The Optimal Pilot Power Allocation Strategy for Multi-IRS Assisted Communication Systems

Intelligent reflecting surface (IRS) is a promising technology that enables the precise control of the electromagnetic environment in future wireless communication networks. To leverage the IRS effectively, the acquisition of channel state information (CSI) is crucial in IRS-assisted communication systems, which, however, is challenging. In this paper, we propose the optimal pilot power allocation strategy for the channel estimation of IRS-assisted communication systems, which is capable of further improving the achievable rate performance with imperfect CSI. More specifically, first of all, we introduce a multi-IRS-assisted communication system in the face of practical channel estimation errors. Furthermore, the ergodic capacity with imperfect CSI is derived in an explicit closed-form expression under the single-input single-output (SISO) consideration. Secondly, we formulate the optimization problem of maximizing the ergodic capacity with imperfect CSI, subject to the constraint of the average uplink pilot power. Thirdly, the method of Lagrange multipliers is invoked to solve the ergodic rate maximizing problem and thus to obtain the optimal pilot power allocation strategy. The resultant pilot power allocation solution suggests allocating more amount of power to the pilots for estimating the weak reflection channels. Besides, we also elaborate on the expense of the proposed pilot power allocation strategy upon analyzing the peak-to-average-power ratio (PAPR) increase quantitatively. Finally, the extensive simulation results verify our analysis and reveal some interesting results. For example, for the user in the vicinity of a large IRS, it is suggested to switch off other IRSs and only switch on the IRS nearest the user; For the user near a small IRS, it is better to switch on all IRSs and perform the optimal pilot power allocation for enhancing the achievable rate performance.