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

The problem of constructing frequency hopping patterns for use in time division multiple access-frequency division multiple access (TDMA-FDMA) cellular systems that employ frequency diversity to minimize bursty errors occurring due to the fading channel is discussed. Conditions under which two frequency and time channels fade independently in a mobile fading channel 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 Groupe Speciale Mobile (GSM) cellular system are given.