New Insights into Channel vs Subspace Codes for Large-Scale Beamspace MIMO Channel Sensing

TL;DR

This paper analyzes channel and subspace coding strategies for large-scale beamspace MIMO channel sensing, revealing key design principles and introducing beamspace subspace codes for improved performance.

Contribution

It provides a theoretical framework linking subspace and Hamming distances, explains limitations of existing codes, and proposes new beamspace subspace codes based on sparse antenna patterns.

Findings

Maximum likelihood angle estimator performance depends on subspace and beam gain.

Reed-Muller codes have poor sensing performance due to zero subspace distance.

Beamspace subspace codes using Golomb rulers achieve near-optimal subspace distance.

Abstract

This paper provides novel insights into channel and subspace codes in nonadaptive channel sensing with a single RF chain. Observing that this problem naturally maps to a noncoherent decoding problem, we show that the sensing performance of the maximum likelihood (ML) angle estimator, which does not require knowledge of the typically unknown channel coefficient, is governed by two key terms: the minimum subspace distance and beam gain of the used beamformers. We derive an exact expression for the subspace distance of binary linear channel codes mapped to BPSK, which illuminates the relationship between subspace and Hamming distance, used to design subspace and channel codes, respectively. Our result also reveals why good Hamming distance alone is insufficient for sensing, and shows that well-known families of channel codes such as Reed-Muller codes, yield zero subspace distance and thereby poor sensing performance when used naively without proper codebook pruning. Finally, we introduce so-called beamspace subspace codes based on sparse antenna selection patterns (Golomb rulers), which we show provide near-optimal subspace distance. We demonstrate that this property of judiciously designed sparse arrays can be leveraged together with beamforming gain via convolutional beamspaces, enabling hardware- and sample-efficient channel sensing with theoretical guarantees in large-scale multiantenna communications.