Frequency Offset Estimation in Ofdm Using Sample Covariance

In this paper we consider the performance of the Parametric Weighted Least Square (lW?LS) algorithm for frequency oflset estimation in Orthogonal 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 will 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. 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 <L. Any mathematical model can be exploited for channel description; here we use the Moving Average (MA) process as a most commonly used model for the LTI channel. The frequency difference between the local oscillators in the transmitter and the receiver is expressed by cq which denotes the normalized frequency as a fraction of the intercarrier frequency spacing l/N. In the following analysis we assume that the channel is a real-valued linear fiker and the transmitted signal is disturbed only by the complex additive white Gaussian noise (AWGN) Wn with power density iV/2. The purpose of the frequency offset estimator is to evaluate u on the basis of receiving symbols cin in order to preset the Carrier Recovery System, which then compensates the residual fi-equency offset and tracks the random phase to make coherent demodulation possible. In particular, as a result of such a compensation and tracking process the ICI is substantially reduced. 0-7803-4902-4/98/$10.00 (c) 1998 IEEE