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This paper presents a flexible method of achieving either fixed or self-adaptive antenna beamforming. It involves the use of an array image factor Â¿d, 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 Â¿d 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 Â¿d 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.