Abstract:
Direction of arrival (DOA) estimation has been an active
field of research for many decades. If the field is modeled as a
superposition of a few planar wavefronts, the DOA estimation
problem can be expressed as a sparse recovery problem and the
Compressed Sensing (CS) framework can be applied. Many
powerful CS-based DOA estimation algorithms have been
proposed in recent years.
However, they all face one common problem. Although,
the model is sparse in a continuous angular domain, to apply
the CS framework we need to construct a finite dictionary
by sampling this domain with a predefined sampling grid.
Therefore, the target locations are almost surely not located
exactly on a subset of these grid points.
Early solutions to this problem include adaptively refining
the grid around the candidate targets found with an initial,
mismatched grid [1]. Recent papers try to model the mismatch
error explicitly and fit it to the observed data either statistically
[2] or by interpolating between grid points [3].
In this paper we take an analytical approach to investigate
the effect of recovering the spectrum of a source not contained
in the dictionary. Unlike earlier works on the sensitivity of
compressed sensing to basis mismatch [4] that have provided
a quantitative analysis of the approximation error, we focus
on the shape of the resulting spectrum, considering one target
source for simplicity. We show that the recovered spectrum
is not sparse but it can be well approximated by the closest
two dictionary atoms on the grid and their coefficients can be
exploited to estimate the grid offset.
