Joint design method for MIMO radar and interference integrated system transceiver

Abstract

The invention discloses a joint design method for an MIMO radar and interference integrated system transceiver, and belongs to the technical field of radar signal processing and electronic warfare. Aiming at the problems of spectrum resource waste, equipment redundancy and electromagnetic compatibility caused by separation of radar detection and interference functions in the prior art, the invention provides an AOFP-based combined waveform and filter design method. A multi-target optimization problem is constructed under energy constraint and peak-to-average ratio limitation, SJNR of a minimum interference target and SJNR of an IRAJ system are taken as targets, a closed-form solution is generated by using a scaling technology, fractional programming and a PML method, and dynamic balance of radar detection and interference functions is realized. The designed waveform has high anti-interference capability and concealment, supports space diversity and time-frequency joint modulation of an MIMO system, and analyzes and verifies strong target echo characteristics and interference suppression performance through a fuzzy function. The calculation complexity of the algorithm and the number of antennas are in a cubic relationship, the convergence speed is high, the comprehensive efficiency of a combat platform in a complex electromagnetic environment can be remarkably improved, and the method is suitable for a new generation of cognitive electronic warfare systems.

Description

Technical Field

[0001] The present invention belongs to the field of electronic warfare and radar signal processing, and relates to a MIMO radar and interference system with both target detection and interference functions, and specifically relates to a joint design method for the transmit waveform and receive filter of a MIMO IRAJ system based on Alternating Optimization Fractional Programming (AOFP). Background Art

[0002] With the increasing urgency of the demand for multi-functional integrated platforms in modern electronic warfare, the IRAJ system has become the core development direction of the new generation of electronic countermeasure technologies due to its advantages of sharing spectrum resources and synergistically optimizing interference and detection capabilities. Traditional interference methods mainly suppress interference targets through high-power signals, but their one-way interference mode is difficult to take into account the radar detection function of themselves, and the single-antenna architecture cannot achieve accurate azimuth interference and is easily identified and suppressed by cooperative radar networks. In contrast, the MIMO technology can flexibly control the spatial radiation energy distribution through spatial diversity and waveform diversity characteristics, providing a key degree of freedom for simultaneously achieving directional coverage of interference signals and radar target detection.

[0003] Waveform and filter co - design is a core technical challenge in MIMO - IRAJ systems. Radar detection requires high - gain waveforms to suppress signal - dependent interference (such as clutter and threat interference), while long - range jamming requires optimizing the signal spectral characteristics to reduce the SJNR of the jammed targets. Waveform constraints under hardware limitations (such as constant modulus CM or PAR constraints) further increase the design complexity. The literature "K. Wang, J. Xu, K. Wang, and Q. Kan, "Detection - jamming integrated waveform design based on multi - dimensional joint constraints," in 2024 7th International Conference on Information Communication and Signal Processing (ICICSP), pp. 539–543" uses the coordinate - descent algorithm to jointly optimize the spectral matching and autocorrelation characteristics, but its computational complexity is high and it is only applicable to single - antenna scenarios; the literature "L. Wu, P. Babu, and D. P. Palomar, "Transmit waveform / receive filter design for MIMO radar with multiple waveform constraints," IEEE Transactions on Signal Processing, vol. 66, no. 6, pp. 1526–1540" proposes a waveform design based on power - type methods, but does not consider the active interference suppression requirements of the jammed targets. The main deficiencies of the existing technologies include: 1) It is difficult for single - antenna IRAJ systems to achieve optimal trade - off between jamming and detection performance; 2) Existing MIMO waveform design methods do not take the suppression of the SJNR of jammed targets as an optimization goal, resulting in insufficient jamming effectiveness; 3) The solution efficiency of multi - constraint non - convex optimization problems is low and it is difficult to meet the real - time requirements; 4) The flexible handling ability of PAR constraints is limited, leading to poor hardware compatibility. Summary of the Invention

[0004] To address the above problems, the present invention proposes a co - design method for MIMO IRAJ systems based on AOFP. By using scalarization and multi - fractional programming techniques, maximizing the SJNR of our radar and minimizing the SJNR of jammed targets are transformed into solvable optimization problems. Combining PML and FFT techniques reduces the computational complexity, and at the same time supports PAR constraints to adapt to the characteristics of actual power amplifiers, ultimately achieving the optimal trade - off between jamming and detection functions.

