Adaptive Sparse Channel Estimation for RIS-Assisted mmWave Massive MIMO Systems

The integration of reconfigurable intelligent surfaces (RISs) with millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems holds significant promise for future wireless communication methods aiming to achieve high-speed data transmission and expand communication coverage. However, channel estimation (CE) in RIS-assisted wireless communication systems faces many challenges due to the limited signal processing capability of the RIS. Existing methods often fail to fully capture the non-uniform sparsity of mmWave channels. To address this limitation, we propose an adaptive sparse CE scheme involving two progressive algorithms, i.e., normalized least mean squares–log sum (NLMS-LOG) and normalized least mean squares–normalized least mean fourth–log sum (NLMS-NLMF-LOG), for RIS-assisted mmWave massive MIMO systems. The proposed scheme selectively adjusts the channel coefficients to improve the accuracy of the estimation, enabling more efficient exploitation of the inherent non-uniform sparsity in mmWave channels. The NLMS-LOG algorithm innovatively incorporates a log-sum penalty term into the cost function of the NLMS algorithm, thereby increasing the convergence rate. Building upon NLMS-LOG, the NLMS-NLMF-LOG algorithm employs a mixed error function to achieve superior performance across different SNR conditions. The simulation results demonstrate that the proposed scheme outperforms existing methods, such as the NLMS, sparse exponential forgetting window least mean square, and sparse hybrid adaptive filtering algorithms, in terms of CE accuracy and convergence speed.