Continuous Surface Matched Filtering: A Finite Dimensional Analysis

Building on recent trends in multiple-input multiple-output and reconfigurable intelligent surfaces, where densely spaced element arrays are considered, this paper focuses on con-tinuous antenna systems where the receive antenna is modelled as a continuous line (in the one-dimensional case) or a continuous surface (in the two-dimensional case). Considering a spatially-correlated Rayleigh process for the communication channel, we conduct an analytical investigation based on matched filtering. More specifically, we derive an approximated distribution for the instantaneous received signal-to-noise ratio (SNR) at the continuous surface. Furthermore, we derive approximations to the achievable rate, average symbol error rate for Mary phase shift keying (MPSK) and an upper bound for the achievable rate. We use extensive numerical examples to illustrate the accuracy of our approximation to the SNR distribution as well as the performance analysis.