WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 2012; 12:236–247 Published online 15 April 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.953 RESEARCH ARTICLE Sequence design for MPG QS-CDMA systems based on heuristic combinatorial optimization André S. R. Kuramoto 1,2† , Fernando Ciriaco 1,2 , Taufik Abrão 3*,‡ and Paul Jean E. Jeszensky 1,2§ 1 Department of Telecommunications and Control Engineering, Escola Politécnica of University of São Paulo (LCS-PTC-EPUSP), São Paulo, Brazil 2 LCS-Laboratório de Comunicações e Sinais, São Paulo, Brazil 3 Department of Electrical Engineering, State University of Londrina (DEEL-UEL), Londrina, Parana, Brazil ABSTRACT This paper deals with a quasi-synchronous code division multiple access (QS-CDMA) system with a multiple processing gain (MPG) variable data rate scheme in the uplink direction and subject to multipath fading channels. An analytic expression is obtained for the signal-to-noise plus interference ratio (SNIR) at the Rake receiver output (finger). In order to maximize the SNIR, three combinatorial optimization methods applied to sequences selection are compared. Then, sequence selection methodology for this class of system is evaluated, comparing the local search optimization results with unitary Hamming distance (1-opt LS), evolutionary programming with cloning (EP-C), and simulated annealing (SA) ones. The contribution of this work consists of considering the self-interference (SI) effect, besides the multiple access interference (MAI), in the description of the proposed objective function for sequence selection and a compared analysis of three heuristic algorithms maximizing that SNIR. Also, numeric results have demonstrated the effectiveness of the proposed method for the QS-CDMA sequences selection. Copyright © 2010 John Wiley & Sons, Ltd. KEYWORDS CDMA; quasi-synchronous; spreading sequences selection; combinatorial optimization * Correspondence Taufik Abrão, Department of Electrical Engineering, State University of Londrina (DEEL-UEL), Londrina, Parana 86051-990, Brazil. E-mail: taufik@uel.br † Petrobras – Petróleo Brasileiro S/A, Brazil. ‡ Adjunct Professor. § Full Professor. 1. INTRODUCTION In quasi-synchronous code division multiple access (QS- CDMA) systems, all users transmit in a synchronized form using a reference signal. As a result, the delays among all received signals will be limited in a time interval, which can be lower than the symbol period depending on the channel characteristics. Thus, all spreading sequences will be almost synchronized and, therefore, the multiple access interference (MAI) and the self-interference (SI), which limit the system’s performance, can be reduced substantially by choosing sets of appropriated sequences with good correlation properties. Some works suggest sequences that have reduced correlation values for small shifts among the sequences [1,2]. In most of these works the correlation functions among sequences of same length are studied (see Reference [3] and references inside). Recently, sequence design based on generalized orthogonality and generalized quasi- orthogonality applied to both single-rate direct sequence QS-CDMA systems and time/frequency hopping (TH/FH) QS-CDMA systems was investigated [4]. In systems with variable data rate schemes, like multiple processing gain (MPG) [5], the correlations involved in the detection and recovery process are accomplished with partial cross-correlation of users sequences. Three situations are possible: (i) sequences with the same length if the interfering user employs the same data rate as the desired user; (ii) a sequence and a fragment from another sequence with larger length if the interfering user employs a lower data rate than the desired user; (iii) a sequence and some periods from another sequence with smaller length if the interfering user employs a higher data rate than the desired user. In the last two cases, general correlation properties 236 Copyright © 2010 John Wiley & Sons, Ltd.