12001 FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 37, No 2, June 2024, pp. 277- 287 https://doi.org/10.2298/FUEE2402277S © 2024 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper COMPARISON OF THE PERFORMANCE OF ARTIFICIAL NEURAL NETWORK WITH VARIABLE STEP-SIZE ADAPTIVE ALGORITHMS FOR THE BEAMFORMING OF SMART ANTENNA FOR CELLULAR NETWORKS Barsa Samantaray1, Kunal Kumar Das2, Jibendu Sekhar Roy3 1,2ECE Department, ITER, SOA University, Bhubaneswar, Odisha, India 3School of Electronics Engineering, KIIT University, Bhubaneswar, Odisha, India ORCID iDs: Barsa Samantaray https://orcid.org/0000-0001-7184-2123 Kunal Kumar Das https://orcid.org/0000-0003-2832-2768 Jibendu Sekhar Roy https://orcid.org/0000-0003-2911-2383 Abstract. A smart antenna is an antenna array that uses spatial diversity to identify the desired mobile station (MS) and reject the unwanted interference signal in a cellular network. Generally, adaptive signal processing algorithms are used for smart antenna beamforming, and one of the most common algorithms is the least mean square (LMS) algorithm. Here, the artificial neural network (ANN) is used for beamforming of smart antennas, and the performance of the ANN is compared with the performance of variable step-size LMS (VS-LMS) and variable step-size sign LMS (VS-SLMS) algorithms. The ANN has better performance than the VS-LMS and VS-SLMS algorithms for the determination of user and null directions. Lower side lobe levels (SLLs) are achieved using ANN compared to the VS-LMS and VS-SLMS algorithms. The reduction of SLL from about 3.5 dB to 8.5 dB is achieved using ANN compared to signal processing algorithms. Key words: Smart antenna, artificial neural network, signal processing, variable step-size, beamforming, SLL 1. INTRODUCTION Smart antenna technology improves overall service quality in cellular communication which provide radiation beams to users while producing nulls for interferers [1]. The function of a smart antenna system in a 3-sector cellular network is shown in Fig. 1. The system uses a signal processing algorithm [1-4] to achieve this adaptive system. The smart antenna is the key technology for 4th generation (4G) wireless access and beyond [5, 6]. Received July 17, 2023; revised August 25, 2023; accepted September 11, 2023 Corresponding author: Jibendu Sekhar Roy School of Electronics Engineering, KIIT University, Bhubaneswar, Odisha, India. E-mail: drjsroy@kiit.ac.in https://orcid.org/0000-0001-7184-2123 https://orcid.org/0000-0003-2832-2768 https://orcid.org/0000-0003-2911-2383 278 B. SAMANTARAY, K. K. DAS, J. S. ROY Fig. 1 Smart antenna in an cellular network The adaptive SAS first identifies the signal's DOA before forming a retro-directive main beam [1]. Multiple Signal Classification (MUSIC) and Estimation of Signal Parameter via Rotational Invariance Technique (ESPRIT) are widely used DOA estimation algorithms [7, 8]. In a cellular network, instead of sending power over the whole cellular zone, a smart antenna produces a beam towards the desired user only. The applications of machine learning (ML) algorithms in smart antenna design is reported in [1]. 2. RELATED WORK There are several beamforming algorithms [9, 10] which include the LMS [1, 11, 12], the recursive least square (RLS) [13], and the sample matrix inverse (SMI) algorithms [14]. The VS-LMS algorithm provides [11] lower SLL. In [14, 15], the VS-LMS algorithm is used for the improved adaptive beamforming of doubly crossed uniform linear arrays. In order to achieve better convergence in adaptive beamforming, variable step-size LMS and its variants are proposed in [16]. Based on past data, in the ML method, a machine learns and improves on its own [17, 18, 19]. The use of ANN for SAS design is suggested in the review paper [20-22]. An overview of the application