An approach to PAPR Reduction in OFDM using Goppa codes

Abstract

Orthogonal frequency division multiplexing (OFDM) is a widely used modulation and multiplexing technology applied in many telecommunications standards due to its spectral efficiency and robustness against multipath fading. The multicarrier aspect of OFDM signal is characterized by high peak-to-average power ratio (PAPR), which renders the power amplifier (PA) inefficient and causes distortion in the transmitted signal. Several techniques to overcome and reduce PAPR such as signal distortion, signal scrambling, coding etc. are proposed and implemented on multipath fading channels. Coding methods does not affect system complexity as forward error correction is an inherent block in any digital communication system. The frequency diversity benefits of OFDM is not utilized well unless channel coding is used. Several codes like Hamming, Golay, BCH, RS, Reed Muller etc. have been investigated so far. Goppa codes were needed to be explored in OFDM systems. In this paper, its ability to reduce the peak power is studied for conventional OFDM signal. These codes are used in computer and telecommunication based applications owing to its useful properties required for cryptography. The PAPR reduction of Goppa coded OFDM (GOFDM) is found to be satisfactory for higher order constellation mapping of binary information. A look up table can also be created to select Goppa code words on the basis of a desired threshold of PAPR in dB. A mathematical analysis of the relationship of input data and its PAPR is also executed and certain conclusions are drawn as shown in the lemmas. But coding methods solely cannot achieve substantial PAPR reduction and therefore most of the literature on PAPR reduction methods have combined coding with other techniques. In this paper, G-OFDM is extended to a hybrid method of constant amplitude modulated (CAM)-G-OFDM to completely mitigate the PAPR problem. But it is achieved at the cost of transmitter and receiver complexity and performance parameters like bit error rate (BER), dependency on modulation index etc. which can be taken care of by making some amendments in the system design.