Estimating frequency correlation functions from propagation measurements on fading radio channels: a critical review

A significant number of propagation and channel modeling papers have reported channel parameters like RMS delay spread, correlation bandwidth, and the Rician K factor, derived by various new methods from instantaneous, or snapshot measurements. This conflicts with the original definitions of these parameters, which formally should be derived from time averages, under an assumption of ergodicity and applied for the assessment of time-averaged link performance. It appears that the origins of fading channel characterization parameters, and the conditions under which they can be estimated and applied are now often ignored, leaving interpretation of new results subject to skepticism. This paper, therefore, provides a critical review of the estimation of frequency correlation and one of these parameters, correlation bandwidth, using channel impulse response estimates derived from propagation measurements. The practical application for knowledge of frequency correlation is summarized. Then, the derivation of the equation relating a channel's average power delay profile to its frequency correlation function via a Fourier transform is reviewed, with emphasis on conditions needed for validity. An alternate method, free from most of these conditions is also reported. Examples are given and comparisons are made of results from analyses using the two methods to estimate frequency correlation on Rayleigh and Rician mobile radio channels, which are shown to have significantly different frequency correlation characteristics. Finally, a measure of frequency correlation that is free from ambiguity concerning the value (e.g., 0.5, 0.75, or 1/e) at the correlation band edges is recommended.

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