A MIMO waveform design method with equalized coherent gain and diversity gain
By designing waveforms that balance coherent gain and diversity gain in a MIMO radar system and optimizing waveform parameters using a block coordinate rotation algorithm, the problem of insufficient flexibility in existing technologies is solved, enabling flexible adjustment and performance improvement of the radar system.
Patent Information
- Application Number
- CN202410532665.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-30
- Publication Date
- 2025-12-26
- Estimated Expiration
- 2044-04-30
AI Technical Summary
In existing MIMO radar systems, the optimization methods for coherent gain and diversity gain lack flexibility and are difficult to adjust quickly to adapt to dynamically changing application scenarios, increasing the complexity and cost of system design.
A MIMO waveform design method that balances coherent gain and diversity gain is adopted. By initializing and generating optimal coherent gain and diversity gain waveforms, constructing an equalized waveform model, and optimizing waveform parameters using a block coordinate rotation algorithm, flexible adjustment of coherent gain and diversity gain is achieved.
It achieves a flexible balance between coherent gain and diversity gain in MIMO radar systems, adapts to dynamic environmental changes, and improves radar detection performance and parameter estimation accuracy.
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Figure CN118209933B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of radar communication, and particularly relates to a MIMO waveform design method with balanced coherent gain and diversity gain. BACKGROUND
[0002] Multiple-input multiple-output (MIMO) radar has attracted extensive attention from scholars at home and abroad since its inception. MIMO radar uses multiple transmitting and receiving antennas, and each transmitting antenna can simultaneously transmit multiple radar signal waveforms. Compared with traditional phased array radars, MIMO radars have the advantage of waveform diversity and higher transmission freedom. In a MIMO radar system, coherent gain and diversity gain are two key technical indicators that are crucial to the improvement of system performance.
[0003] Coherent gain improves signal quality by coherently superimposing multiple received signals, thereby enhancing the target detection and tracking capabilities of the system. Diversity gain utilizes spatial diversity to improve the robustness and anti-interference capability of the system, which can effectively deal with complex environments and interference. These two gain technologies are of great significance in optimizing radar system performance, improving target detection probability, and enhancing signal quality. In current radar systems, research on the optimization problem of balancing coherent gain and diversity gain often uses optimization of array element deployment and planning adjustment of subarrays. This approach lacks flexibility, is limited by hardware constraints, is difficult to quickly adjust and optimize the system to meet new requirements, and increases the complexity and cost of system design. In complex and variable practical application scenarios, it is often necessary to adjust the waveform optimization strategy to meet the changing needs of practical tasks. Therefore, it is necessary to study the use of waveform design technology to balance and optimize coherent gain and diversity gain in order to achieve better radar performance and target detection capability. SUMMARY
[0004] The technical problem to be solved by the application is to propose a MIMO waveform design method that can flexibly balance coherent gain and diversity gain from the perspective of application scenarios.
[0005] The technical solution adopted by the application to solve the above technical problem is a MIMO waveform design method with balanced coherent gain and diversity gain, comprising the following steps:
[0006] Initialization step: initializing the number of transmitting antennas N in the uniform linear array MIMO antenna, the number of samples L of each transmitting waveform, and the proportion parameter p;
[0007] Optimal coherent gain waveform S1 generation step: under the constant modulus condition, the ratio of the maximum minimum main lobe level to the maximum peak side lobe level is taken as the objective function to construct the optimization model of the optimal coherent gain waveform S1, and the optimal coherent gain waveform S1 is obtained by solving the optimization model of S1.
[0008] The generating step of the optimal diversity gain waveform S2: under the constant modulus condition, the weighting matrix is determined, the weighted distance sidelobe level in the frequency domain form which is minimized is taken as the objective function to construct the optimization model of the optimal diversity gain waveform S2, and the optimization model of S2 is solved to obtain the optimal diversity gain waveform S2;
[0009] The constructing step of the optimization model of the equalization waveform S: under the constant modulus condition, the equalization waveform model is constructed based on the weight parameter p, the optimal coherent gain waveform S1 and the optimal diversity gain waveform S2 as follows:
[0010]
[0011]
[0012] Wherein, vec represents the vectorization function, the weight parameter p is in the range of [0, 1], s.t. is a constraint condition, s(i) is the ith term of vec(S), the serial number variable i = 1,..., NL, |·| represents the modulus, and ||·|| represents the 2-norm;
[0013] The MIMO waveform generating step: the optimization model of S is solved to obtain the phase parameter phi(i) corresponding to the uniform linear array MIMO antenna, so that the equalization waveform S is obtained, and the directivity pattern, the autocorrelation sidelobe level and the cross-correlation sidelobe level curve of the MIMO antenna are determined through the obtained equalization waveform S.
