A new fuzzy logic application to search the optimal step size for NLMS beamforming

This paper proposes a new application based on fuzzy logic to search the optimal Step Size of the Normalized Least Mean Square (NLMS) algorithm for beamforming systems. The searching of the step size depends on the fuzzy inference results of an estimation of the final value of the cost function (J_E) instead of using its instantaneous value. The update of the step-size is performed outside of the adaptive algorithm and given it feedback by the fuzzy inference system; therefore the step-size is still fixed for the NLMS algorithm but variable for the complete searching scheme. Simulation experimental results show that a useful approximation of the optimal step-size can be obtained for different conditions of signal-to-noise plus interference ratios (SINR) and the minimization of the mean square error for the adaptive beamforming algorithm is also achieved.