  In traditional compressed sensing theory, the dictionary matrix is given a
priori, whereas in real applications this matrix suffers from random noise and
fluctuations. In this paper we consider a signal model where each column in the
dictionary matrix is affected by a structured noise. This formulation is common
in direction-of-arrival (DOA) estimation of off-grid targets, encountered in
both radar systems and array processing. We propose to use joint sparse signal
recovery to solve the compressed sensing problem with structured dictionary
mismatches and also give an analytical performance bound on this joint sparse
recovery. We show that, under mild conditions, the reconstruction error of the
original sparse signal is bounded by both the sparsity and the noise level in
the measurement model. Moreover, we implement fast first-order algorithms to
speed up the computing process. Numerical examples demonstrate the good
performance of the proposed algorithm, and also show that the joint-sparse
recovery method yields a better reconstruction result than existing methods. By
implementing the joint sparse recovery method, the accuracy and efficiency of
DOA estimation are improved in both passive and active sensing cases.