[0014] When p = 0, the S output is the optimal diversity gain waveform; when the parameter p = 1, the S output is the optimal coherent gain waveform; when the value range of the p parameter is (0, 1), the output waveform should be between the optimal coherent gain waveform and the optimal diversity gain waveform. Therefore, the proportion of the coherent gain and the diversity gain of the transmitted signal can be balanced by adjusting the weight parameter p.
[0015] The present application has the advantages of reasonable allocation of the proportion of the coherent gain and the spatial diversity gain in the MIMO radar system, flexibility, wide practicability, high calculation efficiency and the like, and has more advantages than the array element optimization deployment, can be adjusted and optimized in real time by adjusting the parameters, and is suitable for dynamic channel environment and target scene. BRIEF DESCRIPTION OF DRAWINGS
[0016] Figure 1 The scheme flowchart of the present application;
[0017] Figure 2 The comparison chart of the directivity pattern before and after optimization and the expected directivity pattern;
[0018] Figure 3 The comparison chart of the autocorrelation sidelobe level and the cross-correlation sidelobe level before and after optimization;
[0019] Figure 4 A comparison of the radiation patterns after optimization with different parameters. Detailed Implementation
[0020] To better describe the implementation of this invention, the following definitions and explanations are provided first:
[0021] MIMO radar: Multiple input multiple output radar has multiple transmit and receive antennas. Each transmit antenna can transmit different signals. At the receiver, the echoes of each waveform channel can be received and separated simultaneously to form a virtual aperture, which improves the radar's angular resolution and interference suppression capability. It has the advantages of waveform diversity and higher transmission freedom.
[0022] BCD Algorithm: Block Coordinate Cyclic Approach. The basic idea of this algorithm is to divide the optimization variables into several blocks, updating only the variables in one block at a time while keeping the variables in the other blocks fixed. By iteratively updating the variables in each block, the optimal solution to the optimization problem is eventually reached.
[0023] This invention is primarily verified using simulation experiments; all steps and conclusions are verified on the MATLAB simulation platform. The specific implementation methods of this invention are described in detail below with reference to the accompanying drawings.
[0024] like Figure 1 The flowchart shown below illustrates a MIMO waveform design method for coherent gain and diversity gain equalization according to the present invention, which specifically includes the following steps:
[0025] Step 1: Set the parameters required for the problem;
[0026] The MIMO radar system in this embodiment consists of N transmitting elements, all placed on a uniform linear array, where L is the number of waveform samples per pulse. The system signal is constructed as an L×N transmitted signal matrix S, and the weighting parameter ρ is set. The system simulation parameters used in this embodiment are shown in Table 1.
[0027] Table 1
[0028]
[0029]
[0030] Step 2: Generate the optimal coherent gain waveform S1;
[0031] Assuming the total energy of the transmitted signal is 1, under constant modulus conditions, the ratio of the minimum main lobe level to the maximum peak sidelobe level is maximized as the objective function to construct an optimization model:
[0032]
[0033]
[0034]
[0035]
[0036] where ε denotes the minimum mainlobe level, η denotes the maximum peak sidelobe level, M mainlobe angles θ m mainlobe region consisting of the set S sidelobe angles θ s sidelobe region consisting of the set
[0037] According to the directional diagram of the transmit signal at direction θ:
[0038] P(θ) = s1 H A(θ)A H (θ)s1
[0039] where s1 = vec(S1), s1(i) is the ith item of vec(S1), · H is the conjugate transpose, the transmit steering vector a(θ) = [1, e j2πdsinθ / λ ,..., e j2π(N-1)dsinθ / λ ] T , d denotes the distance between array elements, and λ denotes the wavelength of the transmit signal. The transmit steering matrix at angle θ is the Kronecker product, a(θ) is the transmit steering vector, and I L is the L x L unit matrix. From s1 H A(θ)A H (θ)s1 = ||A H (θ)s1|| 2 , the model is further equivalently transformed as:
[0040]
[0041]
[0042] z m =Α m H s1,||z m || 2 ≥ ε, m = 1,..., M
[0043] y s =Λ s H s1,||y s || 2≤ η, s = 1,..., S
[0044] where the main lobe region θ m The average power P(θ m ) = ||A m H s1|| 2 ≥ ε, make z m = A m H s1, m = 1,..., M, the side lobe region θ s The average power P(θ s ) = ||Λ s H s1|| 2 ≤ η, make y s = Λ s H s1, s = 1,..., S. Convert to Lagrange function, use ADMM algorithm to optimize solution to get S1.
