Transient Performance of the Bidirectional LMS Over Quasi-Static Wireless Networks

This paper considers the transient performance of the bidirectional least-mean squares (BiLMS) algorithm for unknown parameter estimation over quasi-static wireless networks, where the unknown parameter to be estimated is time-invariant. The algorithm is employed in two different configurations to minimize the mean-square error (MSE) while keeping the convergence speed relatively high. The analytical closed-form expressions for the transient MSE are rigorously derived as a function of training block length. The theoretical results are shown to exactly match the simulation data. At the steady state, BiLMS in the first configuration is observed to achieve an MSE half of the second one. On the other hand, the second configuration is shown to achieve a better convergence rate which makes it more appropriate for short acquisition intervals. An analytical decision rule is accordingly proposed to choose the appropriate configuration in advance based on the signal-to-noise ratio, adaptation step-size and block length.