PACKET ERROR PROBABILITIES IN FREQUENCY-HOPPED SPREAD-SPECTRUM PACKET RADIO NETWORKS - MEMORYLESS FREQUENCY-HOPPING PATTERNS CONSIDERED

The packet error probability induced in a frequency-hopped spread-spectrum packet radio network is computed. The frequency spectrum is divided into q frequency bins. Each packet is exactly one codeword from an (M,L) Reed-Solomon code left bracket M equals number of codeword symbols (bytes); L equals number of information symbols (bytes) right bracket . Every user in the network sends each of the M bytes of his packet at a frequency chosen among the q frequencies with equal probability and independently of the frequencies chosen for other bytes (i. e. , memoryless frequency-hopping patterns). Statistically independent frequency-hopping patterns correspond to different users in the network. Provided that K users have simultaneously transmitted their packets on the channel and a receiver has locked on to one of these K packets, the probability that this packet is not decoded correctly is evaluated. It is also shown that although memoryless frequency-hopping patterns are utilized, the byte errors at the receiver are not statistically independent; instead they exhibit a Markovian structure.