on the outage capacity distribution of correlated keyhole mimo channels keyhole multiple input multiple output mimo channels have recently received significant attention since they can model to a certain extend some practically important propagation scenarios and also relay channels in the amplify and forward mode this paper investigates instantaneous signal to noise ratio snr and outage capacity distributions of spatially correlated keyhole mimo channels with perfect channel state information csi at the receive end and with or without csi at the transmit end for a small number of antennas the impact of correlation on the capacity distribution can be characterized by the effective average snr this snr as well as the outage capacity decreases with correlation for a large number of transmit receive antennas the keyhole channel is asymptotically equivalent in terms of capacity to the rayleigh diversity channel with a single transmit receive antenna and multiple receive transmit antennas the outage capacity of the keyhole channel is upper bounded by that of the equivalent rayleigh diversity channel when the number of both transmit and receive antennas is large the outage capacity distribution of the keyhole channel is asymptotically gaussian in some cases the asymptotic gaussian approximation is accurate already for a reasonably small number of antennas the perfect transmit csi is shown to bring a fixed snr gain a more general channel model with multiple keyholes is proposed for a large number of antennas the capacity of a multikeyhole channel is a normally distributed sum of the capacities of single keyhole channels the fact that despite the strong degenerate nature of the keyhole channel its outage capacity distribution is asymptotically normal indicates that gaussian distribution has a high degree of universality for the capacity analysis of mimo channels

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

on gaussian mimo bc mac duality with multiple transmit covariance constraints owing to the special structure of the gaussian multiple input multiple output mimo broadcast channel bc the associated capacity region computation and beamforming optimization problems are typically non convex and thus cannot be solved directly one feasible approach is to consider the respective dual multiple access channel mac problems which are easier to deal with due to their convexity properties the conventional bc mac duality has been established via bc mac signal transformation and is applicable only for the case in which the mimo bc is subject to a single transmit sum power constraint an alternative approach is based on minimax duality which can be applied to the case of the sum power constraint or per antenna power constraint in this paper the conventional bc mac duality is extended to the general linear transmit covariance constraint ltcc case which includes sum power and per antenna power constraints as special cases the obtained general bc mac duality is applied to solve the capacity region computation for the mimo bc and beamforming optimization for the multiple input single output miso bc respectively with multiple ltccs the relationship between this new general bc mac duality and the minimax duality is also discussed and it is shown that the general bc mac duality leads to simpler problem formulations moreover the general bc mac duality is extended to deal with the case of nonlinear transmit covariance constraints in the mimo bc

power allocation for a mimo relay system with multiple antenna users a power allocation or scheduling problem is studied for a multiuser multiple input multiple output mimo wireless relay system where there is a non regenerative relay between one access point and multiple users each node in the system is equipped with multiple antennas the purpose of this study is to develop fast algorithms to compute the source covariance matrix or matrices and the relay transformation matrix to optimize a system performance we consider the minimization of power consumption subject to rate constraint and also the maximization of system throughput subject to power constraint these problems are nonconvex and apparently have no simple solutions in this paper a number of computational strategies are presented and their performances are investigated both uplink and downlink cases are considered the use of multiple carriers is also discussed moreover a generalized water filling gwf algorithm is developed to solve a special class of convex optimization problems the gwf algorithm is used for two of the strategies shown in this paper

the capacity of gaussian mimo channels under total and per antenna power constraints the capacity of a fixed gaussian multiple input multiple output mimo channel and the optimal transmission strategy under the total power tp constraint and full channel state information are well known this problem remains open in the general case under individual per antenna pa power constraints while some special cases have been solved these include a full rank solution for the mimo channel and a general solution for the multiple input single output miso channel in this paper the fixed gaussian miso channel is considered and its capacity and optimal transmission strategies are determined in a closed form under the joint total and pa power constraints in the general case in particular the optimal strategy is hybrid and includes two parts first is equal gain transmission and second is maximum ratio transmission which are responsible for the pa and tp constraints respectively the optimal beamforming vector is given in a closed form and an accurate yet simple approximation to the capacity is proposed finally the above results are extended to the mimo case by establishing the ergodic capacity of fading mimo channels under the joint power constraints when the fading distribution is right unitary invariant of which i i d and semi correlated rayleigh fading are special cases unlike the fixed miso case the optimal signaling is shown to be isotropic in this case

