  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.
