How Many RF Chains Does a Microwave Linear Analog Computer (MiLAC) Need to Match the Fully-Digital Cramér-Rao Bound?

2026-06-22

AI Summary

This study investigates the minimum number of radio-frequency (RF) chains required for a microwave linear analog computer (MiLAC) to achieve the Cramér–Rao bound (CRB) of a fully digital receiver in direction-of-arrival estimation. By modeling a tunable, lossless, reciprocal MiLAC front-end and leveraging Fisher information matrix analysis combined with subspace projection theory, the work establishes—for the first time—that exact attainment of the fully digital performance limit is possible with only 2K RF chains for K far-field sources, a feat unattainable by conventional phase-shifter-based architectures. The authors further introduce a dimension-counting argument to determine the minimal number of tunable components and prove that stem-connected MiLAC configurations asymptotically approach this bound under linear scaling of both antenna elements and source count. Numerical experiments corroborate the theoretical findings.

Abstract

A microwave linear analog computer (MiLAC) is a tunable microwave network that performs linear operations directly on radio-frequency signals through wave propagation. Used as an antenna-array front end, it can map many antenna signals to a small number of active RF chains. While lossless reciprocal MiLACs have been shown to provide flexible or capacity-achieving beamforming for wireless communications, their sensing performance remains largely unexplored. We analyze direction-of-arrival estimation for $K$ far-field targets using a tunable receive-side lossless reciprocal MiLAC combiner. We show that the Fisher information matrix depends on the combiner only through the orthogonal projector onto its row space and never exceeds that of a fully digital receiver. Equality holds when the row space contains the $2K$-dimensional joint steering--derivative subspace, establishing a zero-gap threshold of two RF chains per target. A dimension-counting argument lower-bounds the number of tunable components required to achieve the digital Cramér--Rao bound for every target configuration. The stem-connected MiLAC attains this bound asymptotically, up to an antenna-count-independent additive overhead, while scaling linearly with the antenna and target counts. Unlike a phase-shifter front end with the same number of RF chains, MiLAC can exactly attain the fully digital bound. Numerical results validate the analysis.

Problem

• MiLAC
• RF chains
• Cramér-Rao Bound
• direction-of-arrival estimation
• Fisher information matrix

Innovation

• Microwave Linear Analog Computer
• Cramér–Rao Bound
• Direction-of-Arrival Estimation
• RF Chain Reduction
• Fisher Information Matrix