# Keywords: Adaptive Antennas, Beam forming Algorithm, Signal Nulling, Performance Evaluation.

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5 limits the usefulness of the algorithm in dynamic environment where the signal must be captured quickly. A faster converging CMA algorithm similar in form to the Recursive Least Square (RLS) method is the Orthogonalized-CMA. Another fast converging CMA is the Least Square CMA (LS-CMA) which is a block update iterative algorithm that is guaranteed to be stable and easily implemented. At the n-iteration, n- temporal samples of the beamformer output are generated using the current weight vector. This gives (33) minimum value of the Mean Square Error (MSE). The LMS algorithm is important because of its simplicity and ease of computation, because it does not require off-line gradient estimations or repetition of data. One of the drawbacks of the LMS adaptive scheme is that the algorithm must go through many iterations before satisfactory convergence is achieved. If the signal characteristics are rapidly changing, the LMS algorithm may not allow the tracking of the desired signal in a satisfactory manner. The rate of convergence of the weight is dictated by the Eigen value spread of the correlation matrix, given as The initial weight vector can be taken as (40) (34) if no a priori information is available. The nth signal estimate is then hard limited to yield (35) and a new weight vector is formed according to Where, (38) (36) (37) Equations (26) and (27) denote a time average over. The update weight vector minimizes the mean square error. The iteration described above continues until either the change in the weight vector is smaller than some threshold or until the envelope variance of the output signal is deemed sufficiently small. When the iteration is performed using a new block of data it is known as dynamic LSCMA. But when it is re-applied to the same block of data it is known as static LSCMA. 4. Least Mean Square (LMS) Algorithm The Least Mean Square (LMS) algorithm uses a gradient based method of steepest decent [12]. This algorithm uses the estimate of the gradient vector from the available data. This algorithm computes the complex weights vector recursively using the equation, given as; (39) Where is the step size parameter and controls the convergence characteristics of the LMS algorithm. The LMS algorithm is initiated with an arbitrary value of for the weight vector at. The successive corrections of the weight vector eventually leads to Where matrix. is the largest egien value of the correlation 5 Recursive Least Square Algorithm (RLS) The Recursive Least Square (RLS) algorithm was developed to solve the problem of slow convergence speed in an environment yielding an array correlation matrix with large Eigen value spread. This is achieved by making its convergence independent of the Eigen values distribution of the correlation matrix. In RLS algorithm, the weights are updated using the equation below, (41) Where is referred to as the gain vector and is a prior estimation error which is given as (42) The RLS algorithm does not require any matrix inversion computations as the inverse correlation matrix is computed directly. It requires reference signal and correlation matrix information. An important feature of the RLS is that its rate of convergence is typically an order of magnitude faster than that of the LMS algorithm, due to the fact the RLS algorithm convergence is independent of the Eigen values distribution of the correlation matrix. This improvement however is achieved at the expense of an increase in the computational complexity of the Recursive Least Square algorithm. V. SIMULATION AND PERFORMANCE EVALUATION For simulation purpose and analysis the uniform linear array with (N = 8) number of elements is considered. The inter-element spacing is considered to be half wavelength. It is considered that the desired user is arriving at an angle of 30 degrees and an interferer at an angle of -60 degrees. The simulation is carried out on MATLAB platform. Figure 3 shows the beam pattern form with the DMI beamforming algorithm and figure 4 shows that according to equations (28) and (29) that the accuracy 421

6 and the performance of the DMI algorithm increases as the number of sample data received increases. Fig 3 Array Factor Plot For DMI Algorithm When The Desired User With AOA 30 Deg And Interferer With AOA - 60 Deg, The Spacing Between The Elements Is And The Block Sample Is K =50 Fig 5 Array Factor Plot For CMA Algorithm When The Desired User With AOA 30, The First Multipath With AOA -60 And The Second Multipath With AOA 0, The Spacing Between The Elements Is And Number Of Iteration Is 25 Fig 4 Array Factor Plot For DMI Algorithm When The Desired User With AOA 30 Deg And Interferer With AOA - 60 Deg, The Spacing Between The Elements Is And The Block Sample Is K =100 Figure 5 shows the array factor plot and how the CMA algorithm has suppressed the multipath signals while directing maximum to the direct path signal. From this figure we can verify that the CMA algorithm has a slow convergence time, and to overcome this problem of the CMA a fast convergence algorithm LSCMA is introduced as shown in figure 6 Fig 6 Array Factor Plot For A Static LSCMA Algorithm When The Desired User With AOA 30, The First Multipath With AOA -60 And The Second Multipath With AOA 0, The Spacing Between The Elements Is And Step Size Is And Number Of Iteration Is 5. Figure 7 shows the polar plot of the LMS algorithm, while figure 8 shows the weighted LMS array plot, Figure 9 shows the array factor plot and how the LMS algorithm places deep null in the direction of the interfering signal and maximum in the direction of the desired signal. Fig.10 shows that according to the condition stated in (40) using a larger value for the LMS adaptive step size 422

