A beam scanning sparse array antenna synthesis method based on low-bit phase quantization

Abstract

The application belongs to the technical field of communication, and particularly relates to a kind of beam scanning sparse array antenna synthesis methods based on low bit phase quantization, comprising: using iterative Fourier algorithm to solve the initial array element position distribution of sparse array, ensure that array has good beam scanning basic performance under ideal phase control;For the quantization error introduced by low resolution phase control, the difference between the ideal phase and the quantized phase of each array element in the beam scanning range is calculated, the array elements with larger difference are screened out, and the quantized phase of these error larger array elements is optimized through genetic algorithm to minimize the influence of phase quantization error on beam performance, to realize beam scanning under low resolution phase constraint. The application realizes the collaborative optimization of low resolution phase constraint, array sparsity constraint and wide-angle beam scanning performance, reduces the hardware cost, volume and power consumption of phased array system, and guarantees the excellent radiation performance in the beam scanning range.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to a method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization. Background Technology

[0002] Sparse arrays, by reducing the number of array elements, can effectively reduce the hardware cost, size, and power consumption of phased array radar, communication base stations, and other systems, and have broad application prospects in modern electronic systems. Beam scanning is the core function of a phased array system. By applying specific phase weighting to each array element, directional coverage and flexible scanning of the beam in space can be achieved. However, in practical engineering, the phase resolution of phase control devices such as digital phase shifters is discrete, making continuous phase weighting impossible. At the same time, using low-resolution phase control introduces phase quantization errors, leading to beam main lobe broadening, peak level reduction, gain loss, sidelobe level increase, and reduced pointing accuracy. In severe cases, it can even induce grating lobes, significantly weakening the system's anti-interference capability.

[0003] Due to the lack of array elements, sparse arrays exhibit significantly increased beam control complexity and are far more sensitive to phase quantization errors than full arrays. The performance degradation caused by low-resolution phase control is further amplified in sparse arrays. In existing technologies, sparse array synthesis and low-resolution phase optimization are mostly designed independently, failing to achieve synergistic optimization of array sparse layout, low-resolution phase control, and beam scanning performance. High-performance solutions suffer from issues such as the need for unequal amplitude feeding and high hardware implementation difficulty. Low-cost solutions, on the other hand, struggle to achieve low sidelobes and high pointing accuracy within the beam scanning range under low-resolution phase constraints and high sparsity, failing to balance engineering feasibility, hardware cost, and array radiation performance. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization, comprising:

[0005] S1: Based on the iterative Fourier algorithm, with the preset sidelobe level and array sparsity as the target, the initial array element position distribution of the sparse array is determined by iterative solution of the radiation pattern and array excitation, and the initial sparse array construction is completed.

[0006] S2: Set the beam scanning pointing angle set, combine it with low bit phase resolution, calculate the ideal phase and quantized phase of each element in the initial sparse array at each pointing angle, obtain the corresponding phase difference, and convert the phase difference into a percentage of the phase resolution.

[0007] S3: Set a percentage threshold to filter out key array elements whose phase difference percentage exceeds the threshold. With the goal of minimizing the maximum sidelobe level within the beam scanning range, use a genetic algorithm to optimize the quantization phase of the key array elements.

[0008] S4: Calculate the error variance between the excitation phase of each pointing angle and the ideal phase after optimization, remove individual array elements one by one, recalculate the error variance and compare the difference, and turn off the array element with the smallest variance difference to adjust the array layout.

[0009] S5: Iterate through steps S1 to S4 until the preset sidelobe level constraint or the maximum number of iterations is met, and output the optimal sparse array layout and the excitation phase corresponding to each scanning angle.

[0010] The beneficial effects of this invention are:

[0011] This invention achieves synergistic optimization of low-resolution phase constraints, array sparsity constraints, and wide-angle beam scanning performance, while reducing the hardware cost, size, and power consumption of the phased array system and ensuring excellent radiation performance within the beam scanning range.