of ML methods for antenna and antenna array modelling is explained in [23]. A recurrent neural network is proposed to minimize SLL [24]. In [25-27], neural network and deep learning based neural network for adaptive beamforming are reported. According to reported related work, signal processing algorithms appear to be used for the design of SAS in the majority of cases [1]. The design of SAS using machine learning avoids the use of signal processors. The use of machine learning algorithms for SAS design is relatively new, and not many investigations have been reported on it to date. Also, reports on the performance comparison between ANN and signal processing algorithms for the design of smart antennas are not available in the literature. In this paper, the performance of the ANN method for the design of smart antennas is compared with the signal processing algorithms. The ANN, VS-LMS, and VS-SLMS algorithms are implemented using MATLAB programming. The deviation of beam directions using ANN is negligible from the desired beam directions compared to signal processing methods. The reduction of SLL is necessary for minimizing interference in communication, and using ANN, reduced SLLs are achieved compared to VS-SLMS and VS-LMS algorithms. Comparison of the Performance of Artificial Neural Network with Variable Step-Size … 279 3. ARTIFICIAL NEURAL NETWORK AND SIGNAL PROCESSING ALGORITHMS Artificial neural network (ANN) is a widely used ML algorithm [27, 28], and ANN is a sub-category of deep learning. In a multi-layer neural network, ANN consists of an input layer, multiple hidden layers, and an output layer. The simple model of a multilayer perceptron network for ANN is shown in Fig. 2 using random weights and the weighted sum of inputs is passed through a non-linear activation function. The signal flows from left to right, which is ‘forward pass’. The output is compared with the training data to calculate the error. Then in the ‘backward pass’, from right to left, it propagates the error to every node using back propagation. Accordingly, to reduce the error, weights are adjusted unless the required output is obtained [1]. Mainly, the signal processing algorithm is used to design a smart antenna [3, 29, 30]. In this paper, the performance of ANN for the beamforming of smart antennas is compared with the performances of the VS-SLMS and VS-LMS algorithms. Fig. 2 Artificial neural network architecture The LMS algorithm incorporates an iterative procedure for successive corrections to the weight vector to obtain minimum mean square error [2, 11, 29]. The error e(n) between the desired signal d(n) and array output y(n) is [15] 𝑒(𝑛) = 𝑑(𝑛) − 𝑦(𝑛) (1) The weight vector update equation in the LMS algorithm is 𝑤(𝑛 + 1) = 𝑤(𝑛) + 𝜇 𝑥(𝑛) 𝑒∗(𝑛) (2) here, μ is the step-size parameter, complex conjugate of e(n) is e*(n) and x(n)= [x1(n), x2(n) ------xN(n)] is the signal, received by the antennas [31]. The rate of convergence is determined by the step-size parameter μ, which is fixed in the LMS algorithm. In variable step-size algorithms, μ varies, and convergence becomes better. In the VS-LMS algorithm, μ varies during weight updating according to the formula [31]  𝑛+1 = 𝛼μ𝑛 + 𝛿휀𝑛, if 0<μn+1 < μmax = 𝜇𝑚𝑎𝑥, otherwise (3) 280 B. SAMANTARAY, K. K. DAS, J. S. ROY where, maximum value of μ is μmax and ‘α’ and ‘δ’ are the constant parameters [11, 32, 33] and in simulation, δ =0.0003 and α =0.95. The weight update equation in VS-LMS algorithm is [1] 𝑤(𝑛 + 1) = 𝑤(𝑛) + µ𝑛+1 𝑥(𝑛) 𝑒∗(𝑛) (4) In the Sign LMS (SLMS), the sign of the error is used for weight update. Sign (also called signed regressor) LMS is used for a faster adaptation process [34]. In VS-SLMS algorithm, the step size 𝜇 varies according to (3). The weight updating in the VS-SLMS algorithm is 𝑤(𝑛 + 1) = 𝑤(𝑛) + 𝜇𝑛+1𝑒∗(𝑛)𝑠𝑔𝑛[𝑥(𝑛)] (5) 