_{1}

Efficient nonlinear companding transform (NCT) scheme for reducing peak-to-average power (PAPR) of orthogonal frequency division multiplexing (OFDM) signals is proposed. This scheme transforms the Gaussian-distributed signals into the specified statistics form defined as a piecewise function. By adjusting the transform parameters, it enables more design flexibility in companding form so that a favorable trade-off between PAPR and bit error rate (BER) can be offered. Compared to existing techniques, the scheme can achieve an effective reduction in PAPR as well as an improved BER performance simultaneously.

Orthogonal frequency division multiplexing (OFDM) technique has been widely adopted in modern wireless communications due to its high spectral efficiency and immunity to the multipath fading effects. However, a critical drawback of OFDM system is the high peak-to-average power ratio (PAPR) of the transmitted signals. The high PAPR results in the in-band distortion and out-of-band interference when the nonlinear power amplifier (HPA) is utilized at the transmitter. Various PAPR reduction methods have been proposed for OFDM systems over the past decade [

NCT method was first introduced in [

Both PAPR and moderate performance degradation are critical challenges for a well-designed companding scheme [

Suppose the complex-value vector

Based on the central limit theory, when

The PAPR of OFDM signal in a given time-domain symbol is defined as

In this section we first derive the generic formulas of the proposed scheme. Then, its theoretical performance is characterized with the achievable PAPR gain. The main idea of the scheme is to transform the statistics of the signal amplitude into a specified PDF form defined by a piecewise function with an inflexion point. Assume that the inflexion point and cutoff point of this target PDF are

where

From the CDF definition, namely

where

where

is

To reduce the implementation complexity, both functions in Equation (7) and Equation (8) can be numerically pre-computed and performed through the look- up tables in practice. Moreover, in order to keep the input and output signal with an unchanged power level, i.e.

The ultimate PAPR of the companded signal with this scheme is given by

where

According to Equation (11), the achievable G in PAPR is more than 7.7 dB.

In this section, we present numerical simulations to evaluate the performance of the proposed scheme. We consider an un-coded OFDM system with the number of subcarriers

where

CCDFs of the PAPR with different schemes for QPSK. As shown in the figure, our scheme can effectively reduce the PAPR while simultaneously obtaining sharp drops in CCDFs.

_{b}/N_{0} curves with different

schemes over the additive Gaussian white noise (AWGN) channel for QPSK and 16QAM, respectively. As observed, our scheme can obtain better BER performance than the referred schemes. For example, at BER = 10^{−}^{4} for QPSK, the required E_{b}/N_{0} for our scheme with

In this paper, we have proposed and evaluated a new NCT scheme. Both the theoretical analysis and simulations show that it offers an improved BER performance while reducing the PAPR significantly. Moreover, by properly adjusting the transform parameters, a favorable trade-off between PAPR and BER can also be obtained.

Li, X.G. (2017) Efficient Nonlinear Companding Transform Scheme for Reducing PAPR of OFDM Signals. Int. J. Communications, Network and System Sciences, 10, 293-298. https://doi.org/10.4236/ijcns.2017.108B031