Performance of FH SS radio networks with interference modeled as a mixture of Gaussian and alpha-stable noise

We consider the performance of frequency-hopping spread spectrum (FH SS) radio networks in a Poisson field of interfering terminals using the same modulation and power. The problem is relevant to wireless random-access communication systems where little information about transmitters requires stochastic modeling of their positions. Assuming that the signal strength is attenuated over distance r on average as 1/r ^m, we show that the interference in the network could be modeled as a mixture of Gaussian and α-stable noise. Based on this modeling, we derive expressions for the probability of error (P_e ) for systems with M-ary frequency shift keying (FSK) which use conventional envelope detectors. Because conventional envelope detectors are optimum only in Gaussian noise and are suboptimum in the noise considered, we also investigate noncoherent detectors which offer improved performance. We examine receivers with limiting nonlinearities and detectors which are optimal in Cauchy noise. Numerical calculations and Monte Carlo simulations are provided to confirm the accuracy of the analysis presented. The results obtained are useful in the performance evaluation of multiple-access radio networks in environments varying from urban settings to office buildings with deterministic and stochastic propagation laws such as lognormal shadowing and Rayleigh fading