Emerging technologies, such as holographic multiple-input multiple-output (HMIMO) and stacked intelligent metasurface (SIM), are driving the development of wireless communication systems. Specifically, the SIM is physically constructed by stacking multiple layers of metasurfaces and has an architecture similar to an artificial neural network (ANN), which can flexibly manipulate the electromagnetic waves that propagate through it at the speed of light. This architecture enables the SIM to achieve HMIMO precoding and combining in the wave domain, thus significantly reducing the hardware cost and energy consumption. In this letter, we investigate the channel estimation problem in SIM-assisted multi-user HMIMO communication systems. Since the number of antennas at the base station (BS) is much smaller than the number of meta-atoms per layer of the SIM, it is challenging to acquire the channel state information (CSI) in SIM-assisted multi-user systems. To address this issue, we collect multiple copies of the uplink pilot signals that propagate through the SIM. Furthermore, we leverage the array geometry to identify the subspace that spans arbitrary spatial correlation matrices. Based on partial CSI about the channel statistics, a pair of subspace-based channel estimators are proposed. Additionally, we compute the mean square error (MSE) of the proposed channel estimators and optimize the phase shifts of the SIM to minimize the MSE. Numerical results are illustrated to analyze the effectiveness of the proposed channel estimation schemes.

翻译：新兴技术，如全息多输入多输出(HMIMO)和堆叠智能超表面(SIM)，正推动无线通信系统的发展。具体而言，SIM通过在物理上堆叠多层超表面构建而成，其架构类似于人工神经网络(ANN)，能够以光速灵活操控穿过其中的电磁波。该架构使SIM能够在波域实现HMIMO预编码与合并，从而显著降低硬件成本与能耗。本文研究了SIM辅助多用户HMIMO通信系统中的信道估计问题。由于基站(BS)的天线数量远小于SIM每层的超原子数量，在SIM辅助多用户系统中获取信道状态信息(CSI)具有挑战性。为解决该问题，我们收集了多个穿过SIM的上行导频信号副本。此外，我们利用阵列几何结构识别张成任意空间相关矩阵的子空间。基于信道统计的部分CSI，提出了两种基于子空间的信道估计器。同时，计算了所提信道估计器的均方误差(MSE)，并优化SIM的相移以最小化MSE。数值结果展示了所提信道估计方案的有效性。