  The problem of off-grid direction-of-arrival (DOA) estimation is
investigated. We develop a grid-based method to jointly estimate the closest
spatial frequency (the sine of DOA) grids, and the gaps between the estimated
grids and the corresponding frequencies. By using a second-order Taylor
approximation, the data model under the framework of joint-sparse
representation is formulated. We point out an important property of the signals
of interest in the model, namely the proportionality relationship, which is
empirically demonstrated to be useful in the sense that it increases the
probability of the mixing matrix satisfying the block restricted isometry
property. Simulation examples demonstrate the effectiveness and superiority of
the proposed method against several state-of-the-art grid-based approaches.
