A DECISION-DIRECTED ESTIMATION OF TIME AND FREQUENCY SELECTIVE CHANNELS FOR OFDM SYSTEMS El Kefi Hlel, Fethi Tlili, Sofiane Cherif, Mohamed Siala {el-kefi.hlel, fethi.tlili, sofiane.cherif, mohamed.siala}@supcom.rnu.tn High School of Communications, Tunis, 2083 cit´ e El-Ghazala/Ariana, TUNISIA ABSTRACT We propose in this paper a decision-directed channel es- timation technique for OFDM systems operating in time and frequency selective channels. This technique exploits both frequency and time correlation of the channel trans- fer function. The frequency correlation is achieved by ap- plying a Karhunen-Lo` eve (KL) expansion which performs the separation of the channel space from the noise space and generates an uncorrelated representation of the chan- nel transfer function. At the output of the KL expansion stage, elementary linear single-input single-output (SISO) predictors are developed by exploiting the channel time correlation. The performance of the proposed estimation algorithm is assessed through computer simulations in out- door environment. Test results show that our technique presents a better performance compared with some basic decision-directed channel estimates. Index Terms— Estimation, Decision-directed, OFDM, Time and frequency selective channels 1. INTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) has been successfully applied to a wide variety of digi- tal communications systems [1]. It is being commercially applied for wireless local area network (IEE802.11a and HIPELAN/2), terrestrial digital audio broadcasting (DAB- T), and terrestrial digital video broadcasting (DVB-T), and it is being considered for wireless broadband access sys- tems by the IEEE802.16 work group. 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 [2]. In this context, several works dealt with this problem by using training data based Least Squares (LS) channel estimation or Min- imum Mean-Square Error (MMSE) channel estimation [3, 4]. The training data-based channel estimation has the dis- advantage of a reduced net data rate because the training data consists either of pilot symbols that are continually multiplexed into data stream, or of a training data block at the beginning of each packet. An alternative approach is IDFT DFT ✲ ✲ ✲ x 0,i x 1,i x N-1,i CP ✲ h(τ,t) CP ❣ ✲ ✲ ✲   ❩ ❩ ✲ ✲ ✲ ✲ y 0,i y 1,i y N-1,i ❄ b(t) Figure 1. Baseband model of an OFDM system. the decision-directed channel estimation where the train- ing data is replaced by the previously detected data. In this paper, we propose a novel technique for decision- directed channel estimation in OFDM systems operating in time-varying and frequency selective channels. The KL expansion is applied to take into account the frequency correlation of the channel transfer function and to perform the separation of the channel space from the noise space. A set of elementary and independent SISO predictors are developed by exploiting the uncorrelated channel coeffi- cients resulting from the KL transform. This paper is organized as follows: In Section II, the OFDM system is reviewed. We introduce the proposed channel estimation scheme in Section III, where we also discuss the convenient channel representation by KL ex- pansion and the computational formulation of the elemen- tary SISO predictors. In Section IV, we assess the per- formance of our technique through computer simulations. Finally, Section V concludes the paper. 2. OFDM SYSTEM MODEL We consider an OFDM system consisting of N subcarri- ers. Each transmission subcarrier is modulated by a data symbol x k,i , where k ∈{0, 1, ..., N - 1} represents the subcarrier number and i ∈ Z is the OFDM symbol index. The transmitted symbols x k,i are supposed independent and identically distributed with variance E s . The base- band model of our OFDM system is presented in Figure 1. At the transmitter, Inverse Fast Fourier Transform (IFFT) is applied to each OFDM symbol with duration T u , and subsequently a guard interval with duration ∆ in the form