CN118171442A - Phased array radar main lobe widening method based on trigonometric function weighting - Google Patents
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Abstract
The invention discloses a phased array radar main lobe widening method based on trigonometric function weighting, and belongs to the field of array radar signal processing. The invention constructs a convex constraint iterative algorithm weighted by trigonometric function by utilizing the equivalent form of complex modulus, and obtains a weight vector for controlling the main lobe width in a desired range by constraining a given target angle and utilizing a cvx solver. The invention does not utilize any array structure information when the main lobe stretching is carried out, so that the invention is applicable to any antenna array form; no extra super parameter is introduced in the main lobe stretching solving process, so that the optimal solution can be converged without parameter adjustment, and the method has the advantages of high solving speed and good convergence performance.
Description
Technical Field
The invention belongs to the field of array radar signal processing, and particularly relates to a method for expanding the width of a main lobe of a phased array radar by using angle constraint and a trigonometric function as a weighting coefficient. The invention constructs a convex constraint iterative algorithm weighted by trigonometric function by utilizing the equivalent form of complex modulus, and obtains a weight vector for controlling the main lobe width in a desired range by constraining a given target angle and utilizing a cvx solver.
Background
Due to the advantages of flexible beam control, higher signal gain, extremely strong interference suppression capability, higher spatial resolution capability and the like, array signal processing gradually becomes an important branch in the field of signal processing, and has wide application in various military and civil aspects. With increasingly complex electromagnetic environments, radar detection is one of the research directions of great interest in practical applications, where optimizing array antenna designs plays a vital role in improving system performance and reducing costs. In practical applications, the antenna array may operate in a wider frequency band, and the main lobe width of the conventional beam forming method may be narrowed with the increase of frequency, so that the width of the main lobe needs to be controlled in a desired range in wideband beam forming, so that the main lobe width does not change with the change of frequency.
The prior main lobe widening method of the phased array radar mainly comprises a discrete beam forming method, a space-time beam forming method and a main lobe unfolding method based on intelligent optimization. Wherein the discrete beamforming method forms a wider main lobe by selecting a portion of the antenna elements in the array. This increases the width of the beam, making it immune to frequency variations. The disadvantage of discrete beamforming is that continuous main lobe broadening cannot be achieved and that energy losses occur during beamforming. The space-time beam forming method performs a main lobe widening by weighting the signals in time and space. Space-time beamforming may achieve a wider main lobe by introducing additional degrees of freedom in the beamforming process. However, space-time beamforming requires more complex signal processing algorithms and hardware implementations, and may face multipath effects and challenges for delay estimation. The weight or the phase of the array antenna can be adjusted through an intelligent optimization algorithm, so that the main lobe widening is realized. Common optimization algorithms include genetic algorithms, particle swarm optimization algorithms, and the like. These algorithms can find the optimal antenna weights or phase configurations according to specific requirements and constraint conditions. However, intelligent optimization algorithms require long computation times and may suffer from locally optimal solutions.
In summary, the existing main lobe widening methods have some disadvantages to different degrees, and an appropriate method needs to be selected according to specific application scenes and requirements so as to improve the system performance and reduce the cost.
Disclosure of Invention
The invention aims to construct a convex constraint iterative algorithm weighted by a trigonometric function by utilizing the equivalent form of complex modulus, and obtain a weight vector for controlling the width of a main lobe within a desired range by constraining a given target angle and utilizing a cvx solver.
