Theoretical lower bound on average periodic partial Hamming correlations of frequency-hopping sequence set

Owing to the limited synchronisation time and hardware complexity of frequency-hopping multiple access (FHMA) systems, partial Hamming correlation of the frequency-hopping sequence (FHS) set applied by the FHMA system plays an increasingly important role in measuring the performance of the system. A new lower bound on the average periodic partial Hamming correlation which is tighter than the existing one in a particular case is introduced. The new lower bound includes some earlier theoretical lower bounds on the average Hamming correlation of the FHS set as special cases. A necessary and sufficient condition for obtaining optimality with regard to the new bound is also presented.