On Clutter Rank Observed by Arbitrary Arrays

This paper analyzes the rank and eigenspectrum of the clutter covariance matrix observed by space-time radar systems with arbitrarily configured arrays and varying look geometry. Motivated by recent applications that suggest use of nonuniform antenna arrays, a generalized theory of clutter rank is derived and demonstrated. First, a one-dimensional effective random process is defined by projecting the measurements obtained by an arbitrary space-time radar system into an equivalent one-dimensional sampling structure. Then, this projection and the Karhunen-Loeve representation of random processes are used to predict clutter rank based on effective aperture-bandwidth product. Simulated results are used to confirm the theory over a wide range of scenarios, and along the way, the well-known Brennan's rule for clutter rank is shown to be a special case of the proposed aperture-bandwidth product