7 Mean square error ISSN: µ=0.02 yields better results when compared to a smaller step size µ= Fig 7 Polar Plot Of Beam Pattern Of The LMS Algorithm When The Desired User With AOA 30 Deg And Interfere With AOA -60 Deg, The Spacing Between The Elements Is Fig 10 Shows That According To Equation (40) That Using A Larger Value For The LMS Adaptive Step Size Yields Better Result When Compared To A Smaller Step Size Figure 11 shows that the rate of convergence of RLS algorithm is typically an order of magnitude faster than that of the LMS algorithm, due to the fact the RLS algorithm convergence is independent of the Eigen values distribution of the correlation matrix, as shown by equation (41) Iteration no. Fig8 Weighted LMS Array Plot Fig 11 Array factor plot for RLS algorithm when the desired user with AOA 30 deg and interferer with AOA -60 deg, the spacing between the elements is Fig 9 Array Factor Plot For LMS Algorithm When The Desired User With AOA 30 Deg And Interferer With AOA - 60 Deg, The Spacing Between The Elements Is And Step Size Is VI. CONCLUSION The significance of LMS algorithm cannot be ruled out in generating better main lobe in a specified direction of user and nulls in the interfering signal, The LMS is important because of its simplicity and ease of computation, however, its slow convergence presents an acquisition and tracking problem for cellular system. Simulation results revealed that RLS algorithm involves more computations than LMS; it provides safe side towards main lobe and has better response towards co channel interference. It has been revealed as well that convergence rate of RLS is faster than LMS. The effect of changing step size for LMS algorithm has also been 423

8 studied. RLS Algorithm is found to have minimum BER and error signal magnitude, therefore it has been proved the best algorithm for implementation on Base Station While Constant Modulus Algorithm (CMA) has satisfactory response towards beamforming and it gives better outcome for interference rejection, but one of its major draw backs is the slow convergence which the LSCMA implementation tends to address. REFERENCES [1] R. H. ROY, An overview of Smart Antenna Technology: The next Wave in Wireless Communications, in Proc.1998 IEEE Aerospace Conference, vol. 3, May 1998, pp [2] Joseph C. Liberti, Theodore S. Rappaport. Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications, Prentice Hall PTR, 12 April, [3] Bellofiore, S., Balains, C. A., Foutz, J., Spanins, A. S. Smart Antenna Systems for Mobile Communication Network, part I: Overview and Antenna Design. Antenna and propagation magazine, IEEE, June 2002, 44 (3): [4] M. Chryssomallis, Democritus University, Electrical Engineering Department, Microwave Laboratory, Greece, Smart Antennas, IEEE Antennas and propagation magazine, Vol. 42, No 3, pp. 130, [5] G. V. Tsoulos, Smart Antennas for Mobile Communication Systems: Benefits and Challenges, Electronic and Communication Engineering Journal, pp.1, 2, April [6] Santhi Rani, Subbaiah P. V., Chennakesava R.K, Sudha Rani S. LMS and RLS Algorithms for Smart Antennas in a W-CDMA mobile Communication Environment, ARPN Journal of Engineering and Applied Sciences, vol. 4, No 6, August [7] Sidi Bahiri, Fethi Bendimerad. Performance of Adaptive Beamforming Algorithm for LMS-MCCDMA MIMO Smart Antennas. The international Arab Journal of Information Technology, vol. 6, No. 3, July [8] Raed M. Shubair, Mahmoud A. AL-Qutayri, Jassim M. Samhan. A Setup for the Evaluation of MUSIC and LMS Algorithms for a Smart Antenna System. Journal of Communications, vol.2, No.4, June [9] Susmita Das. Smart Antenna Design for Wireless Communication using Adaptive Beamforming approach. Department of Electrical Engineering, National Institute of Technology Rourkela , Orissa,India. May, [10] Thomas E. Biedka, Analysis and Development of Blind Adaptive Beamforming Algorithms. Department of Electrical Engineering Virgina Polytechnic Institute. October, [11] Zhijun Zhang, Magdy F. Iskander, Zhengqing Yun, Hybrid Smart Antenna Systems, IEEE Transactions on Antenna and Propagation, Vol.51, No.10, Oct [12] Rameshwar Kawitar, D. G. Wakde, Advances in Smart Antenna System, Journal of Scientific & Industrial Research, vol. 64, September 2005, pp [13] Xiao Jian, Yu Lei, Smart antenna technology in 3G system, Journal of Communication and Computer, vol.4, No.7, July [14] Lal C. Godora. Application of Antenna Arrays to Mobile Communications, part I: Performance Improvement, Feasibility, and System Consideration Proceedings of the IEEE, July 1997, 85 (7): [15] A.C.O Azubogu, C.C. okezie. Adaptive Filtering Technique for Noise Cancellation. International Journal of Electrical & Telecommunication System Research, vol.3 No. 3, July [16] Winters J. H, Smart Antennas for Wireless Systems, IEEE Pers Communication Magazine, 5 (1)

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