Training-Throughput Tradeoff in Stacked Intelligent Metasurface-Assisted Multi-User MISO Systems

Abstract

Unlike conventional massive multiple-input multiple-output (MIMO) architectures, stacked intelligent metasurface (SIM)-assisted communication systems can realize large-scale beamforming with a limited number of radio frequency chains by adaptively reconfiguring the meta-atom phase shifts across multiple layers. However, this reconfiguration requires channel state information, which is challenging to acquire for SIM-assisted systems and comes with a significant training overhead. This paper investigates the trade-off between training duration and achievable rates in SIM-assisted multi-user multiple-input single-output (MISO) systems, where channel estimation (CE) is performed in the hybrid digital-wave domain while downlink linear precoding is implemented purely in the electromagnetic wave domain by the SIM. The proposed estimator requires multiple CE sub-phases to estimate the channels for all users with high accuracy. We then utilize the derived estimates to develop an efficient optimization algorithm that designs the SIM response to realize regularized zero-forcing precoding in the wave domain. Analytical expressions of achievable rate bounds at the users are presented, and exhibit dependence on the training overhead and the channel coherence time. Numerical results demonstrate that carefully optimizing the number of training sub-phases yields significant rate gains compared to fixed training schemes, highlighting the importance of jointly designing training protocols and SIM phase shift configurations in SIM-assisted multi-user MISO systems. Additionally, we show that the optimal number of sub-phases to maximize net achievable sum-rate decreases when the channels exhibit high spatial correlation and thereby low rank.