An improved mean-square performance analysis of the diffusion least stochastic entropy algorithm

The diffusion least stochastic entropy (DLSE) algorithm yields a better performance than the diffusion complex-valued least mean-square (DCLMS) algorithm for second-order noncircular noise. The existing theoretical steady-state mean-square deviation (MSD) shows a low accuracy due to the use of improper estimations and approximations. Besides, its transient MSD has not been thoroughly studied. This paper provides an improved performance analysis. We first improve the method of estimating the circularity coefficient (CC) of the error signal, which is required for the update equation of the DLSE. This improvement leads to a better match between the theoretical and simulated MSD and makes the transient MSD analysis mathematically tractable. The MSD analysis is performed by using the Gaussian moment factorizing theorem with some statistical assumptions. Besides, another key performance measure, i.e., the excess mean-square error (EMSE) of the DLSE is also analyzed. Simulation results validate the theoretical findings of the DLSE algorithm for second-order noncircular input signals and noise.