Subspace Coding for Spatial Sensing

TL;DR

This paper introduces a novel subspace coding framework for spatial sensing, particularly DoA estimation, demonstrating how sensor array design can optimize code properties and improve resolution.

Contribution

It establishes a new connection between subspace coding and spatial sensing, proposing sensing subspace codes and leveraging Golomb rulers for improved array geometries.

Findings

Sensing subspace codes can be controlled by array geometry.

Golomb ruler-based codes achieve near-optimal minimum distance.

Conventional arrays are suboptimal for high-resolution sensing.

Abstract

A subspace code is defined as a collection of subspaces of an ambient vector space, where each information-encoding codeword is a subspace. This paper studies a class of spatial sensing problems, notably direction of arrival (DoA) estimation using multisensor arrays, from a novel subspace coding perspective. Specifically, we demonstrate how a canonical (passive) sensing model can be mapped into a subspace coding problem, with the sensing operation defining a unique structure for the subspace codewords. We introduce the concept of sensing subspace codes following this structure, and show how these codes can be controlled by judiciously designing the sensor array geometry. We further present a construction of sensing subspace codes leveraging a certain class of Golomb rulers that achieve near-optimal minimum codeword distance. These designs inspire novel noise-robust sparse array geometries achieving high angular resolution. We also prove that codes corresponding to conventional uniform linear arrays are suboptimal in this regard. This work is the first to establish connections between subspace coding and spatial sensing, with the aim of leveraging insights and methodologies in one field to tackle challenging problems in the other.