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.

中文翻译：

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RIS辅助URLLC系统上的短数据包通信中的平均速率和错误概率分析

在本文中，针对有限块长（FBL）机制，研究了可重构智能表面（RIS）辅助系统的平均可实现率和错误概率。还讨论了由于有限的量化级别引起的相位误差以及RIS元件的硬件损伤而导致的性能损失。首先，表征包含直接路径加上通过RIS的反射通道乘积的复合通道。然后，将接收到的信噪比（SNR）的分布与Gamma随机变量匹配，该变量的参数取决于RIS元素的总数，相位误差和通道的路径损耗。接下来，通过考虑FBL制度，根据建议的信噪比分布，确定了可达到的速率表达和错误概率，并阐述了相应的平均速率和平均错误概率。此外，还讨论了由于有限的量化级别或硬件缺陷导致的相位误差对平均速率和误差概率的影响。数值结果表明，对于足够大量的RIS元素，蒙特卡洛模拟符合匹配的Gamma分布，以符合接收到的SNR。另外，当利用RIS时，特别是当仅存在反射通道时，由SNR分布的紧密度表示的系统可靠性会提高。这凸显了RIS辅助通信在超可靠和低延迟系统中的优势。还讨论了FBL体制下Shannon能力与可实现率之间的差异。另外，当执行相移而没有错误时，在FBL机制中实现所需错误概率所需的RIS元素数量将大大减少。