Perturbation analysis and compensating algorithm for subspace fitting array signal processing methods

Although the eigen-based subspace algorithms such as MUSIC and ESPRIT has been proven to be superior over other conventional methods, they are prone to model errors and system uncertainties which are ubiquitous in practical situations. Therefore recently much attention has been put on analyzing the behaviour and evaluating the performance of these subspace fitting method under the presence of random perturbations. Though much work has been done by researchers on these aspects, most of them have employed the additive Gaussian error model which may not be physically justifiable. Moreover, the algorithm they proposed to compensate for the errors under this perturbation model is computationally extensive and therefore cannot be put into practice. In this thesis, a novel and more realistic error model is introduced. Despite the fact that the novel idea is generally applicable to a wide variety of array signal processing problems and subspace methods, for the sake of presentation, focus has been made on problem of direction-of-arrivals estimation by MUSIC and ESPRIT. By using the new error model, together with certain assumptions, a compact expression for the perturbed data covariance matrix is derived. Based on this expression, a simple and robust compensating algorithm is proposed which proves to have good performance when the perturbation parameter is known. The case of unknown parameter is also considered and a new algorithm is devised for estimating this unknown parameter. To study the performance of the proposed compensating and estimating algorithms, the Cramer-Rao Bound for the parameters being estimated are derived. Simulated and theoretical results are then compared. Finally, to show the generality of our idea, the compensating algorithm is applied with slight modifications to the field of blind deconvolution. Promising simulation results are obtained