FREQUENCY OFFSET ESTIMATION IN OFDM USING SAMPLE COVARIANCE G. Levin D. Wulich Communications Laboratory Department of Electrical and Computer Engineering Ben-Gurion University of the Negev Beer-Sheva, ISRAEL Tel: ++972-7-646 1537; Fax: ++972-7-6472949; E-Mail:
[email protected] ABSTRACT In this paper we consider the performance of the Parametric Weighted Least Square (lW?LS) algorithm for Orthogonal frequency oflset estimation in Frequency-Division Multiplexing (OFDM). No training sequence or redundant information is needed. The correlation between symbols is achieved due to channel spreading, which is assumed to be a Linear Time Invariant (ZTfl jilter with known impulse response. We show that the frequency estimator based on a PWLS algorithm may be used in a tracking mode of the OFDM receivers. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) systems have recently gained increased interest. They are widely used in HDSL, DAB and for digital transmission at HF. One of the main problems in the design of an OFDM receiver is the mismatch of the oscillators in the transmitter and the receiver. The demodulation of a signal with an offset in the carrier frequency can cause a high bit error rate due to degradation in the perilorrnance of the symbol synchronizer and to Inter Channel Interference (ICI) [1]. Many ffequency offset compensation methods have been proposed recently; a training sequence [1,2,3,4] or redundant information [5] is required in many of them. In this paper we consider the Parametric Weighted Least Square (PWLS) algorithm for the frequency offset estimation [6, 7] based on matching, in the weighted least square sense, a sequence of sample correlation to the theoretical values. No training sequence or redundant information is needed. A correlation between symbols is achieved due to channel influence. We suppose that the channel is well described by a Linear Time Invariant (LTI) system and has an a priori known impulse response. The problem of the estimation of the random amplitude complex exponent frequency is very well known in estimation theory and has many solutions [6,8,9]. Here we
use, as stated, the Parametric Weighted Least Square (PWLS) algorithm [6]. It is always very interesting to establish the ultimate statistical performance that can be achieved by a given estimation method. The Cramer-Rao Bound (CRB) [10, 11] has proved to be a usefhl tool because it provides a lower bound on the covariance of any unbiased estimate of the parameters vector in question. We use CRB as a criterion of successfid estimation. will
THE OFDM SYSTEM BASEBAND MODEL Fig. 1 illustrates the discrete-time baseband equivalent OFDM system. Complex data symbols ~k transformed by the Inverse Discrete Fourier Transform (IDFT) yield a string of symbols bn , which represent the baseband equivalent of an OFDM signal with N-parallel subcarriers. Symbols bn are serially transmitted over a discrete-time channel whose impulse response h(z)
is known and
assumed to be of length
