Zuling Chang

Xuanyu Liu, Pinhui Ke, Zuling Chang

Sequences exhibiting favorable ambiguity function characteristics play a critical role in radar detection systems and modern mobile communication applications. As a newly developed sequence family, Doppler resilient complementary sequence sets (DRCSSs) can effectively suppress ambiguity function sidelobes by coherently combining the ambiguity functions of their constituent subsequences. The objective of this paper is to present five classes of asymptotically optimal aperiodic DRCSSs with novel parameters based on trace functions over finite fields and column orthogonal complex matrices. Compared with existing asymptotically optimal aperiodic DRCSSs in the literature, the proposed aperiodic DRCSSs deliver superior or novel parameters. Notably, for three families of the constructed aperiodic DRCSSs, the column sequence peak-to-average power ratio (PAPR) is upper bounded by p by selecting suitable column orthogonal complex matrices.

Zuling Chang, Martianus Frederic Ezerman, San Ling et al.

We study a class of Linear Feedback Shift Registers (LFSRs) with characteristic polynomial $f(x)=p(x)q(x)$ where $p(x)$ and $q(x)$ are distinct irreducible polynomials in $\F_2[x]$. Important properties of the LFSRs, such as the cycle structure and the adjacency graph, are derived. A method to determine a state belonging to each cycle and a generic algorithm to find all conjugate pairs shared by any pair of cycles are given. The process explicitly determines the edges and their labels in the adjacency graph. The results are then combined with the cycle joining method to efficiently construct a new class of de Bruijn sequences. An estimate of the number of resulting sequences is given. In some cases, using cyclotomic numbers, we can determine the number exactly.