Convergence evaluation of a random step-size NLMS adaptive algorithm in system identification

A new and simple method to adjust the step-size (μ) of the standard Normalized Least Mean Square (NLMS) adaptive algorithm is proposed here. The value of μ is totally controlled by the use of a Pseudorandom Noise (PRN) uniform distribution that is defined by values from 0 to 1. Randomizing the step-size parameter eliminates much of the trade-off between residual error and convergence speed compared with the fixed step-size. The mean-square error (MSE) of using the new algorithm in the adaptation process of system identification over a defined communication channel is investigated here. The proposed uniformly distributed step-size variation in the adaptation process of the NLMS algorithm makes it possible to have similar convergence rate but lower steady state error compared with fixed μ.