A discrete phase phased array antenna beam synthesis method

Abstract

The present application belongs to the technical field of information science, and particularly relates to a phased array antenna beam synthesis method of discrete phase. The method considers the discrete phase scenario of digital phase shifter in engineering application, first represents the excitation phase of array element as the weighted sum of discrete phase, and determines the final phase by optimizing the weight value. The weight value is a 0-1 integer variable with constraints, and by introducing a new parameterization scheme, the problem is converted into a non-constrained continuous variable programming problem. The continuous variable programming problem can be efficiently solved by gradient algorithm. In order to obtain discrete phase values, design variable projection is introduced and a penalty function about design variable is constructed. The present application converts the phased array antenna beam synthesis problem of discrete phase into a non-constrained continuous problem by constructing a reasonable parameterization model, and solves the problem by using gradient algorithm, so that excellent beams can be synthesized even in the case of small number of digital phase shifter bits.

Description

Technical Field

[0001] This invention belongs to the field of information science and technology, and in particular relates to a method for beamforming of discrete-phase phased array antennas. Background Technology

[0002] Phased array antennas have wide applications in communications, military, and other fields. Phased array antennas use phase shifters to control the phase of array elements to achieve beamforming; therefore, the phase shifting accuracy of the phase shifter has a significant impact on the beam radiation performance of the phased array antenna. Ideally, continuous phase shifters are used in phased array beamforming to achieve continuous phase adjustment. However, continuous phase shifters are large and heavy, and are not conducive to computer control. Compared to continuous phase shifters, digital phase shifters have advantages such as simple structure, fast phase shifting speed, and ease of computer control, and have been widely used in practical engineering applications. Digital phase shifters cannot perform continuous phase shifting; their phase shift value can only take a certain minimum phase value Δ (Δ = 2π / 2). p , where p is an integer multiple of the number of bits in the digital phase shifter, i.e., a series of discrete phase values.

[0003] Beamforming in a phased array antenna with discrete phase is a difficult integer programming problem. The main difficulties lie in: 1) For a given number of array elements and phase shifter bit depth (even with array elements, the phase shifter bit depth is relatively small; a p-bit digital phase shifter can only produce 2...), the beamforming of a phased array antenna with discrete phase is a challenging problem. p The problem has two main characteristics: 1) The number of feasible phase combinations is too large, resulting in a large solution space; 2) This problem is a highly non-convex nonlinear problem. To avoid the complexity of discrete phase combinations, existing phase array antenna beamforming methods that consider discrete phases do not directly solve this integer programming problem. Instead, they directly use continuous phases for beamforming design and then normalize the designed continuous phase values ​​to the actual discrete phases. Since the actual discrete phases are not considered in the design process, this phase quantization method will introduce quantization errors, causing the main beam of the phase array antenna to deviate from the ideal direction, reducing the beam pointing accuracy. At the same time, the quantization error also leads to an increase in the sidelobe level, further degrading the performance of the phase array antenna. In addition, some intelligent algorithms have also been used to solve the discrete phase phase array beamforming problem. Intelligent algorithms have slow convergence speed and poor optimization ability when solving such highly non-convex nonlinear problems. Moreover, as the array size increases, intelligent algorithms are almost unable to solve the problem effectively. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for beamforming discrete-phase phased array antennas. This method considers the discrete-phase scenario of digital phase shifters in engineering applications. First, the excitation phase of the array elements is represented as a weighted sum of discrete phases, and the final phase is determined by optimizing the weights. These weights are constrained 0-1 integer variables. By introducing a new parameterization scheme, this problem is transformed into an unconstrained continuous variable programming problem. This continuous variable programming problem can be solved efficiently using a gradient algorithm. To obtain discrete phase values, a design variable projection is introduced, and a penalty function with respect to the design variables is constructed. This invention, by constructing a reasonable parameterization model, transforms the discrete-phase phased array antenna beamforming problem into an unconstrained continuous problem, which is then solved using a gradient algorithm. Even with a small number of bits in the digital phase shifter, it can synthesize high-performance beams, making the discrete-phase phased array beamforming problem solvable efficiently and effectively.

