In this paper, a new family of hopping sequences with very large family size suitable for use in time/frequency-hopping (TH/FH) code-division multiple-access (CDMA) systems is proposed and investigated. The construction of the new hopping sequences is based upon the polynomial theory over the finite field, and the new hopping sequences are called the polynomial hopping sequences. It is shown that the new time/frequency-hopping sequences include the well-known cubic hopping sequences, quadratic hopping sequences, and linear hopping sequences as special cases, and are good candidates for the large-capacity ultrawide-bandwidth (UWB) radio systems.
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Fan et al. (2005) studied this question.
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