<inline-formula><tex-math notation="LaTeX">$\mathtt {{SYMMeTRy}}$</tex-math><alternatives><mml:math><mml:mi mathvariant="monospace">SYMMeTRy</mml:mi></mml:math><inline-graphic xlink:href="zheleva-ieq1-3065891.gif"/></alternatives></inline-formula> : Exploiting MIMO Self-Similarity for Under-Determin

Modulation recognition (modrec) seeks to identify the modulation of a transmitter from coresponding spectrum scans. It is an essential functional component of future spectrum sensing with critical applications in dynamic spectrum access and spectrum enforcement. While predominantly studied in single-input single-output (SISO) systems, practical modrec for multiple-input multiple-output (MIMO) communications requires more research attention. Existing MIMO modrec impose stringent requirements of fully- or over-determined sensing front-end, i.e., the number of sensor antennas should exceed that at the transmitter. This poses a prohibitive sensor cost even for simple 2x2 MIMO systems and will severely hamper progress in flexible spectrum access. We design a MIMO modrec framework that enables efficient and cost-effective modulation classification for under-determined settings involving fewer sensor antennas than those used for transmission. Our key idea is to exploit the inherent multi-scale self-similarity of MIMO modulation <inline-formula><tex-math notation="LaTeX">$\mathtt {IQ}$</tex-math><alternatives><mml:math><mml:mi mathvariant="monospace">IQ</mml:mi></mml:math><inline-graphic xlink:href="zheleva-ieq4-3065891.gif"/></alternatives></inline-formula> constellations, which persists in under-determined settings. Our framework, called <inline-formula><tex-math notation="LaTeX">$\mathtt {{SYMMeTRy}}$</tex-math><alternatives><mml:math><mml:mi mathvariant="monospace">SYMMeTRy</mml:mi></mml:math><inline-graphic xlink:href="zheleva-ieq5-3065891.gif"/></alternatives></inline-formula> (<underline>S</underline>elf-similarit<underline>Y</underline> for <underline>M</underline>IMO <underline>M</underline>odula<underline>T</underline>ion <underline>R</underline>ecognition), designs domain-aware classification features with high discriminative potential by summarizing regularities of symbol co-location in the MIMO constellation. To this end, we summarize the fractal geometry of observed samples to extract discriminative features for supervised MIMO modrec. We evaluate <inline-formula><tex-math notation="LaTeX">$\mathtt {{SYMMeTRy}}$</tex-math><alternatives><mml:math><mml:mi mathvariant="monospace">SYMMeTRy</mml:mi></mml:math><inline-graphic xlink:href="zheleva-ieq6-3065891.gif"/></alternatives></inline-formula> in a realistic simulation and in a small-scale MIMO testbed. We demonstrate that it maintains high and consistent performance across various noise regimes, channel fading conditions and with increasing MIMO transmitter complexity. Our efforts highlight <inline-formula><tex-math notation="LaTeX">$\mathtt {{SYMMeTRy}}$</tex-math><alternatives><mml:math><mml:mi mathvariant="monospace">SYMMeTRy</mml:mi></mml:math><inline-graphic xlink:href="zheleva-ieq7-3065891.gif"/></alternatives></inline-formula>’s high potential to enable efficient and practical MIMO modrec in spectrum sensing infrastructures with mixed-complexity sensors.