Estimation of space-time clutter rank for subarrayed data

In this paper, a new expression is provided for the rank of the space-time clutter covariance matrix when spatial subarrays are employed to combine the antenna array elements. The new results are applicable to subarrays that are overlapped, adjacent to one another, or separated with a gap in the underlying element structure. It is only assumed that the underlying element structure is uniform and that the subarrays are constructed in an identical fashion with uniform spacing. It is recognized that the case in which the subarrays are separated corresponds to a regularly spaced "sparse" collection of subarrays. Conditions are provided to indicate when the new expression is exact and when it is an upper bound. The situations where the new expression for clutter rank is exact correspond to new families of scenarios (beyond those previously described in the literature) in which the clutter rank "collapses" due to spatial aliasing. In situations where the new expression is an upper bound, simulations have shown that the new expression is significantly tighter than previously published results. It is expected that the reader may utilize these results to select system parameters to minimize the complexity of the clutter mitigation structure, for airborne or spaceborne radar applications.