In this paper, a generalized superimposed training (GST) is proposed for an uplink cell-free multiple-input multiple-output orthogonal frequency-division multiplexing (mMIMO-OFDM) system, which is aided by reconfigurable intelligent surfaces (RISs) to enhance the spectral efficiency in the system. For the GST scheme, the pilots and data symbols are transmitted simultaneously in the coherence time. This scheme is different from traditional separate transmission methods, such as regular pilots (RP) transmission. In the OFDM multi-carrier case, a part of the subcarriers is based on the GST, whereas the other part of subcarriers is used for data transmission only. The channel and data estimations are carried out and the normalized mean-squared error (NMSE), bit error rate (BER), and sum-rate in different schemes are compared. Different receiver cooperation levels are analyzed in this case, including fully centralized processing and local processing. The distributed time processing and iterative process are also used to improve the performance of the data estimation in this system.
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