De Bruijn sequences as Zero Correlation Zone codes for satellite navigation systems

Abstract

This paper discusses the possible application of an innovative set of binary sequences, the De Bruijn ones, as spreading codes in satellite navigation systems. Binary De Bruijn sequences feature inherent Zero Correlation Zone property, that may be effectively exploited to strongly limit the impact of multipath and interference. Simulation results are presented, referred to span 5 De Bruijn sequences, to show the orthogonality and correlation-related properties of these codes, that may properly fit the requirements of satellite based navigation systems.

Full-length non-linear binary sequences with Zero Correlation Zone for multiuser communications

“…, where n is the span of the sequences, allows to apply suitable strategies to select the spreading codes providing the best performance in terms of minimal error probability at the receiver. The results herein presented also integrate the preliminary analysis developed in [11], where an Additive White Gaussian Noise (AWGN) channel was assumed. The paper is organized as follows: Section 2 discusses related work, whereas Section 3 presents the main properties of the binary DB sequences investigated by the paper.…”

“…Asynchronous systems, or frequency selective propagation channels, may destroy or severely impact the orthogonality of the NO spreading codes used, thus causing an increasing interference, being both Inter Symbol Interference (ISI) and MAI generated by random time offsets among the signals, that make unfeasible the code waveforms to be completely orthogonal. Well-known families of linear spreading sequences, such as m-sequences, Kasami, Gold, and Walsh codes, traditionally employed as channelization codes, exhibit non-zero and sometime non negligible auto-and cross-correlation out-of-phase values, which limit the achievable performance, in asynchronous or in quasisynchronous scenarios [11]. On the other hand, full length sequences obtained through non-linear generation, such as binary De Bruijn (DB) sequences [12], [13], provide attractive features as well, such as long periods and large complexities, great cardinality of the set [14], and good randomness properties, that can be fruitfully exploited in communication systems, coding theory, and cryptography [15].…”

A large set of orthogonal codes for the V2V scenario

“…This paper investigates the adoption of a specific set of binary codes, the De Bruijn (DB) sequences, to be used as vehicle signatures in a CDMA communication framework. DB codes are selected for their huge cardinality to cope with dense scenarios; it is possible to select extended subsets of DB sequences featuring orthogonality-related properties, and a Zero Correlation Zone (ZCZ) that may favor the correct detection of the specific sequence at the receiver [6]. Section II describes the CDMA system model and the criteria adopted to select different sets of sequences; Section III discusses the simulations performed and related results.…”