Note that in Eqs. 1 and 2, both the uplinkand downlink capacities are random variables,conditioned on both the CSI and the MT position(or the distances from the RAUs that areinvolved). Furthermore, the downlink capacity isa function of the transmit power, {ρn, n = 1, 2, …, N}, at the individual RAUs. The exact probabilitydensity functions (pdfs) of the channelcapacities are difficult to obtain. However, it hasbeen shown in [7, 8] that the channel capacitiescan be approximated as a Gaussian random variableat large signal-to-noise ratios (SNRs) and alog-normal random variable at small SNRs,respectively. Figures 3a and 3b show the pdfs ofthe uplink channel capacity for large SNR andsmall SNR, respectively. The median of the averagedSNR over microscopic fading at the referencedistance R is a chosen parameter in oursimulations throughout this article, where R isthe equivalent radius of the GN-cell [9]. It canbe seen that the Gaussian and lognormal approximationsare very accurate.
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