Confidence bounds for signal-to-noise ratios from magnitude-squared coherence estimates

Coherence is used frequently to determine the degree to which one observed voltage is related to another observed voltage. Typically, in practice, these observables are degraded by system noise that is often independent, white, and Gaussian. Often, in measuring coherence, the interest is to determine the fraction of the observed power that is due to coherent signals and the fraction that is due to the uncorrelated noise floor. The term "signal" as used here describes a component of voltage of interest to an observer. With accurate coherence estimates, uncorrelated noise power can be separated from coherent signal power. Therefore, the concern in this article is with the accuracy of signal-to-noise ratio (SNR) calculations made from magnitude-squared coherence (MSC) estimates. Use is made of a report by Carter and Scannel (1) in which they determined confidence bounds of MSC estimates for stationary Gaussian processes. From their results, this article derives corresponding confidence bounds for SNR calculations without recourse to the complicated details of the underlying SNR statistics.