Non-uniform sampling for high resolution spectrum analysis

An important problem in the theory of non-uniform array design is that of finding the sensor locations which minimize the peak sidelobe in the power gain pattern, for given resolution and number of sensors. In this paper it is shown that the sidelobe maxima correspond in a one-to-one manner to the points of a lattice in the N-dimensional space defined by the set of sensor phase vectors. The relationship between this lattice and the array geometry is completely described, and it is shown that the density of this lattice is directly related to the array resolution and field of view. The problem of minimizing the peak sidelobe for given resolution and field of view is shown to be equivalent to finding array designs whose phase space lattices achieve the maximum distance between the nearest neighbors, while simultaneously achieving the density dictated by the resolution and field of view requirement. Examples of the design procedure and the performance achieved in spectrum estimation are given.