Reconfigurable intelligent surface (RIS) is a promising technique to improve the performance of future wireless communication systems at low energy consumption. To reap the potential benefits of RIS-aided beamforming, it is vital to enhance the accuracy of channel estimation. In this paper, we consider an RIS-aided multiuser system with non-ideal reflecting elements, each of which has a phase-dependent reflecting amplitude, and we aim to minimize the mean-squared error (MSE) of the channel estimation by jointly optimizing the training signals at the user equipments (UEs) and the reflection pattern at the RIS. As examples the least squares (LS) and linear minimum MSE (LMMSE) estimators are considered. The considered problems do not admit simple solution mainly due to the complicated constraints pertaining to the non-ideal RIS reflecting elements. As far as the LS criterion is concerned, we tackle this difficulty by first proving the optimality of orthogonal training symbols and then propose a majorization-minimization (MM)-based iterative method to design the reflection pattern, where a semi-closed form solution is obtained in each iteration. As for the LMMSE criterion, we address the joint training and reflection pattern optimization problem with an MM-based alternating algorithm, where a closed-form solution to the training symbols and a semi-closed form solution to the RIS reflecting coefficients are derived, respectively. Furthermore, an acceleration scheme is proposed to improve the convergence rate of the proposed MM algorithms. Finally, simulation results demonstrate the performance advantages of our proposed joint training and reflection pattern designs.

翻译：可重构智能表面（RIS）是一种以低能耗提升未来无线通信系统性能的前沿技术。为充分挖掘RIS辅助波束赋形的潜在优势，提高信道估计精度至关重要。本文考虑具有非理想反射元件的RIS辅助多用户系统（每个反射元件存在相位依赖的反射幅度），通过联合优化用户设备（UE）的训练信号与RIS的反射模式，以最小化信道估计的均方误差（MSE）。作为示例，分别采用最小二乘（LS）与线性最小均方误差（LMMSE）估计器。由于非理想RIS反射元件涉及的复杂约束条件，所考虑的问题难以获得简单解。针对LS准则，我们首先证明正交训练符号的最优性，进而提出基于最大-最小化（MM）的迭代方法设计反射模式，并在每次迭代中获得半闭式解。针对LMMSE准则，我们采用基于MM的交变算法处理联合训练与反射模式优化问题，分别导出训练符号的闭式解与RIS反射系数的半闭式解。此外，提出加速方案以提升所提MM算法的收敛速度。仿真结果验证了所提联合训练与反射模式设计方案的性能优势。