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Is there any solution for estimating Confidence interval of coherence derived by Welch method with overlapping segments?

Moreover, the window length is not same for all the observations, only the number of segments are fixed for all observations

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You might look at

G. Carter, C. Knapp and A. Nuttall, "Statistics of the estimate of the magnitute-coherence function," in IEEE Transactions on Audio and Electroacoustics, vol. 21, no. 4, pp. 388-389, Aug 1973.

doi: 10.1109/TAU.1973.1162487

Abstract: Expressions for the statistics of the estimate of magnitude coherence between two random stationary Gaussian processes are presented. These statistics include the probability density function, the cumulative distribution function, the bias, and the variance of the estimator. The expressions presented are in convenient and accurate forms for digital computer evaluation. Graphical examples of the bias and variance are included. Simple approximations are also given for the maximum bias, variance, and mean-square error.

keywords: {Density functional theory;Distribution functions;Gaussian processes;Mean square error methods;Probability density function;Random processes;Random variables;Statistical distributions;Statistics;Upper bound},

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