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A new adaptive algorithm, called least mean square- least mean square (LLMS) algorithm, which employs an array image factor, , sandwiched in between two least mean square (LMS) algorithm sections, is proposed for different applications of array beamforming. It can operate with either prescribed or adaptive . The convergence of LLMS algorithm is analyzed for two different operation modes; namely with external reference or self-referencing. The range of step size values for stable operation has been established. Unlike earlier LMS algorithm based techniques, the proposed algorithm derives its overall error signal by feeding back the error signal from the second LMS algorithm stage to combine with that of the first LMS algorithm section . Computer simulation results show that LLMS algorithm is superior in convergence performance over earlier LMS based algorithms, and is quite insensitive to variations in input signal-to-noise ratio and actual step size values used. Furthermore, LLMS algorithm remains stable even when its reference signal is corrupted by additive white Gaussian noise (AWGN). In addition, the proposed LLMS algorithm is robust when operating in the presence of Rayleigh fading. Finally, the fidelity of the signal at the output of an LLMS algorithm beamformer is demonstrated by means of the resultant values of error vector magnitude (EVM) and scatter plots.