170 IEEE TRANSACTIONS ON BROADCASTING, VOL. 49, NO. 2, JUNE 2003 SER Performance Evaluation and Optimization of OFDM System With Residual Frequency and Timing Offsets from Imperfect Synchronization Xianbin Wang, Member, IEEE, T. T. Tjhung, Senior Member, IEEE, Yiyan Wu, Fellow, IEEE, and Bernard Caron Abstract—This paper deals with the effects of residual timing and frequency offsets on the symbol error rate (SER) performance of orthogonal frequency division multiplexing (OFDM) system. The synchronization of an OFDM system generally consists of a coarse frequency and timing acquisition stage and a refine stage. Due to the presence of Gaussian noise, channel distortions and implementation losses of synchronization and equalization algorithms, residual frequency and timing offsets always exist for an OFDM receiver. The residual frequency and timing offsets are proven to be Gaussian distributed, with their corresponding variances determined. The reception process of OFDM signal with frequency and timing offsets is analyzed. A closed-form analytical result on the symbol error rate (SER) of OFDM system with residual synchronization errors is derived. Computer simulations and analyses show that the frequency and timing offsets affect the OFDM sub-carriers differently. With this observation, a new technique is proposed to minimize the SER of the OFDM systems by adjusting the distribution of transmission power among the sub-carriers. Index Terms—Frequency and timing offsets, Orthogonal Fre- quency Division Multiplexing (OFDM), synchronization. I. INTRODUCTION O RTHOGONAL frequency division multiplexing (OFDM) [1], [2] has recently received considerable attention for its robustness against inter-symbol interference (ISI) and impulse noise, low implementation complexity and high spectral effi- ciency. One of the principal disadvantages of OFDM is its sen- sitivity to synchronization errors, represented by the so-called frequency and timing offsets. Frequency offset causes a reduc- tion of desired signal amplitude in the output decision variable and introduces inter-carrier interference (ICI) due to the loss of orthogonality among sub-carriers. Timing offset results in the rotation of the OFDM sub-carrier constellation. As a result, an OFDM system cannot recover the transmitted signal without a near perfect synchronization, especially when high order of QAM modulation is implemented. The OFDM synchronization process can be divided into a coarse frequency and timing acquisition and a fine frequency and timing offsets estimation. At the initialization stage, an OFDM receiver achieves coarse frequency and timing synchronization by correlating the received and original Manuscript received August 26, 2002; revised January 23, 2003. X. Wang, Y. Wu, and B. Caron are with Communications Research Centre, Ottawa, Ontario, Canada, K2H 8S2. T. T. Tjhung is with the Institute for Communications Research, TeleTech Park, Singapore Science Park II, Singapore 117674. Digital Object Identifier 10.1109/TGRS.2003.810271 synchronization preamble in frequency and time domain, respectively. After initial acquisition, the frequency and timing offsets are usually quite small. For example, the frequency offset could be less than one half of the carrier spacing and timing offset will be within few sampling intervals. Due to the extremely high synchronization requirement of the system, these small remaining frequency and timing offsets still have to be estimated and compensated. This can be done either by the demodulation of the OFDM synchronization preamble, which is an OFDM symbol for training purpose, or some pilot carriers inserted within the OFDM symbols. By dividing the demodulated OFDM symbols with the transmitted ones, the fine estimation of these offsets can be realized. Recently, a number of studies have been reported on OFDM synchronization [3]–[11]. In [9] and [10], synchronization er- rors has been studied in terms of three different effects, i.e., car- rier error, clock error and sampling timing error. Carrier error is the difference between the local-oscillator (LO) in the receiver and the carrier frequency of the transmitted signal. The differ- ence of the sampling clock in the receiver and transmitter is usu- ally called clock error. Besides these two effects, there is an- other synchronization error due to the difference between the optimum sampling time in the receiver and the actual sampling time, which is called sampling timing error. Different techniques have been proposed to track and correct these synchronization errors [3]–[8]. The impacts of these synchronization errors on the performance of OFDM system have also been analyzed in [9]–[11]. In these studies, carrier error and clock error are usu- ally combined as frequency offset, while sampling timing error is identified as timing offset. However, residual synchronization frequency and timing offsets, which are the difference between the estimated and the correct offsets, have never been studied. These residual offsets always exist no matter what kind of syn- chronization technique is employed. Due to the high sensitivity of OFDM systems to the synchronization errors, it is worthwhile to investigate the effects of residual frequency and timing offsets from imperfect synchronization on the OFDM system perfor- mance, as these are the actual errors the receiver has to tolerate. In Section II, the OFDM reception process with arbitrary frequency and timing offsets is analyzed. The effects from car- rier frequency error and clock error are combined as frequency offset during the analysis. The statistical properties of the residual synchronization offsets from the fine synchronization procedure are studied in Section III. Combining the analysis in Sections II and III, a closed-form expression for the symbol error rate (SER) with the residual synchronization errors is 0018-9316/03$17.00 © 2003 IEEE