Non uniform linear arrays for improved identifiability in cumulant based DOA Estimation

Direction of arrival (DOA) estimation methods based on arbitrary even order (2q, q ≥ 2) cumulants of the received data are known to be capable of identifying many more non Gaussian sources (O(N^q)) than the physical number (N) of sensors. However, in this paper, it is shown that the identifiability of 2qth order cumulant based DOA estimation can be significantly higher than this. This is due to the fundamental connection of the 2qth order cumulants with the concept of a 2qth order difference co-array, which is a virtual array determined solely by the physical array geometry. Depending on the sensor orientations, the 2qth order difference co-array can contain as many as O(N^2q) elements. In order to find a class of linear physical arrays which achieves this, a new generic class of non uniform linear arrays, namely the 2qth order nested array, is proposed, whose 2qth order difference co-array is proved to contain an uniform linear array (ULA) segment with O(N^2q) sensors. Also, to exploit these increased degrees of freedom of the co-array, a new algorithm for DOA estimation is developed, which starts from the same 2qth order cumulant matrix as the earlier methods and can yet identify O(N^2q) sources.