IEEE SIGNAL PROCESSING LETTERS, VOL. 14, NO. 5, MAY 2007 321 A New OFDM Synchronization Symbol for Carrier Frequency Offset Estimation Amine Laourine, Student Member, IEEE, Alex Stéphenne, Senior Member, IEEE, and Sofiène Affes, Senior Member, IEEE Abstract—This letter proposes a new data-aided carrier fre- quency offset (CFO) estimation scheme for orthogonal frequency division multiplexing (OFDM) communications suitable for frequency-selective channels. The proposed method is based on the transmission of a specially designed synchronization symbol that generates a particular signal structure between the received observation samples at the receiver. This structure is exploited to derive a closed-form expression of the CFO. The proposed solu- tion offers a wide acquisition range with reduced computational load. Simulations over frequency-selective channels confirm the superiority of the proposed method compared to recent data-aided synchronization algorithms. Index Terms—Frequency-division multiplexing, synchroniza- tion. I. INTRODUCTION O RTHOGONAL frequency division multiplexing (OFDM) performance suffers from a pronounced sensitivity against carrier frequency offsets (CFOs) [1]. The CFO should therefore be estimated and compensated before any further processing in the receiver. Different data-aided schemes of CFO estimation in OFDM systems have been appraised. These methods hinge on the periodic transmission of known data blocks that allows for the estimation of the CFO from the estimation of the phase rotation between these blocks at the receiver. The most known of these methods is the M&M method [3], which constitutes an improvement to Schmidl’s [2]. The M&M method was also se- lected by [4] to provide a joint robust estimation of the timing and the frequency offset. More recently, a new synchroniza- tion symbol proposed in [5] allowed for performance gains over Schmidl’s algorithm. In this letter, we propose a new synchronization symbol struc- ture and a new CFO estimator that offer a wide acquisition range and a high accuracy at a very reduced computational cost. Based on the original shape of the new synchronization symbol, a closed-form CFO estimator is derived. Our method has an ac- quisition range that can reach the subcarrier spacing, where is a user-selected parameter characterizing our synchro- nization symbol, and is the number of OFDM subcarriers. As Manuscript received July 4, 2006; revised September 21, 2006. This work was supported by a Canada Research Chair in High-Speed Wireless Commu- nications. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Gerald Matz. A. Laourine and S. Affes are with the INRS-EMT, Montréal, QC H5A 1K6, Canada (e-mail: laourine@emt.inrs.ca; affes@emt.inrs.ca). A. Stéphenne is with Ericsson Canada, Montreal, QC H4P 2N2, Canada (e-mail: stephenne@ieee.org). 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/LSP.2006.888353 supported by simulations, our algorithm provides higher accu- racy compared to the well-known M&M method [3] as well as the method in [5]. More specifically, our estimator proved to be robust against low SNRs (below 0 dB). Such low SNR values are of great practical interest since next-generation wireless sys- tems attempt to operate in MIMO multi-access multi-cell envi- ronments, which are characterized by low operating SNRs. In this regard, OFDM needs reliable synchronization techniques that operate well in a low SNR regime. This letter is organized as follows. In Section II, the OFDM system model is described. The designed synchronization symbol and the resulting structure in the received samples are described in Section III. The CFO estimator and the different derivations are presented in Section IV. Section V analyzes the performance of the proposed estimator. Numerical examples are illustrated in Section VI. Conclusions are given in Section VII. II. SYSTEM MODEL We consider a discrete-time OFDM system with subcar- riers. At the transmitter, complex-valued symbols , which belong to a QAM or PSK constellation, modulate orthogonal subcarriers using the inverse fast Fourier transform (IFFT). Be- fore transmission, a cyclic prefix is appended at the beginning of the signal, yielding if if where . At the receiver, the cyclic prefix is discarded, leading to the following received samples: (1) (2) (3) where is the transfer function of the channel at the frequency of the th subcarrier, corresponds to the channel length, is the relative carrier frequency offset (the ratio of the actual frequency offset to the intercarrier spacing), and is an additive complex white Gaussian noise (with variance ) independent of . III. SYNCHRONIZATION SYMBOL DESIGN To estimate the CFO, we propose to transmit the following synchronization symbol: (4) 1070-9908/$25.00 © 2007 IEEE