𝑠𝑔𝑛[𝑥(𝑛)] = 1; 𝑓𝑜𝑟 𝑥(𝑛) > 0 = 0; 𝑓𝑜𝑟 𝑥(𝑛) = 0 = −1; 𝑓𝑜𝑟 𝑥(𝑛) < 0 (6) 4. SMART ANTENNA DESIGN USING ANN, VS-LMS, AND VS-SLMS ALGORITHMS In this work, smart antennas with a uniform linear array (ULA) of isotropic antennas are considered (Fig. 3). The uniform antenna separation is ‘d’. Fig. 3 Uniform linear antenna array The array factor (AF) with a principal beam at an angle θ, is [3] 𝐴𝐹(𝜃) = ∑ 𝐼0𝑒𝑗(𝑛−1)(𝛽𝑑𝑠𝑖𝑛𝜃+𝛼) 𝑁 𝑛=1 = ∑ 𝐼0𝑒𝑗(𝑛−1)( 2𝜋𝑑 𝜆 𝑠𝑖𝑛𝜃+𝛼) 𝑁 𝑛=1 (7) where, ‘N’ is the total number of antenna elements, I0 is the amplitude of current fed to the antennas, and phase factor β=2π/λ at wavelength λ and the required progressive phase shift in the desired beam direction θ0 from the broadside direction is [11] α = -βdsinθ0. The cost function for beamforming using ANN and signal processing methods is (7). The ratio of array factor (AF) to maximum value of array factor (AFmax) [11] is the normalized array factor, 𝐴𝐹𝑛𝑜𝑟𝑚 = | 𝐴𝐹 𝐴𝐹𝑚𝑎𝑥 | In this work, ULAs of 10, 12, 16, and 20 elements (N=10, N=12, N=16, N=20) with spacing of d=λ/2 is considered at 1800 MHz [1]. The desired beam (user) direction (BD) is θs and the desired null (interferer) direction (ND) is θI. For the beamforming using ANN, from the different combinations of f, d, θs and θI, data set of matrix dimension [2205X25] is created. The ANN network consists of 3 input parameters, 2 input variables, 2 hidden Comparison of the Performance of Artificial Neural Network with Variable Step-Size … 281 layers, and 20 output variables (in the case of N=10) [1]. The first and second hidden layers have 20 neurons and 5 neurons, respectively. The two independent input variables are θs, the BD , and θI, the ND. The three input parameters are frequency (f), inter-element spacing (d), and phase constant (β). The 20 output variables are for an antenna array of 10 antenna elements. 10 variables are for the real parts of the weight, and 10 variables are for the imaginary parts of the weight. In ANN simulation, the resilient back propagation algorithm [26] is used as a training algorithm. In ANN, number of run is 1000, learning rate initialization is 0.01 and the tolerance value is 10-5. After training and testing, 10 complex weights are found, and these weights are used for beamforming using the cost function [1]. The VS-SLMS, and VS-LMS algorithms are used for the beam generation of the ULA [11]. Four ULAs with the number of antenna elements N=10, N=12, N=16 and N=20 are considered with different BD and ND. Weight updating equations (4) and (5) with a cost function of (7) are used for beamforming. The number of iterations is 1000 in all cases. The flowchart for the implementation of variable step-size algorithms is shown in Fig. 4. Fig. 4 Flowchart for the implementation of VS-LMS and VS-SLMS algorithms Adaptive beams of smart antennas of N=10, N=16, and N=20 with inter-element spacing of d=0.5λ obtained using ANN, VS-LMS, and VS-SLMS algorithms are plotted in Figs. 5, 6, and 7 respectively. In Fig. 5, BD=00, ND=120, in Fig.6 BD=100, ND=220; and in Fig. 7, BD=200, ND=320. To obtain the results of Figs. 5-7, ANN, VS-LMS, and VS-SLMS are simulated for 1000 iterations/epochs. In Fig. 5, for N=10, the maximum SLLs obtained for ANN, VS- SLMS, and VS-LMS are -13.3 dB, -9.98 dB, and -4.7 dB, respectively. In Fig. 6, for N=16, the maximum SLLs obtained for ANN, VS-SLMS, and VS-LMS are -13.05 dB, -8.72 dB, and -9.4 dB respectively. In Fig. 7, for N=20, the maximum SLLs obtained for ANN, VS- 282 B. SAMANTARAY, K. K. DAS, J. S. ROY SLMS, and VS-LMS are -13.4 dB, -9.88 dB, and -9.0 dB, respectively. In all the cases deviations of BD and ND from desired values are minimum ANN. Therefore, the performance of ANN for beamforming of smart antennas is better than that of VS-SLMS, and VS-LMS algorithms. Fig. 5 Radiation beam using ANN, VS-LMS, and