A Subarray MIMO Radar Waveform Design Method Based on Wide Pulse Compressed Main Lobe

Abstract

This invention discloses a subarray MIMO radar waveform design method based on wide pulse compression main lobe. The implementation steps are as follows: using the constructed system signal, calculate the difference between the signal pulse compression main lobe value and the desired pulse compression main lobe value; calculate the autocorrelation sidelobe level and cross-correlation sidelobe level of the angular domain signal respectively; calculate the difference between the multi-beam transmission pattern and the desired transmission pattern; construct an objective function based on the difference between the pulse compression main lobe value and the desired pulse compression main lobe value, the autocorrelation and cross-correlation sidelobe levels of the angular domain signal, and the difference between the multi-beam transmission pattern and the desired transmission pattern; and optimize the subarray MIMO radar waveform using a sequential quadratic programming algorithm. The subarray MIMO radar waveform designed in this invention can effectively match the desired transmission beam pattern while suppressing the autocorrelation and cross-correlation sidelobe levels of the angular domain signal, thereby improving the radar's detection performance and parameter estimation accuracy.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and further relates to a waveform design method for subarray MIMO radar based on wide pulse compression main lobe. This invention can be applied to designing the transmit waveform of a subarray MIMO radar system, effectively matching the radiation pattern of the desired transmit beam while suppressing the autocorrelation and cross-correlation sidelobe levels of the angular domain signal. Background Technology

[0002] In a subarray MIMO radar system, the subarray antennas operate in phased array mode. Phase weighting of the array is typically achieved using phase shifters. However, for large arrays with a large number of elements, element-level phase weighting is difficult to implement due to high costs. Therefore, subarray-level phase weighting can significantly reduce radar system costs and is an ideal approach. Furthermore, current radar systems have low energy efficiency, affecting their target detection and tracking performance. Optimizing the waveform to match the desired transmission pattern can effectively control the spatial distribution of signal energy and improve the radar system's energy efficiency. Simultaneously, high angular domain signal sidelobe levels are detrimental to effective target detection. Optimizing the waveform to suppress autocorrelation and cross-correlation sidelobes in the angular domain can improve radar detection performance and parameter estimation accuracy.

[0003] In his paper "Research on MIMO Radar Waveform Optimization Design Based on Phase Coding" (Lanzhou University of Technology, Master's Thesis, 2023), Dong Bingliang proposed a MIMO radar waveform design method based on signal sidelobe optimization and constraint by mismatch filter loss. The method's implementation steps are as follows: Logical mapping is used for updating the initial population, ensuring the generated population satisfies the requirements of randomness and ergodicity. Nonlinear inertial weights are introduced into the algorithm's iterative process by using the convergence coefficients of the nonlinear transformation. These nonlinear inertial weights are then updated according to the update expression, establishing an optimization model based on peak sidelobes and sidelobe energy. The multi-objective optimization problem is transformed into an optimization design of peak sidelobes and a linearly weighted problem constrained by mismatch filter loss. While this method can obtain MIMO radar waveform sequences with better peak sidelobe performance, it still has shortcomings. Since the optimization degrees of freedom affect the algorithm's optimization effect, this method only has one parameter to be optimized, resulting in low degrees of freedom. This leads to a non-concentrated transmission pattern beam, affecting the radar system's energy utilization and causing a deterioration in target detection or tracking performance.

[0004] Xi'an University of Electronic Science and Technology disclosed a centralized MIMO radar waveform optimization method based on main lobe broadening in its patent application "A Centralized MIMO Radar Waveform Optimization Method Based on Main Lobe Broadening" (Patent Application No. CN 201910718225.3, Publication No. CN 110456314 A). The implementation steps of this waveform design method are to construct a waveform optimization method with the objective function of matching the desired transmit pattern, suppressing the peak sidelobe levels of autocorrelation in the same angular domain signal and the peak cross-correlation levels in different directions, and approximating the desired autocorrelation main lobe, thereby reducing the sidelobe level of the angular domain signal. While this method can reduce the sidelobe level of the angular domain signal while matching the desired transmit pattern, it still has shortcomings. The method's scenario is too simplistic, only considering element-level radar systems with a small number of array elements and single-beam pattern scenarios, and not considering subarray-level MIMO radar systems with a large number of array elements and multi-beam pattern scenarios. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a MIMO radar waveform design method based on wide pulse compression main lobe. This method aims to solve the problems of low energy utilization in radar systems due to low degrees of freedom in waveform optimization, and the complexity of waveform optimization in large subarray MIMO radar systems and multi-beam scenarios.

