On-Off Digital Noise Modulation: Optimal Likelihood Threshold and Exact BEP in AWGN and α - μ Fading

Recently proposed on-off digital noise (OODN) modulation encodes bit 1 as synthetic Gaussian noise and bit 0 as silence. This approach enables ultra–low–power, non-coherent detection and positions OODN as a promising candidate for next-generation internet of things (IoT) networks. In this letter, we further the study of OODN. We derive the exact empirical-variance distributions and a closed-form optimal likelihood-ratio test (LRT) threshold that minimizes the bit error probability (BEP) for OODN. A closed-form expression for the exact BEP under additive white Gaussian noise (AWGN) channels is also obtained in terms of incomplete Gamma functions and validated against Monte Carlo simulations. The analysis is extended to α–μ fading to capture medium nonlinearity, and its performance is assessed in a practical indoor non-line-of-sight (nLoS) 60 GHz mmWave channel. The results highlight the significant potential of OODN for extreme-low-power IoT radios.