A matrix-based algorithm for estimating multiple coherence of a periodic signal and its application to the multichannel EEG during sensory stimulation

The coherence between the stimulation signal and the electroencephalogram (EEG) has been used in the detection of evoked responses. The detector´s performance, however, depends on both the signal-to-noise ratio (SNR) of the responses and the number of data segments (M) used in coherence estimation. In practical situations, when a given SNR occurs, detection can only be improved by increasing M and hence the total data length. This is particularly relevant when monitoring is the objective. In the present study, we propose a matrix-based algorithm for estimating the multiple coherence of the stimulation signal taking into account a set of N EEG channels as a way of increasing the detection rate for a fixed value of M. Monte Carlo simulations suggest that thresholds for such multivariate detector are the same as those for multiple coherence of Gaussian signals and that using more than six signals is not advisable for improving the detection rate with M=10. The results with EEG from 12 normal subjects during photic stimulation at 10 Hz showed a maximum detection for N greater than 2 in 58% of the subjects with M=10, and hence suggest that the proposed multivariate detector is valuable in evoked responses applications.