Analysis of beamspace transform on uniform circular array

In this paper we analyze the error introduced by beamspace transform when it is applied to uniform circular array (UCA). Several algorithms for direction of arrival (DoA) estimation exploit this modal transform. The performance of such estimators is degraded if the array has a small number of elements. The beamspace transform is based on the phase-mode excitation principle (Davies, DEN, 1983). Here we introduce a generalized beamspace transform 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. Finally, we introduce a first order approximation of the bias in the DoA estimates that arises after the beamspace transform. An expression for the bias is provided.