VS-SLMS for N=10 Fig. 6 Radiation beam using ANN, VS-LMS, and VS-SLMS for N=16 Comparison of the Performance of Artificial Neural Network with Variable Step-Size … 283 Fig. 7 Radiation beam using ANN, VS-LMS, and VS-SLMS for N=20 The results, obtained using ANN, are compared with the signal processing algorithms in Table 1. Table 1 Comparison of results between ANN and signal processing algorithms No. of elements Algorithm Desired BD Obtained BD Desired ND Obtained ND SLLmax N=10 ANN 0° 0.0° 12° 11.9° -13.3 dB VS-SLMS 0° 0.7° 12° 12.3° -9.98 dB VS-LMS 0° 0.9° 12° 11.7° -4.70 dB N=12 ANN 15° 15.1° 30° 30.1° -13.02 dB VS-SLMS 15° 14.5° 30° 29.5° -8.69 dB VS-LMS 15° 15.4° 30° 27.6° -9.15 dB N=16 ANN 10° 10.1° 22° 22.1° -13.05 dB VS-SLMS 10° 10.4° 22° 22.3° -8.72 dB VS-LMS 10° 9.6° 22° 21.6° -9.40 dB N=20 ANN 20° 20.0° 32° 32.0° -13.40 dB VS-SLMS 20° 19.0° 32° 31.8° -9.88 dB VS-LMS 20° 19.6° 32° 26.5° -9.00 dB In Table 1, the deviations of BD and ND from the desired values are less for ANN than for VS-LMS and VS-SLMS. Lower SLLs are obtained for ANN in all the cases. The variations in maximum SLLs with the number of antennas in the array are compared in Fig. 8. Using ANN, an SLL reduction of about 8.5 dB is achieved for N=10 compared to VS-LMS. For N=12, N=16, and N=20, a SLL reduction of about 3.5 dB is obtained in ANN compared to signal processing algorithms. 284 B. SAMANTARAY, K. K. DAS, J. S. ROY Fig. 8 Variation of maximum SLL with number of antenna elements in the array The mean square error (MSE) graphs for VS-LMS, VS-SLMS, and ANN are shown in Fig. 9 for N=10, BD=0° and ND=12°. (a) (b) (c) Fig. 9 MSE curves for (a) VS-LMS (b) VS-SLMS (c) ANN The convergence of the ANN algorithm is faster than that of the variable step-size adaptive algorithms. Comparison of the Performance of Artificial Neural Network with Variable Step-Size … 285 The results for the beamforming of the smart antennas, using ANN are compared with the published results [16, 17, 25, 27, 35] in Table 2. Table 2 Performance comparison of ANN with other published results References Beamforming method Parameters Maximum SLL Ref [16] VS-SLMS ULA with N=4, d=λ/2, BD=200 -11.5 dB Ref [17] VS-NLMS ULA with N=10, d=λ/2, BD=00 -12.1 dB Ref [25] Recurrent neural network (RNN) ULA with N=32, d=λ/2, BD=00 -7.5 dB Ref [25] RNN ULA with N=16, d=λ/2, BD=-100 -8.5 dB Ref [27] RNN based on the gated recurrent unit ULA with N=16, d=λ/2, BD=1000 -11.5 dB Ref [35] Elman RNN ULA with N=5, d=λ/2, BD=300 -11.5 dB This paper ANN ULA with N=10, d=λ/2, BD=00 -13.3 dB This paper ANN ULA with N=16, d=λ/2, BD=100 -13.05 dB This paper ANN ULA with N=20, d=λ/2, BD=200 -13.4 dB One of the main sources of interference in a cellular network is the side lobes of the desired radiation beam. In Table 2, lower SLLs are achieved using ANN, presented in this paper. 5. CONCLUSION The performance of the ANN method for the design of smart antennas is compared with the signal processing algorithms. The ANN shows better performance for achieving the desired BD and ND than other methods. For low interference low SLL is desired in a cellular network, and using ANN, lower SLLs are achieved compared to VS-LMS and VS- SLMS algorithms. The ML method of beamforming avoids the use of a signal processor in the SAS. The theory and simulation are easier for the ANN method than other ML algorithms. But the simulation time in the ANN algorithm is longer than in the signal processing methods. The average time in ANN simulation is 66 seconds, whereas for VS- LMS or VS-VSSLMS, it is 25 seconds. REFERENCES [1] B. Samantaray, K. K. Das, and J. S. Roy, "Designing Smart Antennas Using Machine Learning Algorithms", Journal of Telecommunication and Information Technology, vol. 2023, no. 4, pp. 46–52, Oct 2023. [2] S. Bellofiore, J. Foutz, C. A. Balanis, and