Channel estimation for RIS-aided MIMO systems in MmWave wireless communications with a few active elements

Accurate channel estimation poses a significant challenge in the reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) wireless communication system. The fully passive nature of the RIS primarily relies on cascaded channel estimation, given its limitation in transmitting and receiving signals. Although the advantageous of this approach, the increase in the number of RIS elements leads to an exponential growth in the channel coefficient, resulting in costly pilot overhead. To address this challenge, the paper proposes a two-phase framework for separate channel estimation. The framework involves incorporating a few active elements within the passive RIS, enabling the reception and processing of pilot signals at the RIS. Through leveraging the difference in coherence time of the channel, the estimation of the time-varying channel among user equipment (UE) and RIS, as well as the estimation of the pseudo-static channel among RIS and base station (BS), can be performed separately. The two-phase separate channel estimation framework operates as follows: In the first phase, the BS-RIS channel is estimated at the RIS through the utilization of the few active elements. An iterative weighting methodology is employed to formulate the mathematical optimization problem for estimating the BS-RIS signal model. Subsequently, a proposed algorithm grounded on gradient descent (GD) is introduced to efficiently address and solve the optimization problem. In the second phase, the estimation of the UE-RIS channel is achieved by transforming the signal model of the received channel into an analogous tensor model known as Parallel Factor (PARAFAC). This transformation is followed by the application of the least squares (LS) algorithm within this tensor-based representation at BS. The effectiveness of the proposed framework is demonstrated through simulation findings, considering minimum pilot overhead, average spectral efficiency, and normalized mean square error (NMSE). A comparative analysis is performed with three other state-of-the-art existing schemes.