[0012] This invention significantly improves the beam performance of sparse arrays under low-resolution phase control, effectively suppressing performance degradation caused by phase quantization errors. In a 100-element linear array scenario with 2-bit low-resolution phase control and 25% sparsity, the maximum sidelobe level can be suppressed to below -15.87dB. This invention achieves synergistic optimization of array sparsity, low-resolution phase constraints, and wide-angle beam scanning performance. While reducing system hardware costs with high sparsity, it can stably maintain excellent beam characteristics. Attached Figure Description

[0013] Figure 1 This is a flowchart of a beam scanning sparse array antenna synthesis method based on low-bit phase quantization according to the present invention.

[0014] Figure 2 This is a schematic diagram of the iterative Fourier algorithm of the present invention;

[0015] Figure 3 The element distribution diagram of the present invention with a sparsity of 0.5 and a 2-bit phase is shown.

[0016] Figure 4 The present invention employs a 2-bit phase scanning pattern with a sparsity of 0.5.

[0017] Figure 5 The element distribution diagram of the present invention with a sparsity of 0.25 using 2-bit phase is shown.

[0018] Figure 6 The present invention employs a 2-bit phase scanning pattern with a sparsity of 0.25. Detailed Implementation

[0019] 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.

[0020] A method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization includes:

[0021] S1: Based on the iterative Fourier algorithm, with the preset sidelobe level and array sparsity as the target, the initial array element position distribution of the sparse array is determined by iterative solution of the radiation pattern and array excitation, and the initial sparse array construction is completed.

[0022] S2: Set the beam scanning pointing angle set, combine it with low bit phase resolution, calculate the ideal phase and quantized phase of each element in the initial sparse array at each pointing angle, obtain the corresponding phase difference, and convert the phase difference into a percentage of the phase resolution.

[0023] S3: Set a percentage threshold to filter out key array elements whose phase difference percentage exceeds the threshold. With the goal of minimizing the maximum sidelobe level within the beam scanning range, use a genetic algorithm to optimize the quantization phase of the key array elements.

[0024] S4: Calculate the error variance between the excitation phase of each pointing angle and the ideal phase after optimization, remove individual array elements one by one, recalculate the error variance and compare the difference, and turn off the array element with the smallest variance difference to adjust the array layout.

[0025] S5: Iterate through steps S1 to S4 until the preset sidelobe level constraint or the maximum number of iterations is met, and output the optimal sparse array layout and the excitation phase corresponding to each scanning angle.

[0026] like Figure 1This is a flowchart of the method. It reveals that the core of this method is to use a three-stage iteration to ensure that the peak sidelobe level of the array factor meets preset constraints, while simultaneously satisfying the requirements for sparsity, phase control bit depth, and different main lobe pointing. First, the excitation array ω is randomly initialized, updated via IFFT, and truncated to determine the active array elements. Then, theoretical and actual phase shift values ​​are calculated based on formulas, and the phase region is divided and adjusted according to a threshold. Finally, a genetic algorithm is used to optimize the phase population through crossover and mutation, selecting the optimal individuals. This process is repeated for each target main lobe pointing, and the sparse array layout is adjusted based on the phase error variance. The entire process terminates when PSLL is met and the maximum number of iterations is reached, ultimately outputting a sparse array layout and phase values ​​that satisfy the constraints. The specific design idea consists of three steps:

[0027] First, the initial sparse array is constructed based on the iterative Fourier method. With the preset sidelobe level and sparsity as the target, the array element positions of the sparse array are determined by iteratively solving the radiation pattern and excitation, thus completing the initial array design and providing the array foundation for subsequent phase optimization.

[0028] Secondly, quantization phase optimization is performed by determining multiple pointing angles, calculating the ideal phase of each element in the initial array at these pointing angles, and obtaining the quantized phase of each element by combining it with the given phase resolution and calculating the phase difference.

