142
IEEE COMMUNICATIONS LETTERS, VOL. 9, NO. 2, FEBRUARY 2005
Semi-Analytical Approach of Asynchronous MC-CDMA Systems with a Cyclic Prefix Kyunbyoung Ko, Member, IEEE, Taeyoung Kim, Student Member, IEEE, Sooyong Choi, Member, IEEE and Daesik Hong, Member, IEEE
Abstract— In this letter, asynchronous multicarrier-code division multiple access (MC-CDMA) systems with a cyclic prefix (CP) are analyzed over frequency-selective multipath fading channels, and the average bit error rate is evaluated. The derived results show that a CP is required for MC-CDMA systems in order to mitigate intersymbol interference (ISI) and fully obtain the achievable path diversity as the frequency diversity. Index Terms— Asynchronous MC-CDMA, CP, ISI.
I. I NTRODUCTION
F
OR asynchronous MC-CDMA systems, semi-analytical approaches have been proposed in [1] and [2]. Furthermore, the upper and lower bounds on the average bit error rate (BER) are derived in [3], and performance in correlated fading among subcarriers is analyzed in [2]. However, the analyses in [1], [2], and [3] do not include consideration of a cyclic prefix (CP). In MC-CDMA systems, the path diversity can be obtained as the frequency diversity over frequency-selective multipath fading channels. As the number of multipaths increases, the frequency diversity increases [4]. However, if MC-CDMA systems do not use a CP, the effect of intersymbol interference (ISI) increases in proportion to the number of multipaths and causes performance degradation. Therefore, in order to mitigate ISI in MC-CDMA systems, a CP can be inserted similar to orthogonal frequency division multiplexing (OFDM) [5][6]. This letter presents our evaluation for the performance of asynchronous MC-CDMA systems with a CP over frequencyselective multipath fading channels. II. A SYNCHRONOUS MC-CDMA SYSTEMS
factor N , and a CP is added. Therefore, the transmitted signal for the mth user can be written as [6] ∞ N −1
sm (t) =
Manuscript received April 16, 2004. The associate editor coordinating the review of this letter and approving it for publication was Dr. Paul Cotae. Support for this work was provided by the Basic Research Program (R012002-000-00153-0(2002)) of the Korea Science and Engineering Foundation. Kyunbyoung Ko is with Samsung Electronics Co., Ltd., Korea (e-mail:
[email protected]). Taeyoung Kim and Daesik Hong are with the Center for Information Technology of Yonsei University (CITY), Information and Telecommunication Lab., Dept. of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea (e-mail: {tykim and daesikh}@itl.yonsei.ac.kr). Sooyong Choi is with the ACSEL and OCLNB Lab., School of Electrical Computer Engineering, Oklahoma State University. Digital Object Identifier 10.1109/LCOMM.2005.02017.
(1)
where p(t) is the pulse waveform which is uniform in the interval [−TCP , Tb ), and zero otherwise. Tb , TCP , and TS (= Tb + TCP ) are the bit interval, the cyclic prefix interval, and the MC-CDMA symbol interval, respectively. With respect to CP, g(t) is defined as (t + Tb ) − kTS for kTS − TCP ≤ t < kTS g(t) = (2) t − kTS for kTS ≤ t < kTS + Tb . The low-pass time-variant impulse response for the multipath fading channel of the mth user can be defined as hm (τ ; t) =
L−1
gm,l (t)δ (τ − lTc )
(3)
l=0
where L is the number of paths and Tc (= Tb /N ) is the tap interval [7]. The slow time-varying tap weights {gm,l (t)} are assumed to be complex-valued stationary random processes, for which the magnitudes are Rayleigh-distributed and the phases are uniformly distributed at any instant t. By discrete Fourier transform (DFT) of (3), the transfer of the L−1function [k] [k] nth subcarrier can be written as hm,n = l=0 gm,l e−j2πnl/N [k] with gm,l (t)kT −T ≤t
