Bộ định dạng và điều khiển búp sóng thích nghi sử dụng thuật toán đàn dơi nhị phân để đặt điểm “không” trên giản đồ bức xạ của mảng anten

Nội dung text: Bộ định dạng và điều khiển búp sóng thích nghi sử dụng thuật toán đàn dơi nhị phân để đặt điểm “không” trên giản đồ bức xạ của mảng anten

1. SCIENCE - TECHNOLOGY P-ISSN 1859-3585 E-ISSN 2615-9619 AN ADAPTIVE BEAMFORMER UTILIZING BINARY BAT ALGORITHM FOR ANTENNA ARRAY PATTERN NULLING BỘ ĐỊNH DẠNG VÀ ĐIỀU KHIỂN BÚP SÓNG THÍCH NGHI SỬ DỤNG THUẬT TOÁN ĐÀN DƠI NHỊ PHÂN ĐỂ ĐẶT ĐIỂM “KHÔNG” TRÊN GIẢN ĐỒ BỨC XẠ CỦA MẢNG ANTEN Tong Van Luyen1,*, Nguyen Van Cuong2 enhance performance by improving radio signal spectrum ABSTRACT efficiency, suppressing interferences, and saving utilization In this paper, we propose an adaptive beamformer based on a binary bat power. Moreover, adaptive beamformers are capable of algorithm (BBA) for pattern nulling of uniformly linear array (ULA) antennas. The producing appropriate weights for antenna arrays to optimized array pattern is obtained by controlling the phase of each array obtain desired patterns [1]. It is apparent that the gradual excitation weight. Several scenarios have been conducted to evaluate the increase of wireless devices is causing serious pollution in performance of the proposal including convergence speed and pattern nulling the electromagnetic propagation environment, which ability. The simulation results show that proposed beamformer is able to leads to the emergence of null-steering capabilities in precisely impose nulls at arbitrary directions of interferences while suppressing smart antenna systems as a promising solution for sidelobes and maintaining the main lobe. Furthermore, the proposal is faster and interference suppression in radar, sonar, and wireless more efficient than binary particle swarm optimization (BPSO)-based one with communications applications. respect to pattern nulling in array pattern synthesis. Several adaptive pattern nulling approaches have been Keywords: Beamforming, ULA antennas, binary bat algorithm, pattern nulling, widely researched and implemented, such as position-only interference suppression, array pattern synthesis. control, array thinning, excitation weights control [1, 2]. TÓM TẮT Each method has its advantages and limitations where the position-only method [3] needs a mechanical driving Trong bài báo này, chúng tôi đề xuất bộ định dạng và điều khiển búp sóng system as servomotors for adjusting the position of thích nghi dựa trên thuật toán đàn dơi nhị phân (BBA: Binary Bat Algorithm) để antenna elements, which leads to more complicated and đặt điểm “không” trên giản đồ bức xạ của mảng anten tuyến tính cách đều (ULA: difficult to accurately control. The array thinning method Uniformly linear array). Bức xạ tối ưu của mảng thu được bằng cách điều khiển does not require digital beamformers due to leveraging the pha của các trọng số tác động vào từng phần tử trong mạng. Một số kịch bản robustness of adaptive algorithms to turn array elements được thực hiện để đánh giá hiệu năng của đề xuất bao gồm tốc độ hội tụ và khả on (active) or off (inactive) but this is not an appropriate năng đặt điểm “không” trên giản đồ bức xạ. Các kết quả mô phỏng cho thấy bộ solution for small antenna arrays [4]. định dạng và điều khiển búp sóng được đề xuất có khả năng đặt điểm “không” chính xác tại các hướng nhiễu bất kỳ đồng thời nén búp sóng phụ và duy trì The amplitude-only control [5-7] unique adjusts the hướng và độ rộng búp sóng chính. Hơn nữa, đề xuất này nhanh hơn và hiệu quả amplitude excited at each array element; also, this hơn bộ định dạng và điều khiển búp sóng dựa trên thuật toán tối ưu bầy đàn nhị approach is less flexible in placing various kinds of nulls, phân (BPSO: Binary Particle Swarm Optimization) về khả năng đặt điểm “không” and the main lobe cannot be steered. The complex-weight trên giản đồ bức xạ trong quá tình tổng hợp giản đồ bức xạ của mảng anten. control has been acknowledged as the most effective and flexible one; however, this approach is required to have Từ khóa: Định dạng tia, ăng-ten ULA, thuật toán dơi nhị phân, vô hiệu hóa mẫu, controllers, phase shifters, and attenuators for each array triệt nhiễu, tổng hợp mẫu mảng. element, so it is the most complicated and costly [8-10]. 1Faculty of Electronic Engineering, Hanoi University of Industry The phase-only control is attractive for the phased array 2Hanoi University of Industry systems despite low complication and no extra cost [7, 11, *Email: luyentv@haui.edu.vn 12]; moreover, the main lobe direction can be steered by Received: 20/01/2021 adjusting the phase of excitation weights. Revised: 18/6/2021 Recently, the optimal pattern has been achieved by Accepted: 15/11/2021 applying various optimization techniques where nature- inspired optimization approaches have been proved as promising global optimization solutions in terms of 1. INTRODUCTION flexibility and efficiency [8, 13-28]. Specifically, particle Adaptive beamformers are being widely applied in swarm optimization (PSO)-based solutions were introduced radar, sonar, and wireless communication systems to for array pattern synthesis [17, 20], adaptive interference 52 Journal of SCIENCE & TECHNOLOGY ● Vol 57 - Special (Nov 2021) Website:
