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arXiv · 2606.23986

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

Yuchen Zhang·Yu Ge·Bruno Clerckx·Tareq Y. Al-Naffouri
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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 Cram\'er--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.

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Yuchen Zhang, Yu Ge, Bruno Clerckx, Tareq Y. Al-Naffouri. 2026-06-22. How Many RF Chains Does a Microwave Linear Analog Computer (MiLAC) Need to Match the Fully-Digital Cram\'er-Rao Bound?. https://arxiv.org/abs/2606.23986

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