Construction of optimal frequency hopping sequences for minimising bit errors in selective fading channels characteristic to digital cellular systems

The author discusses the problem of constructing frequency hopping patterns for use in TDMA-FDMA cellular systems that employ frequency diversity to minimise bursty errors occurring due to the fading channel. Conditions under which two frequency and time channels fade independently in mobile fading channels are reviewed. The construction of a family of effective frequency hop sequences for achieving maximum diversity is given. The construction is based on the theory of linear congruences, and the number of sequences for every integer is established. It is shown that when sequences are constructed using prime numbers they are also orthogonal. Examples of constructed sequences applicable to the GSM cellular system are given.