Performance Analysis of Coarray-Based MUSIC in the Presence of Sensor Location Errors

Sparse linear arrays, such as co-prime and nested arrays, can resolve more uncorrelated sources than the number of sensors by applying the MUtiple SIgnal Classification (MUSIC) algorithm to their difference coarray model. We aim at statistically analyzing the performance of the MUSIC algorithm applied to the difference coarray model, namely, the coarray-based MUSIC, in the presence of sensor location errors. We first introduce a signal model for sparse linear arrays in the presence of deterministic unknown location errors. Based on this signal model, we derive a closed-form expression of the asymptotic mean-squared error of a commonly used coarray-based MUSIC algorithm, SS-MUSIC, in the presence of small sensor location errors. We show that the sensor location errors introduce a constant bias that depends on both the physical array geometry and the coarray geometry, which cannot be mitigated by only increasing the signal-to-noise ratio. We next give a short extension of our analysis to cases when the sensor location errors are stochastic and investigate the Gaussian case. Finally, we derive the Cramér–Rao bound for joint estimation of direction-of-arrivals and sensor location errors for sparse linear arrays, which can be applicable even if the number of sources exceeds the number of sensors. Numerical simulations show good agreement between empirical results and our theoretical results.