[0005] The technical solution of the present invention is: a transceiver joint design method for a MIMO radar and interference integration system, the method comprising the following steps:

[0006] S1: Establish a MIMO IRAJ system model, and construct a received signal model including target echo, signal-related interference of interference sources, and interference target interference;

[0007] S2: Construct a multi-objective optimization problem, with maximizing the output signal-to-jamming-plus-noise ratio (SJNR) of the IRAJ system and minimizing the SJNR of interference targets as multi-objective optimization goals;

[0008] S3: Transform the multi-objective problem into a single-objective optimization problem through scalarization, and jointly optimize the transmit waveform and receive filter using the alternating optimization and fractional programming (AOFP) framework;

[0009] S4: Apply transmit power and peak-to-average power ratio (PAR) constraints during the optimization process to generate waveforms adapted to the hardware platform.

[0010] The specific steps of step S1 include:

[0011] Construct a MIMO IRAJ system, including N T transmit antennas and N R receive antennas, supporting the co-optimization of radar detection and interference. The system realizes the dynamic balance of target detection performance and interference effectiveness through the joint design of the transmit waveform matrix X and the receive filter W. The transmit waveform matrix is composed of discrete-time waveform vectors of each antenna

[0012]

[0013] where represents the transmit waveform vector of the m-th antenna, L is the code length, and the received signal expression is

[0014] z = ξ0A0x + d + j + v,

[0015] where ξ0 represents the target radar cross section (RCS), satisfying represents the modulation matrix of the target signal; represents the signal-related interference from K interference sources; represents the interference from N I interference targets; v represents the receiver thermal noise;

[0016] The interference modulation matrix expression is

[0017]

[0018] where is the delay shift matrix, at () and a r () are the transmitting and receiving vectors respectively; p(v) = [1, e j2πν ,..., e j2πv(L-1 )] T is the Doppler modulation vector, and ν is the normalized Doppler frequency;

[0019] The output SJNR of the IRAJ system is

[0020]

[0021] where the interference plus noise covariance matrix Φ(x) is defined as

[0022]

[0023] The received signal model of the i-th interfering target is

[0024]

[0025] Its maximum SJNR can be expressed as

[0026]

[0027] where, is the Fourier transform of s i (l), X i (f) and V i (f) are the energy spectral densities of interference and noise respectively; assuming that the energy spectral density is concentrated within the bandwidth B s , the SJNR is discretized, and the expression is as follows

[0028]

[0029] where is the normalized DFT basis vector, is the matching discrete frequency point, and the extended signal vector is constructed as follows

[0030]

[0031] where is the zero-padded signal vector.

[0032] The specific steps of step S2 include:

[0033] Taking the minimization of the SJNR of the interfering target and the maximization of the SJNR of the IRAJ system as the objectives, an optimization problem is established:

[0034]

[0035] where the constraint set Ω includes: energy constraint: ||x m ||2 = L(m = 1, 2, ..., N T ); PAR constraint: Convert the multi-objective optimization problem into a scalarized single-objective problem

[0036]

[0037] The weight factor b i ≥ 0, which is used to balance the priorities of radar detection and interference suppression.

[0038] The specific steps of step S3 include:

[0039] Step S3.1:

[0040] Initialize the transmitted waveform x (0) and the weight coefficient b i , and set the convergence threshold ∈;

[0041] Step S3.2:

[0042] The closed-form solution of the receive filter

[0043]

[0044] Optimize the transmitted waveform and convert it into a multiple ratio fractional programming problem:

[0045]

[0046] where

[0047]

[0048] Use the PML method to correct the non-positive definite matrix R, let M = R - λ min (R)I, then the problem can finally be converted into

[0049]

[0050] Step S3.3:

[0051] Decompose the global problem into N T independent sub-problems:

[0052]

[0053] where The optimal solution is updated through the projection operator

[0054]

[0055] ​Step S3.4:

[0056] Repeat steps S3.2 - S3.3 until the termination condition ||x (n+1) -x (n) || ≤ ∈ is satisfied.

