simple finite element method in vorticity formulation for incompressible flows a very simple and efficient finite element method is introduced for two and three dimensional viscous incompressible flows using the vorticity formulation this method relies on recasting the traditional finite element method in the spirit of the high order accurate finite difference methods introduced by the authors in another work optimal accuracy of arbitrary order can be achieved using standard finite element or spectral elements the method is convectively stable and is particularly suited for moderate to high reynolds number flows

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

sum power iterative water filling for multi antenna gaussian broadcast channels in this correspondence we consider the problem of maximizing sum rate of a multiple antenna gaussian broadcast channel bc it was recently found that dirty paper coding is capacity achieving for this channel in order to achieve capacity the optimal transmission policy i e the optimal transmit covariance structure given the channel conditions and power constraint must be found however obtaining the optimal transmission policy when employing dirty paper coding is a computationally complex nonconvex problem we use duality to transform this problem into a well structured convex multiple access channel mac problem we exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the mac which can easily be mapped to the optimal bc policies

two level method based on finite element and crank nicolson extrapolation for the time dependent navier stokes equations a fully discrete two level finite element method the two level method is presented for solving the two dimensional time dependent navier stokes problem the method requires a crank nicolson extrapolation solution u h tau 0 p h tau 0 on a spatial time coarse grid j h tau 0 and a backward euler solution u h tau p h tau on a space time fine grid j h tau the error estimates of optimal order of the discrete solution for the two level method are derived compared with the standard crank nicolson extrapolation method the one level method based on a space time fine grid j h tau the two level method is of the error estimates of the same order as the one level method in the h1 norm for velocity and the l2 norm for pressure however the two level method involves much less work than the one level method

dirty paper coding versus tdma for mimo broadcast channels we compare the capacity of dirty paper coding dpc to that of time division multiple access tdma for a multiple antenna multiple input multiple output mimo gaussian broadcast channel bc we find that the sum rate capacity achievable using dpc of the multiple antenna bc is at most min m k times the largest single user capacity i e the tdma sum rate in the system where m is the number of transmit antennas and k is the number of receivers this result is independent of the number of receive antennas and the channel gain matrix and is valid at all signal to noise ratios snrs we investigate the tightness of this bound in a time varying channel assuming perfect channel knowledge at receivers and transmitters where the channel experiences uncorrelated rayleigh fading and in some situations we find that the dirty paper gain is upper bounded by the ratio of transmit to receive antennas we also show that min m k upper bounds the sum rate gain of successive decoding over tdma for the uplink channel where m is the number of receive antennas at the base station and k is the number of transmitters

user selection with zero forcing beamforming achieves the asymptotically optimal sum rate in this paper we propose a generalized greedy g greedy algorithm based on zero forcing beamforming zfbf for the multiple input multiple output mimo broadcast channel this algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations as previous results only give the scaling law of the sum rate of dirty paper coding dpc with the help of the g greedy structure we are able to obtain the exact limit of the dpc sum rate for a large number of users we also prove that the difference between the sum rates obtained by g greedy user selection and by dpc goes to zero as the number of users increases in addition to this we investigate one particular greedy user selection scheme called sequential water filling swf for this algorithm a complexity reduction is achieved by an iterative procedure based on an lq decomposition which converts the calculation of the moore penrose matrix inverse to one vector matrix multiplication a sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction with the help of the g greedy algorithm we prove that swf achieves the full dpc sum rate for a large number of users for a moderate number of users simulation demonstrates that compared with other user selection algorithms swf achieves a higher sum rate that is close to the maximal sum rate achievable by zfbf with the same order of complexity

optimal upward planarity testing of single source digraphs a digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures which frequently arise in software engineering project management and visual languages in this paper we investigate upward planarity testing of single source digraphs we provide a new combinatorial characterization of upward planarity and give an optimal algorithm for upward planarity testing our algorithm tests whether a single source digraph with n vertices is upward planar in o n sequential time and in o log n time on a crcw pram with n log log n log n processors using o n space the algorithm also constructs an upward planar drawing if the test is successful the previously known best result is an o n2 time algorithm by hutton and lubiw proc 2nd acm siam symposium on discrete algorithms siam philadelphia 1991 pp 203 211 no efficient parallel algorithms for upward planarity testing were previously known

