Intelligent metasurfaces may be harnessed for realizing efficient holographic multiple-input and multiple-output (MIMO) systems, at a low hardware-cost and high energy-efficiency. As part of this family, we propose a hybrid beamforming design for stacked intelligent metasurfaces (SIM) aided wideband wireless systems relying on the near-field channel model. Specifically, the holographic beamformer is designed based on configuring the phase shifts in each layer of the SIM for maximizing the sum of the baseband eigen-channel gains of all users. To optimize the SIM phase shifts, we propose a layer-by-layer iterative algorithm for optimizing the phase shifts in each layer alternately. Then, the minimum mean square error (MMSE) transmit precoding method is employed for the digital beamformer to support multi-user access. Furthermore, the mitigation of the SIM phase tuning error is also taken into account in the digital beamformer by exploiting its statistics. The power sharing ratio of each user is designed based on the iterative waterfilling power allocation algorithm. Additionally, our analytical results indicate that the spectral efficiency attained saturates in the high signal-to-noise ratio (SNR) region due to the phase tuning error resulting from the imperfect SIM hardware quality. The simulation results show that the SIM-aided holographic MIMO outperforms the state-of-the-art (SoA) single-layer holographic MIMO in terms of its achievable rate. We further demonstrate that the near-field channel model allows the SIM-based transceiver design to support multiple users, since the spatial resources represented both by the angle domain and the distance domain can be exploited.

翻译：智能超表面可用于实现高效的全息多输入多输出（MIMO）系统，其硬件成本低且能量效率高。作为该技术体系的一部分，我们提出了一种基于近场信道模型的、用于堆叠智能超表面（SIM）辅助宽带无线系统的混合波束成形设计。具体而言，全息波束成形器通过配置SIM每一层的相移来设计，以最大化所有用户基带特征信道增益之和。为优化SIM相移，我们提出了一种逐层迭代算法，以交替优化每一层的相移。随后，数字波束成形器采用最小均方误差（MMSE）发射预编码方法来支持多用户接入。此外，数字波束成形器还通过利用其统计特性，考虑了SIM相位调谐误差的抑制。每个用户的功率分配比例基于迭代注水功率分配算法进行设计。此外，我们的分析结果表明，由于不完善的SIM硬件质量导致的相位调谐误差，所实现的频谱效率在高信噪比（SNR）区域趋于饱和。仿真结果表明，SIM辅助的全息MIMO在可达速率方面优于最先进的单层全息MIMO。我们进一步证明，近场信道模型使得基于SIM的收发机设计能够支持多用户，因为可以利用由角度域和距离域共同表示的空间资源。