[0057] Advantages of the present invention:

[0058] Multi - objective joint optimization ability: The present invention proposes a framework based on alternating optimization and fractional programming (AOFP) to achieve the joint optimization of the transmitted waveform and the receiving filter in a MIMO integrated radar and jammer (IRAJ) system. It simultaneously improves the radar detection signal - to - noise ratio (SJNR) and suppresses the performance of interfering targets in a signal - dependent jamming environment, solving the problem that it is difficult to synergistically optimize the radar and jammer functions in the prior art.

[0059] Enhanced anti - jamming performance: By introducing spatial diversity and signal spectrum optimization, the designed waveform forms a wide - band suppression jammer at the receiving end of the interfering target, and its output SJNR can be reduced by more than 15 dB (see Figure 2 ), significantly superior to traditional single - antenna or fixed - waveform jamming schemes.

[0060] Hardware compatibility and flexibility: The proposed peak - to - average power ratio (PAR) constraint optimization method supports the design of non - constant - modulus waveforms. While ensuring the efficiency of the power amplifier (such as when PAR = 2), it can additionally improve the detection performance by 3 dB compared with constant - modulus waveforms (PAR = 1), breaking through the limitation of the lack of flexibility in the existing constant - modulus waveform design.

[0061] Computational efficiency advantage: The AOFP algorithm achieves fast convergence through closed - form iterative updates. Its computational complexity grows linearly with the number of iterations and is related to the cube of the code length, saving more than 80% of the running time compared with traditional genetic algorithms. Description of the drawings

[0062] Figure 1 It is the system model diagram of MIMO IRAJ for the transceiver joint design method of a MIMO radar and jammer integrated system of the present invention.

[0063] Figure 2 It is the change of the objective function value with the number of iterations for the transceiver joint design method of a MIMO radar and jammer integrated system of the present invention.

[0064] Figure 3 It is the MIMO radar ambiguity function diagram for the transceiver joint design method of a MIMO radar and jammer integrated system of the present invention.

[0065] Figure 4This is the Pareto curve of the radar detection and interference performance for the transceiver joint design method of a MIMO radar and interference integration system according to the present invention, showing the trade-off relationship between the target SJNR and the threat SJNR under different PAR constraints. Specific implementation manner

[0066] The specific implementation steps of the present invention are described as follows:

[0067] Step 1: Establish a MIMO IRAJ system model

[0068] Step 1.1: Signal model

[0069] Construct a MIMO IRAJ system, which includes N T transmitting antennas and N R receiving antennas, and supports the collaborative optimization of radar detection and interference. The system realizes the dynamic balance of target detection performance and interference effectiveness by jointly designing the transmitting waveform matrix X and the receiving filter W. The transmitting waveform matrix is composed of the discrete-time waveform vectors of each antenna

[0070]

[0071] where represents the transmitting waveform vector of the m-th antenna, and L is the code length. The received signal expression is

[0072] z = ξ0A0x + d + j + v

[0073] where ξ0 represents the target radar cross section (RCS), satisfying represents the modulation matrix of the target signal; represents the signal-related interference from K interference sources; represents the interference from N I interference targets; v represents the receiver thermal noise.

[0074] The interference modulation matrix expression is

[0075]

[0076] where is the time-delay shift matrix, a t (θ) and a r (θ) are the transmitting and receiving vectors respectively. p(v) = [1, e j2πν ,..., e j2πv(L-1) T is the Doppler modulation vector, and v is the normalized Doppler frequency. The output SJNR of the IRAJ system is

[0077] ​

[0078] where the interference plus noise covariance matrix Φ(x) is defined as

[0079]

[0080] Step 1.2: Interference target SJNR

[0081] The received signal model of the i-th interference target is

[0082]

[0083] Its maximum SJNR can be expressed as

[0084]

[0085] where is the Fourier transform of s i (l), and X i (f) and V i (f) are the energy spectral densities of interference and noise respectively. Assuming that the energy spectral density is concentrated within the bandwidth B s , the SJNR is discretized, and the expression is as follows

[0086]

[0087] where is the normalized DFT basis vector. To match the discrete frequency points, the extended signal vector is constructed as follows

[0088]

[0089] where is the zero-padded signal vector.