an optimally accurate discrete regularization for second order timestepping methods for navier stokes equations abstract we propose a new optimally accurate numerical regularization stabilization for a family of second order timestepping methods for the navier stokes equations nse the method combines a linear treatment of the advection term together with stabilization terms that are proportional to discrete curvature of the solutions in both velocity and pressure we rigorously prove that the entire new family of methods are unconditionally stable and o t 2 accurate the idea of curvature stabilization is new to cfd and is intended as an improvement over the commonly used speed stabilization which is only first order accurate in time and can have an adverse effect on important flow quantities such as drag coefficients numerical examples verify the predicted convergence rate and show the stabilization term clearly improves the stability and accuracy of the tested flows

low complexity user selection algorithms for multiuser mimo systems with block diagonalization block diagonalization bd is a precoding technique that eliminates interuser interference in downlink multiuser multiple input multiple output mimo systems with the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission the number of simultaneously supportable users with bd is limited by the ratio of the number of base station transmit antennas to the number of user receive antennas in a downlink mimo system with a large number of users the base station may select a subset of users to serve in order to maximize the total throughput the brute force search for the optimal user set however is computationally prohibitive we propose two low complexity suboptimal user selection algorithms for multiuser mimo systems with bd both algorithms aim to select a subset of users such that the total throughput is nearly maximized the first user selection algorithm greedily maximizes the total throughput whereas the criterion of the second algorithm is based on the channel energy we show that both algorithms have linear complexity in the total number of users and achieve around 95 of the total throughput of the complete search method in simulations

design modeling and performance analysis of multi antenna heterogeneous cellular networks this paper presents a stochastic geometry based framework for the design and analysis of downlink multi user multiple input multiple output mimo heterogeneous cellular networks with linear zero forcing transmit precoding and receive combining assuming rayleigh fading channels and perfect channel state information the generalized tiers of base stations may differ in terms of their poisson point process spatial density number of transmit antennas transmit power artificial biasing weight and number of user equipments served per resource block the spectral efficiency of a typical user equipped with multiple receive antennas is characterized using a non direct moment generating function based methodology with closed form expressions of the useful received signal and aggregate network interference statistics systematically derived in addition the area spectral efficiency is formulated under different space division multiple access and single user beamforming transmission schemes we examine the impact of different cellular network deployments propagation conditions antenna configurations and mimo setups on the achievable performance through theoretical and simulation studies based on the state of the art system parameters the results highlight the inherent limitations of baseline single input single output transmission and conventional sparse macro cell deployment as well as the promising potential of multi antenna communications and small cell solution in interference limited cellular environments

space division multiple access with a sum feedback rate constraint on a multiantenna broadcast channel simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput which grows double logarithmically with the number of users the sum rate for channel state information csi feedback however increases linearly with the number of users reducing the effective uplink capacity to address this problem a novel space division multiple access sdma design is proposed where the sum feedback rate is upper bounded by a constant this design consists of algorithms for csi quantization threshold based csi feedback and joint beamforming and scheduling the key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small csi quantization errors such that the sum feedback rate constraint is satisfied despite this constraint the proposed sdma design is shown to achieve a sum capacity growth rate close to the optimal one moreover the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates numerical results show that the proposed sdma design is capable of attaining higher sum capacities than existing ones even though the sum feedback rate is bounded

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

multiuser diversity for successive zero forcing dirty paper coding greedy scheduling algorithms and asymptotic performance analysis dirty paper coding dpc scheme is the capacity achieving transmission technique in multiuser mimo downlink channels as a suboptimal solution to dpc successive zero forcing dpc szf dpc has been proposed recently the zero interference constraint in designing the precoding matrices limits the number of supportable users in this correspondence we propose three low complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in szf dpc as the number of users grows the first algorithm greedily maximizes the true sum rate the second algorithm is based on eigenvalues the third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a hermitian matrix have a strong relationship simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution furthermore the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of dpc

advances in the theory and practice of graph drawing the visualization of conceptual structures is a key component of support tools for complex applications in science and engineering foremost among the visual representations used are drawings of graphs and ordered sets in this talk we survey recent advances in the theory and practice of graph drawing specific topics include bounds and tradeoffs for drawing properties three dimensional representations methods for constraint satisfaction and experimental studies

