Finite-Resolution Microwave Linear Analog Computer (MiLAC)-Aided Multiuser Beamforming
Abstract: Large-scale antenna arrays are essential to future wireless networks but impose significant hardware and digital-processing burdens. The microwave linear analog computer (MiLAC) offers a promising architecture for addressing these challenges. In a MiLAC, beamforming is realized entirely in the analog domain through a reconfigurable multiport microwave network comprising tunable admittance elements. However, existing studies assume that these elements are continuously tunable, whereas practical implementations can support only finitely many configurable states. This paper investigates finite-resolution MiLAC-aided multiuser beamforming under lossless and reciprocal constraints with prescribed connectivity patterns. Each tunable susceptance is selected from a symmetric uniform finite-resolution codebook. We formulate an online problem that jointly optimizes the discrete susceptances and power allocation for a prescribed codebook, and an offline problem that designs the codebook based on channel statistics. By exploiting the odd-uniform codebook structure, we express each multilevel susceptance as a weighted sum of two-level variables and develop exact continuous penalty models for both the online beamforming and offline codebook design problems. We prove that, for sufficiently large penalty parameters, these penalty models are globally equivalent to their original discrete counterparts. Building on these formulations, we develop efficient ADMM-based algorithms for solving the two problems. Numerical results demonstrate that the performance of an unquantized fully-connected MiLAC can be approached with substantially reduced connectivity and finite resolution. In particular, a 3-bit stem-connected MiLAC achieves more than 95% of the sum-rate performance of the unquantized fully-connected MiLAC while requiring only 22% of its tunable components.