[0006] The specific approach to achieving the objective of this invention is as follows: This invention constructs a large-scale subarray MIMO radar system scenario. Given a phase-coded signal pulse width and maintaining a constant range resolution, the degree of freedom is increased by increasing the symbol length of the phase-coded signal. This optimizes the autocorrelation and cross-correlation sidelobe levels and the transmission pattern of the large-scale subarray MIMO radar system's transmitted waveform, increasing the types of parameters to be optimized. This solves the problem of unfocused beam pointing in the transmission pattern caused by low optimization freedom. This invention constructs waveform optimization parameters for transmitting beam pattern matching and reducing autocorrelation and cross-correlation sidelobe levels, and establishes a waveform optimization objective function. A minimax algorithm based on Sequential Quadratic Programming (SQP) is used for optimization to obtain the final subarray MIMO radar waveform.

[0007] The specific steps of this invention include the following:

[0008] Step 1: Using the constructed system signal, calculate the difference between the main lobe value of the compressed signal pulse and the expected main lobe value of the compressed pulse pulse.

[0009] Step 2: Calculate the autocorrelation sidelobe level and cross-correlation sidelobe level of the angular domain signal, respectively;

[0010] Step 3: Calculate the difference between the multi-beam transmission pattern and the desired transmission pattern;

[0011] Step 4: Construct the objective function based on the difference between the pulse compression main lobe value and the desired pulse compression main lobe value, the autocorrelation and cross-correlation sidelobe levels of the angular domain signal, and the difference between the multi-beam transmission pattern and the desired transmission pattern.

[0012] Step 5: Use the Sequential Quadratic Programming (SQP) algorithm to optimize the MIMO radar waveform of the multi-element subarray.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] First, this invention optimizes the autocorrelation and cross-correlation sidelobe levels and transmission pattern of the transmitted waveform of a large subarray MIMO radar system, increasing the types of parameters to be optimized during optimization. This overcomes the shortcomings of low optimization freedom and overly simple waveform forms in existing technologies, enabling the subarray MIMO radar waveform designed in this invention to match the desired transmitted beam pattern well while suppressing the autocorrelation and cross-correlation sidelobe levels of the angular domain signal, thereby improving the radar's detection performance and parameter estimation accuracy.

[0015] Secondly, this invention is applicable to large subarray MIMO radar systems with a large number of array elements and multi-beam scenarios. It overcomes the shortcomings of existing waveform optimization techniques, such as the small number of array elements in MIMO radar systems and the overly simple single-beam pattern scenarios. This allows the MIMO radar waveform designed in this invention to still have low autocorrelation and cross-correlation sidelobe levels in subarray MIMO radar systems with a large number of array elements and multi-beam pattern scenarios, while also matching the pattern of the desired transmitted beam well. Attached Figure Description

[0016] Figure 1 This is a flowchart of an embodiment of the present invention;

[0017] Figure 2 This is a comparison chart of the main lobe value of the compressed signal pulse in this invention and the expected main lobe value of the compressed pulse.

[0018] Figure 3 This is a graph showing the autocorrelation sidelobe level and cross-correlation sidelobe level results of the angular domain signal of this invention;

[0019] Figure 4 This is a comparison diagram of the multi-beam transmission pattern of the present invention and the desired transmission pattern. Detailed Implementation

[0020] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0021] Reference Figure 1 The implementation steps of the embodiments of the present invention will be described in further detail below.

[0022] Step 1: Using the constructed system signal, calculate the difference between the main lobe value of the compressed signal pulse and the expected main lobe value of the compressed pulse pulse.

[0023] The system signal is N s ×N t The phase-coded signal matrix, N s N represents the number of symbols contained in each phase-coded signal. t This indicates the total number of subarrays in a MIMO radar system.

[0024] The difference between the compressed main lobe value of the signal pulse and the desired compressed main lobe value is obtained by the following formula:

[0025]

[0026] Where z1 represents the difference between the compressed main lobe value of the signal pulse in all subarrays and the desired compressed main lobe value, and vec(·) represents the vectorization operation. Represents all subarray signals S t The pulse compression main lobe value after the k-th shift distance, k∈[-m, m], where m represents the boundary between the main lobe region and the side lobe region of the pulse compression value.

[0027] s i Let (·) represent the phase-coded signal of the i-th subarray. H J represents the conjugate transpose operation. k Represents a shift matrix. I represents the identity matrix, f m (·) indicates an m-fold linear interpolation operation. Indicates length is The desired pulse compression main lobe value after the k-th shift distance of the arbitrary phase-encoded signal x0.

