Spectral-Domain Spreading via Hadamard Transform for Robust Downlink Non-Orthogonal Multiple Access

Non-orthogonal multiple access (NOMA) systems allowing multiple users sharing the same resource block offer significant gains in spectral efficiency which can enable the required massive access in future wireless systems. However, they face several challenges due to their sensitivity to power allocation coefficients, fading effects, and imperfect channel state information (CSI). To address these limitations, this paper proposes Hadamard-NOMA, an approach leveraging the Hadamard Transform (HT) at the source level prior to modulation. By introducing HT, the system mitigates the adverse impact of fading and CSI imperfections, reducing bit error rates (BER) and enhancing overall system reliability. Theoretical analysis and Monte Carlo simulations validate the effectiveness of this technique, demonstrating robust NOMA transmission in dynamic wireless environments. The proposed method offers a promising solution for next-generation wireless networks, ensuring more reliable performance under diverse transmission conditions. Simulation results confirm analytical predictions, demonstrating significant performance improvements over state-of-the-art T-NOMA and Usman-NOMA schemes. Specifically, for the Near user, a gain of 15 dB is achieved at a Bit Error Rate (BER) of $10^{-2}$, while the Far user benefits from a 10 dB gain at a BER of $10^{-1}$. Compared to Usman-NOMA, the proposed method provides an improvement of 15 dB for the Far user at BER $10^{-1}$. Additionally, in a two-user scenario with imperfect Successive Interference Cancelation (SIC), user 1 requires an SNR at least 14 dB lower than user 2 to achieve a BER of $10^{-3}$. These findings highlight the effectiveness of applying HT at the source stage, significantly mitigating CSI errors and making NOMA more resilient for next-generation wireless networks.

Fractional Filtering and Anomaly-Guided Diagnostics: The Local Damage Mode Extractor (LDME) for Early Gear Fault Detection

Early and reliable detection of gear faults in complex drivetrain systems is critical for aviation safety and operational availability. We present the Local Damage Mode Extractor (LDME), a structured, physics-informed signal processing framework that combines dual-path denoising, multiscale decomposition, fractional-domain enhancement, and statistically principled anomaly scoring to produce interpretable condition indicators without supervision. LDME is organized in three layers: (i) dual-path denoising (DWT with adaptive Savitzky-Golay smoothing) to suppress broadband noise while preserving transient fault structure; (ii) multi-scale damage enhancement using a Teager-Kaiser pre-amplifier followed by a Hadamard-Caputo fractional operator that accentuates non-sinusoidal, low-frequency fault signatures; and (iii) decision fusion, where harmonics-aware Fourier indicators are combined and scored by an unsupervised anomaly detector. Evaluation using the Case Western Reserve University (CWRU) bearing dataset, the HUMS 2023 planetary gearbox benchmark, and a controlled simulated dataset shows that LDME consistently distinguishes nominal, early-crack, and propagated-crack stages under various operating conditions. LDME identifies the primary detection event earlier (198 cycles) than HT-TSA (284 cycles) and advances maintenance recommendation time from 383 to 365 cycles. We discuss its relation to prior art, limitations, and future theoretical directions. All code and experimental configurations are documented for reproducibility.

Local damage detection in rolling element bearings based on a Single Ensemble Empirical Mode Decomposition

A Single Ensemble Empirical Mode Decomposition (SEEMD) is proposed for locating the damage in rolling element bearings. The SEEMD does not require a number of ensembles from the addition or subtraction of noise every time while processing the signals. The SEEMD requires just a single sifting process of a modified raw signal to reduce the computation time significantly. The other advantage of the SEEMD method is its success in dealing with non-Gaussian or non-stationary perturbing signals. In SEEMD, initially, a fractional Gaussian noise (FGN) is added to the raw signal to emphasize on high frequencies of the signal. Then, a convoluted white Gaussian noise is multiplied to the resulting signal which changes the spectral content of the signal which helps in extraction of the weak periodic signal. Finally, the obtained signal is decomposed by using a single sifting process. The proposed methodology is applied to the raw signals obtained from the mining industry. These signals are difficult to analyze since cyclic impulsive components are obscured by noise and other interference. Based on the results, the proposed method can effectively detect the fault where the signal of interest (SOI) has been extracted with good quality.

Non-parametric Ensemble Empirical Mode Decomposition for extracting weak features to identify bearing defects

A non-parametric complementary ensemble empirical mode decomposition (NPCEEMD) is proposed for identifying bearing defects using weak features. NPCEEMD is non-parametric because, unlike existing decomposition methods such as ensemble empirical mode decomposition, it does not require defining the ideal SNR of noise and the number of ensembles, every time while processing the signals. The simulation results show that mode mixing in NPCEEMD is less than the existing decomposition methods. After conducting in-depth simulation analysis, the proposed method is applied to experimental data. The proposed NPCEEMD method works in following steps. First raw signal is obtained. Second, the obtained signal is decomposed. Then, the mutual information (MI) of the raw signal with NPCEEMD-generated IMFs is computed. Further IMFs with MI above 0.1 are selected and combined to form a resulting signal. Finally, envelope spectrum of resulting signal is computed to confirm the presence of defect.