algorithms for plane representations of acyclic digraphs abstract acyclic digraphs are widely used for representing hierarchical structures examples include pert networks subroutine call graphs family trees organization charts hasse diagrams and isa hierarchies in knowledge representation diagrams we investigate the problem of representing acyclic digraphs in the plane in such a way that all edges flow in the same direction e g from the left to the right or from the bottom to the top three plane representations are considered straight drawings visibility representations and grid drawings we provide efficient algorithms that construct these representations with all edges flowing in the same direction the time complexity is o n for visibility representations and grid drawings and o n log n for straight drawings where n is the number of vertices of the digraph for covering digraphs of lattices the complexity of constructing straight drawings is o n we also show that the planar digraphs that admit any one of these representations are exactly the subgraphs of planar st graphs

nearly optimal monotone drawing of trees abstract a monotone drawing of a graph g is a straight line drawing of g such that for every pair of vertices u w in g there exists a path p u w in g that is monotone in some direction l namely the order of the orthogonal projections of the vertices of p u w on l is the same as the order they appear in p u w the problem of finding monotone drawings for trees has been studied in several recent papers the main focus is to reduce the size of the drawing currently the smallest drawing size is o n 1 205 o n 1 205 in this paper we present an algorithm for constructing monotone drawing of trees on a grid of size at most o n log n o n log n

precoding for full duplex multiuser mimo systems spectral and energy efficiency maximization we consider data transmissions in a full duplex fd multiuser multiple input multiple output mu mimo system where a base station bs bidirectionally communicates with multiple users in the downlink dl and uplink ul channels on the same system resources the system model of consideration has been thought to be impractical due to the self interference si between transmit and receive antennas at the bs interestingly recent advanced techniques in hardware design have demonstrated that the si can be suppressed to a degree that possibly allows for fd transmission this paper goes one step further in exploring the potential gains in terms of the spectral efficiency se and energy efficiency ee that can be brought by the fd mu mimo model toward this end we propose low complexity designs for maximizing the se and ee and evaluate their performance numerically for the se maximization problem we present an iterative design that obtains a locally optimal solution based on a sequential convex approximation method in this way the nonconvex precoder design problem is approximated by a convex program at each iteration then we propose a numerical algorithm to solve the resulting convex program based on the alternating and dual decomposition approaches where analytical expressions for precoders are derived for the ee maximization problem using the same method we first transform it into a concave convex fractional program which then can be reformulated as a convex program using the parametric approach we will show that the resulting problem can be solved similarly to the se maximization problem numerical results demonstrate that compared to a half duplex system the fd system of interest with the proposed designs achieves a better se and a slightly smaller ee when the si is small

eigen based transceivers for the mimo broadcast channel with semi orthogonal user selection this paper studies the sum rate performance of two low complexity eigenmode based transmission techniques for the mimo broadcast channel employing greedy semi orthogonal user selection sus the first approach termed zfdpc sus is based on zero forcing dirty paper coding the second approach termed zfbf sus is based on zero forcing beamforming we first employ new analytical methods to prove that as the number of users k grows large the zfdpc sus approach can achieve the optimal sum rate scaling of the mimo broadcast channel we also prove that the average sum rates of both techniques converge to the average sum capacity of the mimo broadcast channel for large k in addition to the asymptotic analysis we investigate the sum rates achieved by zfdpc sus and zfbf sus for finite k and show that zfdpc sus has significant performance advantages our results also provide key insights into the benefit of multiple receive antennas and the effect of the sus algorithm in particular we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second order behavior of the multi user diversity gain for finite k the benefit can be very significant we also show the interesting result that the semi orthogonality constraint imposed by sus whilst facilitating a very low complexity user selection procedure asymptotically does not reduce the multi user diversity gain in either first k or second order k terms

good spanning trees in graph drawing introduces a good spanning tree of a plane graph solves two open problems on monotone drawings using good spanning trees finds a 2 visibility drawing of a planar graph using a good spanning tree gives algorithms to find an spike vpg and t shaped drawings of a planar graph a plane graph is a planar graph with a fixed planar embedding in this paper we define a special spanning tree of a plane graph which we call a good spanning tree not every plane graph has a good spanning tree we show that every connected planar graph has a planar embedding with a good spanning tree using a good spanning tree we show that every connected planar graph g of n vertices has a straight line monotone grid drawing on an o n o n 2 grid and such a drawing can be found in o n time our results solve two open problems on monotone drawings of planar graphs posed by angelini et al using good spanning trees we also give simple linear time algorithms for finding a 2 visibility representation of a connected planar graph g of n vertices on a 2 n 1 2 n 1 grid and for finding a spike vpg representation of g on a 2 n 1 n grid

