Performance analysis of diffusion LMS algorithm for cyclostationary inputs

As a well-known non-stationary signal, the cyclostationary white Gaussian signal widely exists in many practical applications, which is defined as a particular Gaussian noise whose autocorrelation function is cyclically time-varying. This paper presents the performance analysis of the diffusion least mean squares (DLMS) algorithms in distributed networks while the input signals are the cyclostationary white Gaussian process. We analyze mean and mean square behaviors of the DLMS algorithm. It is found that the time-variations of steady-state mean square deviation (MSD) of DLMS algorithm can be ignored when the input signals have the fast variations of input autocorrelation function. Moreover, the robustness of the DLMS algorithm in the H∞ sense for cyclostationary inputs over networks is analyzed. The bound of convergence time of the DLMS algorithm for cyclostationary white Gaussian inputs is also provided in this paper. The simulated results show the validity of the analytical results.