Outage Probability in Mobile Telephony Due to Multiple Log-Normal Interferers

The mobile radio channel is characterized by three important factors: path losses larger than free space, fading typically taken as Rayleigh, and shadowing generally characterized as lognormal. For cellular systems, in order to determine acceptable reuse distances between base stations and to compare modulation methods, the probability of unacceptable cochannel interference (outage probability) has to be determined in the realistic situation where both fading and shadowing occur. In this paper, the average outage probability is computed for centrally located base stations when multiple log-normal interferers are present. This is done for both the mobile-to-base and base-to-mobile communication links. An unexpected result of this study is that the outage probabilities for the two cases do not differ in a significant way. Cumulative probability curves of the short-term average-signal-toaverage-interference ratio (SIR) are presented for a variety of system parameters: channel set number, propagation law exponent (γ), and dB spread (σ) of the log-normal distribution for the signal and interferers. An important observation is the large sensitivity of the performance curves to the propagation parameters: for a system with seven channel sets with a 10 dB SIR threshold, the average outage probability varies from 10 percent for dB, to 70 percent for dB. Alternatively, for a fixed outage objective of 10 percent, the required SIR threshold value ranges from -17 dB to 11 dB, depending on the propagation parameters. These variations make it imperative that accurate measurements of these parameters be obtained for the different service areas. Outage probabilities are also easily related to specific modulation methods and diversity approaches; detailed results are given for several representative cases.