A fitness function construction method for array antenna beamforming

Abstract

A kind of array antenna beamforming fitness function construction method, the scale of measuring antenna array unit, set the optimization variable of antenna array unit, control the amplitude and phase of each array unit, to control the direction of radar beam, by the angle of antenna beam and its corresponding amplitude value, construct antenna far field pattern function, sketch the desired antenna pattern, with target curve function representation, with fitness function describe the relationship between antenna far field pattern function and target curve function, set the threshold of fitness function value, iteratively optimize the amplitude and phase of array unit, if the antenna far field pattern generated by optimization does not satisfy performance index, continue iteration.

Description

Technical Field

[0001] This invention belongs to the field of antenna beamforming technology, specifically relating to a fitness function construction technique. Background Technology

[0002] In the fields of communications and radar, phased array antennas are a widely used type of antenna. Compared to two-dimensional phase-scanned antennas, one-dimensional phase-scanned array antennas only scan beams in the elevation plane. One-dimensional phase-scanned radars receive multiple beams in the elevation plane, while the azimuth beam is mechanically scanned by the antenna turntable.

[0003] To ensure sufficient airspace search frequency, the azimuth mechanical rotation speed is relatively fast, and it can only maintain a certain continuous rotation speed, meaning the beam cannot be flexibly pointed in any direction. The beam dwell time in a certain azimuth is short, and during the dwell time, the transmitted beam needs to cover the entire search airspace in the elevation plane. If time is spent scanning the elevation plane beam, there will not be enough time for pulse accumulation during reception, affecting detection capability. Generally, radar needs to perform cosecant square beamforming in the elevation direction to efficiently cover the detection airspace, covering both the elevation plane airspace and not wasting transmitted energy.

[0004] Because the output power of the transmitting component cannot be arbitrary, transmit beamforming generally only uses phase shaping. Since the feed phase of the array cannot be solved from the equations, an optimization algorithm is needed to obtain the most ideal phase distribution of the transmit channel.

[0005] Common optimization methods such as genetic algorithms, simulated annealing, particle swarm optimization, and differential evolution can optimize the output electromagnetic wave phase of each transmission channel. Regardless of the algorithm used, a fitness function needs to be constructed. The appropriateness of the fitness function directly determines the quality of the optimization results. Summary of the Invention

[0006] To address the technical problems of insufficient flexibility of fitness functions, excessive optimization resources, and unsatisfactory results in existing technologies, this invention proposes a fitness function construction method for array antenna beamforming. This method employs a technical solution that constructs an optimal objective function to make the process radiation pattern infinitely close to the desired beamforming. This results in reduced iteration steps in the optimization algorithm, smoother curve ripples, higher detection stability, closer approximation to the target curve, better adaptability, applicability to both genetic algorithms and particle swarm optimization, and effectiveness for both beam broadening and beam nulling function curves.

[0007] Step 1: Measure the size of the antenna array elements.

[0008] Step two: Set the optimization variables for the antenna array elements, controlling the amplitude and phase of each array element to control the direction of the radar beam.

[0009] Step 3: Construct the antenna far-field radiation pattern function based on the angle of the antenna beam and its corresponding amplitude value.

[0010] Step four: Draw the desired antenna pattern and represent it using a target curve function.

[0011] Step 5: Use a fitness function to describe the relationship between the antenna far-field radiation pattern function and the target curve function.

[0012] Step 6: Set the threshold of the fitness function and iteratively optimize the amplitude and phase of the array cells.

[0013] Step 7: If the optimized antenna far-field pattern does not meet the performance requirements, continue the iteration.

[0014] Step one includes: measuring the number N, spacing dx, and frequency f of the antenna array elements. Without shaping, the beamwidth and shape of the array antenna are directly related to the electrical aperture of the array antenna, i.e., the maximum size of the antenna. Let M be the number of wavelengths corresponding to the maximum size of the antenna, then M = N*dx / (c / f), where c is the speed of light. The beamwidth of a uniform weighted array antenna is approximately 48° / M.

[0015] The shaping region is the desired antenna beam coverage space, which is independent of the antenna size. Generally, 0 to 40° above the ground plane is selected as the shaping region. The larger the antenna size, the narrower the beam and the more sidelobes, and the greater the shaping difficulty. For example, the beamwidth of a 16-wavelength array antenna is 3°, while the shaping region width can reach 40°. Therefore, shaping requires mastering the size of the antenna array elements.

[0016] Step two includes: given a fixed antenna size, let the optimization variable for the nth array element be a complex weight. Where a n , For complex weight A n The two parameters, because the excitation voltage of each array element cannot be changed, are used during emitter shaping. n It is a set of fixed values.

