Stacked intelligent metasurface (SIM) is an emerging programmable metasurface architecture that can implement signal processing directly in the electromagnetic wave domain, thereby enabling efficient implementation of ultra-massive multiple-input multiple-output (MIMO) transceivers with a limited number of radio frequency (RF) chains. Channel estimation (CE) is challenging for SIM-enabled communication systems due to the multi-layer architecture of SIM, and because we need to estimate large dimensional channels between the SIM and users with a limited number of RF chains. To efficiently solve this problem, we develop a novel hybrid digital-wave domain channel estimator, in which the received training symbols are first processed in the wave domain within the SIM layers, and then processed in the digital domain. The wave domain channel estimator, parametrized by the phase shifts applied by the meta-atoms in all layers, is optimized to minimize the mean squared error (MSE) using a gradient descent algorithm, within which the digital part is optimally updated. For an SIM-enabled multi-user system equipped with 4 RF chains and a 6-layer SIM with 64 meta-atoms each, the proposed estimator yields an MSE that is very close to that achieved by fully digital CE in a massive MIMO system employing 64 RF chains. This high CE accuracy is achieved at the cost of a training overhead that can be reduced by exploiting the potential low rank of channel correlation matrices.

翻译：堆叠智能超表面（SIM）是一种新兴的可编程超表面架构，能够在电磁波域直接实现信号处理，从而以有限的射频（RF）链路数量高效实现超大规模多输入多输出（MIMO）收发器。由于SIM具有多层结构，且需通过有限RF链路估计SIM与用户间的大维信道，信道估计（CE）对SIM赋能通信系统极具挑战性。为高效解决该问题，我们提出一种新型混合数字-波域信道估计器，其中接收训练符号首先在SIM层内进行波域处理，随后进入数字域处理。以所有超原子在各层施加的相位偏移为参数的波域信道估计器，通过梯度下降算法优化以最小化均方误差（MSE），其中数字部分实现最优更新。对于配备4条RF链路、6层SIM（每层64个超原子）的多用户系统，所提估计器获得的MSE与采用64条RF链路的全数字CE大规模MIMO系统性能极为接近。这种高精度CE以训练开销为代价实现，而该开销可通过利用信道相关矩阵的潜在低秩特性加以降低。