[0090] Step 2: Construct a multi-objective optimization problem;

[0091] Taking the minimization of the SJNR of the interference target and the maximization of the SJNR of the IRAJ system as the objectives, an optimization problem is established:

[0092]

[0093] where the constraint set Ω includes: energy constraint: ||x m || 2 = L (m = 1, 2,..., N T ); PAR constraint: Transform the multi-objective optimization problem into a scalarized single-objective problem

[0094]

[0095] Weight factor b i ≥0, used to balance the priorities of radar detection and interference suppression.

[0096] Step 3: Optimize the problem using the AOFP method

[0097] Step 3.1:

[0098] Initialize the transmitted waveform x (0) and the weight coefficient b i , and set the convergence threshold ∈;

[0099] Step 3.2:

[0100] Closed-form solution of the receiving filter

[0101]

[0102] Optimize the transmitted waveform, and transform it into a multi-ratio fractional programming problem:

[0103]

[0104] where

[0105]

[0106] After ignoring the irrelevant constant terms, the problem can be equivalently transformed into

[0107]

[0108] where is the discrete Fourier transform (DFT) basis matrix;

[0109]

[0110] R0 is the interference plus noise covariance matrix; f p is the p-th DFT basis vector. For any vector and the function g(b) is defined as:

[0111]

[0112] Therefore, the problem can be equivalently transformed into:

[0113]

[0114] where

[0115]

[0116] Use the PML method to correct the non - positive definite matrix \(R\), let \(M = R-\lambda min (R)I\), then the problem can be transformed into

[0117]

[0118] and is further equivalently rewritten as:

[0119]

[0120] where \(g (t) = Mx (t) . After decomposing , the global problem can be decomposed into \(N r independent sub - problems

[0121]

[0122] The optimal solution of sub - problem \(P 6,m is

[0123]

[0124] where the projection operator is defined as

[0125]

[0126] where

[0127]

[0128] u k is the sparse direction vector, is the amplitude scaling threshold.

[0129] Step 3.4:

[0130] Repeat steps 3.2 - 3.3 until the termination condition \(\|x (n+1) -x (n) \|\leq\epsilon\) is satisfied.

[0131] The effects of the present invention are further illustrated through simulation below.

[0132] Simulation parameters: Consider an IRAJ system with a bandwidth of 180 MHz and a carrier frequency \(f c = 3\times10 8 / \lambda\). The number of transmit antennas \(N T = 4\), the number of receive antennas \(N R = 4\), the transmit array element spacing \(d T =\lambda / 2\), the receive array element spacing \(d R = N T dT 。The waveform code length L = 180, and the total transmit power constraint is ||x m || 2 = L. The target is located at (0, -15°) with a power of 20 dB; two signal-related interference sources are located at ([-5:5], 30°) and ([15:25], -60°) respectively, both with a power of 20 dB. Two interfering targets are located at (-30°, -40°) and (70°, 50°), and the transmit carrier frequencies are f c -50 MHz and f c +50 MHz linear frequency modulation (LFM) waveforms with a bandwidth of 80 MHz and a duration of 1 microsecond. The algorithm stop criterion is set as ||x (t+1) -x (t) || < 10 -3 , and the maximum number of iterations is 10000.

[0133] Figure 2 Shows the variation of the total objective function value with the number of iterations for γ = 1, 2, 4, which is used to evaluate the convergence characteristics and computational complexity of the proposed AOPF algorithm. Figure 3 Shows the ambiguity function diagram of the MIMO radar.

[0134] Figure 4 Shows the Pareto curve, which is marked by the symbols '×', and '+' for the cases of γ = 1, 2, 4 respectively. In particular, for γ = 4, b0 = 10 -4 、10 -3 、10 -2 、10 -1 、1、10 1 、10 2 、10 3 and b i = 1, (i = 1, 2) Pareto points are highlighted by different symbols listed in the legend. These curves reveal the performance trade-off between target detection ability and interference effectiveness, where the weight parameter b0 plays a key role in the selection of Pareto points. Enhancing the detection performance of the IRAJ system by increasing the value of b0 will directly reduce the detection accuracy of interfering targets, while giving priority to interference quality will weaken the detection ability.

