Wave-Domain Precoding for MU-MIMO Systems via Beyond-Diagonal Stacked Intelligent Metasurfaces

This letter studies beyond-diagonal stacked intelligent metasurfaces (BD-SIM) for wave-domain precoding in downlink multi-user multiple-input multiple-output (MU-MIMO) systems. By exploiting beyond-diagonal RIS (BD-RIS) layers, BD-SIM reduces the required number of layers and mitigates cascaded attenuation of stacked intelligent metasurfaces (SIM). To realize regularized zero-forcing (RZF) precoding, we consider two complementary designs that respectively emphasize approximation accuracy and effective channel gain and solve the resulting coupled nonconvex problems via layer-wise alternating optimization using Takagi decomposition and manifold gradient descent. Numerical results show that BD-SIM outperforms the SIM and BD-RIS baselines; approximation accuracy dominates in interference-limited regimes, while effective channel gain becomes dominant in noise-limited regimes.