Peak Power Reduction of OFDM Signals Using Chaotic Baker Maps Naglaa F. Soliman *, Abdelhamid A. Shaalan *, Sayed El-Rabaie # and Fathi E. Abd El-samie # * Faculty of Engineering, Zagazig University, Zagazig, Egypt. # Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, Menouf, 32952, Egypt. E-mails: nagla_soliman@yahoo.com, dr_shaalan2005@yahoo.com, srabie1@yahoo.com and fathi_sayed@yahoo.com Abstract— This paper presents a new approach for peak to average power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems. This approach is based on the chaotic Baker map. It is known that OFDM transmitted signals are in complex format, having in-phase and in- quadrature components. If a chaotic randomization process is performed on each component, separately, prior to transmission, the likelihood that both the real and imaginary components of the transmitted signal at a certain time are of large amplitude gets lower. As a result, a reduction of the PAPR can be achieved. Simulation results show that the proposed PAPR reduction method achieves a performance improvement in the OFDM system. Index Terms— OFDM, Chaotic Baker map, PAPR. I. INTRODUCTION OFDM is successfully used in many wireless digital communication systems [l-3]. It is a promising solution for high data rate transmission in frequency selective fading channels. A main disadvantage of OFDM is potentially the high PAPR. A large PAPR leads to an increase in the complexity of the analog-to-digital (A/D) converter, and a reduction in the efficiency of the radio frequency (RF) amplifier. The analog hardware at the transmitter of the OFDM system requires an expensive high-power amplifier (HPA) to avoid clipping and/or soft thresholding that cause nonlinearity in the output [4]. Another alternative to the use of sophisticated power amplifiers is to use a PAPR reduction technique prior to the power amplifier. Several PAPR reduction techniques have been proposed [5- 8]. Clipping is an efficient and simple method to reduce the PAPR of OFDM signals, but it causes distortion and out-of- band radiation. Filtering of the oversampled and clipped signal can reduce the out-of-band noise, but may also cause a peak regrowth [8, 9]. The distortion on each tone could be bounded by modifying repeated clipping and filtering [5, 6]. Moreover, the decrease in the SNR due to clipping could be avoided by using optimal coding and reducing the information rate [10]. Multiple signal representation (MSR) techniques have also been proposed by several researchers to reduce the PAPR. Partial transmit sequences (PTS), selective mapping, interleaving, selective scrambling are some of the schemes, which use MSR to reduce the PAPR. These are all distortionless PAPR reduction techniques. In these techniques, several replicas of the OFDM symbol of a given data frame are formed and the one with the minimum PAPR is chosen for transmission [11-16]. Various methods of adaptive interleaving for PAPR reduction are discussed in [17, 18]. The chaotic Baker map has been utilized in several different ways in cryptography [19, 20]. This map is used for generating sequences of pseudo-random numbers, which can be used as time pads for the randomization process. A chaotic Baker map is first generalized by introducing parameters and then discretized to a finite square lattice of points, which represents pixels or some other data items. To encrypt an N × N image, the ciphering map is iteratively applied to the image. It is shown that the permutations induced by the Baker map behave as typical random permutations. Highly correlated data frames of OFDM signals have large PAPRs. If the long correlation patterns of the in-phase and the in-quadrature components are broken down, a reduction in the PAPR can be achieved. Interleaving can be used to break these correlation patterns [11, 14]. In this paper, the chaotic Baker map is used for the randomization of both components, separately. Both the in-phase and in-quadrature components of the time signal after the IFFT step are randomized separately, using the chaotic Baker map, after they are arranged in a 2-D format. The Baker map used in this paper is based on the method proposed by Fridrich [19]. The chaotic randomization step generates permuted sequences with lower correlation between their samples. Moreover, the chaotic Baker map adds a degree of encryption to the transmitted signal. Various images are used to test the proposed chaotic randomization approach and compare it with the traditional OFDM scheme. This method can be extended to study the transmission of other sources of multimedia such as digital audio and video data. The peak signal to noise ratio (PSNR) is used to measure the quality of the reconstructed images at the receiver. It is the ratio between the maximum possible power of the received image and the power of the corrupting noise, which affects the fidelity of this image. Because many images have a very wide dynamic range, the PSNR is usually expressed in terms of the logarithmic decibel scale. It can be defined as follows: ｸ ｸ ｹ ｷ ｨ ｨ ｩ ｧ  MSE PSNR f 2 10 max log 10 (1) 978-1-4244-5844-8/09/$26.00 ©2009 IEEE 593