2. P-ISSN 1859-3585 E-ISSN 2615-9619 SCIENCE - TECHNOLOGY suppression in continuous optimization [21], and in the discrete optimization of complex communication scenarios [22]. Moreover, other pattern nulling solutions were conducted such as ant colony optimization [10],  backtracking search[24], and bat algorithm (BA) [8, 13, 14, 15, 25]. BA, which was proposed by Xin-She Yang in 2010, is a metaheuristic algorithm for global optimization techniques. It has been developed on the natural behavior of microbats manipulating echolocation to detect prey, avoid obstacles, and locate their roosting crevices in the Figure 1. The geometry of the 2N elements ULA antennas dark. So far, this algorithm has been successfully utilized to In order to obtain faster convergence, the minimum deal with various types of engineering problems and weight perturbation phase-only synthesis requires odd proved to be more powerful than other methods like the phase shift (δ = −δ ) [32]. Thus, an asymmetrical pattern genetic algorithm (GA) and PSO [26, 27]. Q. Yao and Y. Lu through the main lobe direction (θ = 0°) is obtained. When first employed BA for adaptive beamforming [28], and BA- a = a and δ = −δ , the array factor in (1) can be based design of a double-sided printed dipole antenna expressed as follows: array with a low first sidelobe level has been performed in [15]; also, adaptive BA-based beamformers for the pattern nulling have been demonstrated and successfully AF(θ) = 2 a cos(ndksin(θ) + δ) (2) implemented for ULAs in [8, 13, 14]. The authors of [8, 13, 14] proved that BA-based According to (2), the number of phase shifters is equal beamformers are more effective than GA and accelerated to the number of elements, yet the number of controllers, particle swarm optimization (APSO)-based one about attenuators, and computational time will be reduced by pattern nulling but optimized weight vectors are real half. Moreover, this approach can be implemented for the number while the phase of each array element is generally actual phased array systems without extra cost, which is the adjusted by digital phase shifters. So as to conveniently highlight of phase-only control compared to amplitude- apply in phased array systems, a basic BBA [29], is used to only control and complex-weight control. determine the phase of weights and is leveraged to The objective function O has been built in [8, 13, 14] as suppress interference in the sidelobe region while follows: maintaining the main lobe and keeping the sidelobes at low levels. Five scenarios will be performed to verify the ⎧ 10,000 [|AF (θ )|] , for θ = θ (3) proposal where the beamformer based on BBA will be ⎪ compared to the beamformer based on a basic BPSO [30]. O = The simulation results will show that the BBA-based ⎨ (4) beamformer performs pattern nulling more powerful than ⎪ [|AF(θ) − AF(θ)| ], elsewhere the BPSO-based one. ⎩ The remains of this work are organized as follows: In where: AF and AF are the optimized array factor Section 2, the formulation of the problem is depicted, and achieved by using optimization algorithms, which will be the proposed beamformers employing BBA are presented BBA and the desired array factor (Chebyshev pattern) in this in Section 3. Section 4 demonstrates the numerical results work, respectively; θ and I correspond to the angles and of the proposal before concluding the work in Section 5. the total number of null points. (3) is used for setting null 2. PROBLEM FORMULATION point, and (4) is to suppress the sidelobe level (SLL) and to keep the beamwidth of the main lobe. In this study, ULA antennas of 2N isotropic elements have been employed and illustrated in Figure 1. The 3. PROPOSAL OF THE BEAMFORMER elements are symmetrically located across the center of the Initialize the parameters of arrays; termination array, so the array factor can be expressed as [31]: condition; objective function ; bat population {frequency ( ), velocity ( ), pulse emission rate ( ) () (1) AF θ = ω e ( ), loudness (), and location/solution ()}; Define an initial location vector ( ) based on the where: ω = ω + jω = ae is the excitation weight vector of Chebyshev array. weight (complex-weight) of the nth element; λ is While (the termination condition is not satisfied) wavelength; k = is the wavenumber; d is the distance Update positions. between adjacent elements. Website: Vol. 57 - Special (Nov 2021) ● Journal of SCIENCE & TECHNOLOGY 53
