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The co-prime array is a sub-Nyquist acquisition scheme for the estimation ofsecond order statistics. It cannot generate all the difference values in theco-prime range and hence, one of the sub-array is extended to enable theestimation of the second order statistics at each difference value in theco-prime range. Recently, the difference set for the co-prime array was studiedand low latency temporal spectrum estimation was demonstrated. In this paper,the fundamentals of the difference set of the extended co-prime array, alsoknown as the conventional co-prime array, is developed. The closed-formequations for the weight function, correlogram bias window, and the varianceare described. This is provided for the entire difference set, continuousdifference set and for the prototype co-prime period. It is shown that thechoice of $M\approx \frac{N}{2}$ generates a bias function with a largerelative amplitude between the main-lobe and side-lobe peaks, where $M$ and $N$are co-prime pairs. The expressions for the number of multiplications andadditions required to compute the autocorrelation for the entire, continuous,and prototype range is derived. Simulation results demonstrate low latencyspectrum estimation using the correlogram method.

Extended (Conventional) Co-Prime Arrays and Difference Set Analysis: Low Latency Approach