Joint carrier frequency offset, doubly selective channel estimation and data detection for RIS assisted MIMO OFDMA uplink system

With the presence of an array of passive elements embedded in a reconfigurable intelligent surface (RIS), estimation of time-varying channels between a fast-moving user and the fixed base station (BS) is more challenging than conventional static channels. In this paper, we propose a joint technique for the estimation of carrier frequency offset (CFO) and doubly selective channel (DSC), and data detection in the RIS-assisted multiple input multiple output (MIMO) orthogonal frequency division multiple access (OFDMA) uplink system. The time variations of the channel within the OFDMA symbol are represented using the basis expansion model (BEM), significantly reducing the number of estimated parameters. An autoregressive (AR) model is used to characterize the variations in BEM coefficients and CFOs over successive OFDMA symbols. A novel technique of combining the Schmidt extended Kalman filtering (SEKF) and Gaussian particle filtering (GPF) integrated with an iterative detector and decoder (IDD) receiver structure (IDD-SKGPF) is proposed to estimate the BEM coefficients, CFOs and to detect the symbols in two stages. Performance of the proposed method is evaluated using normalized mean square error (NMSE) and compared with the derived Bayesian Cramer-Rao bound (BCRB) and modified BCRB. Furthermore, the reflection coefficient is optimized in the time domain by maximizing the achievable rate to demonstrate that the exploitation of RIS may result in significant bit error rate (BER) performance improvement of $6dB$ in SNR over non optimized RIS scenario even under high mobility scenarios.