Abstract-In this paper, we describe a patent pending, fine carrier frequency synchronization algorithm based on a minimum mean-squared error (MMSE) ...
Roh, Cheun, and Park: An MMSE Fine Carrier Frequency Synchronization Algorithm for O m M Systems
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AN MMSE FINE CARRIER FREQUENCY SYNCHRONIZATION ALGORITHM FOR OFDM SYSTEMS Heejin Roh’, Kyungwhoon Cheun’, and Jaehong Park2 ’Communications Systems Lab., Dept. of Electronic and Electrical Engineering Pohang University of Science and Technology (POSTECH) San-31, Hyoja-dong, Nam-ku, Pohang, Kyungbook, 790-784, Korea email: cheun Bvision.postech.ac.kr 2Electronicsand Telecommunications Research Institute, Taejeon, Korea
Abstract-In this paper, we describe a patent pending, fine carrier frequency synchronization algorithm based on a minimum mean-squared error (MMSE) approach for OFDM systems which is insensitive t o symbol timing offsets. In order to obtain these attributes, the proposed algorithm adopts a cost function similar t o the CMA (Constant Modulus Algorithm) used for blind channel equalization. Another advantage of the algorithm is that the transmission of a known training pattern is unnecessary, thus, improving the transmission efficiency. A hardware efficient version of the proposed algorithm is also developed. Computer simulations are performed to evaluate the performance with QPSK and 64-QAM modulations under a frequency selective multipath channel.
I. INTRODUCTION
0
NE of the major drawbacks of orthogonal fre-
quency division multiplexing (OFDM) modulation is the high sensitivity to carrier frequency offsets [I]. A carrier frequency offset of Afc may be decomposed into an integer multiple of the subcarrier spacing denoted f d and a residual frequency offset Sfc, i.e., Afc = k f d + S f c , where k is an integer and lSfc(< f d / 2 . The carrier frequency offset of an integer multiple of the subcarrier spacing, IC f d , simply shifts the transmitted signal in the frequency domain by IC times the subcarrier spacing. On the other hand, the residual carrier frequency offset Sfc not only results in a decrease in the signal power at the receiver discrete Fourier transform (DFT) output but also incurs interchannel interference (ICI,) severely degrading the system performance [l] - [3]. In this paper, we concentrate on compensating the residual carrier frequency offset Sfc which we will simply refer to as the carrier frequency offset for the remaining of the paper. A known training pattern, such as those used for channel equalization, can be used to estimate and recover the carrier frequency offset of an integer multiple of the subcarrier spacing [4]. Most of the recent work on estimating the residual carrier frequency offset focus on the utilization of a This work was supported by Electronics and Telecommunications Research Institute (ETRI) of KOREA.
Manuscript received June 13, 1997
known training pattern, which we classify as data aided (DA) estimators, or take the maximal likelihood estimation approach. For example, P. Moose in [2] proposed transmitting a known pattern for two consecutive OFDM symbols and showed that the frequency offset is proportional t o the phase shift between the DFT outputs of the two OFDM symbols. M. Luise in [5] proposed a decision-directed fine carrier frequency synchronization with periodically inserted known symbol sequences. F. Daffara in [6], suggested a maximum likelihood frequency detector. M. Okada in [7],proposed a maximum likelihood criterion based on the cyclostationarity of OFDM signals. Our criterion for carrier frequency synchronization is the minimization of IC1 induced by the carrier frequency offset using a non-data aided (NDA) approach. In developing an algorithm for minimizing the ICI, it is necessary to consider the effect of symbol timing offsets since a symbol timing offset causes a linear phase rotation of the receiver DFT outputs [8] and introduces intersymbol interference (ISI.) The sensitivity to symbol timing offsets is minimized by adopting a cost function similar to the CMA [9] used for blind channel equalization. The organization of the paper is as follows. The description of the OFDM system under consideration is presented and OFDM related terminologies are defined in Section 11. In Section 111, the relationship between the carrier frequency offset and IC1 is quantified and an MMSE based carrier frequency synchronization algorithm is developed. A modification to the proposed frequency error estimation algorithm resulting in low implementation complexity is also derived. In Section IV, the performance of the proposed algorithm is evaluated through simulations under a frequency selective multipath channel and conclusions are drawn in Section V.
11. SYSTEM DESCRIPTION In an OFDM transmission system, M parallel data symbols are modulated onto N ( N > M ) subcarriers
0098 3063/97 $10.00
1997 IEEE
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JEEE Transactions on Consumer Electronics, Vol. 43; No. 3, AUGUST 1997
via an N-point DFT. The remaining N - M subcarriers are not used for data modulation in order to avoid aliasing problems a t the receiver [lo]. The N DFT outputs are given as
-
M-I
; n = 0 , 1 , 2,...,N - 1 ,
NLM,
{X-P, z-P+l,
=
' ' ' 7
(XN-P, XN-P+l,
I%-1,X O , '
' '