[0028] Step 2: Calculate the autocorrelation sidelobe level and cross-correlation sidelobe level of the angular domain signal, respectively.

[0029] The aforementioned angular domain signal is obtained by the following formula:

[0030]

[0031] in, Indicates the directions of all subarrays as The angular domain signal, where θ represents the pitch angle. Indicates azimuth, A T Represents the transmit modulation diagonal matrix of all subarrays. diag(·) represents the fast diagonal matrix operation. Indicates the direction of the i-th subarray. The transmit modulation vector at that time, exp(•) denotes an exponential operation with the natural constant e as the base, j denotes the imaginary unit sign, λ denotes the radar wavelength, and u denotes the azimuth cosine vector. (·) T P represents the transpose operation. i，l This represents the position of the l-th element in the i-th subarray in three-dimensional space. Indicates that all subarrays are in the direction of The guiding vector at that time,

[0032] The autocorrelation sidelobe level of the angular domain signal is obtained by the following formula:

[0033]

[0034] in, Indicates direction as The autocorrelation sidelobe level of the angular domain signal after the k-th shift distance. This represents the set of beamformer spatial pointers for all subarrays.

[0035] The cross-correlation sidelobe level of the angular domain signal is obtained by the following formula:

[0036]

[0037] in, Indicates direction as and The cross-correlation sidelobe level of the angular domain signal after the k-th shift distance. This represents the set of directions of arrival for the angular domain signal beam.

[0038] Step 3: Calculate the difference between the multi-beam transmission pattern and the desired transmission pattern according to the following formula.

[0039]

[0040] Where z4 represents the difference between the multi-beam transmission pattern and the desired transmission pattern. This indicates the desired transmission pattern beam direction is... Gain at that time.

[0041] Step 4: Construct the objective function based on the difference between the pulse compression main lobe value and the desired pulse compression main lobe value, the autocorrelation and cross-correlation sidelobe levels of the angular domain signal, and the difference between the multi-beam transmission pattern and the desired transmission pattern.

[0042] The objective function is as follows:

[0043]

[0044] Where J represents the objective function, Y represents the waveform set of all subarrays, and the value range of Y is [exp(j0), exp(j2π)), w represents the weighted value corresponding to each optimization vector, ⊙ represents the dot product, z represents the matrix formed by each optimization vector, z = [z1, z2, z3, z4], z1 represents the vector formed by the difference between the main lobe value of the compressed signal pulse and the desired compressed signal pulse, z2 represents the vector formed by the autocorrelation sidelobe level of the angular domain signal, z3 represents the vector formed by the cross-correlation sidelobe level of the angular domain signal, and z4 represents the vector formed by the difference between the multi-beam transmission pattern and the desired transmission pattern.

[0045] Step 5: Use the Sequential Quadratic Programming (SQP) algorithm to optimize the MIMO radar waveform of the multi-element subarray.

[0046] The steps for optimizing the waveform of the multi-element subarray MIMO radar are as follows:

[0047] The first step is to construct a K×G matrix, where the elements are random values ​​within the range [exp(j0), exp(j2π)). The value of K is related to the value of N. s Equal to each other, the value of G is the same as that of N. t equal;

[0048] The second step is to use the aforementioned objective function J as the objective function, and to use S... t As the independent variables of the fminimax optimization function, we set the maximum number of optimization iterations *a*, the error threshold between optimal points *b*, and the function option "Algorithm=SQP". This optimizes the S... t Let it be the matrix mentioned in the first step;

[0049] The third step is to iteratively calculate the objective function and select the signal corresponding to the minimum value in the iteration results as the optimal signal S. t .

[0050] The technical effects of the present invention will be explained in detail below with reference to simulation experiments.

[0051] 1. Simulation experimental conditions.

[0052] The software platform for the simulation experiment of this invention is: Windows 10 operating system and Matlab R2020a.

[0053] The subarray MIMO radar system used in simulation experiment 1 of this invention comprises 16 subarrays with a total of 1020 elements, a carrier frequency of f0 = 8 GHz, a pulse compression half-main lobe width of m = 4, and a weighting ratio of 0.4:0.2:0.2:0.2 for each optimization vector of the objective function. tThe independent variable of the fminimax optimization function takes values ​​in the range [exp(j0), exp(j2π)). The optimization result is the optimal value obtained by executing the optimization function 5 times.

[0054] 2. Simulation content and result analysis.

