On the equivalence of uniform circular arrays and uniform linear arrays

The problem of estimating the directions of arrivals of narrowband plane waves impinging on a uniform circular array with N identical sensors uniformly distributed around a circle is considered. It is shown that for this problem the uniform circular array is equivalent to a uniform linear array with N elements. Specifically, if the number of sensors N is odd and large enough then a linear combination of the inverse discrete Fourier transform of the sensor outputs yields a sequence of measurements z(n)= Sigma A/sub m/ exp(jn theta m), where theta /sub m/ is the angle of arrival of the mth plane wave. This sequence can then be processed using ROOT MUSIC or any other modern line spectral estimation technique as if it came from a uniform linear array. An advantage of using the transformed sequence is that it has a higher signal-to-noise ratio than the array output sequence.<>