Performance bounds evaluation 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 mobile communication systems where the mobility of users requires random modeling of transmitter positions in the network. Assuming logarithmic attenuation of the signal strength over distance between the transmitter and receiver, we show that the interference in the network could be modeled as a mixture of Gaussian and circularly symmetric α-stable noise. Based on this model, we derive union bound approximations for the probability of error for FH systems with M-ary frequency shift keying (FSK). We generalize some of the results of Sousa (see IEEE Trans. I.T., vol.38, no.6, p.1743, 1992), where the focus was limited to Cauchy random variables (RVs), a special subclass of stable distributions, and where the effect of a background (Gaussian) noise was neglected. Numerical calculations and Monte Carlo simulations confirm the accuracy of our analysis. The results obtained allow the prediction of wireless system performance in environments varying from urban settings to office buildings