  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 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 allows accurate estimation of 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
BS antennas. Using least-squares (LS) estimation with the obtained CFO values,
the channels of all users are jointly estimated. For optimization of the RIS
phase shifts at the data transmission stage, we propose a projected gradient
method (PGM). 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.
