  Direction of arrival (DOA) estimation in array processing using
uniform/sparse linear arrays is concerned in this paper. While sparse methods
via approximate parameter discretization have been popular in the past decade,
the discretization may cause problems, e.g., modeling error and increased
computations due to dense sampling. In this paper, an exact discretization-free
method, named as sparse and parametric approach (SPA), is proposed for uniform
and sparse linear arrays. SPA carries out parameter estimation in the
continuous range based on well-established covariance fitting criteria and
convex optimization. It guarantees to produce a sparse parameter estimate
without discretization required by existing sparse methods. Theoretical
analysis shows that the SPA parameter estimator is a large-snapshot realization
of the maximum likelihood estimator and is statistically consistent (in the
number of snapshots) under uncorrelated sources. Other merits of SPA include
improved resolution, applicability to arbitrary number of snapshots, robustness
to correlation of the sources and no requirement of user-parameters. Numerical
simulations are carried out to verify our analysis and demonstrate advantages
of SPA compared to existing methods.
