Beamspace transform for UCA: Error analysis and bias reduction

In this paper, we analyze the error caused by the beamspace transform (BT) when it is applied to uniform circular array (UCA) configuration. Several algorithms for direction of arrival (DoA) estimation exploit this modal transform because it allows using computationally efficient techniques such as polynomial rooting and dealing with coherent sources. The BT is based on the phase-mode excitation principle. The performance of such DoA estimators is degraded if the array has a small number of elements. We introduce a modified beamspace transform (MBT) that performs mapping from element-space to beamspace domain taking into account the error caused by the transform. Justification of the difference in the statistical performances of MUSIC and root-MUSIC algorithms for UCA is also given. Moreover, we show that there is a significant difference in the performance of the UCA root-MUSIC technique depending on whether an even or odd number of elements is used. We derive an expression approximating the bias in the DoA estimates that is caused by the beamspace transform. Some design guidelines are provided for choosing the key UCA configuration parameters such as number of sensors, array radius, and interelement spacing in order to reduce the error. Finally, we propose a novel technique for bias removal. It allows practically bias-free DoA estimation.