Reconfigurable intelligent surface (RIS) is a promising technology that enables the customization of electromagnetic propagation environments in next-generation wireless networks. In this paper, we investigate the optimal pilot power allocation during the channel estimation stage to improve the ergodic channel gain of RIS-assisted systems under practical imperfect channel state information (CSI). Specifically, we commence by deriving an explicit closed-form expression of the ergodic channel gain of a multi-RIS-aided communication system that takes into account channel estimation errors. Then, we formulate the pilot power allocation problem to maximize the ergodic channel gain under imperfect CSI, subject to the average pilot power constraint. Then, the method of Lagrange multipliers is invoked to obtain the optimal pilot power allocation solution, which indicates that allocating more power to the pilots for estimating the weak reflection channels is capable of effectively improving the ergodic channel gain under imperfect CSI. Finally, extensive simulation results corroborate our theoretical analysis.

翻译：可重构智能表面（RIS）是一种能够定制下一代无线网络电磁传播环境的前沿技术。本文研究在信道估计阶段优化导频功率分配，以提升实际非完美信道状态信息（CSI）条件下RIS辅助系统的遍历信道增益。具体而言，我们首先推导出考虑信道估计误差的多RIS辅助通信系统遍历信道增益的显式闭式表达式。随后，构建了在平均导频功率约束下最大化非完美CSI遍历信道增益的导频功率分配问题。进而采用拉格朗日乘子法求解最优导频功率分配方案，结果表明为弱反射信道的估计分配更多导频功率，能有效提升非完美CSI下的遍历信道增益。最后，大量仿真结果验证了我们的理论分析。