Theory of parametric receiving arrays processing utilizing sum and difference frequencies

The majority of highly directive receive arrays obtains their directivity from an often fully populated (lambda/2 spacing) array in one or more dimensions. Digital beamforming allows for steering of these densely populated arrays in multiple directions; however, if there is only one primary direction of interest, a similar highly directive receiver can be generated with just a few elements. Parametric receivers, such as parametric sources, can obtain enhanced directivity via a “virtual aperture” or a region in the medium where nonlinear mixing of a high intensity pump wave and a signal wave interact. For a parametric receiver, the pump element(s) with a frequency, F, and receiver element(s) are separated by a distance, L, and the signals of interest are the sum and difference frequency ( F + /− f) between the pump frequency and an incoming signal frequency, f. The directivity of these parametric receivers are comparable to the end fire response of a line array of similar length, L. This paper will review the highlights of parametric receivers as well as detail the analysis to extend this phenomenon to include the sum and difference frequencies for single element pairing and arrays of pumps and receivers.