A. S. Spanias, "Smart Antenna System for Mobile Communication Network. Part 2. Beamforming and Network Throughput", IEEE Antenna and Propagation Magazine, vol. 44, no. 4, pp. 106–114, 2002. [3] T. K. Sarkar, M. C. Wicks, and M. Salazar-Palma, Smart Antenna, Wiley-IEEE Press, 2003. [4] C. A. Balanis, Antenna Theory: Analysis and Design, Ch-16, 3rd Ed., Wiley-Interscience, Hoboken, NJ, 2005. [5] M. Chryssomallis, "Smart Antennas", IEEE Antenna and Propagation Magazine, vol. 42, no. 3, pp. 129– 136, 2000. [6] W. Liu, A. Madanayake, L. Wu, Q. Shen, and J. Cai, "Recent Advances In Design And Signal Processing For Antenna Arrays 2020", International Journal of Antennas and Propagation, vol. 2023, Article ID: 9843456, 2023. 286 B. SAMANTARAY, K. K. DAS, J. S. ROY [7] A. Dhar, A. Senapati, and J. S. Roy, "Direction of Arrival Estimation for Smart Antenna Using a Combined Blind Source Separation and Multiple Signal Classification Algorithm", Indian Journal of Science and Technology (IJST), vol. 9, no. 18, 2016, pp. 1–8. [8] M. Rzymowsky, K. Nyka, and L. Kulas, "Direction of Arrival Estimation Based on Received Signal Strength Using Two-Row Electronically Steerable Parasitic Array Radiator Antenna", Sensors, vol. 22, no. 5, 2022, pp. 1–20. [9] M. Abualhayja’a, and M. Houssain, "Comparative Study of Adaptive Beamforming Algorithms for Smart Antenna Applications", In Proceedings of the Intl. Conference on Communications, Signal Processing, and their Applications (ICCSPA), Sharjah, UAE, 16-18 March 2021, IEEE Xplore, 2021, pp. 1–5. [10] M. Atzemourt, A. Farchi, Y. Chihab, and Z. Hachkar, "Performance Evaluation of LMS and CM Algorithms for Beamforming", Advances in Materials Science and Engineering, vol. 2022, Article ID 7744625, pp. 1–6, 2022. [11] B. Samantaray, K. K. Das, and J. S. Roy, "Performance of Smart Antenna in Cellular Network Using Variable Step Size Algorithms, " International Journal of Microwave and Optical Technology (IJMOT), vol. 15, no. 2, pp. 179–186, 2020. [12] K. Pirapaharan, N. Ajithkumar, K. Sarujan, X. Fernando, and P. R. P. Hoole, "Smart, Fast, and Low Memory Beam-Steering Antenna Configurations for 5G and Future Wireless Systems" Electronics, vol.11, 2658, 2022, pp. 1–8. [13] B. C. Banister, and J. R. Zeidler, "Tracking Performance of the RLS Algorithm Applied to an Antenna array in a Realistic Fading Environment", IEEE Trans. on Signal Processing, vol. 50, no. 10, pp. 1037– 1050, 2002. [14] J. Gao, J. Zhen, Y. Lv, and B. Guo, "Beamforming Technique Based on Adaptive Diagonal Loading in Wireless Access Networks", Ad hoc Networks, vol. 107, p. 102249, 2020. [15] M. Mishra, and J. S. Roy, "Investigations on the Effect of Mutual Coupling in Smart Antenna Using Adaptive Signal Processing Algorithm", In Proceedings of the 2018 IEEE International Conference on Applied Electromagnetics, Signal Processing and Communication (AESPC), Oct. 22-24, 2018, IEEE Xplore, pp. 1–4. [16] R. M Shubair, and A. Hakam, "Adaptive Beamforming Using Variable Step-Size LMS Algorithm With Novel ULA Array Configuration", In Proceedings of the 15th IEEE International Conference on Communication Technology, Guilin, China, 17-19 Nov., 2013, IEEE Xplore, 2013, pp. 1–4. [17] Veerendraa and M. Bakharb, "A Novel LMS Beamformer for Adaptive Antenna Array", In Proceedings of the 7th Intl. Conf. on Advances in Computing & Communications (ICACC-2017), 22-24 August 2017, Cochin, India, Proceedia Computer Science, vol. 115, 2017, pp. 94–100. [18] D. Knežević, M. Blagojević, "Application of Deep Extreme Learning Machine in Network Intrusion Detection Systems", Facta Universitatis Series Electronics and Energetics, vol. 32, no. 4, 2019, pp. 529–538. [19] F. Z. Fagroud, H. Toumi, E. Lahmar, K. Achtaich, S. Filali, and Y. Baddi, "Connected Devices Classification Using Feature Selection with Machine Learning", IAENG