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 RISaided multi-user massive multiple-input multiple-output (MIMO) systems. To the authors’ knowledge, this represents the first work in the literature on CFO estimation for RIS-aided multiuser communication 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 joint estimation of multiple users’ CFOs, a correlation-based approach is devised using the received signals at all the BS antennas. Using leastsquares (LS) estimation with the obtained CFO values, the channels of all the users are jointly estimated. 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 the more computationally demanding grid search technique while requiring a significantly lower computational load. 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. Furthermore, we analyze the computational complexity and the pilot resource efficiency of the proposed method, and show that the proposed approach requires no extra cost in computational load or pilot overhead.