Time-Hopping and Frequency-Hopping Multiple-Access Packet

Abstract

Time-hopping and frequency-hopping multiple-access (TH/FH MA) can be regarded as a hybrid product of timehopping multiple-access (THMA) and frequency-hopping multiple-access (FHMA) schemes. In THEHMA communication systems, a message of duration T seconds is encoded into n subpackets each of duration T/k seconds via a (n,k) Reed-Solomon error correcting code. The codewords are interleaved so that all the symbols in the same coordinate of the codewords are contained in the same subpacket. Thus, the information in the message packet can be recovered from any k of the n subpackets. The channel time is slotted into time slots of duration equal to TA seconds and the time interval [iT/k,(i+l)T/k) is referred to as the ith time slot. The available frequency spectrum is slotted into q noninterfering frequency slots of equal bandwidth. If the system is slot-synchronous, then subpackets are transmitted and received within the time slots. The n subpackets are transmitted in some n time slots via some n frequencies chosen according to a time- hopping pattern and a frequency-hopping pattern, respectively. Different terminals can be assigned different time-hopping and frequency-hopping patterns, or the terminals can be divided into groups with every member in the same group using the same time-hopping and frequency-hopping patterns. Since the terminals are hopping in both the time and the frequency domains, a subpacket hit occurs when and only when two or more terminals are transmitting in the same time slot and also in the same frequency slot. In this paper, it is assumed that the channel is noiseless and all the subpacket hits are correctly detected and erased. The received message packet will be correctly decoded by the receiver unless it suffers more than n-k subpacket hits. The results in this talk can be easily extended to include undetected hits and a noisy channel. It is possible to design time-hopping and frequency-hopping patterns such that if two terminals transmit at the same time, then they rarely transmit at the same frequency. Conversely, it can also be arranged that if two transmissions are to be transmitted at the same frequency, then such transmissions will seldom occur at the same time. If only a few subpacket transmissions are erased in the collisions, then the receiver will be able to reconstruct the message packet from the uncollided subpackets using an erasure- correcting decoder.