# Investigation of Multibeam Forming Algorithm for Cylindrical Conformal Array Antenna

Authors: Ke Zhao; Lizhe Liu; Lirong Mei
Journal: International Journal of Antennas and Propagation
 (2022)

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## Abstract

A multibeam forming algorithm based on cylindrical conformal array antenna is proposed in this paper. A comprehensively optimized algorithm of Taylor weights is used to reduce sidelobes. Multiple beams pointed at different azimuth angles are formed based on a reconfigurable overlapping array division method of subarrays, therefore each beam can get the maximum excitation of subarrays and ensure the pointing accuracy of the main lobe. Finally the cylindrical array antenna realizes the multibeam scanning and area coverage. The experimental results show that the sidelobe level after comprehensive optimization is 7.37 dB lower than that without optimization and 1.71 dB lower than that of traditional optimization when a single beam is formed. The comprehensive optimization can eliminate the grating lobe between two beams and reduce the sidelobe to -15 ∼ -20 dB when the two beams are 30°. The left sidelobe is reduced by 2.75 dB and the right sidelobe is reduced by 1.69 dB after comprehensive optimization when the two beams are separated by 40°.


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## Body

## 1. Introduction

The phased array antenna adjusts the weighting parameters of each element to achieve noise filtering from the input data compared with an antenna element of low gain and weak directivity. The optimal spatial filtering can be realized by forming a null steering stuffing in the interference direction and obtaining the maximum gain in the desired direction. Meeting the requirements of high gain, multidirectional and specific working environment, the performance of the wireless communication system can be further improved [1,2]. The limited spatial coverage and inflexible beam direction of traditional array antenna make the conformal antennas become a new research focus [3].The conformal antenna has the same spatial characteristics as the carrier compared with traditional array antenna, which will not reduce the aerodynamic performance of the original carrier. The conformal array carrier has smaller radar cross section (RCS) and is more convenient for stealth design compared with the same aperture size planar array [4–6]. In addition, the special shape of conformal antenna attached to the carrier surface makes the carrier higher space utilization. Meanwhile, it has a larger beam coverage and more flexible beam pointing ability to realize multitarget tracking and scanning. Nevertheless, the radiation directions of conformal array elements are inconsistent due to the influence of the curvature change of the carrier. The cross-polarization isolation between array elements clearly deteriorated when scanning at a large angle [7, 8]. The conformal array with special structure has shadow effect while transmitting and receiving beams. Thus the conformal array is divided into sub-array areas and forming beams in different directional airspace [9]. For common conformal arrays, cylindrical array [10], conical array [11], spherical array [12] and circular array [13] can all realize 360° omnidirectional scanning. However, the mutual coupling effect and cross-isolation between array elements make the computational complexity of conical array and spherical array too high, which is not conducive for engineering realization. The physical structure and mathematical model of the cylindrical array are the simplest among conformal arrays for omnidirectional scanning. Meanwhile, the reception and transmission of a single beam cannot meet the increasingly complex electromagnetic environment and task requirements under the demand of multitarget tracking in the whole airspace [14], therefore the multibeam forming of cylindrical array antenna is studied.The influence of wavefront curvature will lead to the elevation of sidelobe and the deviation of beam-pointing when conformal array is used for beamforming. The interaction between two beams results in sidelobe lifting and grating lobes while forming multiple beams. In order to eliminate this disadvantage, it is necessary to optimize the beamforming algorithm of conformal array [15–17]. In [18], the authors addressed a constrained multiobjective problem of sparse conformal array design. In [19], the author proposed an optimization method based on genetic algorithm and convex optimization to solve the problem of high sidelobe level of circular array. In [20], a beam design method based on radial basis function neural network is proposed aiming at the problem that sidelobe is easy to rise in the beam pattern of irregular array.In this paper, a comprehensive optimized Taylor weighting algorithm and an overlapping array algorithm with reconfigurable subarrays are proposed to realize multipoint scanning and area coverage of cylindrical conformal array. The experimental results show that the sidelobe can be reduced from -11.27 dB to -18.66 dB when forming a single beam, from -3.3 dB to -15 dB when forming two beams with an interval of 30° and from -10.09 dB to -12.84 dB when forming two beams with an interval of 40°.


