A Systematic Framework for the Construction of Optimal Complete Complementary Codes

The complete complementary code (CCC) is a sequence family with ideal correlation sums which was proposed by Suehiro and Hatori. Numerous literatures show its applications to direct-spread code-division multiple access (DS-CDMA) systems for inter-channel interference (ICI)-free communication with improved spectral efficiency. In this paper, we propose a systematic framework for the construction of CCCs based on $N$-shift cross-orthogonal sequence families ($N$-CO-SFs). We show theoretical bounds on the size of $N$-CO-SFs and CCCs, and give a set of four algorithms for their generation and extension. The algorithms are optimal in the sense that the size of resulted sequence families achieves theoretical bounds and, with the algorithms, we can construct an optimal CCC consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence families. We also discuss the family size, alphabet size, and lengths of constructible CCCs based on the proposed algorithms

Polyphase Radar Signals with ZACZ Based on p-Pairs D-Code Sequences and Their Compression Algorithm

In modern synthetic-aperture radars, signals with the linear frequency modulation (LFM) have found the practical application as probing signals. Utilization of LFM-signals was formed historically since they were the first wideband signals, which found application in radar technology, and their properties have studied a long time ago and in detail. However, the LFM-signals have the “splay” ambiguity function, which results the ambiguity in range. The question of the probing signal choice is also relevant in connection with the problem of weak echoes detection, which are closed by the side lobes of ACF of the strong echoes. In this paper, the polyphase (p-phase, where p is the prime integer number) radar signal, which has an area of zero side lobes in a vicinity of the central peak of autocorrelation function, has been synthesized. It is shown that this signal represents a train from p coherent phase-code-shift keyed pulses, which are coded by complementary sequences of the p-ary D-code. The method of ensemble set formation of the p-ary D-code for signal synthesis is suggested. Correlation characteristics of the synthesized signal are discussed. The compression algorithm of this signal is considered including in its structure the combined algorithm of Vilenkin-Chrestenson and Fourier fast transform