This study focuses on channel estimation for reconfigurable intelligent surface (RIS)-assisted mmWave systems, in which the RIS is used to facilitate base-to-user data transfer. For beamforming to work with active and passive elements, a large-size cascade channel matrix should always be known. Low training costs are achieved by using the mmWave channels’ inherent sparsity. The research provides a unique compressive sensing-based channel estimation approach for reducing pilot overhead issues to a minimum. The proposed technique estimates channel data signals in a downlink for RIS-assisted mmWave systems. The mmWave systems often have a sparse distribution of signal sources due to the spatial correlations of the domains. This distribution pattern makes it possible to use compressive sensing methods to resolve the channel estimation issue. In order to decrease the pilot overhead, which is necessary to predict the channel, the proposed method extends the Re‘nyi entropy function as the sparsity-promoting regularizer. In contrast to conventional compressive sensing techniques, which necessitate an initial knowledge of the signal’s sparsity level, the presented method employs sparsity adaptive matching pursuit (SAMP) techniques to gradually determine the signal’s sparsity level. Furthermore, it introduces a threshold parameter based on the signal’s energy level to eliminate the sparsity level requirement. Extensive simulations show that the presented channel estimation approach surpasses the traditional OMP-based channel estimation methods in terms of normalized mean square error performance. In addition, the computational cost of channel estimation is lowered. Based on the simulations, our approach can estimate the channel well while reducing training overhead by a large amount.
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