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 leverages wave propagation to perform computation directly in the analog domain. MiLAC finds promising applications in beamforming, where it can map the data streams to the antennas without a digital beamformer, using one radio-frequency chain per stream. A fully-connected MiLAC needs a number of tunable components that grows quadratically with the number of antennas, whereas a stem-connected MiLAC needs only a linearly growing number and still achieves the point-to-point capacity. For the multiuser multiple-input single-output downlink, we prove that the stem-connected MiLAC attains the maximum sum-rate of the fully-connected MiLAC whenever $N\ge 2K-1$, where $N$ and $K$ denote the numbers of antennas and users. The proof shows that restricting the design to beamformers with orthonormal columns, which the stem-connected MiLAC realizes in closed form, loses no sum-rate. Based on this restriction, we develop, for every $N\ge K$, a weighted minimum mean-square error algorithm with a Riemannian beamformer update and prove that its accumulation points are stationary. For the bounded, discrete susceptances of practical components, we then propose an alternating refinement that adjusts one susceptance at a time through rank-one updates and never decreases the sum-rate. With $64$ antennas, four users, and ideal components, the stem-connected MiLAC attains the fully-connected sum-rate with $4.5$ times fewer tunable components. With $3$-bit susceptances at a signal-to-noise ratio of $10$~dB, the refinement retains $90\%$ of this sum-rate.