Adaption Penalized Complex LMS for Sparse Under-Ice Acoustic Channel Estimations

Abstract

Accurate channel information is usually required in under-ice acoustic (UIA) communication, which exhibits a sparse characteristic. A type of norm-constrained least mean square (LMS) algorithm performs well in estimating the real-valued (passband) channels but cannot be directly applied to complex-valued (baseband) channels. This paper generalizes norm-constrained complex LMS. Complex-valued zero-attracting LMS and $l_{0}$ -norm LMS (C $l_{0} $ -LMS) are mentioned first. These two algorithms render a fixed penalty to each coefficient, which may deteriorate the performance. Then, we propose a complex-valued adaption penalized LMS (CAP-LMS) to further utilize the sparsity of the UIA channels. The adaption penalty is achieved by dividing $p$ -norm-like constraints into two separate groups according to the $l_{1} $ -norm of each coefficient. For the dominant coefficients in the large group, the norm constraint disappears to reduce the estimation bias. For the small coefficients, the adaption penalty aims to accelerate the convergence speed. Simulation results are presented to demonstrate the superior performance of the CAP-LMS algorithm. Data processing results from two under-ice experiments show the feasibility and validity of the proposed algorithms in practical UIA applications.