A method for synthesizing an array directional diagram weighted by a trigonometric function is provided for a uniform linear array, so that the main lobe is widened. Therefore, the technical scheme of the invention is that the phased array radar main lobe widening method based on trigonometric function weighting comprises the following steps:
Step 1: establishing a beam forming model of the phased array radar:
find w
s.t.Re[wHa(θ0)]＝1
Where w represents the amplitude-phase excitation vector of the antenna, a (θ) represents the array steering vector in the θ direction, θ is the angle with the array normal, for describing a certain spatial orientation, θ 0 represents the main lobe corresponding angle, ψ SL represents the side lobe angle region, ρ (θ) represents the side lobe level upper limit, re [. Cndot ] is the real part taking operation, Represents any angle θ in the set ψ SL;
Step 2: according to step 1, a sidelobe angle region ψ SL is discretized into { θ 1,…,θJ ] firstly, wherein J represents the number of angles after discretization, and a phased array radar main lobe broadening problem solving model is established in the kth iteration process based on the number of angles after discretization:
s.t.Re[wHa(θ0)]＝1
Wherein the method comprises the steps of And/>For trigonometric function weighting, subscripts i and k represent weighting coefficients used in constraining the ith discrete angle θ i during the kth iteration, g is an optimization variable, g represents a lower sidelobe level limit of each angle in the sidelobe angle region ψ SL, θ i represents an angle after discretizing the sidelobe angle, and a specific weighting value is determined by the following formula:
wherein w k-1 denotes that the trigonometric functions are weighted respectively And/>When the method is used, the optimal solution of the main lobe widening problem of the phased array radar is achieved; the angle (·) is used for calculating the phase of the input complex number, and J is expressed as the number of target constraint angles;
Step 3: taking k=1 to obtain the initial triangular weighting coefficient Solving the main lobe widening problem of the convex optimized phased array radar established in the step 2, marking a solution vector as w 1, and marking an optimal value of the problem as g 1;
Step 4: and (3) circularly adding 1 to k on the basis of the step (3) to obtain a triangular weighting coefficient:
solving the main lobe widening problem of the convex optimized phased array radar established in the step 2, marking the solution as w k, and marking the optimal value of the problem as g k;
Step 5, repeating the step 4 until |g k-gk-1 | < epsilon is true, at this time, the judging algorithm converges, and executing the step 6, wherein epsilon represents a set threshold value;
and 6, obtaining an optimal weight vector w k, and calculating a phased array directional diagram by using w k so as to realize main lobe widening.
Further, the method for solving the main lobe widening problem of the convex optimized phased array radar in the step 3 and the step 4 is as follows: and adopting a convex optimization tool bag to solve the problem.
Further, the value of the threshold value e in the step 5 may be determined according to the system parameters, where e=0.001
Further, the specific method for calculating the phased array pattern by using w k in the step 6 is as follows
Compared with the prior art, the invention has the following advantages:
(1) Because the invention does not utilize any array structure information when the main lobe stretching is carried out, the invention is applicable to any antenna array form;
(2) Because no extra super parameter is introduced in the main valve stretching solving process, the method can converge to the optimal solution without parameter adjustment, and has the advantages of high solving speed and good convergence performance.
Drawings
Fig. 1 is a general flow chart of the present invention.
Fig. 2 is a pattern generated in the case of a uniform linear array according to the present invention.
Fig. 3 is a pattern generated in the case of a non-uniform linear array according to the present invention.
Fig. 4 is a diagram of the main lobe spread of different frequency signals in the case of a non-uniform linear array through reasonable main lobe constraint in the present invention.
Detailed Description
The whole idea of the invention is as follows:
(1) For a linear array, the constraint of a main lobe and side lobes is firstly considered by a conventional beam forming algorithm;
(2) Selecting target angles to be constrained according to the expected main lobe width, and maximizing the sum of array responses of the target angles;
(3) Analyzing the non-convex problem by using the idea of 'convexity';
(4) And iteratively solving by using a cvx solver to obtain weight vectors for controlling the main lobe width within a desired range.
Referring to fig. 1, the steps of the present invention are as follows:
step 1, constructing a conventional wave beam forming mathematical model for a linear array;
Wherein θ 0 represents the main lobe corresponding angle, ψ SL represents the side lobe angle region, ρ (θ) represents the side lobe level upper limit, re [ · ] is the real part taking operation.
Step 2, selecting a target constraint angle according to the expected main lobe width and establishing a lower model;
Wherein θ i (i=1, …, J) is the target constraint angle, used for main lobe broadening, and J is the number of target constraint angles. Constraints in the above model Is non-convex. The main lobe broadening problem described above is modeled as the following approximation problem:
Wherein the method comprises the steps of And/>Weighting the trigonometric function, the specific weighting value is determined by:
In the formula (4), w k-1 represents that the trigonometric functions are weighted respectively And/>The optimal solution of problem (3) is obtained.
Step 3, taking k=1 to obtain an initial triangle weighting coefficient (5), solving a convex optimization problem (3) by utilizing a convex optimization solving kit (CVX software), marking a solution vector as w 1, and marking an optimal value of the problem as g 1;
Step 4, let k=k+1, get the triangle weight coefficient (4), use cvx toolkit to get the question, record the solution as w k, record the optimal value of the question as g k;
Step 5, repeating the step 4 until |g k-gk-1 | < epsilon is true, at this time, the judging algorithm converges, and executing the step 6, wherein epsilon represents a certain threshold value;
And 6, obtaining an optimal weight vector w k, and calculating a phased array directional diagram by using w k to realize main lobe widening.
