Using playing cards to estimate interference in frequency-hopping spread spectrum radio networks

Abstract

Many mobile ad hoc networks, wireless LANs, cellular systems, and military radio networks use frequency-hopping spread spectrum (FHSS) to provide multiple access to the channel as well as for anti-jamming, interference suppression, and mitigating other channel effects. Estimates of interference between two networks using the same set of frequencies is often assumed to be 1/ N where N is the total number of available hopping frequencies. However, this simple model does not incorporate the partial spectral or partial temporal overlap that may occur between the hopping sequences or account for the fact that this overlap may be “stable” which will result in a significantly larger (or smaller) probability of interference. We extend an almost 300 year old probability model developed by the French mathematician Pierre Rémond de Montmort to provide a more accurate estimate of interference between such FHSS networks. This improved playing card model, almost as easy to calculate as the commonly used 1/ N model, is more robust because it incorporates the effects due to partial spectral and temporal overlap. Furthermore, since the hopping sequence in each network is independent, our model can easily be used to determine the interference from multiple networks by simply applying it pairwise and combining the results using elementary probability theory.