Direction Finding of Multiple Partially Polarized Signals With a Nested Cross-Diople Array

In this letter, we investigate the problem of direction finding for multiple partially polarized (PP) electromagnetic signals using a linear nested array of $L$ cross-dioples. Due to the rank-2 characteristics of the PP signal correlation matrices, the conventional vectorization operator of the covariance matrix, which is used to produce degrees of freedom enhancement for nested array, no longer works. We propose to construct a set of data correlation sequences with enhanced degrees of freedom by exploiting the difference coarray property of the nested array geometry. The rank-2 signal correlation matrices of the PP signals convert to rank-1 real-valued amplitudes of the constructed complex sinusoid, and thus, conventional subspace-based methods can be applied to estimate directions directly. Moreover, we show that the proposed method can also be applicable to the scenario where both completely polarized and PP signals coexist, without requiring any prior information on the degree of polarization of the signal.