Steady-state analysis of quantized distributed incremental LMS algorithm without Gaussian restriction

In this paper, we analyze the steady-state performance of the distributed incremental least mean-square (DILMS) algorithm when it is implemented in finite-precision arithmetic. Our analysis in this paper does not consider any distribution of input data. We first formulate the update equation for quantized DILMS algorithm, and then we use a spatial-temporal energy conservation argument to derive theoretical expressions that evaluate the steady-state performance of individual nodes in the network. We consider mean-square error, excess mean-square error, and mean-square deviation as the performance criteria. Simulation results are generated by using two types of signals, Gaussian and non-Gaussian distributed signals. As the simulation results show, there is a good match between the theory and simulation.