  Spatial compressive sensing (SCS) has recently been applied to
direction-of-arrival (DOA) estimation owing to advantages over conventional
ones. However the performance of compressive sensing (CS)-based estimation
methods decreases when true DOAs are not exactly on the discretized sampling
grid. We solve the off-grid DOA estimation problem using the deterministic
maximum likelihood (DML) estimation method. In this work, we analyze the
convexity of the DML function in the vicinity of the global solution.
Especially under the condition of large array, we search for an approximately
convex range around the ture DOAs to guarantee the DML function convex. Based
on the convexity of the DML function, we propose a computationally efficient
algorithm framework for off-grid DOA estimation. Numerical experiments show
that the rough convex range accords well with the exact convex range of the DML
function with large array and demonstrate the superior performance of the
proposed methods in terms of accuracy, robustness and speed.