user selection in mimo interfering broadcast channels interference alignment aims to achieve maximum degrees of freedom in an interference system for achieving interference alignment in interfering broadcast systems a closed form solution is proposed in which is an extension of the grouping scheme in in a downlink scenario where there are a large number of users the base station is required to select a subset of users such that the sum rate is maximized to search for the optimal user subset using brute force approach is computationally exhaustive because of the large number of possible user subset combinations we propose a user selection algorithm achieving sum rate close to that of optimal solution the algorithm employs coordinate ascent approach and exploits orthogonality between the desired signal space and the interference channel space in the reciprocal system to select the user at each step for the sake of completeness we have also extended the sum rate approach based algorithm to interfering broadcast channel the complexity of both these algorithms is shown to be linear with respect to the total number of users as compared to exponential in brute force search

newton iterative method based on finite element discretization for the stationary darcy brinkman equations abstract the stationary darcy brinkman equations in the double diffusive convection which model the heat and mass transfer phenomena are considered in this paper based on a suitable contractive operator the existence and uniqueness of the problem are firstly proved by using the fixed point theorem the regularities of the weak solution are also derived then the newton iterative method is studied for solving the nonlinear discrete system generated from the finite element approximation including the stability and the optimal error estimates regarding the spatial mesh size and the iterative factor the analysis indicates that the viscosity coefficient has more impact on the numerical algorithm than the thermal conductivity and the mass diffusivity coefficients finally many numerical examples are shown to confirm the correctness of the theoretical prediction

towards area requirements for drawing hierarchically planar graphs hierarchical graphs are an important class of graphs for modeling many real applications in software and information visualization in this paper we investigate area requirements for drawing hierarchically planar graphs regarding two different drawing standards firstly we show an exponential lower bound for the area needed for straight line drawing of hierarchically planar graphs the lower bound holds even for s t hierarchical graphs without transitive arcs in contrast to the results for upward planar drawing this motivates our investigation of another drawing standard grid visibility representation as a relaxation of straight line drawing an application of the existing results from upward drawing can guarantee a quadric drawing area for grid visibility representation but does not necessarily guarantee the minimum drawing area motivated by this we will present a new grid visibility drawing algorithm which is efficient and guarantees the minimum drawing area with respect to a given topological embedding this implies that the area minimization problem is polynomial time solvable restricted to the class of graphs whose planar embeddings are unique however we can show that the problem of area minimization of grid visibility for hierarchically planar graphs is generally np hard even restricted to s t graphs

zero forcing methods for downlink spatial multiplexing in multiuser mimo channels the use of space division multiple access sdma in the downlink of a multiuser multiple input multiple output mimo wireless communications network can provide a substantial gain in system throughput the challenge in such multiuser systems is designing transmit vectors while considering the co channel interference of other users typical optimization problems of interest include the capacity problem maximizing the sum information rate subject to a power constraint or the power control problem minimizing transmitted power such that a certain quality of service metric for each user is met neither of these problems possess closed form solutions for the general multiuser mimo channel but the imposition of certain constraints can lead to closed form solutions this paper presents two such constrained solutions the first referred to as block diagonalization is a generalization of channel inversion when there are multiple antennas at each receiver it is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high snr the second known as successive optimization is an alternative method for solving the power minimization problem one user at a time and it yields superior results in some e g low snr situations both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined in order to accommodate more general scenarios we also propose a framework for coordinated transmitter receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas while the proposed algorithms are suboptimal they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity

the stabilized extrapolated trapezoidal finite element method for the navier stokes equations abstract we consider a fully discrete stabilized finite element method for the navier stokes equations which is unconditionally stable and has second order temporal accuracy of o k 2 hk spatial error the method involves a simple artificial viscosity stabilization of the linear system for the approximation of the new time level connected to anti diffusion of its effects at the old time level lowering the cell reynolds number of the oseen problem to o 1 the method requires only the solution of one linear system arising from an oseen problem per time step the effectiveness of the method is illustrated in several numerical experiments

a family of second order time stepping methods for the darcy brinkman equations abstract this study presents an efficient accurate effective and unconditionally stable time stepping scheme for the darcy brinkman equations in double diffusive convection the stabilization within the proposed method uses the idea of stabilizing the curvature for velocity temperature and concentration equations accuracy in time is proven and the convergence results for the fully discrete solutions of problem variables are given several numerical examples including a convergence study are provided that support the derived theoretical results and demonstrate the efficiency and the accuracy of the method

