Performance Analysis of Multi-RIS-Aided LoRa Systems With Outdated and Imperfect CSI

Although LoRa has emerged as the leading technology among the rapidly developing low-power wide-area networks, the performance of the LoRa system severely deteriorates over fading channels. To address this problem, in this paper, we introduce multiple reconfigurable intelligent surfaces (multi-RISs) into the LoRa system to improve its performance. Our specific focus is on the impact of outdated channel state information (CSI), the imperfection of estimated CSI, and the design of RIS discrete phase shifts on the performance. To this end, we first use the moment-matching method to obtain the end-to-end (E2E) channel coefficient of the joint outdated channels and erroneous channels over Nakagami-m fading. Moreover, the closed-form bit error rates (BERs) of the proposed system with non-coherent and coherent detections are derived. The results reveal that, in the high signal-to-noise ratio (SNR) regime, coherent detection encounters the error floor and performs worse than non-coherent detection. Furthermore, we also analyze delay outage rate, throughput, and achievable diversity order of the proposed system. The results show that, despite the presence of outdated CSI and channel estimation errors, the proposed system is still superior to RIS-aided LoRa systems adopting blind transmission and RIS-free ones. Finally, we also thoroughly investigate the effects of various important factors such as the correlation factor, channel estimation errors, the number of RIS reflecting elements, and the number of quantization bits for RIS discrete phase shifts on the performance.