Average Rate and Error Probability Analysis in Short Packet Communications Over RIS-Aided URLLC Systems

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. Index Terms-Average achievable rate, block error probability, finite blocklength (FBL), factory automation, reconfigurable intelligent surface (RIS), ultra-reliable low-latency communications (URLLC).

A Functional Architecture for 6G Special-Purpose Industrial IoT Networks

“…In the case of such sparsity, the channel estimation problem can be formulated as a sparse signal recovery problem, and subsequently solved using the rich body of knowledge available on solving compressed sensing problems [43]. The application of ML based approaches to directly observe the impact of the RIS elements phase shifts on the achievable rate (or other performance metrics) without estimating the channel itself has also been proposed as an alternative solution [44], which is further investigated in Section IV-C. there is a mismatch in the phase shifts of the RIS elements, Θ(t), due to channel estimation error. The power is normalized by the ideal case corresponding to perfect CSI estimation.…”

Robust Beamforming Design for IRS-Aided URLLC in D2D Networks

“…Consequently, IRS can be a potential and cost-effective solution to realize URLLC. In [9], the authors presented the performance analysis of the average achievable rate and error probability over an IRS-aided URLLC transmission with/without phase noise. Considering non-linear energy harvesting, the end-to-end performance of the IRS-assisted wireless system was analyzed in [10] for industrial URLLC applications, and the approximate closedform expression of block error rate was derived.…”

Joint Sum Rate and Blocklength Optimization in RIS-Aided Short Packet URLLC Systems

“…Moreover, employing RIS supplies the stringent latency and reliability requirements to enhance the quality of URLLC transmission especially when the direct links are blocked. Hence, RIS can have a key role in wireless systems considering URLLC requirements [6], [7].…”