transmit selection diversity for unitary precoded multiuser spatial multiplexing systems with linear receivers multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference in such a system the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain this paper proposes two precoding methods that use extra transmit antennas beyond the minimum required to provide additional degrees of diversity the approach taken is to solve for a unitary transmit precoder under a zero interuser interference constraint that minimizes an upper bound on the symbol error rate ser for each user solutions where all transmit antennas are employed as well as subsets of antennas to reduce analog components are described numerical results confirm a dramatic improvement in terms of ser and mutual information over single user multiple input multiple output mimo methods and static allocation methods for example the proposed techniques achieve a signal to noise ratio snr improvement of 6 10 db at an uncoded ser of 10 3 with only one extra transmit antenna

parallel transitive closure and point location in planar structures parallel algorithms for several graph and geometric problems are presented including transitive closure and topological sorting in planar st graphs preprocessing planar subdivisions for point location queries and construction of visibility representations and drawings of planar graphs most of these algorithms achieve optimal o log n running time using n log n processors in the erew pram model n being the number of vertices

recent developments in imex methods with time filters for systems of evolution equations this report presents a summary of the numerical analysis of time filters used to control the unstable mode in the crank nicolson leapfrog discretization of evolution equations

a two level method with backtracking for the navier stokes equations we consider a two level method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations the method yields l2 and h1 optimal velocity approximations and an l2 optimal pressure approximation the two level method involves solving one small nonlinear coarse mesh system one oseen problem hence linear with positive definite symmetric part on the fine mesh and one linear correction problem on the coarse mesh the algorithm we study produces an approximate solution with the optimal asymptotic in h accuracy for any fixed reynolds number we do not consider the behavior of the error for fixed h as re rightarrow infty i e for flows in transition to turbulence

on the number of upward planar orientations of maximal planar graphs we consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have we show that every n vertex maximal planar graph has at least w 1 189 n and at most o 4 n upward planar orientations moreover we show that there exist n vertex maximal planar graphs having o 2 n upward planar orientations and n vertex maximal planar graphs having w 2 599 n upward planar orientations further we present bounds for the maximum and the minimum number of acyclic orientations a maximal planar graph can have

upward planar graphs and their duals we consider upward planar drawings of directed graphs in the plane up and on standing sup and rolling cylinders rup in the plane and on the standing cylinder the edge curves are monotonically increasing in y direction on the rolling cylinder they wind unidirectionally around the cylinder there is a strict hierarchy of classes of upward planar graphs up sup rup in this paper we show that rolling and standing cylinders switch roles when considering an upward planar graph and its dual in particular we prove that a strongly connected graph is rup if and only if its dual is a sup dipole a dipole is an acyclic graph with a single source and a single sink all rup graphs are characterized in terms of their duals using generalized dipoles moreover we obtain a characterization of the primals and duals of wsup graphs which are upward planar graphs on the standing cylinder and allow for horizontal edge curves

on embedding a graph in the grid with the minimum number of bends given a planar graph g together with a planar representation p a region preserving grid embedding of g is a planar embedding of g in the rectilinear grid that has planar representation isomorphic to p in this paper an algorithm is presented that computes a region preserving grid embedding with the minimum number of bends in edges this algorithm makes use of network flow techniques and runs in time o n 2 log n where n is the number of vertices of the graph constrained versions of the problem are also considered and most results are extended to k gonal graphs i e graphs whose edges are sequences of segments with slope multiple of 180 k degrees applications of the above results can be found in several areas vlsi circuit layout architectural design communication by light or microwave transportation problems and automatic layout of graphlike diagrams

