On the Theory of Continuous Array Processing

The theory of continuous and discrete array signal processing is considered for tracking and navigational radar (sonar) systems. The purpose of the active array (and the associated filtering) is to detect an echo of a transmitted pulse reflected from a target in the presence of correlated reverberation or clutter and uncorrelated noise, both of which may vary from antenna-array element to antenna-array element, i.e., both of which are space-time varying functions. The array configuration and signal processor can also be used to determine the target location and direction. For the continuous array the receiving "elements," are distributed continuously in the spatial medium, and the linear processor has a frequency response that is a function of the spatial variables. The discrete array is one where each individual point-receiving element in the spatial medium has a linear signal processor. A linear processor following an active continuous array (aperture) is determined by simultaneously considering the array geometry along with the spatial and temporal aspects of the signal processing filters and the spatial and temporal properties of the noise. The optimization criterion used is the maximization of the array output signal-to-noise ratio. The theory for the active continuous array can be used to determine the linear processor for an active discrete array, e.g., phased array radars. The results for the active-discrete and continuous-array processors are compared throughout the development of the theory. Several examples are considered for both the continuous and discrete arrays.