Channel Estimation for Stacked Intelligent Metasurfaces in Rician Fading Channels

The recent combination of the rising architectures, known as stacked intelligent metasurface (SIM) and holographic multiple-input multiple-output (HMIMO), drives toward breakthroughs for next-generation wireless communication systems. Given the fact that the number of elements per surface of the SIM is much larger than the base station (BS) antennas, the acquisition of the channel state information (CSI) in SIM-aided multi-user systems is challenging, especially when a line-of-sight (LoS) component is present. Thus, in this letter, we address the channel procedure under conditions of Rician fading by proposing a protocol in terms of a minimum mean square error (MMSE) estimator for wave-based design in a single phase. Moreover, we derive the normalized mean square error (NMSE) of the suggested estimator, and provide the optimal phase shifts minimising the NMSE. Numerical results illustrate the performance of the new channel estimation protocol.