IMPROVED ESTIMATION OF TIME VARYING AND FREQUENCY SELECTIVE CHANNELS FOR OFDM SYSTEMS El Kefi Hlel, Sofiane Cherif, Fethi Tlili, Mohamed Siala {el-kefi.hlel, sofiane.cherif, fethi.tlili, mohamed.siala}@supcom.rnu.tn Ecole Sup´ erieure des Communications de Tunis, 2083 cit´ e El-Ghazala/Ariana, TUNISIA ABSTRACT In this paper, we deal with channel estimation for OFDM systems operating in time and frequency selective channels. In order to exploit the frequency correlation of the channel transfer function, we use the Karhunen-Lo` eve expansion to separate the signal space from the noise space. Afterwords, we use decision-directed technique for track- ing the time varying coefficients of the transfer function in the signal space. Our simulation results show the robust- ness of the proposed scheme with respect to least square channel estimator. Index Terms: Channel Estimation, OFDM, Karhunen- Lo` eve, Least Square, Decision-Direcetd. 1. INTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) has been applied in wireless communication systems due to its high data rate transmission capability with high bandwidth efficiency and its robustness to multi-path delay. It has been used in wireless LAN standards such as IEEE802.11a and in multimedia wireless services such as Digital Video Broadcasting - Terrestrial (DVB-T) [1, 2]. A dynamic estimation of the channel is necessary be- fore the demodulation of OFDM signals since the radio channel is frequency selective and time-varying for wide- band mobile communication systems. Several works in- vestigated the time varying channel estimation [2, 3, 4]. In this paper we exploit the frequency correlation of the channel transfer function to develop a new channel estimation technique based on least square criterion. A Karhunen-Lo` eve (KL) expansion is used to separate the signal space from the noise space. After KL, a windowing operation is used for noise space removal. This paper is organized as follows. The OFDM sys- tem and the used channel model are briefly described in Section II. We introduce our channel estimator scheme in Section III, where we also discuss the KL expansion and the windowing operation. In Section IV, we evaluate our technique by computer simulation. Finally, Section V con- cludes the paper. 2. SYSTEM DESCRIPTION 2.1. System Model Figure 1 displays our OFDM baseband model. The use of a cyclic prefix (CP) preserves the orthogonality of the tones and eliminates intersymbol interference (ISI) between consecutive OFDM symbols [5]. Furthermore, the chan- nel is assumed to be slowly fading, so that it can be con- sidered constant during one OFDM symbol. The number of sub-carriers in the system is N and the length of the CP is L samples. The parameter i ∈ Z is the OFDM sym- bol (time) index and the parameter k =0, 1, ...N − 1 is the sub-carrier index. The noise b(t) is assumed white and Gaussian with variance σ 2 b . Figure 1. Baseband model of an OFDM system. The transmitted symbols x k,i are supposed indepen- dent and identically distributed with variance E s = E  |x k,i | 2  . 2.2. Wireless Channel Model As shown in Figure 2, we can describe the system as a set of parallel Gaussian channels with correlated attenuations H k,i . The attenuation on each sub-carrier is given by [6]: H k,i = H (f k , iT s ) , (1) where H (., .) is the frequency response of the channel, f k is the k th sub-carrier frequency and T s is the sampling period of the system. The noise components ω k,i are white and Gaussian with variance σ 2 ω = σ 2 b /N . The complex baseband channel representation of the wireless channel impulse response is given by [7]: h (τ,t)= M  k=1 h k (t) δ (τ − τ k ) , (2)