Waveform design method based on weighted fuzzy function

Abstract

The application discloses a waveform design method based on a weighted fuzzy function and relates to the technical field of radar detection. The method comprises the following steps: defining a weighted fuzzy function, constructing an optimization problem based on the weighted fuzzy function, converting a quartic objective function optimization problem into a linear optimization problem through continuous convex approximation, relaxing the constraint, converting the original problem into a convex optimization problem, normalizing the amplitude of the optimization result, repeating the step until the objective function converges, and finally obtaining an optimal waveform. The application can obtain an optimal waveform with an ideal fuzzy function shape through the response weight adjustment of each distance-Doppler pair of the fuzzy function, and supports the clutter suppression in radar coherent processing and other engineering applications.

Description

Technical Field

[0001] This invention relates to the field of radar detection technology. Background Technology

[0002] For single-transmitter, single-receiver radar waveform design, existing literature has proposed numerous algorithms, including the cyclic algorithm new (CAN), the weighted cyclic algorithm new (WeCAN), and the alternating multiplier class algorithm. Petre S. and Song J. et al., in order to minimize the integrated sidelobe level (ISL), used its "almost equivalent" frequency domain expression as the objective function, and proposed efficient cyclic algorithm new (CAN) and weighted cyclic algorithm new (WeCAN) using fast Fourier transform (see Petre S, Hao H, Jian L, New Algorithms for Designing Unimodular Sequences With Good Correlation Properties[J], IEEE Transactions on Signal Processing, 2009(57)4:1415-1425.) and weighted cyclic algorithm new (WeCAN) (see Song J, Babu P, Palomar DP. Optimization Methods for Designing Sequences With Low Autocorrelation Sidelobes[J]. IEEE Transactions on Signal Processing, 2009(57)4:1415-1425.). Processing, 2015, 63(15):3998-4009.) can achieve fast optimization of polyphase code sequences with a length of not less than 104, far exceeding the length of Frank and Golomb sequences. However, it uses an "equivalent" frequency domain objective function and does not directly minimize the autocorrelation integral sidelobes, which cannot guarantee the quality of the optimal solution. Based on the above ISL equivalent results, multiplier-type algorithms represented by alternating optimization (see Liang, Junli, Jian, et al. Unimodular Sequence Design Based on Alternating Direction Method of Multipliers[J]. IEEE Transactions on Signal Processing: A publication of the IEEE Signal Processing Society, 2016, 64(20):5367-5381.) are gradually being applied to low ISL waveform optimization. This method requires iterative minimization of parameters such as dual constants and redundant variables, which has a large computational load.To quickly solve the constant-mode low-ISL waveform design problem, Wang Xinhai et al. used the phase domain coordinate descent method to solve the constant-mode waveform, and achieved higher solution efficiency than the algorithm proposed by Liang Junli (see Wang Xinhai, Wang Chaoyu, Zhang Ning, et al. A phase domain low integral sidelobe radar waveform optimization method [J]. Journal of Radar, 2022(002):011.). All the above methods use autocorrelation sidelobes as the metric to optimize the waveform in a single dimension. Due to the development of modern radar, applications such as weak target detection and two-dimensional clutter suppression require multi-dimensional simultaneous optimization of the waveform. Summary of the Invention

[0003] To address the problem of low signal-to-noise ratio in the detection of weak targets near strong targets, this invention proposes a waveform design method based on a weighted fuzzy function.

[0004] The present invention achieves its objective through the following technical solutions:

[0005] ① Based on the conventional signal ambiguity function, a weighted ambiguity function is defined, which applies constant weights to the responses of each range-Doppler pair. Furthermore, the power capacity in the range-Doppler domain can be adjusted by changing the weights, allowing the power capacity to be adjusted as needed. Let the aperiodic waveform sequence of length N be... Define the (k, d)th element in the weighted fuzzy function as:

[0006]

[0007] Where k represents the number of delay points, M represents the total number of Doppler points, and f d This represents the d-th normalized Doppler frequency. The weighted coefficient vector has the following matrix form:

[0008]

[0009] The weighted fuzzy function A has the same meaning as the conventional fuzzy function if and only if W is an all-one matrix;

[0010] ② Construct a constant modulus optimization problem based on a weighted fuzzy function, let w 0，M / 2 =0, F is a Toeplitz matrix with all 1s on the k-th diagonal; the Doppler matrix is ​​F. d Represented as

[0011]

[0012] ③ A non-convex objective function is equivalently transformed into a convex function.

