Probability of error in frequency-hop spread-spectrum multiple-access communication systems with noncoherent reception

Expressions are developed for the probability of error for asynchronous frequency-hop spread-spectrum multiple-access networks using Markov hopping patterns and binary frequency shift keying (BFSK) with one symbol transmitted per hop. The expressions are exact when there is one interfering user and orthogonal BFSK is used. They provide excellent approximations when there are more than one interfering user. It is also shown that the error probability when Markov hopping patterns are used is a good approximation to the error probability when memoryless hopping patterns are used. By computing the channel capacity and the associated throughput, a simple hard decision receiver is shown to perform much better than a receiver using perfect side-information to erase the symbols transmitted on hops that were hit when all the users have the same power and one binary symbol is transmitted per hop