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Coherence multiplexing (CM) technique for analog signal transmission was proposed but has not been studied comprehensively. In this paper, we investigate RF signal transmission over CM systems (RF over CM) in theory, simulation, and experiments. The transmission performances are analyzed using a single-tone RF signal, and theoretical SNR is developed. It is found that RF over CM systems are limited in performance by both beat noise and fiber chromatic dispersion due to the use of a broadband light source. A broader light source improves the system performance only if fiber dispersion of the system is negligibly small. Otherwise, the performance is seriously degraded by fiber dispersion. The theoretical model is verified experimentally. Finally, an orthogonal frequency division multiplexing ultra-wideband wireless signal over a CM system is verified. It is concluded that CM systems cannot be used for high-frequency RF signal transmission.