[0029] Finally, array elements with phase differences exceeding a set threshold are selected as optimization targets. With minimizing the maximum sidelobe level within the beam scanning range as the core objective, a genetic algorithm is used to optimize the quantized phase of the selected array elements and calculate the variance of the optimized phase error. For array elements with large variances, their excitation states are reconsidered.

[0030] 1. Iterative Fourier Algorithm:

[0031] First, let's introduce the Discrete Fourier Transform (DFT), a mathematical tool for converting time-domain signals into frequency-domain signals. By performing a Fourier transform on a discrete-time signal, we obtain discrete sampled values ​​in the frequency domain. Let x[n] be a finite-length sequence of length M. Let n be the k-th frequency component and n be the number of time-domain sampling points. Then its M-point discrete Fourier transform is defined as:

[0032] (1)

[0033] Its inverse transform can be expressed as:

[0034] (2)

[0035] Combine the above equation with equation (3) for the matrix factor AF( Comparative analysis:

[0036] (3)

[0037] in, For the activation of the array element, is the element spacing, and k is the wave number;

[0038] In the formula Change to And order:

[0039] (4)

[0040] therefore:

[0041] (5)

[0042] It can be observed that there is a clear Fourier transform correspondence between the array factors and the array excitation. Based on this correlation, performing an inverse Fourier transform on the array excitation can directly yield the corresponding array factors. Thanks to the invertible property of the Fourier transform, the corresponding array excitation can be deduced from the known array factors through Fourier transform processing.

[0043] Taking a sparse linear array as an example: Consider a uniform linear array with N elements, an element spacing of d, and a sparsity ratio of f, where f is defined as the ratio of the number of inactive elements to the total number of elements in the array:

[0044] (6)

[0045] in This represents the number of activated elements in the array. The iterative recursive relationship between the array factor and the array excitation can be obtained from the Fourier relation:

[0046] (7)

[0047] in, This represents the array excitation in the t-th iteration. This function represents the adjustment of the array factor pattern corresponding to the current excitation. It uses the set maximum sidelobe level (PSLL) as a reference. Based on whether the normalized sidelobe size exceeds the set maximum sidelobe level (PSL), values ​​are assigned to the excess sidelobe portion, while keeping other parts unchanged. The corresponding formula is as follows:

[0048] (8)

[0049] Generally speaking, adjusting the portion exceeding the set maximum sidelobe level threshold to below the required level can more effectively obtain the desired solution, therefore T is a positive constant. This represents the function that adjusts the excitation corresponding to the adjusted array factor pattern. Since the K-point Fourier transform yields complex excitation weights for K excitations, truncation is necessary to meet the requirements for array size and sparsity. This is achieved by sorting the excitations according to their amplitudes and selecting... A stimulus with a larger amplitude is set to a value of 1, indicating that it is activated, while other stimulus values ​​are set to 0, indicating that they are deactivated. The corresponding formulas are as follows:

[0050] (9)

[0051] in, The order of incentives One incentive, It is the excitation of the m-th array element.

[0052] Figure 2 A schematic diagram of the algorithm is shown, where double arrows represent the main lobe region, single arrows represent the side lobe region, and the two dashed lines represent the set side lobe level and the set value after exceeding the set side lobe level, respectively. As can be seen from the above, the iterative Fourier algorithm is the process of finding the intersection of two subsets: the excitation satisfying the array element amplitude constraints and the preset radiation pattern target.

[0053] 2. Phase difference calculation and array element selection:

[0054] Suppose there exists a b-bit digital phase shifter that has Each discrete phase, the quantization process is as follows:

[0055] (10)

[0056] in, q To quantize the phase, ideal For ideal phase, This refers to the phase resolution.

