JPL's Wireless Communication Reference WebsiteChapter: Wireless Propagation Channels

One can define 'narrowband' transmission also in the time domain, considering the interarrival
times of multipath reflections and the time scale of variations in the signal caused by modulation:
A signal sees a narrowband channel if the bit duration is sufficiently
larger than the interarrival time of reflected waves. In such case, the intersymbol interference is small.
Formally the coherence bandwidth is the bandwidth for which the auto covariance of the signal amplitudes at two extreme frequencies reduces from 1 to 0.5. For a Rayleighfading WSSUS channel with an exponential delay profile, one finds
B_{c} = 1/(2 p T_{rms})where T_{rms} is the rms delay spread. This results follows from the derivation of correlation of the fading at two different frequencies.
Delay Profile < > E [H(f_{1}) H*(f_{2}) ]After some algebraic operations, this can be used to express the autocorrelation and autocovariance of the amplitude, versus frequency separation f_{1}  f_{2}.
Figure: AutoCovariance of the received amplitude of
two carriers transmitted with certain frequency offset.
The normalized covariance of the amplitudes R_{1} and R_{2} of two carriers, one at f_{1} and another at f_{2} is
E R_{1} R_{2}  E R_{1} E R_{2} C =  s(R_{1}) s(R_{2})That is, we normalized for unity standard deviations sigma of R_{1} and R_{2}. One finds, for an exponential delay profile
1 C =  1 + 4 p^{2} (f_{1}  f_{2})^{2} T_{rms}^{2}