Simulation conditions and simulation results are processed;
1. simulation conditions
| System parameters | Value (unit: rice) |
| Wavelength of | λ＝10 |
| Array element spacing | d＝0.5λ＝5 |
| Threshold value | ∈＝0.001 |
2. Simulation data processing
Simulation 1: the invention is a direction diagram in the case of uniform linear array
The main lobe direction is theta 0 =10°, the array element number is 10, the target constraint angle is theta target = [8 DEG 10 DEG 12 DEG ], and the response of the directional diagram at the target angle is increased as can be seen from fig. 2, so that the main lobe widening purpose is achieved.
Simulation 2: the invention is directed to a pattern in the case of a non-uniform linear array
The main lobe direction is set as theta 0 =10°, the non-uniform linear array has 22 array elements, the array aperture is 20λ, the target constraint angle is theta target = [8°10°12 ° ], and the direction diagram is drawn as shown in fig. 3. It can be seen that the present invention can be applied in a non-uniform array scenario.
Simulation 3: under the condition of a non-uniform linear array, the main lobe width of a 10MHz signal pointing to 0 DEG under the same array aperture is used as a reference under the condition of the uniform linear array, and the main lobe width constraint is respectively carried out on 10MHz, 22MHz and 27MHz, and an array directional diagram is shown in figure 4. The invention can realize that the widths of main lobes of signals with different frequencies are kept consistent under the same distribution condition through reasonable target angle constraint.
Claims (4)
1. A phased array radar main lobe widening method based on trigonometric function weighting, comprising:
Step 1: establishing a beam forming model of the phased array radar:
find w
s.t.Re[wHa(θ0)]＝1
Where w represents the amplitude-phase excitation vector of the antenna, a (θ) represents the array steering vector in the θ direction, θ is the angle with the array normal, for describing a certain spatial orientation, θ 0 represents the main lobe corresponding angle, ψ SL represents the side lobe angle region, ρ (θ) represents the side lobe level upper limit, re [. Cndot ] is the real part taking operation, Representing any angle θ in the set ψ SL.
Step 2: according to step 1, a sidelobe angle region ψ SL is discretized into { θ 1,…,θJ ] firstly, wherein J represents the number of angles after discretization, and a phased array radar main lobe broadening problem solving model is established in the kth iteration process based on the number of angles after discretization:
s.t.Re[wHa(θ0)]＝1
Wherein the method comprises the steps of And/>For trigonometric function weighting, subscripts i and k represent weighting coefficients used in constraining the ith discrete angle θ i during the kth iteration, g is an optimization variable, g represents a lower sidelobe level limit of each angle in the sidelobe angle region ψ SL, θ i represents an angle after discretizing the sidelobe angle, and a specific weighting value is determined by the following formula:
wherein w k-1 denotes that the trigonometric functions are weighted respectively And/>When the method is used, the optimal solution of the main lobe widening problem of the phased array radar is achieved; the angle (·) is used for calculating the phase of the input complex number, and J is expressed as the number of target constraint angles;
Step 3: taking k=1 to obtain the initial triangular weighting coefficient Solving the main lobe widening problem of the convex optimized phased array radar established in the step 2, marking a solution vector as w 1, and marking an optimal value of the problem as g 1;
Step 4: and (3) circularly adding 1 to k on the basis of the step (3) to obtain a triangular weighting coefficient:
solving the main lobe widening problem of the convex optimized phased array radar established in the step 2, marking the solution as w k, and marking the optimal value of the problem as g k;
Step 5, repeating the step 4 until |g k-gk-1 | < epsilon is true, at this time, the judging algorithm converges, and executing the step 6, wherein epsilon represents a set threshold value;
and 6, obtaining an optimal weight vector w k, and calculating a phased array directional diagram by using w k so as to realize main lobe widening.
2. The method for widening main lobe of phased array radar based on trigonometric function weighting according to claim 1, wherein the method for solving the main lobe widening problem of convex optimized phased array radar in step 3 and step 4 is as follows: and adopting a convex optimization tool bag to solve the problem.
3. The method for widening main lobe of phased array radar based on trigonometric function weighting as claimed in claim 1, wherein the value of the threshold value e in step 5 is determined according to system parameters, and e=0.001 is taken.
4. The method for widening main lobe of phased array radar based on trigonometric function weighting as claimed in claim 1, wherein the specific method for calculating the phased array pattern by using w k in step 6 is as follows
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