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

iterative precoder design and user scheduling for block diagonalized systems the block diagonalization bd scheme is a low complexity suboptimal precoding technique for multiuser multiple input multiple output mimo downlink channels which completely precancels the multiuser interference accordingly the precoder of each user lies in the null space of other users channel matrices in this paper we propose an iterative algorithm using qr decompositions qrds to compute the precoders specifically to avoid dealing with a large concatenated matrix we apply the qrd to a sequence of matrices of lower dimensions one problem of bd schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints when the number of users is large a set of users must be selected and selection algorithms should be designed to exploit the multiuser diversity gain finding the optimal set of users requires an exhaustive search which has too high computational complexity to be practically useful based on the iterative precoder design this paper proposes a low complexity user selection algorithm using a greedy method in which the precoders of selected users are recursively updated after each selection step the selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices which is related to the eigenvalues by the hadamard and schur inequalities an asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the mimo broadcast channel the numerical results show that the proposed algorithm achieves a good trade off between sum rate performance and computational complexity when users suffer different channel conditions providing fairness among users is of critical importance to address this problem we also propose two fair scheduling fs algorithms one imposing fairness in the approximation of the data rate and another directly imposing fairness in the product of the squared row norms of the effective channel matrices

on the computational complexity of upward and rectilinear planarity testing a directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction and no two edges cross an undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical segment and no two edges cross testing upward planarity and rectilinear planarity are fundamental problems in the effective visualization of various graph and network structures for example upward planarity is useful for the display of order diagrams and subroutine call graphs while rectilinear planarity is useful for the display of circuit schematics and entity relationship diagrams we show that upward planarity testing and rectilinear planarity testing are np complete problems we also show that it is np hard to approximate the minimum number of bends in a planar orthogonal drawing of an n vertex graph with an o n 1 epsilon error for any epsilon 0

the maximum snr optimal weighting matrix for a class of amplify and forward mimo relaying assisted orthogonal space time block coded transmission the optimal weighting matrix design at the relay node for the v blast based amplify and forward af mimo relay transmission scheme has been intensively investigated in literature however there are few papers considering the optimal design of the weighting matrix at the relay node for orthogonal space time block codes ostbcs based af mimo relay transmission scheme in this paper the maximum snr weighting matrix at the relay node is designed for the ostbc based af mimo relay scheme so that for the first time we can quantify the snr gain by optimizing the weighting matrix at the relay node for the ostbc based af mimo relay scheme specifically the canonical form of the optimal linear weighting matrix is derived by exploiting matrix inequality theory and majorization theory furthermore we propose a simulation based gamma approximation method for diversity order analysis the simulation results show that the proposed optimal weighting matrix significantly outperforms the traditional scalar gain weighting matrix for the ostbc based af mimo relay scheme

weighted sum rate maximization for mimo broadcast channels using dirty paper coding and zero forcing methods we consider precoder design for maximizing the weighted sum rate wsr of successive zero forcing dirty paper coding szf dpc for this problem the existing precoder designs often assume a sum power constraint spc and rely on the singular value decomposition svd the svd based designs are known to be optimal but require high complexity we first propose a low complexity optimal precoder design for szf dpc under spc using the qr decomposition then we propose an efficient numerical algorithm to find the optimal precoders subject to per antenna power constraints papcs to this end the precoder design for papcs is formulated as an optimization problem with a rank constraint on the covariance matrices a well known approach to solve this problem is to relax the rank constraints and solve the relaxed problem interestingly for szf dpc we are able to prove that the rank relaxation is tight consequently the optimal precoder design for papcs is computed by solving the relaxed problem for which we propose a customized interior point method that exhibits a superlinear convergence rate two suboptimal precoder designs are also presented and compared to the optimal ones we also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme

multiuser mimo user selection based on chordal distance multiuser mimo mu mimo systems have advantages over single user mimo systems in terms of system performance in mu mimo systems inter user interference needs to be dealt with especially when linear processing is used the block diagonalization bd method is one of techniques that are widely used to eliminate the inter user interference in a cellular system where there are many users the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell in this paper we propose a low complexity mu mimo scheduling scheme using bd with chordal distance for a large number of users the optimal scheduling technique needs an exhaustive search which is impractical one of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms

end to end ber analysis for dual hop ostbc transmissions over rayleigh fading channels in this letter a ber study is presented for the end to end performance of dual hop wireless communication systems employing transmit diversity with orthogonal space time block codes ostbcs where a nonregenerative or regenerative relay is equipped with a single antenna operating over flat rayleigh fading channels more specifically we provide probability density functions pdfs and moment generating functions mgfs for the end to end snr of the dual hop ostbc transmissions and then present its ber performance over m ary qam and psk modulations respectively numerical investigation shows that the analytic ber provided in the letter makes an exact match with the simulation result in various multiple antenna transmission scenarios the result also shows how the number of antennas equipped at the source and destination affects the end to end performance