[0005] The technical solution of the present invention is as follows:

[0006] A method for beamforming a discrete-phase phased array antenna includes the following steps:

[0007] Step 1: Based on the radiation performance of the phased array antenna to be designed, establish the following optimization model:

[0008]

[0009] Where w represents the selection relationship between the phased array antenna elements and the discrete phase values; Ψ represents the objective function for the radiation performance of the synthesized phased array antenna; and AF represents the radiation direction factor of the phased array antenna.

[0010]

[0011]

[0012] Where N is the total number of elements in the phased array, and Q is the number of discrete phases that the digital phase shifter can provide; ψ n Let ψ be the excitation phase of the nth element. q The discrete phase value that a digital phase shifter can provide; w qn (n = 1, ..., N; q = 1, ..., Q) are binary choice variables, w qn =1 indicates that the excitation phase of the nth element is the qth discrete phase value, w qn =0 indicates that the excitation phase of the nth element is not the qth discrete phase value; x n y n , z n θ represents the position of the array element center in the phased array in the spatial rectangular coordinate system; (θ,φ) represents the elevation and azimuth angles in the spherical coordinate system, j is the imaginary unit, and k is the wave number;

[0013] Step 2: Since any array element is excited by at most one discrete phase value, for any array element, an auxiliary function is introduced to ensure that the binary selection variables satisfy the constraints.

[0014] The auxiliary function is:

[0015]

[0016]

[0017] Q w =ceil(log2Q) (6)

[0018] Where, χ sn (s=1,…,Q w ; n = 1, ..., N) are new design variables; ξ qsn (q = 1, ..., Q; s = 1, ..., Q) w ; n = 1, ..., N) is the variable χ sn The coefficient; ceil is the floor function;

[0019] Step 3: The design variable χ in step 2 sn The value of χ is either -1 or 1, making the design variable's value continuous. sn ∈[-1,1];

[0020] Step 4: In step 3, χ sn When taking intermediate values ​​other than {-1, 1}, the designed phase will deviate from the actual discrete phase value. During the optimization process, the χ... sn Perform projection processing; the projection function is:

[0021]

[0022] in, χ represents the projected design variables, where β is the sloping factor controlling the steepness of the projection function; sn After projection, there is no guarantee. If the objective function Ψ takes all values ​​of {-1, 1}, add a penalty term to make it so that... During the optimization design process, it gradually tends towards {-1, 1}; the penalty term function is:

[0023]

[0024] Step 5: Substitute the penalty term function from Step 4 into the optimization model established in Step 1, define the objective function Ψ as minimization, and set the constraint that the design variables satisfy the upper and lower limits. The final optimization model is as follows:

[0025]

[0026] Where p is the penalty factor;

[0027] Step 6: Calculate the objective function Ψ in the final optimization model with respect to the design variable χ. sn The first derivative is used to update the design variables using the gradient algorithm, and then the feed phase of the array element is calculated based on the variable results obtained from the optimization model in step 5. The feed phase is rounded to the discrete phase value that the digital phase shifter can provide.

[0028] Furthermore, in step 5, the established optimization model employs a two-layer optimization process: the inner layer optimizes χ, and the outer layer updates the penalty factor and steepness factor. The penalty factor p starts from 0 and increments, with the increment strategy being p... i+1 =p i +0.2, the steepness factor β increases from 0, and the increasing strategy is β = 2. i (i = 1, ..., m), where i is the number of iterations in the outer optimization and m is the maximum number of iterations in the outer optimization, typically taken as 10.

[0029] Compared with the prior art, the present invention has achieved the following beneficial effects:

[0030] (1) The phased array antenna beamforming method of the present invention has the same design result as the discrete phase value available to the digital phase shifter, and there is no quantization error.

