Degrees of Freedom of Full-Duplex Multiantenna Cellular Networks

We study the degrees of freedom (DoF) of cellular networks in which a full duplex (FD) base station (BS) equipped with multiple transmit and receive antennas communicates with multiple mobile users. We consider two different scenarios. In the first scenario, we study the case when half duplex (HD) users, partitioned to either the uplink (UL) set or the downlink (DL) set, simultaneously communicate with the FD BS. In the second scenario, we study the case when FD users simultaneously communicate UL and DL data with the FD BS. Unlike conventional HD only systems, inter-user interference (within the cell) may severely limit the DoF, and must be carefully taken into account. With the goal of providing theoretical guidelines for designing such FD systems, we completely characterize the sum DoF of each of the two different FD cellular networks by developing an achievable scheme and obtaining a matching upper bound. The key idea of the proposed scheme is to carefully allocate UL and DL information streams using interference alignment and beamforming techniques. By comparing the DoFs of the considered FD systems with those of the conventional HD systems, we establish the DoF gain by enabling FD operation in various configurations. As a consequence of the result, we show that the DoF can approach the two-fold gain over the HD systems when the number of users becomes large enough as compared to the number of antennas at the BS.Comment: 21 pages, 16 figures, a shorter version of this paper has been submitted to the IEEE International Symposium on Information Theory (ISIT) 201

Bishop-Phelps-Bolloba's theorem on bounded closed convex sets

This paper deals with the \emph{Bishop-Phelps-Bollob\'as property} (\emph{BPBp} for short) on bounded closed convex subsets of a Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove that the \emph{BPBp} holds for bounded linear functionals on arbitrary bounded closed convex subsets of a real Banach space. We show that for all finite dimensional Banach spaces $X$ and $Y$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed convex subset $D$ of $X$, and also that for a Banach space $Y$ with property $(\beta)$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of an arbitrary Banach space $X$. For a bounded closed absorbing convex subset $D$ of $X$ with positive modulus convexity we get that the pair $(X,Y)$ has the \emph{BPBp} on $D$ for every Banach space $Y$. We further obtain that for an Asplund space $X$ and for a locally compact Hausdorff $L$, the pair $(X, C_0(L))$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of $X$. Finally we study the stability of the \emph{BPBp} on a bounded closed convex set for the $\ell_1$-sum or $\ell_{\infty}$-sum of a family of Banach spaces