s c,j and s t of

[0117] For the quadratic substitution function of the first expression in Equation (17) can be expressed as:

[0118]

[0119] Among them:

[0120]

[0121] In the formula, is the maximum eigenvalue of denotes the 0 (m - 1) - th iteration, denotes the 0 (m - 1) - th iteration of * () represents the conjugate matrix of a matrix.

[0122] For the second expression in Equation (17) it is a concave function with respect to therefore, the upper - bound framework through the first - order Taylor expansion can be written as:

[0123]

[0124] In the formula, represents the defined symbol, among which,

[0125] By using the property denotes the product of the interference-plus-noise inverse matrix and the channel matrix of the nth user, and is used to calculate the SINR or MI of this user, F n denotes that of all other users The sum is used to quantify the total interference of other users to the current user. Therefore, combining the constraint set That is, removing the constant expression The left term of Equation (12) can be written as

[0126] Let and ensure the positive semi-definiteness of, which can be modified as By using the block component decomposition framework, the optimization problem shown in Equation (12) can be separated for each user, and it is defined as:

[0127] and

[0128] That is, the proof is completed.

[0129] Note that due to the constraint condition the above problem is still non-convex and can be transformed into For the non-convex A convex transformation framework can be written as To ensure the feasibility of the problem in Equation (13), non-negative slack variables {ε n} and penalty factors {ρ n} are introduced, and then there is the following first optimization sub-problem:

[0130]

[0131] where ρ n represents the parameter that controls the penalty effect. Due to the existence of the slack variable ε n the first optimization sub-problem described in Equation (21) is always feasible and separable for each user of the quadratic programming with convex quadratic constraints.

[0132] (2) Optimization of {s t}: Solve the set of {s } with fixed t .

[0133] Following the same reasoning, the expression with respect to s t can be defined as:

[0134]

[0135] Then, the transformed framework exactly corresponds to the expression (15) in Proposition 1, and thus is:

[0136]

[0137] where, represents the largest eigenvalue of the relaxation matrix, which is used to construct the convex upper bound of the non-convex term and support the solution of the optimization problem. represents the relaxed pattern matrix, which is used to transform the non-convex pattern constraint into a convex form. Moreover, there is:

[0138]

[0139] Following the same reasoning, for which is convex with respect to s t and then the surrogate function is obtained by the first-order Taylor expansion around :

[0140]

[0141] where, F t represents the gradient matrix of MI with respect to S t quantifying the marginal impact of radar transmission on communication performance, represents the linear term of the Taylor expansion, which is used to approximate the non-linear mutual information as a linear function and support convex optimization. There is:

[0142]

[0143] For the non-convex constraint Let which can be transformed into For the non-convex constraint a convex transformation framework can be written as Define:

[0144]

[0145] To ensure the feasibility of problem (21), non-negative slack variables and penalty factors are introduced into the optimization problem (21). There is the second optimization sub-problem:

[0146]

[0147] where, represents the parameter controlling the penalty effect. Note that due to the slack variable Due to its existence, the problem shown in formula (27) is always feasible, and for quadratic programming with convex quadratic constraints.

[0148] Therefore, the optimization problem shown in formula (11) constructed through the above proof can be transformed into convex problems as shown in formula (21) and formula (27). Furthermore, the ADMM iterative algorithm can be used to alternately solve the first optimization sub-problem and the second optimization sub-problem until the convergence condition is met, and then the spatio-frequency transmit sequence is determined.

[0149] Specifically, the ADMM algorithm realizes co-design by alternately optimizing the radar and communication transmit vectors: First, the system parameters are initialized, and then two convex sub-problems are alternately solved in each iteration. Sub-problem 1 fixes the radar vector and, with a fixed solves the set {s c,n} (formula 21), optimizes the transmit strategy of the communication users through convex relaxation and semidefinite programming, and maximizes the communication mutual information while satisfying the power and interference constraints; Sub-problem 2 fixes the communication vector and, with a fixed solves the {s t} set (formula 27), linearizes the non-convex terms using Taylor expansion, optimizes the radar beam pattern and satisfies the spatio-frequency power constraint. By introducing auxiliary variables and dual variables through the augmented Lagrangian function, the original variables, auxiliary variables, and Lagrange multipliers are alternately updated to ensure the consistency constraint until convergence.

