On the statistical dependence of hits in frequency-hop multiple access

The statistical dependence of hits due to multiple-access interference in an asynchronous slow-frequency-hop packet radio network in which the radios employ memoryless hopping patterns is described. Models in which hits are conditionally independent given the number of interfering packets are investigated. It is shown that if the conditional probability of a hit is chosen appropriately, the distribution function for the number of hits in a packet for these models can be used to compute upper and lower bounds on the true distribution function for the number of hits. Conditions are described for which these models can be used to compute upper and lower bounds on the codeword and packet error probabilities. It is shown that if the ratio of the number of interfering packets to the number of frequency slots is held constant, hits in the asynchronous frequency-hop network are asymptotically independent in the limit as the number of frequency slots increases. This result suggests that when the number of frequency slots is large, error probabilities can be closely approximated by using the distribution for the number of hits that results from assuming that hits are independent