Quantification of the difference between detection and resolution thresholds for multiple closely spaced emitters

The problem of estimating the parameters of multiple signals closely spaced in either space or frequency has been much researched because it is a difficult case for modern spectral analysis techniques. Based on empirical evidence, it has been noted by others that signal-to-noise ratio (SNR) detection thresholds typically are lower than resolution thresholds. That is, one can detect the occurrence of n closely spaced signals at SNRs lower than those at which one can resolve the signals and reliably estimate their parameters. The difference between detection and resolution thresholds is quantified for the direction-finding problem in which source locations are specified by a single angular coordinate (e.g., azimuth)