[0150] This method has significant advantages and achieves: 1) Non-convex problem convexification: The original NP-hard problem is decomposed into convex sub-problems that can be efficiently solved. The direction uncertainty is addressed through relaxation techniques, enhancing the robustness of the solution; 2) Dynamic co-optimization: The communication capacity and radar detection accuracy are iteratively balanced, supporting parallel computing in multi-user scenarios and significantly reducing the complexity. The Lagrange multiplier mechanism ensures that the constraints are strictly satisfied, enabling efficient resource allocation and stable system operation. The weighting factor can flexibly adjust the functional focus, and numerical verification shows that the algorithm has good convergence, providing a solution with both theoretical guarantee and engineering feasibility for the transmit sequence design of the dual-functional system.

[0151] In this example, by comprehensively considering the performance requirements of the communication system and the radar system, the overall system performance is optimized, and the accuracy of the communication mutual information and the radar beam pattern is improved. Moreover, considering the uncertainty of the channel state information, by designing a robust optimization framework, the performance stability of the system in a complex and changing channel environment is enhanced. The robustness effect is mainly reflected in the explicit limitation of the direction mismatch by the constraint conditions, the dynamic adaptation of the slack variables to the uncertainty, and the forced correction of the variable consistency by the penalty mechanism. These steps jointly ensure that the system can still stably optimize the spatio-frequency transmit sequence in an environment with uncertain channel states. And the design method proposed in the present invention can flexibly adjust the weighting factor according to actual requirements, realize the trade-off between multi-user communication and radar functions, and meet the requirements of different application scenarios.

[0152] In this embodiment, some numerical simulations will be provided to evaluate the performance of the developed design. It is considered that the system has N t transmitting antennas, N = 2 communication users, and the coding length D = 15. Considering the transmit power parameter The reference signal s 0 is an OFDM-LFM code, and the similarity parameter ξ = 0.5(NP C,n +P R ), the noise variance Considering the direction range is [-90°, 90°], the spacing is 1°, and the corresponding weight parameter ζ k = 1 / 180, considering P 1 = P 2 = 5 paths are randomly selected in (-50°, -35°) and (25°, 40°) respectively, and the direction uncertainty Δ n = 3°. Therefore, a radar desired signal θ l = 0° with a width of 6° is considered. Except that the factor within the range of [-3°, 3°] is set to 1, the values of the required beam pattern in other places are zero. Considering the spatio-frequency constraint parameter The radar frequency band constraint [f m,u , f m,l are [0.35, 0.45] and [0.7, 0.8] respectively, and the corresponding spatial range is [0.45, 0.55] and [0.25, 0.35]. The communication frequency band constraint [f n,u , f n,l is [0.1, 0.2] and [0.5, 0.6], and the corresponding spatial range is [0.2, 0.3] and [0.6, 0.7]. Finally, let γ 1 = γ 2 = 0.5, and ζ n = 1 / N to achieve the average user mutual information.

[0153] The convergence performance of the proposed design is evaluated. For fairness, the SDP (Semidefinite Programming) algorithm based on the proposed MM framework (Majorization-Minimization Framework) is studied and compared with the DMM-ADMM iterative algorithm adopted in this embodiment, that is, the power constraint in formula (11e) is relaxed through semidefinite relaxation programming. MM-SDP transforms the non-convex power constraint into a convex form through semidefinite relaxation, while DMM-ADMM directly processes the original constraint through the augmented Lagrangian function, avoiding relaxation errors. MM-SDP relies on a centralized SDP solver with a complexity of DMM-ADMM decomposes the problem through distributed iteration, and its complexity is linearly related to the number of nodes, which is more suitable for large-scale systems. MM-SDP provides a globally optimal relaxed solution but may introduce performance losses; DMM-ADMM approximates the local optimum through alternating optimization, ensuring that the constraints are strictly satisfied and having stronger robustness. The effectiveness of the weighting factor in the proposed formula is also studied. The weighting factor realizes the optimal trade-off of the dual-functional system by dynamically adjusting the weights of radar and communication performance, and simulation verifies that it can effectively balance detection accuracy and communication capacity, improving the system robustness and resource utilization rate. Figure 2 Figure showing the relationship between the objective function value in formula (11) and the number of iterations at different weighting factor levels γ 1 = 0.1, 0.5, 0.9, and the initial points of the Radcom function follow an equal division with 50. The results show that the proposed design achieves both good objective values and convergence performance. The trade-off of the dual functions can also be flexibly controlled by adjusting the weighting factor level. To further analyze the effectiveness of the radar function and the communication function, Figure 3 and Figure 4 respectively give the spectral distribution of the communication function in the spatio-frequency domain and the spectral distribution of the radar function in the spatio-frequency domain, where the weighting factor level γ 1 = 0.5, and the stop bands in the space-frequency domain are represented by rectangular frames. The results show that the zeros of the space-frequency distribution can be precisely controlled.

