Root-Based Nonlinear Companding Technique for Reducing PAPR of Precoded OFDM Signals

Orthogonal frequency division multiplexing (OFDM) signals are characteristically independent and identically distributed Gaussian random variables that follow Rayleigh distribution. The signals also exhibit high peak-to-average power ratio (PAPR) problem due to the infinitesimal amplitude component distributed above the mean of the Rayleigh distribution plot. Since the amplitudes are nonlinearly and non-monotonically increasing, applying roots to the amplitude distribution is shown in this paper to change the probability density function (PDF) and thus reduces the PAPR. We exemplify these by imposing this constraint on standard μ-law companding (MC) technique in reducing PAPR of OFDM signals, which is known to expand the amplitudes of low power signals only without impacting the higher amplitude signals. This limits the PAPR reduction performance of the MC scheme. Since companding involves simultaneously compressing/expanding high/low amplitude OFDM signals, respectively, in this paper, we refer to the new method as a root-based MC (RMC) scheme that simultaneously expands and compresses OFDM signal amplitudes unlike MC. In addition, we express a second transform independent of the MC model. The results of the two proposed schemes outperform four other widely used companding techniques [MC, log-based modified (LMC), hyperbolic arc-sine companding (HASC) and exponential companding (EC)]. Besides these, we precode the OFDM signals using discrete Hartley transform (DHT) in order to further reduce the PAPR limits achieved by RMC by distorting the phase. While preserving the BER, DHT-precoded RMC outperforms all the four other companding schemes (MC, EC, HASC, LMC) in terms of PAPR.