Co-Prime Sampling and Cross-Correlation Estimation

Research in the field of co-prime arrays and samplers has been mainly focused on reconstructing the autocorrelation and the spectral content of a signal at the Nyquist rate from sub-Nyquist data. This has found applications in power spectrum estimation, beamforming, direction-of-arrival estimation, and system identification. However, the use of coprime samplers for cross-correlation estimation has not received much attention. We describe cross-correlation estimation using co-prime samplers and consider two scenarios. In the first, both signals are acquired using co-prime samplers, while in the second scenario we assume one of the signals to be a known signal and thus available at the Nyquist rate, and the second signal is acquired using a co-prime sampler. We determine the number of contributors available for cross-correlation estimation at each difference value as this is a key parameter in determining the estimation accuracy. The work presented in this paper will have applications in time-delay, range, velocity, acceleration, and cross-spectrum estimation, which require cross-correlation estimation.