[0154] Through numerical simulation verification, the design method proposed in the present invention has good convergence performance and can reach the optimal solution in a short time. This design is effective in both the radar function and the communication function in the space-frequency domain, providing new ideas and methods for the design and application of the dual-functional RadCom system, and is expected to play an important role in the fields of wireless communication, radar detection, etc.

[0155] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0156] In addition, the terms "first" and "second" are used for descriptive purposes only and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of these features. In the description of the present invention, "a plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0157] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A space-frequency transmission sequence design method for a dual-function radar communication system, characterized in that: include: For dual-function radar communication systems, the optimization problem of space-frequency transmission sequence is constructed under multiple constraints with mutual information optimization of multiple communication users and simultaneous radar transmission beam pattern control of multiple targets as the objective function. The constraints include directional mismatch interference power constraint, radar transmission vector constraint and power constraint. With fixed Solving the communication transmission vector set in the optimization problem, converting the optimization problem from a non-convex problem to a first optimization sub-problem, where m0 represents an iteration index, represents the radar transmission vector at the m0th iteration, s t represents the radar transmission vector; With fixed Solving the radar emission vector in the optimization problem, converting the optimization problem from a non-convex problem to a second optimization sub-problem, where represents the communication transmission vector at the m0th iteration, s c,n represents the communication transmission vector; The first optimization subproblem and the second optimization subproblem are solved alternately until a convergence condition is met to determine a space-frequency transmission sequence, wherein the first optimization subproblem and the second optimization subproblem are both convex problems.

2. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 1, characterized in that: The optimization problem includes an objective function and constraints, and the formula is expressed as: Where: γ1 and γ2 represent the weighting factors corresponding to the mutual information and square error function, respectively, ζ n and k are the weighting coefficients of multi-user communication and multi-target radar detection, MI n ({s c,n },s t ) is the mutual information of multiple communicating users, F R (β,{s c,n },s t ) is the square error between the radar design beam pattern and the expected beam pattern, β is the proportional factor, Π i represents a matrix in which all factors except the (i,i)th element are 0, It represents the power of the radar signal transmitted to the mth spatial frequency band, It represents the power of the communication user transmitting the signal to the nth spatial frequency band, Represents the frequency-dependent response matrix, which describes the r1 and q r2 The frequency response characteristics at represents the estimated frequency-dependent response matrix, represents the response matrix related to spatial angle, represents the estimated spatial angle-dependent response matrix, η R,m and η C,n They represent the power upper bounds corresponding to the radar function and the communication function respectively, s0 represents the radar transmission vector when the detection signal is x0, that is, the reference vector, ξ represents the similarity parameter, Indicates the transmit power parameter, Indicates the power of the communication user's transmitted signal in the nth spatial frequency band, ∥∥ 2 represents the square of the Euclidean norm of a vector, Represents the convolution between two matrices, M, N, N t , D are the number of radar detection targets, the number of communication users, the number of transmitting units and the code length in the dual-function radar communication system, respectively. H represents a Hermitian operator.

3. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 2, characterized in that: The mutual information disclosure of multiple communicating users is expressed as: Where: represents the inverse matrix of the Nth interference plus noise covariance matrix, represents the Nth interference plus noise covariance matrix, s c,j represents the transmission vector of the jth communication user, s c,i represents the transmission vector of the i-th communication user, H n represents the nth user channel, represents the noise variance of the nth communication user, N r,n ×D-dimensional identity matrix, Denotes the transmission vector s of the nth communication user c,n The complex conjugate transposed matrix of represents the complex conjugate matrix of the nth user channel, Indicates a definition symbol.

4. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 2, characterized in that: The formula for the square error between the radar design beam pattern and the expected beam pattern is expressed as: Where: k represents the weighting parameter of the kth direction, d(θ k ) represents the desired beam pattern, represents the radar transmission vector s t The complex conjugate transposed matrix, R(θ k ) represents the angle θ k The relevant response function or correlation function, Denotes the transmission vector s of the nth communication user c,n The complex conjugate transposed matrix of , K represents the number of targets detected by the radar.

5. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 2, characterized in that: Said and The calculation formula is: Where: q r1 ,q r2 Indicates two different frequency points, represents the complex exponential associated with higher spatial angles, represents the complex exponent related to the lower spatial angle, [f m,u ,f m,l ] represents the frequency band constraint, [sinθ m,u ,sinθ m,l ] represents the spatial angle range, θ m,u Represents a higher spatial angle, θ m,l represents the lower spatial angle, represents the complex exponential associated with higher frequencies, Represents complex exponentials associated with lower frequencies.

6. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 2, characterized in that: Said and The calculation formula is: Where: q cn1 ,q cn2 Represent two different frequency points, θ n,u and θ n,l denote the higher spatial angle and the lower spatial angle respectively, represents the complex exponential associated with higher spatial angles, represents the complex exponent related to the lower spatial angle, f n,u and f n,l Represent the higher and lower frequencies respectively, represents the complex exponential associated with higher frequencies, Represents complex exponentials associated with lower frequencies.

7. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 2, characterized in that: The formula of the first optimization sub-problem is expressed as: Where: represents the estimated transmission vector of the nth communication user, Indicates To optimize the variables, minimize the quadratic function represents the radar performance matrix associated with the nth communication user, represents the communication performance matrix associated with the nth communication user, ε n represents a non-negative slack variable, ρ n represents the penalty factor, I represents the identity matrix, represents the estimated transmission vector of the jth communication user, represents the estimated value of the radar emission vector at the m0th iteration, represents the reference transmission vector, represents the estimated channel matrix at the i+1th iteration, represents the relaxed power constraint of the nth communication user, represents the complex conjugate transpose of the original transmission vector of the nth communication user, represents the complex conjugate transpose of the communication transmission vector at the m0-1th iteration, represents the real part operator.

8. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 2, characterized in that: The formula of the second optimization sub-problem is expressed as: Where: represents the radar emission vector, Indicates To optimize the variables, minimize the quadratic function represents the matrix related to the radar system performance, represents the matrix related to the performance of the communication system, represents the optimized or estimated radar transmit vector, represents an estimated or optimized version of the reference vector s0, represents the parameter controlling the penalty effect, represents the slack variable, represents the complex conjugate matrix of the estimated radar transmit vector, Represents the frequency f m The relevant function matrix is ​​used to describe the correlation of radar signals in the frequency domain, η R,m represents the upper limit of interference caused by the radar transmission vector to the communication system at the mth communication frequency, represents the complex conjugate matrix of the estimated communication transmission vector at the m0th iteration, represents the estimated channel matrix of the i+1th time, s t H represents the complex conjugate matrix of the radar transmit vector, represents the radar's transmit power, represents the complex conjugate matrix of the radar transmit vector at the m0-1th iteration, represents the real part operator, represents the slack variable.

9. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 1, characterized in that: Alternately solving the first optimization subproblem and the second optimization subproblem until a convergence condition is met to determine a space-frequency transmission sequence, including: The first optimization subproblem and the second optimization subproblem are alternately solved based on the ADMM algorithm until a convergence condition is met, and a space-frequency transmission sequence is determined.

10. The space-frequency transmission sequence design method for a dual-function radar communication system as claimed in claim 2, characterized in that: The weighting factors γ1 and γ2 are adjustable, and γ1+γ2=1.

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