[0013] ④ The constant modulus constraint relaxation is a convex constraint.

[0014] ⑤ Constant modulus projection transforms the non-constant modulus optimal solution into a waveform sequence that satisfies constant modulus constraints.

[0015] Furthermore, minimizing the integral sidelobes of the weighted fuzzy function is used as the criterion, and a constant modulus constraint is applied to the optimal waveform sequence. Representing the variables involved in A(k, d) using vectorization or matrix representation, the optimization problem is then constructed as follows:

[0016]

[0017] subjecttoX=xx H

[0018] |x n |=1, n=1, ..., N.

[0019] Furthermore, a continuous convex approximation algorithm is used to perform two consecutive convex approximations on the quartic non-convex objective function using its upper bound quadratic function, transforming the original objective function into an equivalent linear objective function:

[0020]

[0021] Where, λ max (L) represents the largest eigenvalue of matrix L, λ g =λ max (Γ), e k，d =vec(F d E k ), vec(·) denotes the vectorization operator of a matrix, and furthermore, let A -k，M-d+1 Let x be the value of the -kth row and M-d+1th column of the fuzzy function matrix obtained from x. Then:

[0022]

[0023]

[0024] Furthermore, the non-convex constant modulus constraint is transformed into a convex energy finite constraint, that is, |x n Let |=1, n=1, ..., N be relaxed as follows:

[0025] Furthermore, the non-modal optimal solution of the obtained equivalent convex problem is transformed into a modal waveform that satisfies the requirements of the original optimization problem using Euclidean constant modulus projection.

[0026] Compared with the prior art, the beneficial effects of this invention include:

[0027] 1. The optimized waveform has been refined to shape its range-Doppler plane behavior, which can be used for detecting weak targets near strong targets and suppressing moving clutter;

[0028] 2. A constant-modulus waveform optimization model with weighted fuzzy functions was constructed, enriching the relevant content of waveform optimization model research;

[0029] 3. By combining the convex approximation technique of quartic polynomials with the constant modulus constraint relaxation technique, the equivalent transformation of the waveform optimization problem is completed, and the computational efficiency is improved compared with the traditional global algorithm. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 The waveform design method flow is shown in this embodiment of the invention;

[0032] Figure 2 Let be the fuzzy function for a random constant modulus sequence with a sequence length of 32;

[0033] Figure 3 Let be the ambiguity function for optimizing the waveform sequence when the sequence length is 32;

[0034] Figure 4 The convergence curve of the objective function based on the weighted fuzzy function waveform design method when the sequence length is 32;

[0035] Figure 5 For a random constant modulus sequence with a sequence length of 64, the fuzzy function is given.

[0036] Figure 6 Let be the ambiguity function for optimizing the waveform sequence when the sequence length is 64.

[0037] Figure 7 The convergence curve of the objective function based on the weighted fuzzy function waveform design method is given when the sequence length is 64. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] This invention provides a waveform optimization method based on a weighted fuzzy function. The waveform optimization method described herein is as follows: Figure 1As shown: A weighted fuzzy function is defined, and an optimization problem based on the weighted fuzzy function is constructed. Then, the fourth-order objective function optimization problem is transformed into a linear optimization problem through continuous convex approximation. Afterwards, the constraints are relaxed, transforming the original problem into a convex optimization problem, and the amplitude of the optimization result is normalized. This process is repeated until the objective function converges, finally obtaining the optimal waveform. The waveform design method of this invention includes (taking N=32 as an example):

[0040] 1. Weighted fuzzy function and optimization problem construction

[0041] Let a random sequence of length N = 32 be given by... The (k, d)th element in its fuzzy function is:

[0042]

[0043] Weighted fuzzy function expression

[0044]

[0045] Among them, if This represents a real matrix with α rows and β columns. The weighted coefficient vector has the following matrix form:

[0046]

[0047] The distance-Doppler weights for the fuzzy function are designed as shown in Table 1.

