Near-Optimal Piecewise Linear Companding Transform for PAPR Reduction of OFDM Systems

Since the inherent high envelope fluctuation characteristics of OFDM signals present a significant challenge in reducing energy consumption, it is crucial to minimize the range of the envelope fluctuations of OFDM signals. As companding is a well-known technique for reducing the envelope fluctuations of OFDM signals, we explore the optimal companding transform by building a multi-objective optimization model with the goal of minimizing peak-to-average power ratio (PAPR), inner-band distortions, and out-of-band (OOB) radiations in this paper. The solution reveals that the optimal form of companding transform is a piecewise one and closely resembles a linear transform. Furthermore, we find that the average power of the optimal companded signal is never greater than that of the original signal, which contradicts the constraint of constant average signal power usually used in the design of companding transform. Based on the characteristics of the optimal companding transform, we propose a near-optimal piecewise linear companding transform to obviate the extremely high computational complexity of the optimal companding transform. The proposed near-optimal piecewise linear companding transform is a promising solution for mitigating companding distortions while reducing PAPR. However, it should be noted that there may still be some unavoidable distortions after decompanding, which results in a degradation of the BER performance. Thus, we diminish the remaining distortions after decompanding by relaxing the constraint of the proposed near-optimal piecewise linear companding transform on the average power of the companded signals. Simulation results demonstrate that the relaxation can improve the BER performance while ensuring the PAPR performance with only a small sacrifice on OOB radiations.

I. Introduction

Due to the advantages of high spectral efficiency and robustness against multipath fading, OFDM is still a preferable candidate of the baseline physical-layer waveform of 5G New Radio (NR) [1] and Internet of Vehicles (IOV) [2]. As a multicarrier waveform, the overlapped multi-carrier signals make OFDM more prone to severe envelope fluctuations, which demands high power amplifiers (HPAs) with large linear ranges entailing significant cost and power loss. Nowadays, the increasingly urgent requirements on high power efficiency and low cost obligate HPAs to be operated much closer to saturation points. However, when HPAs operate near saturation points, the inherent drawback of high envelope fluctuations in OFDM signals will introduce undesired in-band distortions and out-of-band (OOB) radiations causing serious performance degradation. To keep such nonlinear distortions low, HPAs need to be operated with a large input back-off (IBO). However, this inevitable reduces the power efficiency of HPAs and causes unnecessary energy consumption, which goes against the system energy efficiency requirements. Therefore, it is imperative to reduce the envelope fluctuations of OFDM signals.