A Comparison Of Maximum Likelihood Frequency Offset Estimation Methods For OFDM Systems H. Nezamfar and M. H. Kahaei Department of Electrical Engineering, University of Science and Technology, Tehran, Iran Emails: hnezamfar@ee.iust.ac.ir, kahaei@iust.ac.ir Abstract—Maximum Likelihood (ML) estimation of the frequency offset between the transmitter and the receiver from known trans- mitted preambles is the dominant technique for the estimation of Carrier Frequency Offset (CFO) in OFDM systems. A general formulation of ML detection problem for OFDM systems is provided in this paper and it is described how different ML techniques can be treated as special cases. In addition major newly proposed ML techniques are compared in a unified simulation framework in the presence of AWGN and their performance in terms of estimation range, and their complexity are compared. Index Terms—Orthogonal frequency division multiplexing (OFDM), Carrier Frequency Offset, Maximum Likelihood. I. INTRODUCTION Orthogonal Frequency-Division Multiplexing (OFDM) is the modulation used for many high speed communication systems. OFDM has the main advantages of being bandwidth efficient and robust against multi-path fading, which make it suitable for wireless systems in crowded environments. OFDM has been used in several standards including IEEE802.11, Hiperlan2 [1], IEEE802.16 [2] and DVB-T [3]. However, the main challenge in using OFDM is that the system performance heavily depends on the synchronization between the transmitter and the receiver [4 - 6]. For example, the system performance can substantially degrade due to a small offset in the carrier frequency between the transmitter and the receiver. The doppler effect caused by the mobility of the transmitter or receiver can also introduce a virtual offset. The CFO reduces the system performance since it degrades the orthogonality among the OFDM sub-carriers. Substantial amount of work has been done in order to overcome the CFO problem by estimating and compensating the offset. Most of the proposed methods are based on joint maximum likelihood detection of the channel response and the frequency offset from known preamble sequences [7 - 10]. Preambles are sequences of known data sent at the beginning of a burst of data, especially designed to ease the estimation procedure. Such methods estimate the frequency offset by computing the correlation between several preamble symbols, thus eliminating signal dependent phase information, and maximizing an ML cost function to find frequency offset. These methods differ by the range of frequency offsets that they can estimate, the amount of redundancy they introduce in the preamble sequence, and their estimation complexity. The first major ML-based CFO estimation technique was proposed by Schmidl and Cox [7]. In this method, two identical preamble sequences are transmitted, and the CFO is estimated at the receiver by a simple correlation. However, the range of estimation technique is limited by the OFDM symbol rate since the correlation output is periodic with respect to the frequency offset. A more sophisticated technique was proposed by Morelli and Mengali [9], in which a cascade of several shorter identical preambles are transmitted and the frequency offset is estimated by pair-wise correlation of all the preambles and combining the results. The resulting estimator is still periodic with respect to the frequency offset; however, the period is larger than the former method, leading to larger estimation range at the cost of larger complexity. To eliminate the periodicity, Minn and Tarasak [10] proposed another preamble structure in which redundant symbols are inserted between the preamble symbols of the former method, leading to a less regular preamble structure. This irregularity is desirable as it leads to a larger estimation range. Nonetheless, both methods using multiple preamble symbols require a sophisticated detection hardware incorporating an FFT block with a reasonably large block size. In this paper we formulate the ML CFO estimation technique for an arbitrary preamble sequence and propose a new preamble structure that eliminates the periodicity in the estimation function and requires a simple detection hardware. We further compare the performance and complexity of previously proposed techniques with the proposed technique through MATLAB simulations. The rest of this paper is organized as follows. In Section II, the signal model and the general Maximum likelihood formulation are explained. In Section III, we explain how different estimation techniques can be described as special cases. In Section IV the new preamble structure is presented. In Section V we compare the performance of the three methods explained in Section III with our proposed method in a unified simulation environment and Section VI concludes the paper. 2008 Internatioal Symposium on Telecommunications 978-1-4244-2751-2/08/$25.00 ©2008 IEEE 224