Average Rate and Error Probability Analysis in Short Packet Communications over RIS-aided URLLC Systems

TL;DR

This paper analyzes the performance of RIS-aided URLLC systems in short packet regimes, focusing on achievable rate and error probability, considering phase errors and hardware impairments, and demonstrating the benefits of RIS in reliability and latency.

Contribution

It introduces a Gamma distribution-based SNR model for RIS channels in FBL regimes, accounting for phase errors and hardware impairments, and evaluates their impact on system performance.

Findings

Monte Carlo simulations match the Gamma SNR distribution for large RIS arrays.

RIS significantly improves reliability in URLLC scenarios.

Phase errors increase the required number of RIS elements for target error probabilities.

Abstract

In this paper, the average achievable rate and error probability of a reconfigurable intelligent surface (RIS) aided systems is investigated for the finite blocklength (FBL) regime. The performance loss due to the presence of phase errors arising from limited quantization levels as well as hardware impairments at the RIS elements is also discussed. First, the composite channel containing the direct path plus the product of reflected channels through the RIS is characterized. Then, the distribution of the received signal-to-noise ratio (SNR) is matched to a Gamma random variable whose parameters depend on the total number of RIS elements, phase errors and the channels' path loss. Next, by considering the FBL regime, the achievable rate expression and error probability are identified and the corresponding average rate and average error probability are elaborated based on the proposed SNR distribution. Furthermore, the impact of the presence of phase error due to either limited quantization levels or hardware impairments on the average rate and error probability is discussed. The numerical results show that Monte Carlo simulations conform to matched Gamma distribution to received SNR for sufficiently large number of RIS elements. In addition, the system reliability indicated by the tightness of the SNR distribution increases when RIS is leveraged particularly when only the reflected channel exists. This highlights the advantages of RIS-aided communications for ultra-reliable and low-latency systems. The difference between Shannon capacity and achievable rate in FBL regime is also discussed. Additionally, the required number of RIS elements to achieve a desired error probability in the FBL regime will be significantly reduced when the phase shifts are performed without error.