[0017] The array elements of a phased array radar antenna are arranged according to certain rules. Let the signal voltages of the antenna array elements be coherently superimposed at the beam pointing angle θ. Where AF is the far-field pattern function of an array of M antenna elements, and its formula is similar to that of the Discrete Fourier Transform. m θ m The feed amplitude and phase of the m-th array element are respectively, x m Let θ be the position of the m-th array element, λ be the operating wavelength, and different θ correspond to different AF values. The absolute value of the AF obtained by cosecant square shaping is a smooth monotonic function 1 / sin(θ) in the region [θ1, θ2].2 Ideally, AF should be infinitely close to the cosecant square function in the key regions and as small as possible in the non-key regions.

[0018] Step three includes: placing A n The antenna far-field radiation pattern function is obtained by performing an FFT transform on N discrete-time signals. Where θ k Let θ be the angle of the antenna beam, used as the horizontal axis. k =asin(k*c / (N*f*dx)),k=1,2,3...,N,F(θ k The amplitude value corresponding to the beam angle is used as the vertical axis.

[0019] The radiation pattern is composed of the number of elements N, spacing dx, frequency f, and optimization variable A. n The decision was made that the antenna size was determined during the design phase and cannot be changed; only optimization of A is possible. n optimization and The initial value can be any value within the range of 0 to 360°, determined by... The initial values ​​can be used to obtain the initial radiation pattern of the array antenna.

[0020] Step four includes: using the target curve function Y(θ) k The desired antenna pattern is described, including key and non-key regions. Key regions are covered by the antenna's far-field pattern and are areas where the curve shape is important, such as straight lines or cosecant square curves. Non-key regions are areas with limited amplitude and no requirements on curve shape. Let the interval of the key region of interest be [θ]. m1 ,θ m2 ], where θ m1 Let θ be the starting angle. m2 The termination angle.

[0021] Step five includes: F(θ) k ) and Y(θ k Subtracting the two values ​​yields the sample distribution Δ(θ) of the difference. k )=F(θ k )-Y(θ k ), using the formula Calculate Δ(θ) k The root mean square δ of θ, as the fitness function, is not only θ k The interval function, also known as Y(θ) k ) and F(θ) k The conditional expression.

[0022] Step six includes: setting the threshold for δ and adjusting A. n or If δ is less than the threshold, the optimization ends; otherwise, the iteration continues. Because the antenna pattern is a nonlinear function of multiple variables, the optimized pattern is not completely consistent with the target curve. δ cannot be zero, and the threshold cannot be set to zero, otherwise convergence will not be possible. The threshold cannot be too high or too low. The initial value of the threshold is set relatively large, which is 1 / 10 of the wavelength number M of the largest size of the array antenna. As the optimization progresses, the threshold is gradually lowered. For example, for an array antenna with a size of 16 wavelengths, the initial threshold can be set to 1.5.

[0023] Step seven includes: from the final A n or Generate the antenna far-field radiation pattern. If the performance indicators of the radiation pattern, such as the null penetration depth, number, curve envelope, and sidelobe size in key areas and non-key areas, meet the requirements, the optimization ends; otherwise, reduce the amplitude value in non-key areas and continue iterating. Attached Figure Description

[0024] Figure 1 It is a discrete Fourier transform graph. Figure 2 It is an ideal cosecant square shape diagram. Figure 3 It is a convergence curve graph. Figure 4 Shaping results. Implementation

[0025] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0026] Beam voltage formula for coherent superposition of signals at direction θ of array elements Equivalent to a discrete Fourier transform, it has a regular discrete spectrum, such as... Figure 1 As shown.

[0027] Ideal cosecant square beam, such as Figure 2 As shown, interval 1 is the target curve region, and intervals 2 and 3 are control regions. They do not need to have a specific shape; they only need to have an amplitude less than a certain value.

[0028] The Fourier transform determines the characteristics of the AF function. It has a certain number of zeros in the entire visible space, and the shapes of different regions are mutually constrained, making it impossible to simultaneously satisfy all amplitude distribution requirements.

[0029] In the useless region, the AF function exhibits an irregular and chaotic spectrum due to phase effects. It is only necessary to limit its maximum value, without having to satisfy a certain function curve distribution. This significantly increases the optimization margin for the useful region, resulting in a significant improvement in the smoothness of the optimized shaping curve.

[0030] Step 1: Determine the number of antenna array elements as 64, the working wavelength as λ, and the element spacing as λ / 2. The beamwidth of the uniform weighted array is determined by the wavelength multiple of the array.

