PAPR Reduction in Trigonometric-Based OFDM Systems

A key building block in any OFDM transceiver is the Fast Fourier Transform (FFT) and its inverse. A number of researchers have recently proposed the use of the discrete cosine transform (DCT) and the discrete sine transform (DST), and their inverses as alternative modulating/demodulating bases to improve the BER performance of OFDM schemes while maintaining a low implementation cost. In this paper, we consider the open problem of reducing the peak-to-average power ratio (PAPR) in OFDM systems that deploy these trigonometric transforms. In specific, we show that similar to the FFT case, the complex envelope of a bandlimited DCT/DST- OFDM signal has a chi-square distribution with one degree of freedom and hence converges weakly to a Gaussian random process as the number of sub-carriers becomes large. Using this result, we then derive closed form expressions for the complementary cumulative distribution functions (CCDF) of each system and show that OFDM systems with trigonometric transforms provide higher PAPR reduction than the standard FFT-based system. Simulation results that compare the CCDFs of the different transforms using the partial transmit sequences (PTS) technique confirm our theoretical findings.