Multiple Level Nested Array: An Efficient Geometry for $2q$th Order Cumulant Based Array Processing
Piya Pal, Palghat P. Vaidyanathan · IEEE Transactions on Signal Processing · 2011
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 2qMUSIC algorithm. In particular, it has been shown that the 2qMUSIC algorithm can identifyO(Nq) statistically independent non-Gaussian sources. However, in this paper, it is demonstrated that the processing power of the 2qth-order cumulant based methods can potentially be even larger. It will be shown that the 2qth-order cumulant matrix of the data is directly related to the concept of a 2qth-order difference co-array which can potentially haveO(N2q) virtual sensors, leading to identification ofO(N2q) statistically independent non-Gaussian sources using 2qth-order cumulants. However, the number of actually realizable virtual elements in the 2qth-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 2qth-order nested array, is proposed, whose 2qth-order difference co-array is proved to contain a uniform linear array withO(N2q) 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 2qth-order cumulant matrix as the earlier methods and can yet identifyO(N2q) sources. It is proved that the proposed method can identify the maximum number of sources among all methods that use 2qth-order cumulants.