the calabi yau conjectures for embedded surfaces in this talk i will discuss the proof of the calabi yau conjectures for embedded surfaces this is joint work with bill minicozzi cm9 the calabi yau conjectures about surfaces date back to the 1960s much work has been done on them over the past four decades in particular examples of jorge xavier from 1980 and nadirashvili from 1996 showed that the immersed versions were false we will show here that for embedded surfaces i e injective immersions they are in fact true their original form was given in 1965 in ca where e calabi made the following two conjectures about minimal surfaces see also s s chern page 212 of ch conjecture 1 prove that a complete minimal hypersurface in r must be unbounded calabi continued it is known that there are no compact minimal submanifolds of r or of any simply connected complete riemannian manifold with sectional curvature 0 a more ambitious conjecture is conjecture 2 a complete minimal hypersurface in r has an unbounded projection in every n 2 dimensional flat subspace

mimo cognitive radio a game theoretical approach the concept of cognitive radio cr has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed primary and unlicensed secondary users in the same bandwidth in this paper we propose and analyze a totally decentralized approach based on game theory to design cognitive mimo transceivers who compete with each other to maximize their information rate the formulation incorporates constraints on the transmit power as well as null and or soft shaping constraints on the transmit covariance matrix so that the interference generated by secondary users be confined within the temperature interference limit required by the primary users we provide a unified set of conditions that guarantee the uniqueness and global asymptotic stability of the nash equilibrium of all the proposed games through totally distributed and asynchronous algorithms interestingly the proposed algorithms overcome the main drawback of classical waterfilling based algorithms the violation of the temperature interference limit and they have the desired features required for cr applications such as low complexity distributed implementation robustness against missing or outdated updates of the users and fast convergence behavior

the space of embedded minimal surfaces of fixed genus in a 3 manifold v fixed genus this paper is the fifth and final in a series on embedded minimal surfaces following our earlier papers on disks we prove here two main structure theorems for itnonsimply connected embedded minimal surfaces of any given fixed genus the first of these asserts that any such surface without small necks can be obtained by gluing together two oppositely oriented double spiral staircases the second gives a pair of pants decomposition of any such surface when there are small necks cutting the surface along a collection of short curves after the cutting we are left with graphical pieces that are defined over a disk with either one or two sub disks removed a topological disk with two sub disks removed is called a pair of pants both of these structures occur as different extremes in the two parameter family of minimal surfaces known as the riemann examples

the capacity and optimal signaling for gaussian mimo channels under interference constraints gaussian mimo channel under the joint transmit tx and interference power constraints tpc and ipc is studied a closed form solution for the optimal tx covariance matrix in the general case is obtained using the kkt based approach up to dual variables a number of more explicit closed form solutions are given with optimal dual variables including full rank and rank 1 beamforming cases as well as the case of identical eigenvectors typical for massive mimo settings which differer significantly from the standard water filling solution a whitening filter is shown to be an important part of optimal precoding under interference constraints sufficient and necessary conditions for each constraint to be redundant are given capacity scaling with the snr is shown to be determined by a natural linear algebraic structure of sub spaces induced by channel matrices of multiple users a number of unusual properties of optimal tx covariance matrix under the joint tpc and ipc are pointed out and a bound on its rank is established an interplay between the tpc and ipc is studied including the transition from power limited to interference limited regimes as the tx power increases while closed from solutions for optimal dual variables are given in some special cases an iterative bisection algorithm iba is proposed to find optimal dual variables in the general case and its convergence is proved for some special cases numerical experiments illustrate its efficient performance bounds for the optimal dual variables are given

capacity bounds for the gaussian interference channel the capacity region of the two user gaussian interference channel ic is studied three classes of channels are considered weak one sided and mixed gaussian ics for the weak gaussian ic a new outer bound on the capacity region is obtained that outperforms previously known outer bounds the sum capacity for a certain range of channel parameters is derived for this range it is proved that using gaussian codebooks and treating interference as noise are optimal it is shown that when gaussian codebooks are used the full han kobayashi achievable rate region can be obtained by using the naive han kobayashi achievable scheme over three frequency bands equivalently three subspaces for the one sided gaussian ic an alternative proof for the sato s outer bound is presented we derive the full han kobayashi achievable rate region when gaussian codebooks are utilized for the mixed gaussian ic a new outer bound is obtained that outperforms previously known outer bounds for this case the sum capacity for the entire range of channel parameters is derived it is proved that the full han kobayashi achievable rate region using gaussian codebooks is equivalent to that of the one sided gaussian ic for a particular range of channel parameters

heegaard surfaces and measured laminations i the waldhausen conjecture we give a proof of the so called generalized waldhausen conjecture which says that an orientable irreducible atoroidal 3 manifold has only finitely many heegaard splittings in each genus up to isotopy jaco and rubinstein have announced a proof of this conjecture using different methods

