2-d Sensor Position Perturbation Analysis: Equivalence to Awgn on Array Outputs

In this paper, the performance of a subspace beamformer, namely the multiple signal classification algorithm (MUSIC), is scrutinized in the presence of sensor position errors. Based on a perturbation model, a relationship between the array autocorrelation matrix and the source autocorrelation matrix is established. It is shown that under certain assumptions on the source signals, the Gaussian sensor perturbation errors can be modelled as additive white Gaussian noise (AWGN) for an array where sensor positions are known perfectly. This correspondence can be used to equate position errors to an equivalent signal-to-noise ratio (SNR) for AWGN in performance evaluation. Finally, Cramér-Rao bound for the position perturbations that can be computed using the Cramér-Rao bound relations for the additive Gaussian noise case at high SNR’s.