Coprime Sampling and Arrays in One and Multiple Dimensions

Abstract

his chapter gives an overview of the concept of coprime sampling. The basic idea is that a continuous-time (or spatial) signal is sampled simultaneously by two sets of samplers, with sampling rates 1∕MT and 1∕NT where M and N are coprime integers and T>0. One of the results is that it is possible to estimate the autocorrelation of the signal at a much higher rate (=1/T) than the total sampling rate. Thus, any application which is based on autocorrelation will benefit from such sampling and reconstruction. One example is in array processing, in the context of estimation of direction of arrival (DOA) of sources. Traditionally, an array with L sensors would be able to identify L − 1 independent sources, but with a pair of coprime arrays, one can identify O(L2) sources. It is also shown how to use two DFT filter banks, one in conjunction with each sampling array, to produce a much denser tiling of the frequency domain than each filter bank would individually be able to do. This chapter also discusses the extension of coprime sampling to multiple dimensions by using sampling geometries that are defined based on lattices. In this context the generation of coprime pairs of integer matrices is a very interesting mathematical problem and is dealt with in detail. The use of coprime samplers in system identification is also elaborated upon. A brief review of fractionally spaced equalizers in digital communications, in the context of coprime sampling, is included.

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