Blind adaptive identification and equalization using bias-compensated NLMS methods

In this paper, two new blind adaptive identification and equalization algorithms based on second-order statistics are proposed. We consider a practical case where the noise statistics of each transmission channel is unknown. Resorting to the technique of antennas array, a single-input double-output channel can be obtained. We further convert the problem of blind identification into an errors-in-variables (EIV) parameter estimation problem, then we apply the normalized least-mean squares (NLMS) algorithms to tackle the problem. To improve the performance of the NLMS algorithms, we also develop a variable step-size NLMS (VSS-NLMS) algorithm that ensures the stability of the algorithm and faster convergence speed at the beginning of the iterations process. Under various practical scenarios, noise affects transmission channels; it is necessary to estimate the variance and remove the bias. By modifying the cost function, we present a bias-compensated NLMS (BC-NLMS) algorithm and a bias-compensated NLMS algorithm with variable step-size (BC-VSS-NLMS) to eliminate the bias. The proposed algorithms estimate the variances of the noise online, and therefore, the noise-induced bias can be removed. The estimate of the channel characteristics is available for equalization. Simulation results are presented to demonstrate the performance of the proposed algorithms.