Adaptive scrambling-based hadamard transform for peak-to-average power ratio reduction in sixth-generation orthogonal time-frequency space waveforms

Orthogonal time-frequency space (OTFS) modulation is a promising waveform for sixth-generation (6G) wireless systems owing to its robustness in high-mobility and doubly selective channels. However, the inherent two-dimensional symbol spreading and multicarrier synthesis of OTFS generates a high peak-to-average power ratio (PAPR), severely constraining power amplifier efficiency and causing nonlinear distortion and spectral regrowth. This study proposes an Adaptive Scrambling-Based Hadamard Transform (ASB-HT) framework that enables distortionless and side-information-free PAPR reduction through intrinsic data-driven adaptivity. Unlike static transform precoding or probabilistic candidate generation schemes, the proposed method embeds row-wise energy balancing within an orthogonal Hadamard precoder, structurally reducing the likelihood of deterministic peak alignment prior to inverse symplectic finite Fourier transform (ISFFT) spreading. A theoretical analysis establishes the relationship between excess kurtosis and PAPR tail probability, demonstrating that the proposed precoder reduces the fourth-order signal statistics and systematically suppresses the complementary cumulative distribution function (CCDF) of the PAPR. The scheme preserves signal energy, maintains receiver transparency, and introduces only marginal computational overhead. Simulation results across multiple grid sizes (64--512 subcarriers) demonstrate consistent gains, achieving up to 6 dB PAPR reduction at CCDF = 10 −3 and up to 7 dB signal-to-noise ratio (SNR) improvement at bit error rate (BER) = 10 −3 compared to conventional OTFS, selective mapping (SLM), discrete Fourier transform (DFT)-spread OTFS, genetic algorithm (GA), and deep neural network (DNN)-based approaches. The power spectral density analysis further confirmed the significant suppression of out-of-band emissions, validating the proposed framework for energy-efficient 6G OTFS transceivers.