an iteratively weighted mmse approach to distributed sum utility maximization for a mimo interfering broadcast channel consider the multiple input multiple output mimo interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to each other the basic problem is to design linear beamformers that can maximize the system throughput in this paper we propose a linear transceiver design algorithm for weighted sum rate maximization that is based on iterative minimization of weighted mean square error mse the proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum rate maximization problem furthermore the algorithm and its convergence can be extended to a general class of sum utility maximization problem the effectiveness of the proposed algorithm is validated by numerical experiments

rosenbrock s theorem for systems over von neumann regular rings abstract if a b is a finite system over a commutative von neumann regular ring r the problem of searching for a matrix f such that the pencil s i a b f has some prescribed smith normal form is reduced to the case where r is a field a problem which for controllable systems is described by a well known theorem of rosenbrock on pole assignment 12 and was then generalized to noncontrollable pairs 14 it this paper von neumann regular rings are characterized as the class of commutative rings for which the solution of the above problem over the ring is equivalent to its solution in each residue field

optimized signaling for mimo interference systems with feedback the system mutual information of a multiple input multiple output mimo system with multiple users which mutually interfere is considered perfect channel state information is assumed to be known to both transmitters and receivers asymptotic performance analysis shows that the system mutual information changes behavior as the interference becomes sufficiently strong in particular beamforming is the optimum signaling for all users when the interference is large we propose several numerical approaches to decide the covariance matrices of the transmitted signals and compare their performance in terms of the system mutual information we model the system as a noncooperative game and perform iterative water filling to find the nash equilibrium distributively a centralized global approach and a distributed iterative approach based on the gradient projection method are also proposed numerical results show that all proposed approaches give better performance than the standard signaling which is optimum for the case without interference both the global and the iterative gradient projection methods are shown to outperform the nash equilibrium significantly

effective finiteness of irreducible heegaard splittings of non haken 3 manifolds the main result is a short effective proof of tao li s theorem that a closed non haken hyperbolic 3 manifold n has at most finitely many irreducible heegaard splittings along the way we show that n has finitely many branched surfaces of pinched negative sectional curvature carrying all closed index 1 minimal surfaces this effective result together with the sequel with daniel ketover solves the classification problem for heegaard splittings of non haken hyperbolic 3 manifolds

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

the space of embedded minimal surfaces of fixed genus in a 3 manifold iii planar domains this paper is the third in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed 3 manifold in cm3 cm5 we describe the case where the surfaces are topologically disks on any fixed small scale although the focus of this paper general planar domains is more in line with cm6 we will prove a result here namely corollary iii 3 5 below which is needed in cm5 even for the case of disks roughly speaking there are two main themes in this paper the first is that stability leads to improved curvature estimates this allows us to find large graphical regions these graphical regions lead to two possibilities

on the superiority of improper gaussian signaling in wireless interference mimo scenarios recent results have elucidated the benefits of using improper gaussian signaling igs as compared with conventional proper gaussian signaling pgs in terms of achievable rate for interference limited conditions this paper exploits majorization theory tools to formally quantify the gains of igs along with widely linear transceivers for multiple input multiple output mimo systems in interference limited scenarios the mimo point to point channel with interference is analyzed assuming that received interference can be either proper or improper and we demonstrate that the use of the optimal igs when received interference is improper strictly outperforms in terms of achievable rate and mean square error the use of the optimal pgs when interference is proper then these results are extended to two practical situations first the mimo z interference channel z ic is investigated where a trade off arises with igs we could increase the achievable rate of the interfered user while gracefully degrading the rate of the non interfered user second these concepts are applied to a two tier heterogeneous cellular network where macrocells and small cells coexist and multiple mimo z ics appear

the space of embedded minimal surfaces of fixed genus in a 3 manifold i estimates off the axis for disks this paper is the first in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed riemannian 3 manifold the key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in r3 with the flat metric this study is undertaken here and completed in cm6 these local results are then applied in cm7 where we describe the general structure of fixed genus surfaces in 3 manifolds there are two local models for embedded minimal disks by an embedded disk we mean a smooth injective map from the closed unit ball in r2 into r3 one model is the plane or more generally a minimal graph the other is a piece of a helicoid in the first four papers of this series we will show that every embedded minimal disk is either a graph of a function or is a double spiral staircase where each staircase is a multi valued graph this will be done by showing that if the curvature is large at some point and hence the surface is not a graph then it is a double spiral staircase to prove that such a disk