3. SCIENCE - TECHNOLOGY P-ISSN 1859-3585 E-ISSN 2615-9619 ι (rand > r) In this section, five scenarios will be investigated to Select a solution ( ) among the best evaluate the performance of the proposals for pattern nulling. It is well known that the Chebyshev array weights solutions. distribution produces optimized patterns in terms of a Change some of the dimensions of location vector trade-off between the sidelobe level (SLL) and the first null beamwidth (FNBW) of the main beam for equally spaced with some of the dimensions of . arrays [33]. In this work, the parameters of the Chebyshev ενδιΦ array (the desired pattern AF is to control SLL and the Generate a new solution by flying randomly. beamwidth of the main beam) have been chosen as −30 λ⁄2 ι (rand < A & O() < O(G)) follows: SLL is dB; is adjacent elements spacing; Accept the new solutions. isotropic elements are 20. Other parameters and common items for the proposal are introduced in Table 1. ενδ ιΦ To show the capability of BBA utilization in our Rank the bats and find the final . proposed beamformer for interference suppression, five ενδ ωηιλε scenarios have been built. Scenario1 named Convergence characteristics is the first step to evaluate the operation of Build array element weights from the final and the proposal beamformer by comparing the convergence conduct pattern nulling. rate of the objective functions based on BBA and BPSO. Algorithm 1. Pseudocode of the proposed adaptive pattern nulling approach Scenarios 2 - 5 are for investigating and comparing the ability of null-steering of the proposed beamformer to the Based on studies in [8, 13, 14, 29], the BBA-based BPSO-based one. All simulation scenarios have been beamformer utilizing phase-only control for interference presented in Figure 2 - 7, where the results are the suppression applications have been deployed step-by-step averaged values of Monte Carlo simulations with 1000 in Algorithm 1, in which the termination condition is times for the first scenario, and 100 times for the others. chosen as the max number of iterations in all simulation scenarios except for the computational time in the first 4.1. Convergence characteristics scenario. In the first scenario, the computational capability of the 4. NUMERICAL RESULTS proposed BBA-based beamformer has been evaluated and compared to the BPSO-based one in the case of a single Table 1. Parameters and common items for the proposal null placed at the second sidelobe peak (14.5°) in the Parameters, Details Dolph-Chebyshev array pattern. To do that, at the initial common items step, the location vector of one bat in the population has Applied arrays ULAs: inter-element spacing: λ/2; 20 elements (2N) been initialized as Chebyshev array weights with SLL of Array elements Isotropic elements (Ideal) −30dB; pop is 100; ite is 200. The simulation results of the Array factor (AF) AF in (2) objective function are displayed in Figure 2, and the Control techniques Phase-only computational time of two beamformers has been The objective function (O) O in (3), (4) investigated in case of getting the same value of the objective function (O < 10). The results show that the BBA- The step size of theta angle (θ) is 0.5o; based beamformer and BPSO-based one take 0.52 seconds Population size (pop) is 100; and 14.2 seconds, respectively on Desktop PC (CPU Intel i7- The number of iterations (ite) is 2 (except for 8700, RAM 8GB, and MATLAB 2020a). It is apparent that the simulation results presented in Figure (ite 200); in BBA-based approach converges much faster than the Figure (ite 50)) BPSO-based one. Search value of variables in the range of [-5o, Global parameters 5o] ; One bat (locations) in the population is initialized by weights of the Chebyshev array with the SLL of -30bB. Others are randomly initialized. Variables: 8-bit numbers. Transfer function: V-shaped [20, 21]. Optimization algorithms BBA The step size of random walk is 0.01; boundary frequency values: fmin = 0 and fmax = 2; A = 0.25; r = 0.1 [20] BPSO C1 = C2 = 2; W is linearly decreased from 0.9 to 0.4; max velocity: 6 [21]. Figure 2. The objective function comparisons of BBA and BPSO 54 Journal of SCIENCE & TECHNOLOGY ● Vol 57 - Special (Nov 2021) Website:
