Beamforming Design for Stem-Connected Microwave Linear Analog Computer (MiLAC)-Aided Multiuser MISO Downlinks

A microwave linear analog computer (MiLAC) is a tunable microwave network that performs computation through wave propagation in the analog domain. In beamforming, data streams pass through a reconfigurable admittance network and emerge as antenna signals. For communications, MiLACs are preferably lossless and reciprocal to avoid power dissipation and non-reciprocal components, but these constraints limit the analog beamformers they can realize. Fully-connected MiLACs offer broad flexibility at the cost of a quadratic number of tunable admittances in the antenna count. Stem-connected MiLACs reduce this scaling to linear and preserve point-to-point capacity, but their role in multiuser downlink beamforming and under bounded, discrete hardware constraints has remained open. This paper addresses both questions for the multiuser multiple-input single-output downlink. We show that a stem-connected MiLAC can realize every beamformer on the complex Stiefel manifold and prove that, when $N\ge 2K-1$, this Stiefel-restricted design achieves the same sum-rate as the fully-connected MiLAC, where $N$ and $K$ are the numbers of transmit antennas and users. We then develop a weighted minimum mean-square error solver with a Riemannian Stiefel update, together with a closed-form projection baseline and an alternating refinement for bounded, discrete susceptances. Simulations show that the stem-connected MiLAC matches fully-connected MiLAC performance, approaches the fully digital sum-rate upper bound without symbol-rate digital processing, and recovers most of the loss caused by direct hardware-grid quantization.