Multi-Scale Spatio-Temporal Fractal Modulation (MS-STFM)

This work introduces Multi-Scale Spatio-Temporal Fractal Modulation (MS-STFM), a passive physical-layer signal processing architecture based on recursive self-similarity in both spatial (geometric) and temporal (scale) domains. By engineering a medium where different recursion levels exhibit independent phase velocities, an incident broadband signal undergoes deterministic fragmentation and controlled latency. The architecture enables natural orthogonal multiplexing without digital processing, yielding K = N𝙜 ╳ N𝘴 parallel sub-channels. A continuous, infinite key space is demonstrated for physical-layer encryption. Generalized dispersion relations are derived from a multi-fractional wave equation, and the propagation kernel is shown to be formally dual to an effective inhomogeneous medium with tunable negative effective parameters. Quantitative analyses of spectral efficiency, PAPR reduction, processing gain, latency trade-offs, and diversity order are presented. Validation contexts include high-power radar, underwater acoustic communications, and secure backhaul links. The work establishes a unified framework for wave-structure interaction across acoustics, electromagnetics, and analogue gravity phenomena.