  Distorted sensors could occur randomly and may lead to the breakdown of a
sensor array system. We consider an array model within which a small number of
sensors are distorted by unknown sensor gain and phase errors. With such an
array model, the problem of joint direction-of-arrival (DOA) estimation and
distorted sensor detection is investigated and the problem is formulated under
the framework of low-rank and row-sparse decomposition. We derive an
iteratively reweighted least squares (IRLS) algorithm to solve the resulting
problem in both noiseless and noisy cases. The convergence property of the IRLS
algorithm is analyzed by means of the monotonicity and boundedness of the
objective function. Extensive simulations are conducted regarding parameter
selection, convergence speed, computational complexity, and performances of DOA
estimation as well as distorted sensor detection. Even though the IRLS
algorithm is slightly worse than the alternating direction method of
multipliers in detecting the distorted sensors, the results show that our
approach outperforms several state-of-the-art techniques in terms of
convergence speed, computational cost, and DOA estimation performance.
