Frequency/time hopping sequence sets with optimal partial Hamming correlation properties

Frequency hopping/time hopping(FH/TH) sequences have found wide applications in various modern FH/TH spread spectrum communications, such as digital cellular mobile communication, short-range wireless communication, personal communication, and multi-user radar, sonar systems. In order to evaluate the goodness of FH/TH sequences design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FH/TH sequence, so the study of the partial Hamming correlation of FH/TH sequence is particularly important. In this paper, a new class of FH/TH sequence sets with good partial Hamming correlation properties is proposed and investigated. The construction of new FH/TH sequence sets is based upon the generalized m-sequence and generalized Gordon-Mills-Welch sequence over a polynomial residue class ring. It is shown that new FH/TH sequence sets are optimal with respect to the partial Hamming correlation bound.