[0057] Determine the beam scanning pointing angle set Calculate the ideal phase of each element in the initial array at various angles:

[0058] (11)

[0059] The quantization phase corresponding to each angle is calculated using equation (4-9). q Then calculate the m-th array element in Phase difference at angle:

[0060] (12)

[0061] The ideal phase of the m-th element is calculated as a percentage of the phase resolution based on the phase difference value:

[0062] (13)

[0063] To filter out array elements that have a significant impact on beam performance, a percentage threshold G is set. If a certain array element at a certain angle... p If the threshold is exceeded, the array element is identified as a key array element. If the threshold is not exceeded, its phase is maintained as the quantized phase. Subsequent optimizations are only performed on key array elements, which can ensure a certain beam pointing while reducing computational complexity.

[0064] 3. Overall Algorithm Flow:

[0065] (1) Randomly initialize the array factor excitation array ω with a value of 0 or 1, and perform K-point fast Fourier inverse transform on ω to obtain the array factor AF.

[0066] (2) Calculate the ideal phase shift value corresponding to each array element according to formula (11). .

[0067] (3) Based on the number of phase control bits B, the quantization phase shift value corresponding to the B-bit phase control is calculated using the rounding method and equation (10). q .

[0068] (4) Calculate the quantization according to formula (11) and percentage difference p .

[0069] (5) Apply a maximum value constraint on the peak sidelobe level to the array factor AF, and perform a fast Fourier transform on the array factor AF after applying the constraint to complete the update of the excitation ω.

[0070] (6) Truncate ω according to the array size M, select active array elements according to the sparsity f, set the M×f elements with smaller values ​​to 0, and set the others to 1.

[0071] (7) Compare the positions of the array elements in the two iterations. If there is a difference, repeat steps 2 to 3. If the positions are completely consistent, repeat steps 1 to 3 until the peak sidelobe level meets the preset sidelobe constraint condition or the maximum number of iterations is reached.

[0072] (8) Extracting sparse arrays Corresponding percentage form p .

[0073] (9) Set the difference percentage threshold G, and combine the threshold G with p The excitation phase of the array element is divided into two parts: p For the portion smaller than the threshold G, retain the phase calculated in step 6. p For the portion exceeding the threshold G, its phase is redistributed.

[0074] (10) Initialize the initial population pop based on the phase control state. The total number of phase control states is 2^B, and the state values ​​are integers from 1 to 2^B.

[0075] (11) Sort the initial population pop according to the sidelobe level to complete the population update.

[0076] (12) Perform a two-point crossover operation on the initial population pop to obtain a new population newpop.

[0077] (13) Perform multipoint mutation operation on the new population newpop to complete the update of the new population.

[0078] (14) Merge the initial population pop and the new population newpop, sort them according to the sidelobe level, and select individuals with smaller sidelobe levels to form a new population pop.

[0079] (15) Repeat steps (11) to (14) until the peak sidelobe level meets the specified sidelobe level requirement or the maximum number of iterations is reached. Merge the optimized phase with the retained quantized phase value.

[0080] (16) For each required main lobe maximum direction Execute steps (10) to (15) to obtain the excitation phase corresponding to each direction. .

[0081] (17) First, calculate the excitation phase corresponding to each pointing angle of the array. With ideal phase variance of phase error Then, the variance of the excitation phase error for each direction is calculated one by one after removing the m-th array element. And solve them separately. and The difference is calculated. Select the array element corresponding to the smallest difference and turn it off. Repeat the iterative process of steps (5) to (17) above until the number of iterations reaches the preset maximum value. Finally, from all the iteration results, select the set of excitation phases with the lowest sidelobe level as the optimal result.

[0082] Example 1: A 100-element linear array with a sparsity of 50% and a 2-bit phase control element spacing of 0.5λ.

[0083] Array element distribution as follows Figure 3 As shown, the horizontal axis represents the distribution location of the array elements, ranging from 0 to 100, and the vertical axis represents whether the array element is on or off. A value of 1 indicates that the array element is on, and a value of 0 indicates that the array element is off.

