LINEAR ARRAY PROCESSING IN THE PRESENCE OF COHERENT SIGNALS, AMPLITUDE AND PHASE ERRORS

Abstract

The power inversion array has a particularly simple structure and its principle has been employed in many array processing techniques. Direction of arrival estimation schemes using power inversion arrays are attractive from a computational point of view, since they do not require computationally expensive optimization, root-finding or eigendecomposition procedures. These algorithms converge ideally to the same solution for the direction of arrival estimates by minimizing the overall array output power. In particular, the complex response zeros of the power inversion array are steered such that the nulls in the directional characteristics correspond to the source directions in the steady state. The various schemes for power inversion array processing, their performance, computational complexity and convergence behaviour have been extensively studied earlier. Apart from these aspects, the robustness of the algorithms and the sensitivity of the results with respect to environmental perturbations are extremely important issues in practical implementations. In particular, amplitude and phase errors in the signal measurements at the array elements may arise due to electronic equipment miscalibration, device tolerances, thermal effects, array element position errors or other non-ideal conditions, and it is imperative to examine their impact on direction of arrival estimation. In the first half of this thesis, the effect of amplitude and phase errors on the results obtained using power inversion arrays is investigated. Specifically, the variation of the complex response zeros due to random amplitude and phase errors is investigated. The variance of the response zeros is derived and expressed in terms of the optimum weights and response zeros of power inversion arrays. A simple guideline for the variances of the response zeros is obtained for situations when the sources are well separated and resolvable by the array. This guideline will be useful in defining the specification and evaluating the performance of power inversion arrays. The effect of amplitude and phase errors on the direction of arrival estimates is investigated for signal scenarios with incoherent as well as coherent sources. The case of coherent signals involves a spatial smoothing technique to decorrelate the signals and is analyzed separately. Some simulation results are presented validating the theoretical derivations. In the second half of this thesis, a novel high resolution array processing method is proposed, based on the TLS-ESPRIT algorithm which is a eigenstructure based technique having high resolution capabilities even for low signal to noise ratios. In the proposed method, the TLS-ESPRIT algorithm is combined with forward-backward averaging for the decorrelation of pairs of coherent signals. It is shown that a combination of TLS-ESPRIT processing and forward-backward averaging leads to parameter estimates for the directions of arrival which are constrained on the unit circle and hence better satisfy the postulated data model. A significant advantage of the new algorithm over the original TLS-ESPRIT algorithm is the substantial reduction in the computational complexity. In fact, the computational complexity of the TLS-ESPRIT solution is reduced almost by a factor of four and the new algorithm is formulated entirely over the field of real numbers, Finally, some simulation results are presented to demonstrate the robustness of the proposed technique and to show its performance improvement over the original TLS-ESPRIT method.