Capacity scaling law by multiuser diversity in cognitive radio systems

This paper analyzes the multiuser diversity gain in a cognitive radio (CR) system where secondary transmitters opportunistically utilize the spectrum licensed to primary users only when it is not occupied by the primary users. To protect the primary users from the interference caused by the missed detection of primary transmissions in the secondary network, minimum average throughput of the primary network is guaranteed by transmit power control at the secondary transmitters. The traffic dynamics of a primary network are also considered in our analysis. We derive the average achievable capacity of the secondary network and analyze its asymptotic behaviors to characterize the multiuser diversity gains in the CR system.Comment: 5 pages, 2 figures, ISIT2010 conferenc

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection -- Secure DoF and Jammer Scaling Law

In this paper, we propose opportunistic jammer selection in a wireless security system for increasing the secure degrees of freedom (DoF) between a transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer group consisting of $S$ jammers among which Bob selects $K$ jammers. The selected jammers transmit independent and identically distributed Gaussian signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are independent, we can select the jammers whose jamming channels are aligned at Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more than $KN_j$ receive antennas, where $N_j$ is the number of jammer's transmit antenna each, and hence $KN_j$ can be regarded as defensible dimensions against Eve. For the jamming signal alignment at Bob, we propose two opportunistic jammer selection schemes and find the scaling law of the required number of jammers for target secure DoF by a geometrical interpretation of the received signals.Comment: Accepted with minor revisions, IEEE Trans. on Signal Processin

Deformations of Annuli on Riemann surfaces with Smallest Mean Distortion

Let $A$ and $A'$ be two circular annuli and let $\rho$ be a radial metric defined in the annulus $A'$. Consider the class $\mathcal H_\rho$ of $\rho-$harmonic mappings between $A$ and $A'$. It is proved recently by Iwaniec, Kovalev and Onninen that, if $\rho=1$ (i.e. if $\rho$ is Euclidean metric) then $\mathcal H_\rho$ is not empty if and only if there holds the Nitsche condition (and thus is proved the J. C. C. Nitsche conjecture). In this paper we formulate an condition (which we call $\rho-$Nitsche conjecture) with corresponds to $\mathcal H_\rho$ and define $\rho-$Nitsche harmonic maps. We determine the extremal mappings with smallest mean distortion for mappings of annuli w.r. to the metric $\rho$. As a corollary, we find that $\rho-$Nitsche harmonic maps are Dirichlet minimizers among all homeomorphisms $h:A\to A'$. However, outside the $\rho$-Nitsche condition of the modulus of the annuli, within the class of homeomorphisms, no such energy minimizers exist. % However, %outside the $\rho-$Nitsche range of the modulus of the annuli, %within the class of homeomorphisms, no such energy minimizers exist. This extends some recent results of Astala, Iwaniec and Martin (ARMA, 2010) where it is considered the case $\rho=1$ and $\rho=1/|z|$.Comment: Some misprints are corrected in this version (see Lemma~5.1