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The Reconfigurable Intelligent Surface (RIS) constitutes one of the prominent technologies for the next generation of wireless communications. It is envisioned to enhance the signal coverage in cases when the direct link of the communication is weak. Recently, beam training based on codebook selection is proposed to obtain the optimized phase configuration of the RIS. After that, the data is transmitted and received by using the classical coherent demodulation scheme (CDS). This training approach is able to avoid the large overhead required by the channel sounding process, and it also circumvents complex optimization problems. However, the beam training still requires the transmission of some reference signals to test the different phase configurations of the codebook, and the best codeword is chosen according to the measurement of the received energy of the reference signals. Then, the overhead due to the transmission of reference signals reduces the spectral efficiency. In this paper, a zero overhead beam training for RIS is proposed, relying on data transmission and reception based on non-CDS (NCDS). At the BS, the received differential data can also be used for the determination of the best beam for the RIS. Therefore, the efficiency of the system is significantly enhanced since reference signals are fully avoided. After choosing the best codebook, NCDS is still more suitable to transmit information for high mobility scenarios as compared to the classical CDS. Analytical expressions for the Signal-to-Interference and Noise Ratio (SINR) for the non-coherent RIS-empowered system are presented. Moreover, a detailed comparison between the NCDS and CDS in terms of efficiency and complexity is also given. The extensive computer simulation results verify the accuracy of the presented analysis and showcase that the proposed system outperforms the existing solutions., Comment: Accepted by IEEE Access 2022