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Fading is the time-dependent variations in signal strength measured at a receiver, due to temporally evolving multipath scattering and interference. In our previous work we introduced a statistical fading model for the time-reversal invariant case by combining the predictions of random matrix theory with the random coupling model that includes system-specific properties such as the radiation impedance of the ports and short-orbit effects. In the high-loss limit this random matrix theory model reduced to the most common fading models in the wireless communication field. In this paper we discuss the theoretical model in more detail and extend it to the case of broken time-reversal invariance.
EN
Random matrix theory successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive formula in terms of impedance to combine the predictions of random matrix theory and nonuniversal system-specific features. The statistics of measured wave properties generally have nonuniversal features. However, ratios of the variances of elements of the impedance matrix are predicted to be independent of such nonuniversal features and thus should be universal functions of the overall system loss. In contrast with impedance variance ratios, scattering variance ratios depend on nonuniversal features unless the system is in the high loss regime. In this paper, we present numerical tests of the predicted universal impedance variance ratios and show that an insufficient sample size can lead to apparent deviation from the theory, particularly in the low loss regime. Experimental tests are carried out in three two-port microwave cavities with varied loss parameters, including a novel experimental system with a superconducting microwave billiard, to test the variance-ratio predictions in the low loss time-reversal-invariant regime. It is found that the experimental results agree with the theoretical predictions to the extent permitted by the finite sample size.
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