[0045] Step 3, generate the optimal diversity gain waveform S2;
[0046] Assuming the total energy of the transmitted signal is 1, determine the weight matrix, use the minimum weighted distance sidelobe level WISL as the measurement standard:
[0047]
[0048] where ε r is the signal weighted distance sidelobe level, is the autocorrelation function / mutual correlation function at the lth transmitted signal, γ l represents the weight value of the set lth sidelobe level, according to Parseval theorem, it is transformed into frequency domain form, and an optimization model is constructed:
[0049]
[0050]
[0051] where s n (l) is the element of the nth row and the lth column of S2, the frequency value of the pth frequency point The sequence variable p = 0,..., 2L-1, the frequency domain form · H is the conjugate transpose, · T is the transpose, Γ is the weight matrix, γ0 is the diagonal element value in the weight matrix Γ, I N is an N × N unit matrix, ||·||2 represents the 2-norm, Z(ω p ) = A pS2, transformation matrix Diag denotes a diagonal matrix.
[0052]
[0053] According to Z(ω p ) = A p S2, further simplification is made to the model. Due to the constant modulus constraint, we can get After converting the problem into an unconstrained problem about the phase parameter φ n (l) corresponding to the l-th sampling value of the n-th antenna, the BCD algorithm is used to solve the optimization problem to obtain S2.
[0054] Step 4, construct an equalization waveform S design optimization model;
[0055] Assuming that the total energy of the transmitted signal is 1, based on the constant modulus constraint, the optimization model is constructed as follows:
[0056]
[0057]
[0058] where s1 = vec(S1), s2 = vec(S2), s = vec(S), vec represents a vectorization function, s(i) is the i-th item of s, i = 1,..., NL.
[0059] Due to the constant modulus constraint, the transmitted waveform S can be expressed as:
[0060]
[0061] where φ n (l) ∈ [0, 2π]. Therefore, it can be further converted to:
[0062]
[0063]
[0064] Step 5, use the block coordinate rotation (BCD) algorithm to solve the optimization model of S. In the BCD algorithm, only one block is optimized at each iteration, and other blocks remain unchanged. When fixing other variables, the optimization problem about the variable s(i) can be converted to:
[0065]
[0066]
[0067] where c is a constant term generated when other variables are fixed using the BCD algorithm.
[0068] According to the constant modulus constraint, the signal is expressed as The optimization problem is changed into an unconstrained problem about φ(i) in the form, and thus can be solved by numerical calculation method. Further simplifying:
[0069]
[0070]
[0071] Let c(i) = ρs1(i) + s2(i) - ρs2(i), and finally obtain the expression about φ(i):
[0072]
[0073] Step 6, according to the obtained phase parameter φ(i), the equalized waveform S is obtained, and the directivity pattern, autocorrelation sidelobe level and cross-correlation sidelobe level curve are drawn by the obtained waveform S.
[0074] Steps 3 and 5 use the block coordinate rotation BCD algorithm to obtain the optimal solution of the problem, and the multivariable optimization problem is converted into a single variable optimization problem in turn, other blocks remain unchanged. Compared with other traditional solving algorithms, the BCD algorithm is simple and easy to implement, and is widely used in solving unconstrained problems.
[0075] The optimal coherent gain waveform S1, the optimal diversity gain waveform S2 and the transmission signal S obtained by the algorithm of the application are used to draw the directivity pattern, and the expected directivity pattern is added for comparison, and four curves as shown in Figure 2 are obtained. The autocorrelation sidelobe level and the cross-correlation sidelobe level comparison diagram is shown in Figure 3 . Change the value of the parameter ρ, which is 0, 0.25, 0.5, 0.75 and 1 respectively, and make the comparison of the optimized directivity pattern as shown in Figure 4 .
[0076] From Figure 2 and Figure 3 , it can be seen that the coherent gain of the transmission signal obtained by the algorithm of the application is better than the optimal diversity gain signal, and slightly worse than the optimal coherent gain signal. The autocorrelation and cross-correlation sidelobe levels are opposite. From Figure 4 , it can be seen that when the parameter ρ = 0, the coherent gain effect is good, when ρ = 1, the coherent gain effect is poor. And the coherent gain effect of ρ = 0.25 is better than that of ρ = 0.5. Therefore, the purpose of balancing the proportion of coherent gain and spatial diversity gain of the transmission signal by changing the parameter ρ is achieved.
