Analysis of frequency-hopped packet radio networks with random signal levels - Part I: Error-only decoding

This paper is concerned with the performance analysis of frequency-hopped packet radio networks with random signal levels. We assume that a hit from an interfering packet necessitates a symbol error if and only if it brings on enough energy that exceeds the energy received from the wanted signal. The interdependence between symbol errors of an arbitrary packet is taken into consideration through the joint probability generating function of the so-called effective multiple access interference. Slotted networks, with both random and deterministic hopping patterns, are considered in the case of both synchronous and asynchronous hopping. A general closed-form expression is given for packet capture probability, in the case of Reed-Solomon error only decoding. After introducing a general description method, the following examples are worked out in details: (i) networks with random spatial distribution of stations (a model for mobile packet radio networks), (ii) networks operating in slow fading channels, (iii) networks with different power levels which are chosen randomly according to either discrete or continuous probability distribution (created captures).