Multiple Level Nested Array: An Efficient Geometry for th Order Cumulant Based Array Processing

摘要

Recently, direction-of-arrival estimation (DOA) algorithms based on arbitrary even-order $(2q)$ cumulants of the received data have been proposed, giving rise to new DOA estimation algorithms, namely the $2q$ MUSIC algorithm. In particular, it has been shown that the $2q$ MUSIC algorithm can identify $O(N^{q})$ statistically independent non-Gaussian sources. However, in this paper, it is demonstrated that the processing power of the $2q$th-order cumulant based methods can potentially be even larger. It will be shown that the $2q$th-order cumulant matrix of the data is directly related to the concept of a $2q$th-order difference co-array which can potentially have $O(N^{2q})$ virtual sensors, leading to identification of $O(N^{2q})$ statistically independent non-Gaussian sources using $2q$ th-order cumulants. However, the number of actually realizable virtual elements in the $2q$ th-order difference co-array depends on the geometry of the physical array. In order to ensure that the co-array indeed has the desired degrees of freedom, a new generic class of linear (one dimensional) nonuniform arrays, namely the $2q$th-order nested array, is proposed, whose -ntex Notation="TeX">$2q$ th-order difference co-array is proved to contain a uniform linear array with $O(N^{2q})$ sensors. In order to exploit these increased degrees of freedom of the co-array, a new algorithm for DOA estimation is also developed, which acts on the same $2q$ th-order cumulant matrix as the earlier methods and can yet identify $O(N^{2q})$ sources. It is proved that the proposed method can identify the maximum number of sources among all methods that use $2q$ th-order cumulants.