Tracking Analysis of Normalized Adaptive Algorithms

In this work, tracking analysis of normalized adaptive algorithms is carried out in the presence of two sources of nonstationarites; carrier frequency offset between transmitter and receiver, and random variations in the environment. A unified approach is carried out using a mixednorm-type error nonlinearity. Close agreement between analytical analysis and simulation results is obtained for the case of the NLMS algorithm, which is the only algorithm considered here due to space limitations. The results show that unlike the stationary case, the steady-state excess-mean-square error is not a monotonically increasing function of the step-size, while the ability of the adaptive algorithm to track the variations in the environment degrades by increasing the frequency offset.