The autocorrelation function (ACF) can be useful in evaluating channel behavior. It reveals how self-similar the impulse and frequency response are. The shape of the ACF can be used to determine the coherence time and coherence bandwidth [2]. The results are normalized in such a way that the value of the ACF will always be between -1 and 1. A value of one implies that signal is the same, at ˜t=0 or ˜f=0 its value will always be equal to one.
Temporal ACF
Theoretically the ACF is described by the following function
Raa,i(˜t)=1K+1[J0(2πfD,max˜t)+Kexp(j2πfD,maxcos(θ0)⋅˜t)]
Spectral ACF
The spectral ACF is quite a bit simpler. It can be described using [6]
RHH(t,f)=∑iPτ,i⋅exp[−j2πτi⋅f].
[2] T. S. Rappaport, Wireless Communications: Principles and Practice. Prentice Hall PTR, 2002.
[3] N. C. Beaulieu, Chengshan Xiao, and Yahong Rosa Zheng, “Novel Sum-of-Sinusoids Simulation Models for Rayleigh and Rician fading Channels,”
IEEE Transactions on Wireless Communications, vol. 5, no. 12, pp. 3667–3679, 2006.
[6] R. J. C. Bultitude, “Estimating frequency correlation functions from propagation measurements on fading radio channels: a critical review”,
IEEE Journal on Selected Areas in Communications, vol. 20, no. 6, pp. 1133–1143, 2002.