Virtual-Manifold Ambiguity in HOS-Based Direction-Finding with Electromagnetic Vector-Sensors

Herein derived are the lower and upper bounds for the number of linearly independent (2Q)th-order virtual steering vectors of an array of electromagnetic vector-sensors, with Q being any positive integer over one. These bounds help determine the number of non-Gaussian signals whose directions-of-arrival (DOAs) can be uniquely identified from (2Q)th-order statistics data. The derived lower bounds increase with Q, whereas the derived upper bounds often fall below the maximum number of virtual sensors achievable from (2Q)th-order statistics manipulation. These bounds are independent of the permutation of the (2Q)th-order statistics entries in the higher order cumulant matrix that has a similar algebraic structure of the classical covariance matrix used in the second-order subspace-based direction-finding algorithms.