On frequency-hop multiple access sequence

The design of frequency-hop spread spectrum multiple access sequences is discussed. In particular, it is pointed out that the minimum number of pairwise hits between sequences does not necessarily guarantee good sequences in terms of mutual interference between multiple users. The point is illustrated using pairwise optimum Reed-Solomon sequences with maximum one pairwise hit. It is shown that in this case, one user can even have a hit in every hop in the worst case. Since the worst-case assumption is often too restrict in engineering, the average number of hits appears to be a more appropriate criterion in sequence design. This is particularly true where error-correcting techniques are employed. Hit distributions are given for some hopping sequence sets in a frequency-hop, multiple-access, spread spectrum system. A generating function proves to be a useful tool. A special set of Reed-Solomon sequences is shown to approximate truly random sequences with respect to hit probability distribution, but with a reduced variance