## 2. Cylindrical Conformal Array Model and Pattern Synthesis

The cylindrical conformal array antenna studied in this paper is divided into three layers with 144 array elements. Each layer including 48 uniformly distributed antenna elements with a height of 48 mm, and the radius of the cylinder is 280 mm as shown in Figure1.Figure 1
Cylindrical conformal array antenna consists of 3 layers, each layer containing 48 elements.A sub-array in the cylindrical conformal array consists of 3 rows and 12 columns, and a total number of 36 elements are used for pattern synthesis as shown in Figure2. Each TR module includes an IF input and three RF outputs as shown in Figure 3. The cylinder array patterns are synthesized and the simulation results are demonstrated in Figure 4.Figure 2
A sub-array of the cylindrical array.Figure 3
Each TR module has an IF input and three RF outputs, including filters, mixers and amplifiers.Figure 4
Pattern synthesis of cylindrical conformal array antenna: (a) 3D view, (b) elevation view, and (c) horizontal view.
(a)(b)(c)Gain (G) is an index to measure the ability of the antenna to direct the power input to it in a specific direction, which is measured by the peak radiation intensity. Generally, the gain is related to the antenna pattern. The narrower the main lobe and the smaller the side lobe, the higher the gain. Assuming that the input power is P0, the radiation power density of the omnidirectional antenna at the distance R is(1)S=P04πR2.Since the omnidirectional antenna radiates uniformly in all directions, its radiation power densityS is the radiation power divided by the sphere area, i.e., 4πR2. Assuming that the efficiency of the omnidirectional radiator is 100% and the electric field strength is E.(2)S=P0G4πR2=E2η.Beamwidth is one of the parameters describing antenna performance, which refers to an antenna pattern or beam angle, in which the relative power is 50% or more of the highest power. Beamwidth refers to the angle at which the radiation power on both sides of the maximum radiation direction drops by 3 dB in the horizontal or vertical direction[21].As shown in Figure4, the three elements in the pitch direction form a wide beam with a sidelobe of -15.44 dB and a half-power beamwidth of 36°, which meets the pitch angle scanning requirement, and the sidelobe of the horizontal beam is -12.36 dB.