[0135] ​In summary, the MIMO IRAJ joint optimization method proposed in this invention realizes the collaborative enhancement of radar detection and interference. Numerical simulations evaluate the trade-off between the radar's detection ability for signal-related interference and the interference effectiveness, revealing the performance boundaries jointly determined by shared resources and interference dynamics. The ambiguity function evaluation further validates the effectiveness of this framework for synthetic waveforms - such waveforms can jointly suppress sidelobe interference and achieve precise interference. These research results lay the foundation for dual-functional systems that require both situational awareness and electromagnetic countermeasure capabilities, and are of great significance for the design of next-generation cognitive electronic warfare platforms. Future research directions can explore complex deception interference techniques that combine time-division multiplexing and intra-pulse agile pulses to optimize the IRAJ waveform design and processing methods.

Claims

1. A transceiver design method for an integrated MIMO radar and interference system, characterized in that Including the following steps: S1: Establish an MIMO IRAJ system model and construct a received signal model including the target echo, signal-related interference of the interference source, and interference-target interference; S2: Construct a multi-objective optimization problem with maximizing the output signal-to-jamming-and-noise ratio (SJNR) of the IRAJ system and minimizing the SJNR of the interference target as the multi-objective optimization goals; S3: Transform the multi-objective problem into a single-objective optimization problem through scalarization, and jointly optimize the transmit waveform and receive filter using the alternating optimization and fractional programming (AOFP) framework; S4: Impose transmit power and peak-to-average power ratio (PAR) constraints during the optimization process to generate a waveform adapted to the hardware platform.

2. The transceiver design method of a MIMO radar and interference integration system according to claim 1, characterized in that, The specific content of step S1 includes: Construct an MIMO IRAJ system, including N T transmitting antennas and N R receiving antennas, which supports the co-optimization of radar detection and interference. The system realizes the dynamic balance between target detection performance and interference effectiveness by jointly designing the transmitting waveform matrix X and the receiving filter W. The transmitting waveform matrix is composed of discrete-time waveform vectors of each antenna wherein represents the transmission waveform vector of the m-th antenna, L is the code length, and the received signal expression is z = ξ0A0x + d + j + v, where ξ0 represents the target radar cross section (RCS), satisfying represents the modulation matrix of the target signal; represents the signal-related interference from K interference sources; represents the interference from N I interference targets; v represents the receiver thermal noise; The expression of the interference modulation matrix is Among them is the delay shift matrix, a t (θ) and a r (θ) are the transmit and receive vectors respectively; p(v) = [1, e j2 πv ,..., e j2πv(L-1) T is the Doppler modulation vector, and v is the normalized Doppler frequency;​ The output SJNR of the IRAJ system is where the interference-plus-noise covariance matrix Φ(x) is defined as The received signal model of the i-th interference target is Its maximum SJNR can be expressed as Among them, is the Fourier transform of s i (l), X i (f) and V i (f) are the energy spectral densities of interference and noise respectively; assuming that the energy spectral density is concentrated within the bandwidth B s , the SJNR is discretized, and the expression is as follows Among them is the normalized DFT basis vector, and is the matching discrete frequency point. The extended signal vector is constructed as follows wherein is a zero-padding signal vector.

3. A transceiver design method for a MIMO radar and interference integration system according to claim 1, characterized in that, The specific content of step S2 includes: Establish an optimization problem with the goal of minimizing the SJNR of the interference target and maximizing the SJNR of the IRAJ system: Among them, the constraint set Ω includes: energy constraint: ||x m || 2 = L (m = 1, 2,..., N T ); PAR constraint: Convert the multi-objective optimization problem into a scalarized single-objective problem Weight factor b i ≥ 0, used to balance the priorities of radar detection and interference suppression.

4. A transceiver design method for a MIMO radar and interference integration system according to claim 1, characterized in that The specific content of step S3 includes: Step S3.1: Initialize the transmitted waveform x (0) and the weight coefficient b i , and set the convergence threshold ∈; Step S3.2: Closed-form solution of the receive filter Optimize the transmitted waveform and transform it into a multiple ratio fractional programming problem: where Use the PML method to correct the non - positive definite matrix R, and let M = R - λ min (R)I, then the problem can finally be transformed into Step S3.3: Decompose the global problem into N T independent sub-problems: Among them The optimal solution is updated by the projection operator Update Step S3.4: Repeat steps S3.2 - S3.3 until the termination condition ||x (n+1) -x (n) || ≤ ∈ is satisfied.

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