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Channel Evaluation using Autocorrelation

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)]

where K=0if i0 [3]. The function J0(x) is the Bessel function of the first kind and zeroth order.
The visual appearance of the temporal ACF will differ greatly depending on the amount of symbols NSymbol. By increasing NSymbol the temporal ACF will be calculated for a greater span of time. The temporal ACF is directly computed in the time domain using h(t,0).

Spectral ACF
The spectral ACF is quite a bit simpler. It can be described using [6] RHH(t,f)=iPτ,iexp[j2πτif].

The power Pτ,i is dependent on wi and K. The spectral ACF is directly computed in the frequency domain using H(t,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.