Analysis of MUSIC algorithm with sensor gain and phase perturbations

Direction of arrival (DOA) estimation using eigenstructure based algorithms, such as MUSIC, require exact characterisation of the array in terms of its geometry and sensor gain and phase. In practice, however, the sensor gain and phase differ from their nominal values due to measurement errors, changes in the surrounding environment and sensor misplacement. In this paper, we analyse the mean-square error (MSE) in the DOA estimates obtained with the MUSIC algorithm under sensor gain and phase perturbations, using first-order perturbation analysis. First, we develop the analysis for an arbitrary array and a general signal scenario, i.e., for arbitrarily correlated (excluding the fully correlated case) sources. We then simplify the analysis to one- and two-source cases assuming a uniform linear array with isotropic sensors of unity nominal gain and obtain expressions for MSE. Simulations have been performed to verify the theoretical predictions and the results are in close agreement with the predicted values.