Performance of RLMS Algorithm in Adaptive Array Beam Forming Jalal Abdulsayed Srar and Kah-Seng Chung Department of Electrical and Computer Engineering, Curtin University of Technology, Perth, WA jalal.srar@postgrad.curtin.edu.au, and k.chung@curtin.edu.au Abstract—This paper examines the performance of an adaptive linear array employing the new RLMS algorithm, which consists of a recursive least square (RLS) section followed by a least mean square (LMS) section. The performance measures used are output and input signal-to-interference plus noise ratios (SINR), side lobe level (SLL), and SINR o as a function of the direction of arrival of the interfering signal. Computer simulation results show that the performance of RLMS is superior to either the RLS or LMS based on these measures, particularly when operating with low input SINR. Keywords RLS algorithm, LMS algorithm, RLMS algorithm, adaptive antenna array beam forming. I. INTRODUCTION The continued demand for wireless communication services is spearheading research in new techniques for enhancing spectral utilization. One such technique is the use of adaptive or smart antennas to produce a movable beam pattern that can be directed to the desired coverage areas. This characteristic minimizes the impact of unwanted noise and interference, thereby improving the quality of the desired signal. An adaptive antenna consists of an array of antenna elements. The signals picked up by these individual elements are combined through the use of a signal processing unit to form a beam pattern that can be steered toward the desired coverage direction [1]. The performance of the signal processing unit is generally dictated by the beam forming algorithm used. The LMS or RLS are two commonly used algorithms for adaptive beam forming. The former has good tracking performance with low computational complexity, and is robust against numerical errors. On the other hand, the RLS algorithm can achieve a faster convergence which is independent of the eigen-value spread variations of the input signal correlation matrix [1]. These desirable features offered by both the LMS and RLS algorithms can be jointly realized through the use of a new algorithm, called RLMS [2]. The RLMS algorithm consists of two signal processing sections; an RLS section followed by an LMS section, as shown in Fig. 1. The convergence performance of RLMS is analyzed in [2]. In this paper, the effectiveness of the RLMS algorithm for beam forming in an adaptive linear array consisting of N isotropic antenna elements is evaluated under different operating conditions, including the presence of a cochannel interfering signal, and additive white Gaussian noise (AWGN) of zero mean and variance 2 σ . The performance measures adopted are the signal-to-interference plus noise ratio ( ) SINR , the side lobe level (SLL), and the variation of the output SINR as a function of the angle of arrival (AOA) of the interfering signal. For comparison, corresponding results obtained with the use of only the RLS or LMS algorithm are also presented. The paper is organized as follows. In section II, the RLMS system model for the adaptive array is described. Section III reviews the convergence of the RLMS algorithm. A description of the computer simulation study is provided in Section IV, followed by the results presented in Section V. Section IV concludes the paper. II. RLMS SYSTEM OVERVIEW Fig. 1 shows the block diagram of an N-isotropic element adaptive linear array, which employs RLMS as its beam forming algorithm. Let the desired signal () d s t and a cochannel interference () i s t , both originated from a distance, are impinging on the array at an angle and d i θ θ , respectively, as shown in Fig. 1. The resulting outputs of the individual antenna elements in the presence of AWGN, () t n of variance 2 σ can be expressed as 1 2 () [ ( ), ( ), ..., ( )] () () () T N d d i i t x t x t x t s t s t t = = + + x A A n (1) where and d i A A are the array factors for the desired signal and the cochannel interference, respectively. By referencing with respect to the first element, and d i A A are given by 2 ( 1) [1, , , ...., ] d d d j j N j T d e e e ψ ψ ψ − − − − = A (2) 2 ( 1) [1, , , ...., ] I I I j j N j T i e e e ψ ψ ψ − − − − = A (3) with sin( ) 2 d d d θ ψ π λ = and sin( ) 2 i i d θ ψ π λ = , where d is the antenna element spacing, λ is the carrier wavelength [3] , and ( ) T denotes transpose. 1-4244-2424-5/08/$20.00 ©2008 IEEE ICCS 2008 493