Optimum step size of sign algorithm for nonstationary adaptive filtering

The adaptive filtering sign algorithm is analyzed in the case of nonstationary and correlated data. The excess time average absolute estimation error (EAAE) is used as a performance index of the algorithm. It is proved that the EAAE is the sum of two terms: one proportional to the algorithm step size μ and the other proportional to 1/μ. The optimum step size that minimizes the EAAE is found equal to √Q /P, with Q being the power of fluctuations of the optimal filter weights, and P being the power of filter input. This formula is derived under the assumption that increments of optimal filter weights are white. Computer simulations are used to examine the validity of the formula for other models of variation of the optimal filter. Simulation results show a good fit with the obtained optimum step size formula