Resource Allocation for Channel Estimation in Reconfigurable Intelligent Surface-Aided Multi-Cell Networks

Reconfigurable intelligent surface (RIS) is a promising solution to deal with the blockage-sensitivity of millimeter wave band and reduce the high energy consumption caused by network densification. However, deploying large scale RISs may not bring expected performance gain due to significant channel estimation overhead and non-negligible reflected interference. In this paper, we derive the analytical expressions of the coverage probability, area spectrum efficiency (ASE) and energy efficiency (EE) of a downlink RIS-aided multi-cell network. In order to optimize the network performance, we investigate the conditions for the optimal number of training symbols of each antenna-to-antenna and antenna-to-element path (referred to as the optimal unit training overhead) in channel estimation. Our study shows that: 1) RIS deployment is not `the more, the better', only when blockage objects are dense should one deploy more RISs; 2) the coverage probability is maximized when the unit training overhead is designed as large as possible; 3) however, the ASE-and-EE-optimal unit training overhead exists. It is a monotonically increasing function of the frame length and a monotonically decreasing function of the average signal-to-noise-ratio (in the high signal-to-noise-ratio region). Additionally, the optimal unit training overhead is smaller when communication ends deploy particularly few or many antennas.