Abstract-A new adaptive algorithm, called LLMS, which employs two Least Mean Square (LMS) sections in tandem, is proposed for different applications of array beamforming. 12The convergence of the LLMS algorithm is analyzed, in terms of mean square error, in the presence of Additive White Gaussian Noise (AWGN) for two different operation modes; normal referencing and self-referencing. Computer simulation results show that the convergence performance of LLMS is superior to the conventional LMS algorithms as well some of the more recent LMS based algorithms, such as constrained-stability LMS (CSLMS), and Modified Robust Variable Step Size LMS (MRVSS) algorithms. It is shown that the convergence of LLMS is quite insensitive to variations in both the input signal-to-noise ratio and the step size used. Also, the operation of the proposed algorithm remains stable even when its reference signal is corrupted by AWGN noise. Furthermore, the fidelity of the signal at the output of the LLMS beamformer is demonstrated through the Error Vector Magnitude (EVM) and the scatter plot obtained.

This paper presents a flexible method of achieving either fixed or self-adaptive antenna beamforming. It involves the use of an array image factor ' d A , which interfaces an RLS and LMS sections in cascade to form the RLMS beamforming algorithm. It is shown that an accurate fixed beam can be obtained by prior setting the elements of ' d A with prescribed values for the required direction. Moreover, the beam direction can also be made adaptive to automatically track the target signal. In this case, a convenient and effective method is described for computing the element values of ' d A based on the estimated RLS output signal and tap weights. Analytical and computer simulation results verify these two modes of operation of the RLMS beamforming algorithm. Furthermore, the convergence of RLMS is shown to be quite insensitive to variations in SNR of the input signal as well as the step sizes associated with the RLS and LMS sections.

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This paper presents a flexible method of achieving either fixed or self-adaptive antenna beamforming. It involves the use of the array image factor ' d A , which interfaces the Recursive Least Squares (RLS) and Least Mean Squares (LMS) sections in cascade to form the RLMS beamforming algorithm. It is shown that an accurate fixed beam can be obtained by simply setting the elements of ' d A with prescribed values corresponding to the required direction. Moreover, the beam direction can also be made adaptive to automatically track the target signal. In this case, a simple method is described for estimating the element values of ' d A based on the estimated RLS output signal and tap weights. Computer simulation results verify these two modes of operation of the RLMS beamforming algorithm. Furthermore, the convergence performance of RLMS is shown to be quite insensitive to variations in SNR of the input signal as well as step sizes associated with the RLS and LMS sections. Keywords-Fixed beam, RLMS algorithm, adaptive antenna array beam forming.

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