## 3. Sidelobe Optimization and Overlapping Array Division

The sidelobe level of the cylindrical conformal array is relatively high due to the influence of carrier curvature. In order to make the array antenna energy converge more in the main lobe pointing direction, the sidelobe suppression effect is optimized by amplitude “windowing.” At the moment, the window functions mainly used are Chebyshev weighting and Taylor weighting [22]. Chebyshev weighting causes the excitation amplitude of the two end elements to jump when the number of array elements is large and the required sidelobe level is not very low. A minor error greatly affects the sidelobe level of the radiation pattern, which is not conducive to feeding. Taylor’s weighted pattern shows that the sidelobe level in a certain area near the main lobe is nearly equal and monotonously decreases, which is beneficial to improve the antenna directivity coefficient. Meanwhile, the excitation amplitude distributions are monotonically decreasing from the array center to both ends with a proper design. There will be no jumping of excitation amplitude at both ends of the antenna, which is more suitable in the application scenario of multibeam forming. Therefore, Taylor optimization algorithm is used to suppress the sidelobe in this paper.The traditional Taylor weighting technique is mainly suitable for uniform linear arrays and planar arrays with equally spaced array elements, while the existing nonuniform Taylor weighting algorithm only considers the nonuniform distribution in one-dimensional direction for sparse arrays based on linear arrays. The projection based on conformal surface often ignores the influencing factors in nonhorizontal direction, which makes the sidelobe suppression effect nonoptimal. The Taylor function of discrete sampling continuous line source is used and projecteed in two-dimensional based on conformal array to normalize and weight the obtained two-dimensional optimization weights. Finally the comprehensive optimization weights matching the curvature of the conformal array are obtained, to further reduce the sidelobe of the cylindrical conformal array and raise the main lobe level.A coordinate system is established based on a sub-array of a cylindrical array antenna, ignoring the pitching direction. Horizontal circular array with 48 elements evenly distributed, one sub-array contains 12 elements, and the two-dimensional projection is shown as Figure5.Figure 5
A sub-array of cylindrical conformal array in horizontal section, two-dimensional projection.In Figure5, the projection of A1 to A12, i.e., 12 elements in a subarray, on the X axis is x1 to x12, while the projection of A1 to A6 on the Y axis is y1 to y6. The elements A1 to A6 with elements A7 to A12 are symmetrically distributed around the Y axis.The radius of the cylindrical array and the angle of the sector betweenA1 and A12 are known to be r and θ1, respectively. Then the chord length can be obtained through the formula x1x12 = 2rsin(θ1/2). x2x11 can be obtained through the formula x2x11 = 2rsin(θ2/2) with the angle θ2 correspondingly. The coordinates of 12 array elements projected on the X axis can be obtained. Note x1x12 as d1, x2x11 as d2, x3x10 as d3, x4x9 as d4, x5x8 as d5, and x6x7 as d6. Therefore, it can be known that the projected nonuniform distribution coordinates on the X axis are -d1/2, -d2/2, -d3/2, -d4/2, -d5/2, -d6/2, d6/2, d5/2, d4/2, d3/2, d2/2 and d1/2, and the projection coordinates of the array elements on the Y axis can be obtained from the formula r=(d2+4 h2)/8h.The Taylor space factor is expressed as(3)S¯k=1,k=0n¯−1!2n¯+k−1!⋅n¯−k−1!∏n=1n¯−11−k2σ2A2+n−1/22,0,k≥n¯1≤k≤n¯−1,where R0 means the ratio of the main lobe to side lobe level, A=arccoshR0/π and σ=n¯/A2+n¯−1/22. n¯ means that the first n¯−1 zeros of Taylor pattern are determined by the modified ideal space factor, so that the first n¯−1 sidelobes are nearly equal. The general selection rule of n¯ is n¯≥2A2+1/2, and here take n¯=7. Discretize the continuous Taylor space factor, as shown in Figure 6.Figure 6
Discrete sampling of continuous Taylor function.The current distribution on Taylor continuous line source antenna is as follows.(4)IZ=1LS¯0+2∑k=1n¯−1S¯kcos2kπLZ.Ignoring the coefficient 1/L and make S¯0=1, the excitation amplitude of each unit of the discrete Taylor array is as follows.(5)InZn=1+2∑k=1n¯−1S¯kcoskp,where L is the total length of the linear array, here it is equal to d1. It can be seen from Figure 5 that an equivalent transformation is required in the horizontal and vertical dimensions when the antenna elements of the conformal array are equivalent to linear arrays. In the horizontal direction, the coordinate matrix Zn of the ordinary linear array with equal distance distribution is replaced by the nonuniform distribution coordinate Zn′ obtained by projection.(6)InZn=1+2∑k=1n¯−1S¯kcosk2πd1Zn′.The current excitation amplitudeInn=1,2,…,12 after horizontal nonuniform transformation is obtained from (4), while I6=I7,I5=I8,I4=I9,I3=I10,I2=I11 and I1=I12 according to the symmetry of conformal array. After normalizing the current excitation amplitude in the vertical direction according to different chord heights and integrating the influence factors of two dimensions, the Taylor current excitation amplitude after comprehensive optimization can be obtained as follows.(7)IA6=IA7=I6,IA5=IA8=I5⋅R−y6y5R,IA4=IA9=I4⋅R−y6y4R,IA3=IA10=I3⋅R−y6y3R,IA2=IA11=I2⋅R−y6y2R,IA1=IA12=I1⋅R−y6y1R.Omni-directional multiangle multibeam forming in a cylindrical conformal array antenna needs to be done on the divided sub-array. Since the maximum gain of the subarray antenna unit cannot be completely obtained, the main lobe gain of the formed beam is low, the side lobe is high, and the beam pointing angle will be shifted to a certain extent, because the divided subarray sector is fixed and the main beam pointing is located in the sector edge. The main beam direction is random in actual beamforming due to the uncertainty of target signal orientation, which cannot guarantee the quality of the formed multibeam signal. To solve this problem, the divided subarray is set as Overlapping Subarray (OSA).OSA can be divided into regular overlapping arrays and irregular overlapping arrays [23,24]. The division of overlapping arrays reduces the spacing between subarrays and increases the spacing of the grating lobes of subarrays. At the same time, OSA can reuse among array elements and can form sub-array patterns with “flat-top lobe” effect, thus effectively inhibiting the formation of grating lobes. On the basis of OSA, amplitude weighting is carried out. The diameter and the degree of freedom of the subarrays is increased without increasing the distance between the phase centers of the subarrays, making the calculation of beamforming more flexible [25]. Here, a multibeam forming method of OSA based on reconfigurable subarrays is proposed. On the basis of Taylor comprehensive optimization, it is different from the division method with a fixed number of OSA. The range of divided subarrays and the number of overlapping elements can be changed according to the main lobe direction, which can effectively narrow the main lobe, reduce the side lobe and suppress the grating lobe, and at the same time, form beams with high gain and accurate direction in different directions.Multibeam forming based on reconfigurable subarrays is demonstrated in Figure7.Figure 7
Multibeam forming of cylindrical array antenna based on overlapping array, and the subarray can be reconstructed.Assume that the antenna elementX is multiplexed n times in the overlapping array, its position in the first overlapping array is x1, and its position in the nth overlapping array is xn. The Taylor comprehensive optimization weights of 12 elements are known as [T1,T2,T3,…,T12].Then the weight of the antenna elementX in the overlapping array N is shown as follows.(8)An=TxnTx1+Tx2+Tx3+…+Txn.Equation (7) can be used to synthesize multibeam shaping for a cylindrical conformal array.(9)Fφ,θ;φx,θx=∑m=0M−1∑n=0N−1fmnφ,θAmnexpjkrmsinθmsinθxcosφx−φmn−sinθcosφ−φmn+cosθmcosθx−cosθ.where x=0,1,2,…X, it means that X beams are formed. The directions of X beams are φ0,θ0,φ1,θ1,φ2,θ2,…,φx,θx as shown in Figure 7. fmnφ,θ represents the directed array element optimization function, where only horizontal scanning is considered. fnϕ=1+cosϕ−ϕn/2. As shown in Equation (9), Amn represents the amplitude weighting coefficient after the simultaneous multibeam forming and Taylor optimization synthesis of the overlapping arrays.(10)An=1+2∑k=1n¯−1S¯kcosk2π/dxnZxn'∑n=1N1+2∑k=1n¯−1S¯kcosk2π/dxnZxn'.


