Abstract: In this paper,we suppose that the signal and noise of broadband moving medium reverberation are colored Gaussian signals.When the sample number is large,both the mean and variance of the first power spectrum moment by covariance techniques are obtained.The results obtained by D.S.ZRNIC8are generalized,where he assumed the noise is white.The transmitted signal is pseudo noise (PN) train and consists of two same subtrains between which the difference is only a time delay.In order to simplify the analysis,we also assume that the center frequency and frequency bandwidth of both signal and noise are equal.It is found that the mean of the first power spectral moment estimate is an unbiased estimate and that the variance of this estimate is dependent on the correlation coefficient ρ between two subtrains,the signal-to-noise ratio S/N and ΔfTL,where △f,T and L are the frequency bandwidth,time duration and total number of pulse elements in a subtrain respectively.Three thousand groups of narrow-band-signal data obtained in field are analyzed,then we know the range of ρ.All these results are very useful in designing a BBADCP.