Distributed separated-decorrelation LMS algorithms over sensor networks with noisy inputs

When the input is a highly correlated and noisy signal over sensor networks, it will lead to the severe performance degeneration of traditional distributed algorithms in terms of convergence rate and steady-state error. To tackle such an issue, this paper proposes distributed bias-compensated separated-decorrelation least mean-square (BC-SDLMS) algorithms. Due to the adoption of new separated-decorrelation structure and bias-compensated term, the steady-state mean-square error with the proposed algorithms can be reduced in comparison with the previous decorrelation schemes. The mean-square analysis is also carried out, which indicates that the proposed algorithms can converge to an unbiased solution. Moreover, an effective estimate for the noise variance at the input terminal of every node is designed. Finally, simulation comparisons are made between the proposed BC-SDLMS algorithms and the competing methods in terms of convergence rate and steady-state error for different colored and noisy inputs.