A new LLMS Algorithm for Antenna Array
Beamforming

Jalal Abdulsayed SRAR, Kah-Seng CHUNG and Ali MANSOUR

Dept. of Electrical and Computer Engineering, Curtin University of Technology, Perth, Australia
jalal.srar@google.com, k.chung@curtin.edu.au, and a.mansour@curtin.edu.au

Abstract- A new adaptive algorithm, called LLMS, which
employs an array image factor, I A , 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.

Keywords—Adaptive array beamforming, LLMS algorithm,
EVM, Rayleigh fading.