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.

翻译：子空间码定义为环境向量空间中子空间的集合，其中每个信息编码的码字为一个子空间。本文从新颖的子空间编码视角研究一类空间感知问题，特别是基于多传感器阵列的波达方向估计。具体而言，我们证明了规范（被动）感知模型如何映射为子空间编码问题，其中感知操作为子空间码字定义了独特的结构。我们基于此结构提出感知子空间码的概念，并阐明如何通过精心设计传感器阵列几何结构来控制这些编码。进一步地，我们利用一类特定类型的Golomb标尺构建了感知子空间码，该编码实现了接近最优的最小码字距离。这些设计启发了具有高角度分辨率的抗噪声稀疏阵列几何结构。我们还证明了传统均匀线性阵列对应的编码在此方面是次优的。本研究首次建立了子空间编码与空间感知之间的联系，旨在通过一个领域的见解和方法论来解决另一个领域的挑战性问题。