3450 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 9, SEPTEMBER 2009 Efficient Generation and Correlation of Sequence Pairs With Three Zero-Correlation Zones M. Carmen Pérez, Student Member, IEEE, Jesús Ureña, Member, IEEE, Álvaro Hernández, Member, IEEE, Ana Jiménez, and Carlos De Marziani Abstract—This paper presents three novel methods to efficiently generate and correlate sequence pairs with three zero correlation zones in the sum of their aperiodic correlation functions. These se- quences have achieved great importance in communications sys- tems when the maximum transmission delay is less than the length of these zones, because the multiple access interference (MAI) and the intersymbol interference (ISI) can be removed. The proposed algorithms are based on the properties of complementary sets of sequences (CSS) and they offer an efficient hardware implementa- tion of the corresponding generators and correlators that reduces the total number of operations to be performed in comparison with straightforward implementations. That makes possible real-time operation as well as the use of very long sequences. Index Terms—Code division multiaccess, correlators, genera- tors, pulse compression methods, sequences. I. INTRODUCTION C ODES with favorable correlation properties are of substantial interest in applications based on Code Di- vision Multiple Access (CDMA) techniques, such as radar, sonar, cryptography or mobile and wireless communications. In fact, the performance of these applications is largely con- strained by the chosen codes, requiring ideal properties of Auto-Correlation (AC) and Cross-Correlation (CC) to avoid both the Inter Symbol Interference (ISI) and the Multiple Ac- cess Interference (MAI). Another limitation is imposed by the matched-filter technique used in the reception stage to detect the emitted codes, as it means an increase of signal processing tasks that can put into risk the real-time operation capability of the system. Hence, efforts are being devoted to find new encoding schemes with good correlation properties together with efficient hardware implementations of the corresponding matched-filter correlators. Traditional CDMA pseudo-random codes such as m-se- quences [1], Gold codes [2] or Kasami sequences [3] exhibit non-zero off-peak AC and CC values and were designed based only on their periodic correlation properties. Walsh-Hadamard Manuscript received November 18, 2008; accepted March 02, 2009. First published April 10, 2009; current version published August 12, 2009. The asso- ciate editor coordinating the review of this manuscript and approving it for pub- lication was Prof. An-Yeu Wu. This work was supported by the Spanish Ministry of Science and Technology (RESELAI Project: TIN2006-14986-CO2-01). M. Carmen Pérez, J. Ureña, Á. Hernández, and A. Jiménez are with the Department of Electronics, University of Alcalá, Escuela Politécnica, 28871, Alcaláde Henares, Madrid, Spain (e-mail: carmen@depeca.uah.es; urena@de- peca.uah.es; alvaro@depeca.uah.es; ajimenez@depeca.uah.es). C. De Marziani is with the Department of Electronics Engineering, National University of Patagonia San Juan Bosco (Argentina), Ciudad Universitaria, 9000 Comodoro Rivadavia (Chubut), Argentina (e-mail: marziani@unpata.edu.ar). Digital Object Identifier 10.1109/TSP.2009.2020745 sequences [4] and Gold orthogonal codes [5] have perfect orthogonality at zero time delay and they are only useful in case of accurate synchronism. Consequently, these codes limit the achievable performance in many real applications where aperiodic emissions, asynchronous detection, multi-path effects, etc. are quite common. Since with one single sequence it is impossible to remove completely and simultaneously sidelobes both in the AC and CC functions [6], several authors rely on complementary codes [7]–[9]. Complementary codes were firstly considered by Golay [10] and each one consists of a pair of binary sequences with the same length whose addition of AC and CC functions have per- fect properties. Nevertheless, they provide only two mutually uncorrelated pairs and are not suitable for multi-user environ- ments. Complementary sets of sequences (CSS) [11] are a gen- eralization of Golay pairs containing more than two sequences. The elimination of the constrains in the number of sequences yields on a high process gain and also more than two mutually uncorrelated sets. However, the number of uncorrelated sets is limited by the number of sequences for every set. Besides, in many systems it is not possible to simultaneously transmit the sequences of a set, thus emission schemes that arrange the se- quences of the set by concatenation or by interleaving are used. These transmission schemes degrade the ideal properties of the sum of the correlation functions, so ISI and MAI appear [12]. Recently, interest in codes with Zero Correlation Zones (ZCZ) has increased considerably [13]–[17]. Such kind of codes are thought for applications in quasi-synchronous CDMA (QS-CDMA) systems where the relative time delay among different users does not exceed a certain limit. The correlation functions of these codes have zero values around the in-phase shift, providing null ISI and MAI when the length of the ZCZ is larger than the multipath spread and the rela- tive multiple access delays. Specifically, the codes proposed in [13] and [14] have ZCZ only in periodic correlation and are of reduced interest for applications such as radar pulse compression or synchronization. On the other hand, [15] and [16] are thought for aperiodic emissions, and they need to insert guard intervals (or zero gaps) to maintain their properties when they are periodically emitted. In [17] a set of ternary codes with ZCZ both in the periodic correlation and the odd correlation functions is proposed. Nevertheless, their energy efficiency is limited due to the insertion of zeros. As a solution, in [18] nonzero-valued sequence pairs with ZCZ in the middle and ending parts of the sum of their aperiodic AC and CC functions have been proposed and named T-ZCZ codes (Three Zero Correlation Zone codes). These sequence pairs also avoid to insert extra guard intervals in case of periodic emissions and 1053-587X/$26.00 © 2009 IEEE