Doubly-Dispersive MIMO Channels with Stacked Intelligent Metasurfaces: Modeling, Parametrization, and Receiver Design

Abstract: Introduced with the advent of statistical wireless channel models for high mobility communications and having a profound role in communication-centric (CC) integrated sensing and communications (ISAC), the doubly-dispersive (DD) channel structure has long been heralded as a useful tool enabling the capture of the most important fading effects undergone by an arbitrary time-domain transmit signal propagating through some medium. However, the incorporation of this model into multiple-input multiple-output (MIMO) system setups, relying on the recent paradigm-shifting transceiver architecture based on stacked intelligent metasurfaces (SIM), in an environment with reconfigurable intelligent surfaces (RISs) remains an open problem due to the many intricate details that have to be accounted for. In this paper, we fill this gap by introducing a novel DD MIMO channel model that incorporates an arbitrary number of RISs in the ambient, as well as SIMs equipping both the transmitter and receiver. We then discuss how the proposed metasurfaces-parametrized DD (MPDD) channel model can be seamlessly applied to waveforms that are known to perform well in DD environments, namely, orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), and affine frequency division multiplexing (AFDM), with each having their own inherent advantages and disadvantages. An illustrative application of the programmable functionality of the proposed model is finally presented to showcase its potential for boosting the performance of the aforementioned waveforms. Our numerical results indicate that the design of waveforms suitable to mitigating the effects of DD channels is significantly impacted by the emerging SIM technology.