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This work analyzes the detection performance of autocoherence (i.e., the magnitude-squared complex autocorrelation coefficient estimate) as a nonparametric detector of narrowband signals in broadband noise. The distribution theory of this statistic is derived along with approximations that permit easy analysis of the detection performance. It is shown in particular case studies that only 1 to 2.6 dB additional signal-to-noise ratio is required by autocoherence to achieve performance equivalent to the optimal parametric energy detector. Unlike the mean-level detector, autocoherence does not require a separate pool of noise reference samples and is therefore easier to implement in cluttered environments.