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.