[0055] The simulation experiment of this invention uses the method of this invention to perform simulations on all subarray signals S. t Optimize.

[0056] The obtained compressed main lobe value of the signal pulse and the expected compressed main lobe value of the pulse are plotted as follows: Figure 2 The two curves shown depict the autocorrelation sidelobe levels of the angular domain signal as follows: Figure 3 The four curves shown in (a) plot the cross-correlation sidelobe levels as follows: Figure 3 The six curves shown in (b) plot the multi-beam transmission azimuth map and the desired transmission azimuth map as follows: Figure 4 The two curves shown in (a) plot the multi-beam transmission elevation diagram and the desired transmission elevation diagram as follows: Figure 4 The two curves shown in (b) are shown in the middle.

[0057] Figure 2 The horizontal axis represents the shift distance of the compressed signal pulse, and the vertical axis represents the amplitude, with the unit being dB. Figure 2 The red curve in the figure represents the symbol length N. s =256 signal S t Pulse compression main lobe value k∈[-4, 4], the blue curve represents the symbol length. Phase-coded signal x0 pulse compression main lobe value The result of 4 times linear interpolation.

[0058] from Figure 2 It can be seen that the signal pulse compression main lobe value obtained by the method of the present invention is quite close to the desired pulse compression main lobe value.

[0059] Figure 3 In (a), the horizontal axis represents the shift distance of the autocorrelation sidelobe level of the angular domain signal, and the vertical axis represents the amplitude, in dB. Figure 3 (a) indicates the direction of the angular domain signal. Autocorrelation sidelobe levels at (-10°, -10°), (-10°, 10°), (10°, -10°), and (10°, 10°), respectively.

[0060] Figure 3 In (b), the horizontal axis represents the shift distance of the cross-correlation sidelobe level of the angular domain signal, and the vertical axis represents the amplitude, in dB. Figure 3(b) indicates the direction of the angular domain signal. The cross-correlation sidelobe levels of ((-10°, -10°), (-10°, 10°)), ((-10°, -10°), (10°, -10°)), ((-10°, -10°), (10°, 10°)), ((-10°, 10°), (10°, -10°)), ((-10°, 10°), (10°, 10°)) and ((10°, -10°), (10°, 10°)) are respectively.

[0061] from Figure 3 As can be seen from (a) and (b), the autocorrelation sidelobe level and cross-correlation sidelobe level of the angular domain signal obtained by the method of the present invention are suppressed to be relatively flat.

[0062] Figure 4 In (a), the horizontal axis represents the azimuth angle of the transmission pattern, and the vertical axis represents the amplitude, both in dB. Figure 4 The red curve in (a) represents the desired transmission azimuth of a phased array radar array with beam pointing to (-10°, -10°), (-10°, 10°), (10°, -10°), and (10°, 10°) consisting of 30 half-wavelength intervals. The blue curve represents the multi-beam transmission azimuth of a subarray MIMO radar system with beam pointing to (-10°, -10°), (-10°, 10°), (10°, -10°), and (10°, 10°)

[0063] Figure 4 In (b), the horizontal axis represents the elevation angle of the launch pattern, and the vertical axis represents the amplitude, both in dB. Figure 4 The red curve in (a) represents the desired transmit elevation diagram of a phased array radar array with beam pointing to (-10°, -10°), (-10°, 10°), (10°, -10°), and (10°, 10°) consisting of 30 half-wavelength intervals. The blue curve represents the multi-beam transmit elevation diagram of a subarray MIMO radar system with beam pointing to (-10°, -10°), (-10°, 10°), (10°, -10°), and (10°, 10°)

[0064] from Figure 4 As can be seen from (a) and (b), the multi-beam transmission pattern obtained by the method of the present invention can match the desired transmission pattern very well. The signal-to-noise ratio of the multi-beam transmission pattern and the desired transmission pattern are very close, and the transmission energy is concentrated in the main lobe direction.

Claims

1. A subarray MIMO radar waveform design method based on wide pulse compressed main lobe, characterized in that, The objective function is constructed based on the pulse compression main lobe value, the autocorrelation and cross-correlation sidelobe levels of the angular domain signal, and the multi-beam transmission pattern. The Sequential Quadratic Programming (SQP) algorithm is then used to optimize the waveform of the multi-element subarray MIMO radar. The steps of this design method are as follows: Step 1: Using the constructed system signal, calculate the difference between the main lobe value of the compressed signal pulse and the expected main lobe value of the compressed pulse pulse. Step 2: Calculate the autocorrelation sidelobe level and cross-correlation sidelobe level of the angular domain signal, respectively; Step 3: Calculate the difference between the multi-beam transmission pattern and the desired transmission pattern; Step 4: Construct the objective function based on the difference between the pulse compression main lobe value and the desired pulse compression main lobe value, the autocorrelation and cross-correlation sidelobe levels of the angular domain signal, and the difference between the multi-beam transmission pattern and the desired transmission pattern. Step 5: Use the Sequential Quadratic Programming (SQP) algorithm to optimize the MIMO radar waveform of the multi-element subarray.

