MAXIMUM-LIKELIHOOD REAL PART OF COHERENCE BETWEEN 2 NOISY SENSOR OUTPUTS WITH ZERO-DELAY SIGNAL INPUTS

We seek, in particular at low signal-to-noise ratio, the coherence bet ween the outputs of two sensors that receive a signal with zero time-o f-arrival difference but whose outputs include additive independent no ises. This situation arises when the spectrum of a source is being inv estigated in a laboratory situation. The coherence measure may be used as a detection statistic for power at any FFT or DFT frequency; it ma y also be used indirectly as a signal power estimator since it is a fu nction of SNR, and noise power is known. Because of the zero delay dif ference, ideal complex coherence has a zero imaginary part, and direct estimation of the real part seems appropriate. The maximum likelihood estimator for this and the corresponding Cramer-Rao Bound are derived . Extensive simulations verify the derivations. The small-difference a pproximation to the maximum likelihood solution gives a significant im provement in efficiency. Both the maximum likelihood solution and its small-coherence approximation give computational advantages over the c onventional coherence estimator.