[0048] Table 1 Simulation Parameters

[0049]

[0050] That is, W(24:28, 32:36) = 10, W(36:40, 66:70) = 10, W(32, 51) = 0, and the rest are 1. The optimization problem is:

[0051]

[0052] 2. Convex approximation of the objective function - constraint relaxation - constant modulus projection

[0053] Calculate e k，d =vec(F d E k ) and L, that is:

[0054]

[0055]

[0056] Let λ g Let Γ be the largest eigenvalue. After convex approximation of the objective function and constant modulus relaxation, we obtain:

[0057]

[0058] After solving equation (14), the phase vector of the optimal solution can be taken to form the constant modulus vector as the optimal solution for the current iteration. use Substitute x0 in problem (14) As the initial value for the next iteration, the problem (14) is solved cyclically until the objective function converges, and the optimal waveform with the ideal fuzzy function shape is obtained.

[0059] When the waveform sequence is 32, the average normalized sidelobe power of the unoptimized fuzzy function is -19dB (see...). Figure 2 The average power within the optimized notch is -32dB (see...). Figure 3 This reduces the bandwidth by 13 dB, and the proposed algorithm converges after 10,000 iterations (see...). Figure 4 When the waveform sequence is 64, the average normalized sidelobe power of the unoptimized fuzzy function is -20dB (see...). Figure 5 The average power within the optimized notch is -34dB (see...). Figure 6 This reduces the bandwidth by 14 dB, and the proposed algorithm converges after 4000 iterations (see...). Figure 7 ).

[0060] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A waveform design method based on a weighted fuzzy function, characterized in that: Step 1: Based on the conventional signal ambiguity function, define a weighted ambiguity function, apply constant weights to the responses of each range-Doppler pair, and change the power capacity in the range-Doppler domain with the weights so that the power capacity can be adjusted as needed; Let the length be N Aperiodic waveform sequence is Define the ( ) in the weighted fuzzy function k , d The number of elements is: (1) in, k Indicates the delay points. M Represents all Doppler points. f d Indicates the first d A normalized Doppler frequency, The weighted coefficient vector has the following matrix form: (2) iff W weighted blur function A same meaning as normal blur function; Step 2: Construct a constant modulus optimization problem based on a weighted fuzzy function, let For the first k Toeplitz matrix with all diagonals equal to 1; Doppler matrix F d Represented as: (3) The criterion is to minimize the weighted sidelobe integral of the ambiguity function, and the optimal waveform sequence is subject to constant modulus constraint. A ( k , d ) The variables involved in the form of vectorization or matrix representation, the optimization problem is constructed: (4) Step 3: Transform the non-convex objective function into a convex function; Step 4: Relax the constant modulus constraint to a convex constraint; Step 5: Constant modulus projection transforms the non-constant modulus optimal solution into a waveform sequence that satisfies constant modulus constraints.

2. The waveform design method based on the weighted ambiguity function according to claim 1, characterized in that: Step 3 further includes: using a continuous convex approximation algorithm to perform two consecutive convex approximations on the quartic non-convex objective function using its upper bound quadratic function, thereby transforming the original objective function into an equivalent linear objective function. (5) in, λ max ( L ) represents a matrix L The largest eigenvalue, λ g =λ max (Г), e k,d = vec ( F d E k ), vec ( · ) denotes the vectorization operator of a matrix. Furthermore, let... A -k，M-d+1 For the reason x The calculated fuzzy function matrix has the following digits: -k OK M - d+ The values ​​in column 1, then: (6) (7)。 3. The weighted blurring function based waveform design method of claim 1, wherein: The step 4 further comprises: converting the non-convex constant modulus constraint into a convex energy limited constraint, i.e. converting relaxing to .

4. The weighted blurring function based waveform design method of claim 1, wherein: Step 5, the constant modulus projection, further includes: using Euclidean constant modulus projection to transform the non-constant modulus optimal solution of the obtained equivalent convex problem into a constant modulus waveform that satisfies the requirements of the original optimization problem.

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