IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010 2543 Simplified Multiaccess Interference Reduction for MC-CDMA With Carrier Frequency Offsets Layla Tadjpour, Shang-Ho Tsai, and C.-C. Jay Kuo, Fellow, IEEE Abstract—Multicarrier code-division multiple-access (MC- CDMA) system performance can severely be degraded by multiac- cess interference (MAI) due to the carrier frequency offset (CFO). We argue that MAI can more easily be reduced by employing complex carrier interferometry (CI) codes. We consider the sce- nario with spread gain N , multipath length L, and N users, i.e., a fully loaded system. It is proved that, when CI codes are used, each user only needs to combat 2(L - 1) (rather than N - 1) interferers, even in the presence of CFO. It is shown that this property of MC-CDMA with CI codes in a CFO channel can be exploited to simplify three multiuser detectors, namely, parallel interference cancellation (PIC), maximum-likelihood, and decor- relating multiuser detectors. The bit-error probability (BEP) for MC-CDMA with binary phase-shift keying (BPSK) modulation and single-stage PIC and an upper bound for the minimum error probability are derived. Finally, simulation results are given to corroborate theoretical results. Index Terms—Carrier frequency offset, complexity reduction, decorrelating detection, interferometry codes, maximum likelihood detection, multiaccess interference, multicarrier code- division multiple-access (MC-CDMA), multiuser detection, orthogonal codes, parallel interference cancellation. I. I NTRODUCTION M ULTICARRIER code-division multiple access (MC- CDMA) has emerged as a promising multiaccess tech- nique for high-data-rate communications [2], [10]. MC-CDMA is inherently more robust to intersymbol interference than a conventional CDMA system due to the use of the orthogonal frequency-division multiplexing (OFDM) structure. However, the multipath and/or the carrier frequency offset (CFO) effects tend to destroy orthogonality among users and lead to multiac- cess interference (MAI). Thus, the performance of MC-CDMA can greatly degrade. There has been research on MAI suppression using single- user detection (SUD) techniques. For example, the structural Manuscript received December 10, 2008; revised August 2, 2009; accepted January 8, 2010. Date of publication February 8, 2010; date of current version June 16, 2010. This work was supported in part by the Integrated Media Systems Center, a National Science Foundation Engineering Research Center, under Cooperative Agreement EEG-9529152, and in part by the National Science Council, Taiwan, under Cooperative Agreement 97-2221-E-009-071- MY2. The review of this paper was coordinated by Prof. J. Lie. L. Tadjpour is with Information System Laboratories, Vienna, VA 22182 USA (e-mail: ltadjpour@isl-inc.com). S.-H. Tsai is with the Department of Electrical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan (e-mail: shanghot@mail.nctu.edu.tw). C.-C. J. Kuo is with the Department of Electrical Engineering and Integrated Media Systems Center, University of Southern California, Los Angeles, CA 90089-2564 USA (e-mail: cckuo@sipi.usc.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2010.2042473 differences of interfering users caused by CFO were exploited at the receiver to suppress MAI in [12]. However, this MAI- suppression technique imposes a computational burden on the receiver since a discrete Fourier transform (DFT) of size larger than N is required due to the oversampling of the received signal in the frequency domain. Another way to reduce MAI is achieved by code design while keeping the structure of MC- CDMA unchanged [19]. In [19], a code-design method based on real Hadamard–Walsh (HW) codes was proposed and shown to achieve zero MAI in a multipath environment in MC-CDMA. However, not all users can enjoy MAI-free communications with this design. In addition, suppression of the MAI due to the CFO effect was not considered in this paper. Multiuser-detection (MUD) techniques have been developed to mitigate MAI. However, the complexity of MUD techniques is generally high. Much effort has been made to reduce the complexity of the multiuser detectors. Cai et al. [4] proposed to assign a set of subcarriers to a group of users while preserving the frequency diversity of MC-CDMA as much as possible. A new maximum-likelihood (ML) MUD scheme called sphere decoding was proposed for MC-CDMA whose complexity is a polynomial function of the user number [3]. However, when the user number is large, the sphere-decoding ML algorithm is cumbersome to perform. Moreover, neither of these techniques are shown to be effective in the presence of CFO. In this paper, we show how to suppress MAI with simplified techniques for MC-CDMA in CFO environments using carrier- interferometry (CI) codes. CI codewords were introduced to MC-CDMA in [17], which showed that two sets of orthogonal CI codewords can increase user capacity from N to 2N in MC- CDMA with negligible performance degradation in a multipath fading channel. CI codes were also used as training sequences for channel estimation to decouple the interantenna interference in a CFO-free MIMO-OFDM system [14]. Here, we first show how to completely eliminate MAI by employing CI codes in MC-CDMA with CFO. That is, for CI codes, when the number of active users is less than or equal to N/G, where G is a power of 2 with G ≥ L, N is the spread gain, and L is the multipath length, we demonstrate that a proper choice of CI codewords allows MC-CDMA systems to enjoy MAI-free communication. Second, for a fully loaded MC-CDMA system with CI codes (CI-MC-CDMA), we prove that for L ≤ N/2, each user receives interference from 2(L − 1) users only (instead of other N − 1 active users) in CFO and multipath-fading environments. Third, we demonstrate that by exploiting the sparsity of the cross-correlation matrix of CI-MC-CDMA, we can lower 0018-9545/$26.00 © 2010 IEEE