Comparison of Bearing Estimation Algorithms for a Circular Array Transformed to Have a Vandermonde Manifold Vector

University Hall, Rm 134

Sensor arrays are widely used in estimating the directions of targets of interest, such as submarines and aircrafts, by detecting signals reflected or emitted by such targets. There are many different arrangements for sensors in arrays, and each offers distinct advantages and disadvantages. Uniform circular arrays (UCAs) offer various benefits over uniform linear arrays (ULAs) for direction-of-arrival (DoA) estimation including an increased range of measurement of the azimuth angle and the ability to measure an angle of elevation. Unlike ULAs, UCAs are disadvantaged in that their array manifold vectors do not have the Vandermonde structure which allows for convenient electronic steering of an array. This project utilizes a technique to transform the array manifold vector of a UCA into a Vandermonde vector by using a Butler-type matrix [Davies, November, 1965]. This technique has been known to transform a UCA into an effective ULA. We test this technique for simulated wide sense stationary plane-wave signals in Gaussian white noise. We also build a sixty-three microphone UCA and gather acoustic data to test our results. We implement conventional beamforming (CBF) and eigendecomposition based method such as multiple signal classification (MUSIC) for DoA estimation and compare the performances. The results show that the transformed UCA is equivalent to a ULA for MUSIC but not for CBF. CBF degenerates for particular numbers of sensors whereas MUSIC works well for any number of sensors. However, at unrealistically high signal to noise ratios, CBF is functional.