[0031] Step 2: Determine the cocutter square beam target curve, where the cocutter square interval is [-1.5°, 20°]. The amplitude in the left region of the cocutter is less than -15dB, and the amplitude in the right region is less than -25dB. There are no shape requirements. The cocutter square beam shaping target curve Y(θ) can be obtained from formula 1 / sin(θ). 2 Calculated.

[0032] Step 3: Construct the fitness function by performing an FFT transformation with the initial phase weights.

[0033] Step 4: Use a genetic algorithm to set the number of variables in the fitness function to 64, with fitness as the optimization objective, an initial population size of 100, and a crossover mutation rate of 0.8.

[0034] Step 5: After optimizing for 2000 iterations, if the fitness value doesn't change significantly, end the iteration. Calculate the fitness value again using the genetic algorithm. After multiple calculations, select the optimization result with the smallest fitness value. The smaller the fitness value, the closer the optimization result is to the target curve. The convergence curve is shown below. Figure 3 As shown.

[0035] Step 6: Generate a lobe diagram from the obtained phase and compare it with the target curve. If it is unacceptable, then iterate again to optimize.

[0036] Step 7: Determine the final phase weights as [-67,-61,-51,-38,-20,-4,-20,-63,-69,-65,-53,-30,-23,-40,-31,-5,-2,-173,10,-21-4,21,-4,-26,-12,-3,5,20,38,59,81,123,-1 [61,-71,-7,31,26,63,127-160,-47,79,159,223,-93,-70,-45,-111,-75,-27,26,-22,-14,24,16,38,73,115,80,119,163,202,237], a total of 64 values, consistent with the set array size.

[0037] Step 8: The optimized lobe pattern is as follows Figure 4 As shown, the amplitude ripple in the cocut interval is ±0.7dB, the sidelobe level in the left cocut region is less than -12dB, and the sidelobe level in the right cocut region is less than -17dB. The optimized beamforming is quite ideal and can be used as the actual beamforming phase weight.

[0038] The above are embodiments of the present invention and do not limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention are included within the protection scope of the present invention.

Claims

1. A method for constructing the fitness function for beamforming of an array antenna, characterized in that, include: Step 1: Measure the size of the antenna array elements, including the number of array elements N, the spacing dx, and the frequency f. Let M be the number of wavelengths corresponding to the maximum size of the antenna, then M = N * dx / (c / f), where c is the speed of light. Step 2: Set the optimization variables for the antenna array elements. Let the optimization variable for the nth array element be a complex weight. ,in For complex weights The two parameters control the amplitude and phase of each array element to control the direction of the radar beam; Step 3: Construct the antenna far-field radiation pattern function from the antenna beam angle and its corresponding amplitude value. The antenna far-field radiation pattern function is obtained by performing an FFT transform on N discrete-time signals. ,in The angle of the antenna beam is used as the horizontal axis. k=1,2,3...,N The amplitude value corresponding to the beam angle is used as the ordinate, and... The initial value is used to obtain the initial radiation pattern of the array antenna; Step 4, use the target curve function The desired antenna pattern is described, including key and non-key regions. The key region is covered by the antenna's far-field pattern, while the non-key region is a region with limited amplitude and no requirements on the curve shape. Let the interval of the key region of interest be denoted as . ,in Starting angle, The termination angle; Step 5, and Subtracting them yields the sample distribution of the difference. Using formula calculate root mean square As a fitness function, the relationship between the antenna far-field radiation pattern function and the target curve function is described by the fitness function. Step 6: Set a threshold for the fitness function value and iteratively optimize the amplitude and phase of the array cells; Step 7: If the optimized antenna far-field pattern does not meet the performance requirements, continue the iteration.

2. The method for constructing the fitness function for beamforming of an array antenna according to claim 1, characterized in that, It also includes: setting the antenna array element at the beam pointing angle coherent superposition of signal voltage Where AF is the far-field pattern function of an array of M antenna elements. , These represent the feed amplitude and phase of the m-th array element, respectively. Let m be the position of the m-th array element. For the operating wavelength, different For different AF values, the absolute value of the cosecant squared shape is in The region is a smooth monotonic function. .

3. The method for constructing the fitness function for beamforming of an array antenna according to claim 1, characterized in that, Step six includes: setting The threshold is initially set to 1 / 10 of the wavelength M of the largest antenna array, and is gradually lowered and adjusted. or If the fitness function value is less than the threshold, the optimization ends; otherwise, the iteration continues.

4. The method for constructing the fitness function for beamforming of an array antenna according to claim 1, characterized in that, Step seven includes: from the final or Generate the antenna far-field radiation pattern. If the performance indicators of the radiation pattern do not meet the requirements, reduce the amplitude value of non-critical areas and continue iterating.

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