Hyperbolic Tangent Function-based LMS Channel Estimation for mmWave MIMO Systems

Accurate channel estimation is crucial for millimeter wave multiple-input multiple-output (MIMO) systems. This paper introduces two novel regularization-based block least mean square (BLMS) channel estimation algorithms. Firstly, we propose a hyperbolic tangent function-based regularization (tanhR) to address the inherent multi-parameter trade-off issues associated with the approximate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{0}$</tex>-norm. Then, we apply this regularization into the BLMS algorithm to improve its sparse representation capability. We further present a weighted-tanh-R-based BLMS to strengthen the sparsity-inducing properties. Additionally, we have derived the range of regularization parameters and proved that the tanh-R-based BLMS can effectively narrow the parameter range of the weighted-tanh-R-based BLMS, addressing the multi-parameter trade-off associated with the approximate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{0}$</tex> norm. This significantly reduces the complexity of parameter trade-off during the simulation process while achieving excellent convergence performance. Simulation results validate the theoretical derivations and demonstrate the superiority of the proposed methods.