[0031] (2) The method of the present invention uses a gradient algorithm to solve the beamforming problem, and can synthesize high-performance beams even when the number of bits of the digital phase shifter is small. Attached Figure Description

[0032] Figure 1 This is a schematic diagram illustrating the selection relationship between the binary selection variable control array elements and the discrete phase values ​​in this invention;

[0033] Figure 2 This is a schematic diagram of the projection function under different steepness factors in this invention;

[0034] Figure 3 This is a schematic diagram of the array element arrangement of the phased array to be designed in Example 1;

[0035] Figure 4 This is a schematic diagram of the feeding phase of the 32 array elements in Example 1;

[0036] Figure 5 This is the normalized radiation pattern of the linear array designed based on a continuous phase shifter and a 3-bit digital phase shifter in Example 1. Detailed Implementation

[0037] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0038] This implementation case considers the phased array antenna to be designed as a one-dimensional linear array with uniformly arranged array elements. A 3-bit digital phase shifter is selected, which can provide 8 different discrete phase values. The feed amplitude of each array element is equal, meaning the amplitude is not involved in the design. The radiation performance objective function is set to minimize the sidelobe level of the pencil beam. The elevation and azimuth angles of the main radiation direction of the pencil beam are 10° and 0°, respectively. The sidelobe regions are set as follows: azimuth range of 0°, elevation range of [-90°, 7°] ∪ [13°, 90°]. The array element arrangement of the one-dimensional linear array to be designed is shown in [reference needed]. Figure 3 As shown.

[0039] Step 1: Determine the phased array antenna structure to be designed, with 32 array elements, see... Figure 3 As shown. A 3-phase shifter is used, which can provide 8 different discrete phase values. A binary selection variable w is defined. qn ∈{0,1} to control the selection relationship between array elements and discrete phase (e.g. Figure 1 (As shown). At this point, the formula for calculating the radiation directivity of the phased array antenna is:

[0040]

[0041] Among them, the binary variable w qn (n = 1, ..., 32; q = 1, ..., 8), the discrete phase provided by the digital phase shifter is ψ. q x n ,y n This represents the position of the array element in the phased array in a spatial rectangular coordinate system;

[0042] Step 2: Since any array element is excited by at most one discrete phase feed, there must be constraints. This constraint is difficult to strictly satisfy during the optimization process. Therefore, an auxiliary function is introduced, which holds for each array element:

[0043]

[0044] w qn Represented as the new variable χ sn The constraints described in this step can be automatically and strictly satisfied for the function. At this point, χ... sn (s = 1, ..., 3; n = 1, ..., 32) are the new design variables;

[0045] Step 3: In step 2, the new design variable χ only applies if... snOnly when χ takes a value of -1 or 1 can the final result be guaranteed to be a discrete phase value. Since discrete variables are difficult to handle during optimization, their values ​​are made continuous. In this case, χ... sn ∈[-1,1], the optimization design can proceed smoothly;

[0046] Step 4: In step 3, χ sn When taking intermediate values ​​other than {-1, 1}, the designed phase will deviate from the actual discrete phase value. To force χ... s Differentiating towards {-1,1} ensures the final design result is a discrete phase value; during the optimization process, χ... sn Perform projection processing. The projection function is:

[0047]

[0048] Projection functions under different steepness factors, such as Figure 2 As shown. For the projected design variables, the excitation phase of the array elements is determined by the projected... Calculated. χ sn Projection does not guarantee Since the condition is completely set to {-1, 1}, a penalty term is added to the objective function Ψ to make... During the optimization design process, it gradually approaches {-1, 1}. The penalty term is:

[0049]

[0050] Step 5: Substitute the penalty function from Step 4 into the optimization formula, define the objective function as minimizing the sum of the peak sidelobe level (PSLL) and the penalty term, and set the constraint that the design variables satisfy the upper and lower limits. The optimization model is established as follows:

[0051]

[0052] Where p is the penalty factor.