International Journal of Computer Science, vol. 49, no. 2, pp. 445–452, 2022. [20] P. Ranjan, H. Gupta, S. Yadav, and A. Sharma, "Machine Learning Assisted Optimization and its Application to Hybrid Dielectric Resonator Antenna Design", Facta Universitatis Series Electronics and Energetics, vol. 36, no. 1, 2023, pp. 31–42. [21] A. Rawat, R. N. Yadav, and S. C. Shrivastava. "Neural Network Applications in Smart Antenna Arrays: A Review", AEU-International Journal of Electronics and Communications, vol. 66, no. 11, pp. 903–912, 2012. [22] B. Hamdi, S. Limam, and T. Aguili, "Uniform and Concentric Circular Antenna Arrays Synthesis for Smart Antenna Systems Using Artificial Neural Network Algorithm", Progress In Electromagnetics Research B, vol. 67, pp. 91–105, 2016. [23] F. Andriulli, P.-Y. Chen, D. Erricolo, and J.-M. Jin, "Machine Learning In Antenna Design, Modeling, and Measurements", Guest Editorial, IEEE Transactions on Antennas and Propagation, vol. 70, no. 7, 2022, pp. 4948–4952. [24] H. Che, C. Li, X. He, and T. Huang, "A recurrent neural network for adaptive beamforming and array correction", Neural Networks, vol. 80, pp. 110–117, Aug. 2016. [25] P. Ramezanpour, M. J. Rezaei, and M. R. Mosavi, "Deep-learningbased beamforming for rejecting interferences", Signal Processing, vol. 14, pp. 467–473, Sep. 2020. [26] H. Al Kassir, Z. D. Zaharis, P. I. Lazaridis, N. V. Kantartzis, T. V. Yioultsis, I. P. Chochliouros, A. Mihovska, and T. D. Xenos, "Antenna Array Beamforming Based on Deep Learning Neural Network Architectures" In Proceedings of the 3rd URSI AT-AP-RASC, Gran Canaria, 29 May–3 June 2022, IEEE Xplore, 2022, pp. 1–4. Comparison of the Performance of Artificial Neural Network with Variable Step-Size … 287 [27] I. Mallioras, Z. D. Zaharis, and P. I. Lazaridis, "A Novel Realistic Approach of Adaptive Beamforming Based on Deep Neural Networks", IEEE Trans. on Antennas and Propagation, vol. 70, no. 10, pp. 8833–8848, 2022. [28] S. Haykin, Neural Network and Machine Learning, 3rd Ed., Pearson International, 2009. [29] Y. Han, Y. Tao, W. Zhang, W. Cui, and T. Shi, "Perceptron Neural Network Image Encryption Algorithm Based on Chaotic System", IAENG International Journal of Computer Science, vol. 50, no. 1, pp. 42–50, 2023. [30] K. Ghatak, A. Senapati and J. S. Roy, "Investigations on Adaptive Beam Forming for Linear and Planar Smart Antenna Arrays Using Sample Matrix Inversion Algorithm", International Journal of Computer Applications (IJCA), vol. 117, no. 8, pp. 47–50, May 2015. [31] B. Samantaray, K. K. Das and J. S. Roy, "Performance of Smart Antenna of Dipole Array", In Proceedings of the 2nd Intl. Conf. on Intelligent Computing and Advances in (ICAC-2019), Nov. 15-17, 2019, ITER, SOA Uni., Bhubaneswar, 2019, Springer Lecture Notes in Networking and Systems, vol. 109, 2019, pp. 424–431. [32] A. Khan, A. Senapati, and J. S. Roy, "Adaptive Signal Processing Algorithm Applied to the Design of Smart Antenna in a Cellular Network Considering Phase Quantization Error", In Proceedings of the 2nd Intl. Conf. on Data Science and Applications (ICDSA 2021), Kolkata, Springer Lecture Notes in Networks & Systems, April 10-11, 2021, vol. 288, Nov. 2021, pp. 563–575. [33] Y-S. Lau, Z. M. Hussain, and R. J. Harris, "A Weight-vector LMS Algorithm for Adaptive Beamforming", In Proceedings of the IEEE TENCON Conference, New Jersey, Nov. 2004, pp. 494–498. [34] P. Bhattacharyya, H. G. Sastry, V. Marriboyina, and R. Sharma, "Smart and Innovative Trends in Next Generation Computing Technologies", NGCT 2017, Dehradun, India, Oct. 30-31, 2017, Springer Nature Singapore, 2018. [35] A. H. Sallomi and S. Ahmed, "Elman Recurrent Neural Network Application in Adaptive Beamforming of Smart Antenna System", Intl. Jnl. of Computer Applications (IJCA), vol. 129, no. 11, pp. 38–43, 2015.