BER analysis of tightly packed planar RIS system using the level of spatial correlation and discrete phase shifter

Abstract

In this article, the bit error rate (BER) performance of a tightly packed reconfigurable intelligent surface (RIS) assisted communication system is analyzed in terms of the level of spatial correlation. In conventional models, channels are assumed to be independent and identically distributed and continuous phase shifts are available for phase compensation. However, in practice, as RIS reflecting units are arranged in more compact form (less than 0.5λ$$ \lambda $$) due to space constraints, correlation effects among the reflecting elements are to be considered. Further, discrete phase shifters are widely used to meet practical deployment limitations. These practical constraints severely affect the error performance of the system. It necessitates that the impact of spatial correlation and discrete phase shifts on the BER performance of the system is to be analyzed. The instantaneous signal to noise ratio is the square of the sum of correlated random variables. In order to analyze the BER performance accurately, the exact statistical distribution for the sum of spatially correlated random variables is to be chosen. In this work, appropriate distribution fitting is chosen based on the level of spatial correlation. Numerical BER expressions are derived with the chosen statistical distributions. The analysis on the impact of spatial correlation and discrete phase shifter on BER performance would be more beneficial for design and practicing engineers in the field of 6G wireless communications.