On the Performance Analysis of RIS-Assisted Infinite and Finite Blocklength Communication in Presence of an Eavesdropper

This work investigates the performance of a reconfigurable intelligent surface (RIS) aided communication system under ultra-reliable low-latency communication (URLLC) constraints, where the secrecy performance for communication with multiple legitimate users
$(D)$
, scheduled one at a time, in presence of eavesdropper
$(E)$
is analyzed. The outage probability and block error rate (BLER) at
$D$
and
$E$
are derived for infinite and finite blocklength transmissions assuming that the direct communication links between source
$(S)-D$
and
$S-E$
exist. The expressions for the asymptotic outage probability, secrecy capacity, secrecy outage probability and secure BLER are also obtained. The new expressions for the probability density function (PDF) and the cumulative distribution function (CDF) for the difference of phases of two Nakagami
$-m$
distributed channel envelopes are derived. To validate the correctness of the derived analytical expressions and to analyze the impact of various system parameters including the number of RIS meta-atoms, the magnitude of reflection coefficient, transmit signal-to-noise ratio (SNR) threshold, and quantized phase-shifts, Monte-Carlo simulations are used. The performance of the proposed system is compared with that of the decode and forward relay-based system. It is also shown that RIS significantly improves the performance at
$D$
, whereas degrading the same for
$E$
.