Minimize Age of Information for IRS-Aided Sensor Systems : How Many IRS Elements Are Needed?

rgb0.00,0.00,0.00In this paper, we investigate an intelligent reflecting surface (IRS) assisted sensor system, where the average age of information (AoI) is derived to characterize the information freshness of short packets. Although the IRS can enhance the beamforming gain which improves the AoI performance, it also introduces higher channel estimation overhead which impairs the AoI performance. The quantitative impact of IRS on AoI performance remains unclear. To this end, our work aims to characterize the relationship of the average AoI in terms of the number of IRS elements and optimize the latter to minimize the former. However, the average AoI expression is difficult to obtain due to the complex composite channel distribution. To tackle this difficulty, we employ the moment matching (MM) technique to approximate the composite channel by Gamma distribution. The obtained average AoI expression is still complicated and it is intractable to directly obtain the optimal IRS elements number. To overcome this challenge, we derive the approximated expressions of the average AoI for small and large IRS elements, and then obtain the intersection between the two approximated expressions as a suboptimal solution. Based on them, we prove that the average AoI first decreases and then increases as the number of IRS elements increases, which indicates there is an optimal number of IRS reflecting elements for attaining the optimal AoI performance. Simulation results verify our theoretical results and demonstrate that the proposed scheme for obtaining the number of IRS elements can achieve almost the same performance as the exhaustive search method and outperforms benchmarks.