Perfect Polyphase Sequences Research Articles

Sequences With Good Correlations Based on Circular Florentine Arrays

Sequences and their correlation properties have been extensively studied due to their broad applications. In this paper, we develop a connection between sequences and well-studied combinatorial objects, circular Florentine arrays. This connection allows us to derive two types of sequences with good correlation properties. The first type consists of sequences having optimal correlation with respect to the Sarwate bound. Our constructions are based on perfect polyphase sequences. The number of perfect sequences with optimal correlation depends on the existence of circular Florentine arrays, which improves the previous known results. The second type is about multiple ZCZ sequence sets with low inter-set cross-correlation. Each generated ZCZ sequence set is optimal with respect to the Tang-Fan-Matsufuji bound, and each sequence in each set is perfect. In addition, any two sequences from distinct ZCZ sequence sets possess optimal inter-set cross-correlation with respect to the Sarwate bound. Compared with the previous results, the number of ZCZ sequence sets with optimal inter-set cross-correlation property is improved, because of the existence of circular Florentine arrays.

Optimal Families of Perfect Polyphase Sequences from Cubic Polynomials

Optimal Families of Perfect Polyphase Sequences from Cubic Polynomials

Optimal Families of Perfect Polyphase Sequences From the Array Structure of Fermat-Quotient Sequences

We show that a $p$ -ary polyphase sequence of period $p^{2}$ from the Fermat quotients is perfect. That is, its periodic autocorrelation is zero for all non-trivial phase shifts. We call this Fermat-quotient sequence. We propose a collection of optimal families of perfect polyphase sequences using the Fermat-quotient sequences in the sense of the Sarwate bound. That is, the cross correlation of two members in a family is upper bounded by $p$ . To investigate some relation between Fermat-quotient sequences and Frank-Zadoff sequences and to construct optimal families including these sequences, we introduce generators of $p$ -ary polyphase sequences of period $p^{2}$ using their $p\times p$ array structures. We call an optimal generator to be the generator of some $p$ -ary polyphase sequences which are perfect and which gives an optimal family by the proposed construction. Finally, we propose an algebraic construction for optimal generators as another main result. A lot of optimal families of size $p-1$ can be constructed from these optimal generators, some of which are known to be from the Fermat-quotient sequences or from the Frank-Zadoff sequences, but some families are new for $p\geq 11$ . The relation between the Fermat-quotient sequences and the Frank-Zadoff sequences is determined as a by-product.

Construction of Sparse Representations of Perfect Polyphase Sequences in Zak Space with Applications to Radar and Communications

Sparse representations of sequences facilitate signal processing tasks in many radar, sonar, communications, and information hiding applications. Previously, conditions for the construction of a compactly supported finite Zak transform of the linear FM chirp were investigated. It was shown that the discrete Fourier transform of a chirp is, essentially, a chirp, with support similar to the support of the time-domain signal. In contrast, the Zak space analysis produces a highly compactified chirp, with support restricted to an algebraic line. Further investigation leads to relaxation of the original restriction to chirps, permitting construction of a wide range of polyphase sequence families with ideal correlation properties. This paper contains an elementary introduction to the Zak transform methods, a survey of recent results in Zak space sequence design and analysis, and a discussion of the main open problems in this area.

Bat Chirps With Good Properties: Zak Space Construction of Perfect Polyphase Sequences

Previously, a discretization of the linear FM chirp of length N=KL 2, L and KL isin Z, was given and the conditions for its minimal Zak space support were derived. Chirps satisfying these conditions are known as finite chirps. In this work, subsets of finite chirps of length N=L 2, L a prime, are examined. The investigation leads to a new, Zak space construction of general polyphase sequence sets of size L-1 with optimal auto and cross-correlation properties, known as perfect sequence sets. It is shown that perfect sequence sets are closely related to sets of finite chirps and, in particular, include the sets of Zadoff-Chu sequences (which are identical with subsets of finite chirps) and the sets of generalized Frank sequences (which are identical with sets of modulations of finite chirps), as special cases. The entire collection of perfect sequence sets is then given by a partition of the set of perfect auto correlation sequences, obtained by right coset decomposition of the group of all permutations with respect to a certain cyclic group. The construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group.

New Perfect Polyphase Sequences and Mutually Orthogonal ZCZ Polyphase Sequence Sets

In communication systems, ZCZ sequences and perfect sequences play important roles in removing multiple-access interference (MAI) and synchronization, respectively. Based on an uncorrelated polyphase base sequence set, a novel construction method, which can produce mutually orthogonal (MO) ZCZ polyphase sequence (PS) sets and perfect PSs, is presented. The obtained ZCZ PSs of each set are of ideal periodic cross-correlation functions (PCCFs), in other words, the PCCFs between such two different sequences vanishes, and the sequences between different sets are orthogonal. On the other hand, the proposed perfect PSs include Frank perfect PSs as a special case and the family size of the former is quite larger than that of the latter.

Perfect polyphase sequences with small alphabet

New perfect polyphase sequences with a small phase alphabet and some zero elements are proposed. These sequences are derived from pairs of perfect polyphase sequences with zeroes and odd-perfect ternary sequences of the same length N. They have a length of 4N and possess a peak factor close to 1 as N becomes large. The sequences can be used in digital communication, navigation and radar engineering.