4. P-ISSN 1859-3585 E-ISSN 2615-9619 SCIENCE - TECHNOLOGY −46dB, all SLLs are lower than −24dB, and HPBW roughly equals that of the Chebyshev pattern. The BBA pattern shows advantages over the BPSO one with respect to NDL. Figure 3. The objective function of BBA-based beamformers with various population sizes Furthermore, the objective function of the BBA-based Figure 5. Optimized patterns with three nulls at -48o, 20o, and 40o beamformer has been implemented with various bat population sizes (pop) and is illustrated in Figure 3. The 4.4. Optimized patterns with a broad null objective function takes 35 iterations, 8 iterations, 4 In interference suppression applications, if the direction iterations, and 2 iterations to roughly converge of the interference slightly varies over time or cannot be corresponding to pop = 10, 30, 50, and 100, respectively. exactly known, or a null is continuously steered to obtain an 4.2. Optimized patterns with a single null appropriate signal-to-noise ratio, a broad null is required. In order to show the ability of broad interference suppression, In Scenario 2, the optimized pattern with a single null in the fourth scenario, the pattern with a set broad null at a has been considered. This null can be arbitrarily set at any predefined sector of [30°, 40°] has been obtained and angle, which is chosen at the peak of the second sidelobe illustrated in Figure 6. A broad null (minimum NDL < −38dB) (14.5°) in this test case. The population has been initialized on the BBA pattern at that target sector has been as Chebyshev array weights with −30dB SLL, and Figure 4 successfully placed. The beamwidth is nearly unchanged and demonstrates optimized patterns with a single null the maximum SLL is −24.16dB. The results prove that the obtained by BBA and BPSO. The optimized pattern BBA pattern is better than BPSO one in terms of NDL. preserves almost all characteristics of the initial Chebyshev pattern such as half-power beamwidth (HPBW = 6.3°) and SLL (−30dB). The maximum SLL is −23.89dB, and the null depth level (NDL) at 14.5° is −73.21dB; additionally, Figure indicates that the pattern with a single null optimized by BBA-based approach is better than that of the BPSO-based one in terms of NDL at the desired direction. Figure 6. Optimized patterns with a broad null from 30o to 40o 4.5. Optimized patterns with the steered main lobe Figure 4. Optimized patterns with a single null at 14.5o 4.3. Optimized patterns with multiple nulls In the third scenario, the proposal will be used for separately imposing multiple nulls at −48°, 20°, and 40°, corresponding to the peaks of three sidelobes next to the main lobe of the Chebyshev array pattern. As shown in Figure 5, the patterns with multiple nulls at predefined locations have been obtained. All NDLs are less than Figure 7. Optimized patterns with the steered main lobe at 10o Website: Vol. 57 - Special (Nov 2021) ● Journal of SCIENCE & TECHNOLOGY 55
5. SCIENCE - TECHNOLOGY P-ISSN 1859-3585 E-ISSN 2615-9619 In the situation of fixed main lobe direction, the efficiency [7]. K. Guney, A. Durmus, 2015. Pattern Nulling of Linear Antenna Arrays of the proposed beamformer has been demonstrated above. Using Backtracking Search Optimization Algorithm. International Journal of However, this solution is not only constrained by the fixed Antennas and Propagation. main lobe direction but also able to apply in main lobe [8]. T.V. Luyen, T.V.B. Giang, 2017. Bat Algorithm Based Beamformer for steering. In order to implement pattern nulling while Interference Suppression by Controlling the Complex Weight. REV Journal on steering the main lobe, the process is the same as mentioned Electronics and Communications. vol. 7, no. 3-4, pp. 87-93. above, but the main lobe is steered to the desired direction. [9]. H. Steyskal, R. A. Shore, R. L. Haupt, 1986. Methods for null control and This can be gained by steering the main lobe of the their effects on the radiation pattern. IEEE Trans. Antennas Propagat., vol. 34, pp. Chebyshev pattern in the objective function to the desired 404–409. direction before setting nulls toward interferences. In the fifth scenario, three above adaptive pattern nulling cases [10]. D. Karaboga, K. Guney, A. Akdagli, 2004. Antenna array pattern nulling have been conducted while steering the main lobe to a by controlling both the amplitude and the phase using modified touring ant colony optimisation algorithm. Int. J. Electronics, vol. 91, pp. 241–251. predefine angle, which is 10° in this test case. The simulation results shown in Figure 7 have been proved that the [11]. A. Akdagli, K. Guney, 2004. Null steering of linear antenna arrays by proposal is capable of performing as well as those in the phase perturbations using modified tabu search algorithm. Journal of scenarios presented in Sections 4.2 – 4.4. 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