Joint CFO and Channel Estimation for RIS-Aided Multi-User Massive MIMO Systems

Accurate channel estimation is essential to achieve the performance gains promised by the use of reconfigurable intelligent surfaces (RISs) in wireless communications. In the uplink of multi-user orthogonal frequency division multiple access (OFDMA) systems, synchronization errors such as carrier frequency offsets (CFOs) can significantly degrade the channel estimation performance. This becomes more critical in RIS-aided communications, as the RIS phases are adjusted based on the channel estimates and even a small channel estimation error leads to a significant performance loss. Motivated by this, we propose a joint CFO and channel estimation method for RIS-aided multi-user massive multiple-input multiple-output (MIMO) systems. Our proposed pilot structure makes it possible to accurately estimate the CFOs without multi-user interference (MUI), using the same pilot resources for both CFO estimation
and
channel estimation. For optimization of the RIS phase shifts at the data transmission stage, we propose a projected gradient method (PGM) which achieves the same performance as a more computationally demanding grid search technique while having a significantly lower computational complexity. Simulation results demonstrate that the proposed method provides an improvement in the normalized mean-square error (NMSE) of channel estimation as well as in the bit error rate (BER) performance. Moreover, analyzing the computational complexity and the pilot resource efficiency of the proposed method, we demonstrate that the proposed estimation approach requires low computational load and no extra cost in pilot overhead.