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The revolutionary technology of \emph{Stacked Intelligent Metasurfaces (SIM)}has been recently shown to be capable of carrying out advanced signalprocessing directly in the native electromagnetic (EM) wave domain. An SIM isfabricated by a sophisticated amalgam of multiple stacked metasurface layers,which may outperform its single-layer metasurface counterparts, such asreconfigurable intelligent surfaces (RISd) and metasurface lenses. We harnessthis new SIM concept for implementing efficient holographic multiple-inputmultiple-output (HMIMO) communications that dot require excessiveradio-frequency (RF) chains, which constitutes a substantial benefit comparedto existing implementations. We first present an HMIMO communication systembased on a pair of SIMs at the transmitter (TX) and receiver (RX),respectively. In sharp contrast to the conventional MIMO designs, theconsidered SIMs are capable of automatically accomplishing transmit precodingand receiver combining, as the EM waves propagate through them. As such, eachinformation data stream can be directly radiated and recovered from thecorresponding transmit and receive ports. Secondly, we formulate the problem ofminimizing the error between the actual end-to-end SIMs'parametrized channelmatrix and the target diagonal one, with the latter representing a flawlessinterference-free system of parallel subchannels. This is achieved by jointlyoptimizing the phase shifts associated with all the metasurface layers of boththe TX-SIM and RX-SIM. We then design a gradient descent algorithm to solve theresultant non-convex problem. Furthermore, we theoretically analyze the HMIMOchannel capacity bound and provide some useful fundamental insights. Extensivesimulation results are provided for characterizing our SIM-based HMIMO system,quantifying its substantial performance benefits.

Stacked Intelligent Metasurfaces for Efficient Holographic MIMO Communications in 6G