[0077] In conclusion, the application establishes an equalization target function with optimal coherent gain waveform and optimal diversity gain waveform, and realizes the purpose of reasonably distributing the proportion of coherent gain and spatial diversity gain of the MIMO radar system by changing parameters with the constant modulus constraint as a constraint condition. This method has great flexibility, can be dynamically adjusted according to actual needs and environmental conditions, helps to meet user needs, and improves the detection performance and parameter estimation accuracy of the radar.
Claims
1. A method for MIMO waveform design with equalized co-phasing gain and diversity gain, characterized in that, The method comprises the following steps: An initialization step: initializing the number of transmitting antennas N, the number of samples L of each transmitting waveform and the proportion parameter ρ in the uniform linear array MIMO antenna; An optimal co-phasing gain waveform S1 generation step: under the constant modulus condition, an optimization model of the optimal co-phasing gain waveform S1 is constructed by taking the maximum minimum main lobe level to maximum peak side lobe level ratio as an objective function, and the optimal co-phasing gain waveform S1 is obtained by solving the optimization model of S1; An optimal diversity gain waveform S2 generation step: under the constant modulus condition, a weighting matrix is determined, an optimization model of the optimal diversity gain waveform S2 is constructed by taking the minimum weighted distance side lobe level in the frequency domain as an objective function, and the optimal diversity gain waveform S2 is obtained by solving the optimization model of S2; An optimization model construction step of the equalization waveform S: under the constant modulus condition, the equalization waveform model is constructed based on the proportion parameter ρ, the optimal co-phasing gain waveform S1 and the optimal diversity gain waveform S2 as follows: Wherein, vec represents the vectorization function, s.t. is the constraint condition, s(i) is the ith item of vec(S), the serial number variable i = 1,..., NL, ||·|| represents the modulus, and ||·|| represents the 2-norm; A MIMO waveform generation step: the phase parameter φ(i) corresponding to the uniform linear array MIMO antenna is obtained by solving the optimization model of S, so that the equalization waveform S is obtained, and the directivity diagram, the autocorrelation side lobe level and the cross-correlation side lobe level curve of the MIMO antenna are drawn by the obtained equalization waveform S.
2. The method of claim 1, wherein, The optimization model of the optimal co-phasing gain waveform S1 is: where ε denotes the minimum main lobe level, The average power of the transmit signal in the direction of θ is P(θ) = s1 H A(θ)A H (θ) s1, s1 = vec(S1), vec denotes a vectorization function, s1(i) is the i-th term of vec(S1), the transmit steering matrix in the direction of θ is a Kronecker product, a(θ) is a transmit steering vector, I L is an L x L identity matrix, · H is a conjugate transpose, η denotes the maximum peak side lobe level, M main lobe angles θ m constitute a main lobe region S main lobe angles θ s constitute a side lobe region 3. The method of claim 2, wherein, The method for solving the optimization model of S1 is that, after the optimization model of S1 is equivalently transformed, it is written in the form of an augmented Lagrange function, and then the ADMM algorithm is used to solve the optimization model of S1 in the form of the Lagrange function.
4. The method of claim 1, wherein, The optimization model of the optimal diversity gain waveform S2 is: where s n (l) is an element of the nth row and the lth column of S2, the frequency value of the pth frequency point The sequence variable p = 0,..., 2L-1, frequency domain form · H is the conjugate transpose, · T is the transpose, Γ is a weighting matrix, γ0 is the diagonal element value in the weighting matrix Γ, γ l represents the weight value of the lth side lobe level set, I N is an N×N unit matrix, Z(ω p ) = A p S2, conversion matrix Diag represents a diagonal matrix.
5. The method of claim 4, wherein, In solving the optimization model of the optimal diversity gain waveform S2, the element in the nth row and the 1st column of S2 is expressed as The optimization model of S2 is converted into an optimization model of the phase parameter φ corresponding to the 1st sample value of the nth antenna n the unconstrained problem of (l) is solved again using the block coordinate descent (BCD) algorithm.
6. The method of claim 1, wherein, In solving the optimization model for S, the ith term s(i) of the waveform vec(S) is expressed as Thus, the optimization model for the equalized waveform S is converted into an unconstrained problem in terms of φ(i), which is then solved using the block coordinate descent (BCD) algorithm.