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Title: Schur-convexity of outage capacity for fading wireless channels Authors:  Eduard Jorswieck - TU Dresden (Germany) [presenting]
Abstract: The outage or $\epsilon$-capacity of fading wireless channels describes the data rate which can be reliably transmitted in a slow-fading channel with success probability of at least $1-\epsilon$ if the receiver has perfect channel state information (CSI) while the transmitter has imperfect CSI. In fading channels with multiple degrees of freedom, such as from multiple-antenna or multi-carrier systems, the resulting diversity effect has a different impact on the outage capacity depending on the operating SNR and rate point. For small SNR and high transmission rates, the outage probability is Schur-concave with respect to the diversity weights while for high SNR and low transmission rates, the outage probability becomes Schur-convex. This enables the wireless system design by choosing a proper antenna layout and an optimal number of transmit and receive dimensions. Interestingly, the framework to show order preserving results for majorization can be extended from Rayleigh fading channels to other relevant fading distributions. Furthermore, there exists an intriguing relationship between outage capacity in wireless communications and the level-$q$ Value-at-Risk for risk analysis in economics and finance. Adding antennas or carriers in wireless corresponds to diversification in portfolio allocation.