Optimal sparse sampling for detection of a known signal in ar(2) colored gaussian noise via rank ordering

Abstract

This paper addresses optimal sparse sampling for detection of a known deterministic signal in second-order autoregressive (AR (2)) colored Gaussian noise. We extend the framework of Adhikari and Kay [3]—which solved the sparse sampling problem for AR (1) noise via rank ordering with O (N log N) complexity—to the AR (2) setting, a case explicitly deferred as future work in [3] and unaddressed in the open literature. Results are validated on two signal types—sinusoidal and LFM chirp—confirming that the algorithm generalizes beyond a single waveform. Performance is further evaluated across multiple values of M (M=10, 15, 21), demonstrating consistent improvement with increasing M. For AR (2) noise with coefficients a₁ and a₂, the whitened signal = s(t) + a₁s′(t) + a₂s″(t) is evaluated analytically at each sample , guaranteeing pointwise separability with no coupling between neighboring samples. This property ensures that rank ordering of squared whitened samples yields the globally optimal sparse subset. Optimality is verified numerically and analytically, demonstrating robustness across signal types and parameter variations.