## 4. Realization and Analysis of Multibeam Forming

The proposed beamforming algorithm is tested in a microwave anechoic chamber based on the designed cylindrical conformal array antenna prototype. The conformal antenna operates at 3.915 GHz and the test environment is shown in Figure8.Figure 8
The pattern of cylindrical array antenna was tested in microwave anechoic chamber. There are 3×48 antenna units in the array and some hardware modules are exposed outside while in the preliminary debugging stage.Firstly, the pattern under the conditions of unoptimized traditional optimization and Taylor comprehensive optimization forming a single beam is tested. The measurement results are shown in Figure9.Figure 9
Single beam forming.It can be seen from Figure9 that the sidelobe of the single beam formed is -11.27 dB without optimization, the sidelobe is -16.95 dB after optimization with traditional window function and the sidelobe is -18.66 dB after Taylor comprehensive optimization. It can be seen that the optimization algorithm will lead to a certain degree of broadening of the main lobe while reducing the side lobes, so it is necessary to set the optimization weight size according to the actual needs. The Taylor’s comprehensive optimization can obtain lower sidelobes compared with traditional optimization from the figure, so Taylor’s comprehensive optimization method is adopted to study the multibeam forming.The experimental results before and after optimization are shown in Figure10 when two beams separated by 30°. It can be seen that the main lobe of beam 1 is reduced by 3.258 dB by using the traditional structure to form two beams without optimizing by using the window function. The grating lobe appears between the two beams with a gain of -3.306 dB and the pointing direction of beam 2 is shifted. The two beams are separated by 30° with accurate pointing after optimization, while the left lobe is about -15 dB and the right lobe is about -20 dB.Figure 10
Two beams separated by 30°.The experimental results before and after optimization are as shown in Figure11 when two beams separated by 40°. It can be seen that the left side lobe is -10.09 dB, the right side lobe is -16.6 dB, and the middle lobe of -13.65 dB with traditional structure to form two unoptimized beams. After optimization, the left and right side lobes are reduced to -12.84 dB and -18.29 dB, respectively, and the middle grating lobe is eliminated.Figure 11
Two beams separated by 40°.At the end of this work, the peak sidelobe levels (PSLL) performance of several similar sidelobe optimization algorithms are compared, and the comparison results are shown in Table1.Table 1
Performance statistics of different algorithms in terms of PSLL.
MethodLowest PSLL (dB)Highest PSLL (dB)Average PSLL (dB)PSO in [18]−10.06−6.14−7.68NSFAII in [18]−12.13−9.04−10.12CO in [19]−16.75−12.995−15.10This work−18.66−23.5−21.08


## 5. Conclusions

The multibeam forming algorithm of cylindrical conformal array antennas is studied in this paper. Based on Taylor’s comprehensive optimization algorithm for sidelobe suppression, the overlapping array division method with reconfigurable subarrays is used to realize multibeam. Experimental results show that the algorithm can reduce the sidelobe by 7.39 dB in single beam forming scenario and accurately optimize the sidelobe level of each beam by 2–5 dB in multibeam forming, which proves that the algorithm can realize multibeam scanning of cylindrical conformal array.



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*Source: 5379071-2022-03-29.xml*