A New LLMS Algorithm for Antenna Array Beamforming

A new adaptive algorithm, called LLMS, which employs an array image factor, A_I, sandwiched in between two Least Mean Square (LMS) sections, is proposed for different applications of array beamforming. The convergence of LLMS algorithm is analyzed, in terms of mean square error, in the presence of Additive White Gaussian Noise (AWGN) for two different modes of operation; namely with either an external reference or self-referencing. Unlike earlier LMS based schemes, which make use of step size adaptation to enhance their performance, the proposed algorithm derives its overall error signal by feeding back the error signal from the second LMS stage to combine with that of the first LMS section. This results in LLMS being less sensitive to variations in input signal-to-noise ratio as well as the step sizes used. Computer simulation results show that the proposed LLMS algorithm is superior in convergence performance over the conventional LMS algorithm 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. Also, the operation of LLMS remains stable even when its reference signal is corrupted by AWGN. It is also shown that LLMS performs well in the presence of Rayleigh fading.