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Evaluating super-resolution bounds on the detection of multiple signals

The conventional resolution of individual emitters or frequencies within a cluster is limited by the physical dimensions and electrical aspects (such as the bandwidth) of a sensor system. Super-resolution describes algorithmic techniques that potentially enhance the conventional degree of resolution. Although there has been considerable research into super-resolution techniques (since 1970), there has, in contrast, been very little that addresses the fundamental bound of resolution performance that should theoretically be achievable by a 'perfect' algorithm in ideal conditions. The purpose of this paper is to present a generic method for predicting the fundamental resolution limit. We show that the resolution of closely-spaced signal waveforms is intrinsically linked to the signal-to-noise ratios of those signals. The method can be applied to individual spatial, temporal or spectral discriminants or to multi-discriminant systems. Loss of SNR resulting from the need to separate signals is derived both for the matched filter case and for eigen decomposition.