2. The subarray MIMO radar waveform design method based on wide pulse compressed main lobe according to claim 1, characterized in that, The system signal mentioned in step 1 is The phase-coded signal matrix, This indicates the number of symbols contained in each phase-coded signal. This indicates the total number of subarrays in a MIMO radar system.

3. The subarray MIMO radar waveform design method based on wide pulse compressed main lobe according to claim 2, characterized in that, The difference between the main lobe value of the compressed signal pulse and the desired main lobe value in step 1 is obtained by the following formula: ； in, This represents the difference between the compressed main lobe value of the signal pulse in all subarrays and the desired compressed main lobe value. Indicates vectorization operation, Indicates all subarray signals No. Pulse compression main lobe value after the second shift distance , This indicates the boundary between the main lobe region and the side lobe region of the pulse compression value. express Double linear interpolation operation, Indicates length is Arbitrary phase encoded signal No. The expected pulse compression main lobe value after the second shift distance.

4. The subarray MIMO radar waveform design method based on wide pulse compressed main lobe according to claim 3, characterized in that, The angular domain signal mentioned in step 2 is obtained by the following formula: ； in, Indicates the directions of all subarrays as Angular domain signal, Indicates pitch angle, Indicates azimuth. Represents the transmit modulation diagonal matrix of all subarrays. Indicates that all subarrays are in the direction of The guiding vector at that time.

5. The subarray MIMO radar waveform design method based on wide pulse compressed main lobe according to claim 4, characterized in that, The autocorrelation sidelobe level of the angular domain signal mentioned in step 2 is obtained by the following formula: ； in, Indicates direction as angular domain signal Autocorrelation sidelobe level after the second shift distance This indicates the conjugate transpose operation. This represents the set of beamformer spatial pointers for all subarrays.

6. The subarray MIMO radar waveform design method based on wide pulse compressed main lobe according to claim 5, characterized in that, The cross-correlation sidelobe level of the angular domain signal mentioned in step 2 is obtained by the following formula: ； in, Indicates direction as and angular domain signal Cross-correlation sidelobe level after the second shift distance This represents the set of directions of arrival for the angular domain signal beam.

7. The subarray MIMO radar waveform design method based on wide pulse compressed main lobe according to claim 6, characterized in that, The difference between the multi-beam transmission pattern and the desired transmission pattern in step 3 is obtained by the following formula: ； in, This represents the difference between the multi-beam transmission pattern and the desired transmission pattern. This indicates the desired transmission pattern beam direction is... Gain at that time.

8. The subarray MIMO radar waveform design method based on wide pulse compressed main lobe according to claim 7, characterized in that, The objective function described in step 4 is as follows: ； in, Describe the objective function. Represents the waveform set of all subarrays. The range of values ​​is , This indicates an exponential operation with the natural constant e as the base. The symbol representing the imaginary unit. This represents the weighted value corresponding to each optimization vector. This represents the dot product. This represents the matrix formed by each optimization vector. , This represents the vector formed by the difference between the compressed main lobe value of the signal pulse and the desired compressed main lobe value. This represents a vector composed of the autocorrelation sidelobe levels of the angular domain signal. This represents a vector composed of the cross-correlation sidelobe levels of the angular domain signals. This represents the vector formed by the difference between the multi-beam transmission pattern and the desired transmission pattern.

9. The subarray MIMO radar waveform design method based on wide pulse compressed main lobe according to claim 8, characterized in that, The steps for optimizing the multi-element subarray MIMO radar waveform described in step 5 are as follows: The first step is to build A matrix, the elements of which are Random values ​​within, The value of and equal, The value of and equal; The second step is to convert the objective function into a target function. As the objective function, The maximum number of iterations is set as the independent variable of the fminimax optimization function. Error threshold between optimal points And the function option Algorithm=SQP optimizes the function. Let it be the matrix mentioned in the first step; The third step is to iteratively calculate the objective function and select the signal corresponding to the minimum value in the iteration results as the optimal signal. .

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