Optimal OFDM-IM Signals With Constant PAPR

Orthogonal frequency division multiplexing indexed modulation (OFDM-IM), an emerging multi-carrier modulation technique, offers significant advantages over traditional OFDM. The OFDM-IM scheme exhibits superior performance in terms of bit error rate (BER) at low and medium data rates, while also enhancing resilience to inter-carrier interference in dynamically changing channels. However, the challenge of a high peak-to-average ratio (PAPR) also persists in OFDM-IM. In this study, we propose a novel approach to mitigate PAPR by introducing a small dither signal to the idle subcarrier, leveraging the inherent characteristics of OFDM-IM. Subsequently, we address the nonconvex and non-smooth optimization problem of minimizing the maximum amplitude of dither signals while maintaining a constant PAPR constraint. To effectively tackle this challenging optimization task, we adopt the linearized alternating direction multiplier method (LADMM), referred to as the LADMM-direct algorithm, which provides a simple closed-form solution for each subproblem encountered during the optimization process. To improve the convergence rate of the LADMM-direct algorithm, a LADMM-relax algorithm is also proposed to address the PAPR problem. Simulation results demonstrate that our proposed LADMM-direct and LADMM-relax algorithms significantly reduce computational complexity and achieve superior performance in terms of both PAPR and bit error rate (BER) compared to state-of-the-art algorithms.