The 7 th International Telecommunications Symposium (ITS 2010) Performance of WHT-STC-OFDM in Mobile Frequency Selective Channel Luciano Leonel Mendes Electrical Engineering Inatel Sta. Rita do Sapucai, MG, BR luciano@inatel.br Renato Baldini Filho DECOM UNICAMP Campinas, SP, BR baldini@decom.fee.unicamp.br Abstract— High data rate systems usually employ Or- thogonal Frequency Division Multiplexing and Space-Time Coding to improve the performance on a mobile time-variant frequency-selective channel. Nonlinearities introduced by the power amplifier can be minimized by performing a Wash- Hadamard Transform on the data symbol prior the Inverse Fast Fourier Transform (IFFT) at the transmitter. This pro- cedure reduces the peak-to-average power ratio of the OFDM symbol. An extra advantage of the WHT combined with OFDM is the performance improvement on a frequency-selective channel. The aim of this paper is to present an analytical expression to estimate the performance of the WHT-STC- OFDM taking into account the receiver/transmitter mobility, the channel frequency response and the noise added by the channel. The theoretical results are corroborated by computer simulations. Keywords— Time-variant frequency-selective channel, OFDM, Space-Time Coding, Walsh-Hadamard Transform. I. I NTRODUCTION Broadband wireless communication is an issue that has been the focus of attention for several years. Different standards, such as DVB (Digital Video Broadcasting) [1], ISDB (Integrated Service Digital Broadcasting) [2], Wi-FI (Wireless Fidelity) [3] and Wi-MAX (Worldwide Interop- erability for Microwave Access) [4], use OFDM (Orthogo- nal Frequency Division Multiplexing) [5] to minimize the harmful distortions of the frequency-selective channels [6]. Space-Time coding, as proposed by Alamouti [7], can be integrated to OFDM to minimize the effects of the Doppler spread in a mobile system [4] [9]. OFDM applied to a power limited system, such as cel- lular communication systems, presents high PAPR (Peak- to-Average Power Ratio) [5]. High PAPR means that the signal presents high amplitude peaks that may lead the power amplifier to its saturation. An amplifier operating on a nonlinear region introduces ICI (Intracarrier Interference) [10], that reduces the overall performance of the system. The Walsh Hadamard Transform (WHT) technique can be used to reduce the PAPR of OFDM symbols [11] [12]. The WHT combined with OFDM also improves the performance on frequency-selective channels [13] due the dispersion of the information data in all OFDM subcarriers. The occurrence of a deep frequency notch in the OFDM bandwidth do not destroy all the information transmitted in the affected subcarriers. The aim of this paper is to analyze the performance of the OFDM system combined with the WHT and STC (Space- Time Coding) [14] on a mobile frequency-selective channel. An analytical expression to estimate the performance of this system is devised. Theoretical and simulation results are compared to guarantee its validity. This paper is organized as follows: Section II presents the principles of the OFDM combined with STC and WHT. In Section III, a theoretical expression to estimate the system performance is evaluated and theoretical and simulation curves are presented for comparison and validation. Finally, Section IV presents conclusion and final remarks. II. PRINCIPLES OF WHT-STC-OFDM SYSTEMS OFDM system transforms a high data-rate stream into N slow data-rate sub-streams transmitted by mean of N complex subcarriers. The spectral efficiency is preserved by using sub-carriers spaced by Δf = R mc = R s N , (1) where N is the number of subcarriers, R mc is the subcarrier symbol rate and R s is the overall symbol rate of the OFDM system. Notice that the overall occupied bandwidth of an OFDM signal is practically equals to the bandwidth of an equivalent single carrier signal [5]. The sampled OFDM signal can be stated as s m = s(mT S )= 1 N N−1  i=0 c[i] exp  j 2πi N m  , (2) where c[i] is the complex serial symbols to be transmitted, T s is the time interval between adjacent samples of the OFDM symbol and m is the time index of the samples. Then, a N -point IDFT (Inverse Discrete Fourier Transform) generates the OFDM signal while a N -point DFT (Discrete Fourier Transform) recovers the desired data at the receiver. Assuming that the channel frequency response is H[n], then the signal delivered to the decision device is given by c ′ [i]= H[i]c[i]+ W [i], (3) where W [i] is a sample of the complex gaussian noise in the frequency domain for the i th subcarrier. The detector