Bit Error Probability for Large Intelligent Surfaces Under Double-Nakagami Fading Channels

Ricardo Coelho Ferreira,Eduardo Rodrigues De Lima,Michelle S P Facina,Gustavo Fraidenraich,Felipe A P De Figueiredo

doi:10.1109/ojcoms.2020.2996797

Abstract

In this work, we investigate the probability distribution function of the channel fading between a base station, an array of intelligent reflecting elements, known as large intelligent surfaces (LIS), and a single-antenna user. We assume that both fading channels, i.e., the channel between the base station and the LIS, and the channel between the LIS and the single user are Nakagami-m distributed. Additionally, we derive the exact bit error probability considering quadrature amplitude (M-QAM) and binary phase-shift keying (BPSK) modulations when the number of LIS elements, n, is equal to 2 and 3. We assume that the LIS can perform phase adjustment, but there is a residual phase error modeled by a Von Mises distribution. Based on the central limit theorem, and considering a large number of reflecting elements, we also present an accurate approximation and upper bounds for the bit error rate. Through several Monte Carlo simulations, we demonstrate that all derived expressions perfectly match the simulated results.

Highlights

T HE DEMAND for data rate has increased exponentially in the last years, mainly due to the emergence of new services such as the Internet of things (IoT) and the video on demand
We present some numerical results to validate the Monte Carlo simulations obtained from 106 realizations
We have considered binary phase-shift keying (BPSK) and M-QAM modulations under the effect of Nakagami-m fading channels

Summary

INTRODUCTION

T HE DEMAND for data rate has increased exponentially in the last years, mainly due to the emergence of new services such as the Internet of things (IoT) and the video on demand. Using a massive number of passive reflectors and a small number of active ones, the LIS can learn the channel parameters and autonomously optimize the data transmission Following this idea, Basar et al [6] present closed-form solutions for optimization problems. The authors only consider a phase error with uniform distribution (worst case of phase estimation) and a channel subjected to the Rayleigh fading They do not provide any expression for a small number of reflectors. The expressions derived here allow us to predict how the channel parameters and the phase error distribution impact the performance of the communication between the base station and the enduser.

SYSTEM MODEL

FADING DISTRIBUTION

BIT ERROR PROBABILITY

NUMERICAL RESULTS

CONCLUSION