The linear span of the frequency hopping sequences in optimal sets

Abstract

Frequency hopping (FH) sequences are needed in FH code division multiple access (CDMA) systems. Recently some new constructions of optimal sets of FH sequences were presented. For the anti-jamming purpose, FH sequences are required to have a large linear span. The objective of this paper is to determine both the linear spans and the minimal polynomials of the FH sequences in these optimal sets. Furthermore, the linear spans of the transformed FH sequences by applying a power permutation are also investigated. If the power is chosen properly, the linear span could be very large compared to the length of the FH sequences.

Linear Span of the Optimal Frequency Hopping Sequences from Irreducible Cyclic Codes

“…For any permutation over the finite field, it is not easy to calculate the exact value of the linear span of the transformed sequence in the optimal set, which is left as an open problem [10] . In this paper, using the root representation method [10,11,22] , we have investigated the linear span of the transformed frequency hopping sequences. The exact values of these transformed frequency hopping sequences are determined by the root representation of the sequences.…”

“…Ding and Yin mentioned that a fresh optimal set of frequency hopping sequences having large linear span can be obtained by a proper power permutation [7] . By using the power permutations, several optimal sets of frequency hopping sequences are transformed into new optimal sets of frequency hopping sequences with large linear spans [10,11] . The author stated that "It is also noted that other types of permutation polynomials over GF(q) may be employed in the same way for improving the linear spans of FH sequences in some optimal sets.…”

Design of Receiving Wireless Network for the Application on Recovery of Rocket-Borne Memory

“…In order to solve the Doppler shift, there have been different solutions in different communication networks, for example in Refs [8,9] "CDMA system"; in refs [10] "Bluetooth networks"; in refs [11] "GSM Cellular Phone". In this paper, we use the Spread Spectrum frequency-hopping technique to eliminate this effect.…”