Improved Decoding Scheme for Frequency-Hopped Multilevel FSK System

We have examined a digital spread-spectrum modulation technique employing frequency-hopping and multiple frequency-shift keying (MFSK) for multiple-access satellite communication 1 and for digital mobile radio telephony. 2 Every T seconds each user conveys a K-bit message by transmitting a sequence of L tones chosen from an alphabet of 2k sine waves of duration r ( = T/L). Code-division multiplexing is 1839 used, and the message is modulated onto the address (code) assigned to each user. The receiver, knowing the address, can decode the received signal and extract the message. However, transmissions by other users can combine to cause an erroneous message, resulting in an ambiguous reception. Thus even without channel impairments, the number of simultaneous users the system can support at a given error probability is interference limited. The interference can be minimized by a proper choice of addresses with minimum cross correlation. Schemes for assigning 2 K addresses which guarantee minimum mutual interference between 2 K or fewer users have been proposed. 3 The performance of the system could be improved, in principle, by decoding the addresses of all possible users and analyzing the interference pattern. Such a complete decoding scheme is very complex. This paper describes a simpler decoder which makes use of the welldefined algebraic structure of the sequences 3 to eliminate erroneous messages which come from interference. The result is a significant improvement in the performance of the system with a much smaller complexity than complete decoding.