[0084] like Figure 4 The proposed method can effectively control the sidelobe level at all scanning angles, with the maximum sidelobe level below -14.12 dB, the average 3-dB main lobe width stable at around 2.9°, and the main lobe pointing accuracy deviation less than 0.11°, demonstrating the performance advantages of the proposed method.

[0085] Example 2: A 100-element linear array with a sparsity of 25% and an element spacing of 0.5λ using 2-bit phase control.

[0086] Using the same scanning angle as in Example 1 Figure 5 The element distribution of the sparse array is shown. Figure 6 The normalized beam patterns of the proposed method at all scanning angles are shown. The figures demonstrate that the method effectively controls the sidelobe level, suppressing the maximum sidelobe level below -15.87 dB, maintaining the average 3-dB main lobe width stably at around 1.585°, and achieving a main lobe pointing accuracy deviation of no more than 0.1°. To evaluate the beam performance of the proposed method in this array structure, Figure 4-6 The method proposed in this section is presented using ideal phase, quantized phase, and a phase resolution of 2-bit, with beam pointing... , , , , , , Beamform at that time.

[0087] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization, characterized in that, include: S1: Based on the iterative Fourier algorithm, with the preset sidelobe level and array sparsity as the target, the initial array element position distribution of the sparse array is determined by iterative solution of the radiation pattern and array excitation, and the initial sparse array construction is completed. S2: Set the beam scanning pointing angle set, combine it with low bit phase resolution, calculate the ideal phase and quantized phase of each element in the initial sparse array at each pointing angle, obtain the corresponding phase difference, and convert the phase difference into a percentage of the phase resolution. S3: Set a percentage threshold to filter out key array elements whose phase difference percentage exceeds the threshold. With the goal of minimizing the maximum sidelobe level within the beam scanning range, use a genetic algorithm to optimize the quantization phase of the key array elements. S4: Calculate the error variance between the excitation phase of each pointing angle and the ideal phase after optimization, remove individual array elements one by one, recalculate the error variance and compare the difference, and turn off the array element with the smallest variance difference to adjust the array layout. S5: Iterate through steps S1 to S4 until the preset sidelobe level constraint or the maximum number of iterations is met, and output the optimal sparse array layout and the excitation phase corresponding to each scanning angle.

2. The method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization according to claim 1, characterized in that, The iterative Fourier algorithm is specifically as follows: S11: Randomly initialize the array excitation array with values ​​of 0 or 1, and perform an inverse fast Fourier transform on it to obtain the array factor; S12: Apply a preset maximum sidelobe level constraint to the array factor, and adjust the portion of the sidelobe region that exceeds the threshold. Perform a Fast Fourier Transform on the adjusted array factor to update the array excitation; S13: Truncate and sort the excitations according to array size and sparsity, select the excitations with larger amplitudes as active array elements, and set the rest as closed array elements; S14: Iterate through the above operations until the array element positions are stable or the sidelobe levels meet the preset requirements.

3. The method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization according to claim 1, characterized in that, The formula for calculating the ideal phase is: in, Let d be the ideal phase, λ be the element spacing, λ be the operating wavelength, and θ be the operating wavelength. p This refers to the beam pointing angle.

4. The method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization according to claim 1, characterized in that, The formula for calculating the quantization phase is: in, q To quantize the phase, For phase resolution, This is the ideal phase.

5. The method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization according to claim 1, characterized in that, The formula for calculating the phase difference is: in, For the m-th array element in Phase difference at angle, For the m-th array element in Ideal phase at an angle, For the m-th array element in Quantization phase at an angle.

6. The method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization according to claim 1, characterized in that, Converting the phase difference to a percentage of the phase resolution includes: in, p Phase difference value Percentage of phase resolution This refers to the phase resolution.

7. The method for synthesizing beam-scanning sparse array antennas based on low-bit phase quantization according to claim 1, characterized in that, The genetic algorithm optimization includes: initializing the phase-controlled state population, performing two-point crossover and multi-point mutation operations on the population, and sorting by sidelobe level to select the optimal individual.

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