Asymptotic analysis of the generalized coherence estimate

The generalized coherence (CC) estimate has shown promise as a multiple-channel detection statistic, but analysis of its performance in this role has been hampered because its probability density function is difficult to evaluate under signal absent hypotheses and is unknown under signal-present hypotheses. This paper presents an asymptotic analysis of the GC estimate that provides tractable closed-form expressions for the density of the CC estimate under useful signal-absent and signal-present hypotheses, These expressions are valid as the number of data samples employed in the estimate approaches infinity. Theoretical predictions of detection performance based on these expressions are shown to match closely results obtained by Monte Carlo simulation, even when relatively small numbers of samples are used in the GC estimate. These results are used to further examine the merits of the GC estimate as a multiple-channel detection statistic.