[0053] Step 6: Calculate the first derivative of the objective function with respect to the design variables, and update the design variables using a sequential quadratic programming algorithm. Based on the optimized design variable results, calculate the feed phase of each array element, and round and normalize the feed phase to the discrete phase value that the digital phase shifter can provide. The final normalized discrete excitation phase of the linear array is as follows: Figure 4 As shown. The radiation pattern of the linear array is as follows. Figure 5 As shown, the peak sidelobe level of the radiation beam obtained by the method of the present invention based on a 3-bit digital phase shifter is similar to that of the radiation beam based on a continuous phase shifter.

Claims

1. A method for beamforming a discrete-phase phased array antenna, characterized in that, Includes the following steps: Step 1: Based on the radiation performance of the phased array antenna to be designed, establish the following optimization model: Where w represents the selection relationship between the phased array antenna elements and the discrete phase values; Ψ represents the objective function for the radiation performance of the synthesized phased array antenna; and AF represents the radiation direction factor of the phased array antenna. Where N is the total number of elements in the phased array, and Q is the number of discrete phases that the digital phase shifter can provide; ψ n Let ψ be the excitation phase of the nth element. q The discrete phase value that a digital phase shifter can provide; w qn Let n = 1, ..., N, q = 1, ..., Q, w be binary choice variables. qn =1 indicates that the excitation phase of the nth element is the qth discrete phase value, w qn =0 indicates that the excitation phase of the nth element is not the qth discrete phase value; x n y n , z n θ represents the position of the array element center in the phased array in the spatial rectangular coordinate system; (θ,φ) represents the elevation and azimuth angles in the spherical coordinate system, j is the imaginary unit, and k is the wave number; Step 2: Since any array element is excited by at most one discrete phase value, for any array element, an auxiliary function is introduced to ensure that the binary selection variables satisfy the constraints. The auxiliary function is: Where χ sn ∈{-1,1} (3) Q w =ceil(log2Q) (5) Where, χ sn s=1,…,Q w ξ, n = 1, ..., N, are new design variables; qsn q = 1, ..., Q; s = 1, ..., Q w n = 1, ..., N, where χ is the variable. sn The coefficient; ceil is the floor function; Step 3: The design variable χ in step 2 sn The value of χ is either -1 or 1, making the design variable's value continuous. sn ∈[-1,1]; Step 4: In step 3, χ sn When taking intermediate values ​​other than {-1, 1}, the designed phase will deviate from the actual discrete phase value. During the optimization process, the χ... sn Perform projection processing; the projection function is: in, χ represents the projected design variables, where β is the sloping factor controlling the steepness of the projection function; sn After projection, there is no guarantee. If the objective function Ψ takes all values ​​of {-1, 1}, add a penalty term to make it so that... During the optimization design process, it gradually tends towards {-1, 1}; the penalty term function is: Step 5: Substitute the penalty term function from Step 4 into the optimization model established in Step 1, define the objective function Ψ as minimization, and set the constraint that the design variables satisfy the upper and lower limits. The final optimization model is as follows: Where p is the penalty factor; Step 6: Calculate the objective function Ψ in the final optimization model with respect to the design variable χ. s The first derivative is used to update the design variables using the gradient algorithm, and then the feed phase of the array element is calculated based on the variable results obtained from the optimization model in step 5. The feed phase is rounded to the discrete phase value that the digital phase shifter can provide.

2. The method for beamforming a discrete-phase phased array antenna according to claim 1, characterized in that, In step 5, the established optimization model is a two-layer optimization during the optimization process: the inner layer optimizes χ, and the outer layer updates the penalty factor and steepness factor; the penalty factor p increases from 0, and the increasing strategy is p i+1 =p i +0.2, the steepness factor β increases from 0, and the increasing strategy is β = 2. i , i = 1, ..., m, where i is the number of iterations in the outer optimization and m is the maximum number of iterations in the outer optimization.

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