Strong No-Hit-Zone Sequences for Improved Quasi-Orthogonal FHMA Systems: Sequence Design and Performance Analysis

This paper is focused on the optimal design and performance analysis of a novel class of no-hit-zone frequencyhopping sequences (NHZ-FHSs) in quasi-synchronous FH multiple-access (QS-FHMA) systems. Although traditional NHZ-FHSs can offer interference-free FHMA performance when the signal arrival delay (τ) does not exceed the width of NHZ (Znh), i.e., |τ| ≤ Znh, the same performance cannot be guaranteed for |τ| > Znh in which traditional NHZ-FHZs may have large Hamming correlation (which denotes the total number of frequency hits of sequences) and consequently poor error probability performance. Since the strict quasi-synchronization (i.e., |τ| ≤ Znh) may be hard to maintain at all times in practical FHMA networks (e.g., infrastructureless ad hoc networks), it is also important to minimize the Hamming correlation for time-shifts outside of the NHZ. Such FHSs are called strong NHZ-FHSs (SNHZ-FHSs) in this paper. We derive a lower bound on the maximum Hamming correlation outside of the NHZ and then present a design algorithm for the optimal SNHZ-FHS set meeting our proposed lower bound with equality. We analyze the bit-error-rate (BER) performance of the FHMA system employing the proposed SNHZ-FHS sets using the average Hamming correlation function. The theoretical analysis and simulation results show that the proposed optimal SNHZ-FHS sets are feasible for practical FHMA networks with relaxed timing requirement and enhanced BER performance.