face counting on an acyclic birkhoff polytope in this paper we present some algorithms allowing an exhaustive account on the number of edges and faces of the acyclic birkhoff polytope

smooth approximation of plurisubharmonic functions on almost complex manifolds this note establishes smooth approximation from above for j plurisubharmonic functions on an almost complex manifold x j the following theorem is proved suppose x is j pseudoconvex i e x admits a smooth strictly j plurisubharmonic exhaustion function let u be an upper semi continuous j plurisubharmonic function on x then there exists a sequence u j in c infty x of smooth strictly j plurisubharmonic functions point wise decreasing down to u in any almost complex manifold x j each point has a fundamental neighborhood system of j pseudoconvex domains and so the theorem above establishes local smooth approximation on x this result was proved in complex dimension 2 by the third author who also showed that the result would hold in general dimensions if a parallel result for continuous approximation were known this paper establishes the required step by solving the obstacle problem

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

performance of vector perturbation multiuser mimo systems with limited feedback this paper considers the multiuser multiple input multiple output mimo rayleigh fading broadcast channel we consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via a multiuser technique known as vector perturbation we propose lattice theoretic and rate distortion based approaches to analyze the performance of these systems taking into account the practical restrictions imposed by limited feedback and training we show that performance is primarily determined by the ratio between the number of users and the number of transmit antennas we then propose a new practical low complexity low rate feedback scheme and show that the performance approaches the ideal rate distortion based scheme

linear dispersion codes for mimo systems based on frame theory multiple input multiple output mimo wireless communication systems provide high capacity due to the plurality of modes available in the channel existing signaling techniques for mimo systems have focused primarily on multiplexing for high data rate or diversity for high link reliability in this paper we present a new linear dispersion code design for mimo rayleigh fading channels the proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability this is important because as we show designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view various techniques are presented for finding codes with good error probability performance monte carlo simulations illustrate performance of some example code designs in terms of ergodic capacity codeword error probability and bit error probability

channel quantization using constellation based codebooks for multiuser mimo ofdm in this paper we propose clustered quantization techniques for multiuser multi input multi output mimo orthogonal frequency division multiplexing ofdm using constellation based codebooks constellation based codebooks provide scalability and efficient codeword search capability which are key features for practical multiuser mimo ofdm systems with a large number of antennas the proposed clustered quantization scheme quantizes consecutive subcarriers into a single codeword that minimizes aggregated quantization errors we base our new clustering techniques on two constellation based quantization methods namely equal magnitude angular quantization emaq and squared lattice angular quantization new efficient codebook search algorithms are proposed for the clustered quantization in addition we propose new constellations to guarantee different users quantize channels into distinct codewords one is a rotated m psk constellation suitable for randomly distributed user scenarios and the other is a random phase equal magnitude rpem constellation suitable for ill conditioned user scenarios thus full spatial multiplexing gain can be achievable even with small number of users finally a near sphere codeword search algorithm is proposed for the rpem in simulations the proposed clustered quantization shows up to 50 higher throughput compared to conventional fixed pilot channel quantization also we show our new constellations for emaq improve throughput almost 35 compared to the standard emaq

qam and psk codebooks for limited feedback mimo beamforming this paper considers the problem of beamforming in multiple input multiple output mimo wireless systems assuming perfect channel state information at the receiver the choice of the beamforming vector is made possible through a noiseless limited rate feedback of one or more bits per coefficient to the transmitter this paper proposes the use of beamforming codebooks based on quadrature amplitude modulation qam and phase shift keying psk constellations which essentially eliminates the need for storage of the codebook we show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases and that full diversity order is achieved we demonstrate an equivalence between the beamforming codebook search problem with that of noncoherent sequence detection based on this we propose fast beamforming vector search algorithms monte carlo simulations are presented to show that the performance is comparable to the best known codebooks and that the search complexity can be reduced by several orders of magnitude

symplectic manifolds with contact type boundaries an example of a 4 dimensional symplectic manifold with disconnected boundary of contact type is constructed a collection of other results about symplectic manifolds with contact type boundaries are derived using the theory ofj holomorphic spheres in particular the following theorem of eliashberg floer mcduff is proved if a neighbourhood of the boundary of v is symplectomorphic to a neighbourhood ofs2n 1 in standard euclidean space and if vanishes on all 2 spheres inv thenv is diffeomorphic to the ballb2n

computing the degree of a vertex in the skeleton of acyclic birkhoff polytopes abstract for a fixed tree t with n vertices the corresponding acyclic birkhoff polytope n t consists of doubly stochastic matrices having support in positions specified by t matrices associated with t the skeleton of n t is the graph whose vertices are the permutation matrices associated with t and two vertices permutation matrices a and b are adjacent if and only if e g a e g b e g b e g a is the edge set of a nontrivial path where e g a and e g b are the edge sets of graphs associated with a and b respectively we present a formula to compute the degree of any vertex in the skeleton of n t we also describe an algorithm for computing this number in addition we determine the maximum degree of a vertex in the skeleton of n t for certain classes of trees including paths and generalized stars where the branches have equal length

multi user mimo with limited feedback using alternating codebooks accurate channel information at the transmitter is crucial to multi user mimo performance unfortunately the bandwidth of the control channel by which the feedback is conveyed is often limited an important issue is how to improve multi user mimo performance with minimal feedback conventional feedback techniques focus on improving the quantized codebook performance using various quantization criteria in this paper instead of trying to optimize a single codebook we apply multiple alternating codebooks to effectively reduce the multi user mimo quantization error in addition to the reduction provided by the single codebook optimization techniques that is we use an existing quantization codebook design methodology to create not one but multiple such similar codebooks the codebooks are alternated at each feedback instance creating a larger virtual codebook with the same number of feedback bits as the single smaller codebook simulation results show that significant performance gain in multi user mimo systems is obtained via the alternating codebook scheme

on complementary coverage of ωn t abstract every acyclic birkhoff polytope is represented by a bicolored tree in this paper we use the concept of t component of a tree in order to cover it in addition the definitions of t edge cover respectively t vertex cover subgraphs and of complementary coverage by vertices edges are introduced some consequences related to the dimension of the acyclic birkhoff polytope are also obtained

some remarks about acyclic and tridiagonal birkhoff polytopes abstract for a given tree t we consider the facial structure of the acyclic birkhoff polytope t we also determine the f vector of the polytope n t consisting of all tridiagonal doubly stochastic matrices of order n finally we count the number of combinatorially distinct faces of n t in each dimension

a vector perturbation technique for near capacity multiantenna multiuser communication part ii perturbation recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity we introduce a simple encoding algorithm that achieves near capacity at sum rates of tens of bits channel use the algorithm is a variation on channel inversion that regularizes the inverse and uses a sphere encoder to perturb the data to reduce the energy of the transmitted signal the paper is comprised of two parts in this second part we show that after the regularization of the channel inverse introduced in the first part a certain perturbation of the data using a sphere encoder can be chosen to further reduce the energy of the transmitted signal the performance difference with and without this perturbation is shown to be dramatic with the perturbation we achieve excellent performance at all signal to noise ratios the results of both uncoded and turbo coded simulations are presented

the skeleton of acyclic birkhoff polytopes abstract for a fixed tree t with n vertices the corresponding acyclic birkhoff polytope n t consists of doubly stochastic matrices having support in positions specified by t this is a face of the birkhoff polytope n which consists of all n n doubly stochastic matrices the skeleton of n t is the graph where vertices and edges correspond to those of n t and we investigate some properties of this graph in particular we characterize adjacency of pairs of vertices compute the minimum degree of a vertex and show some properties of the maximum degree of a vertex in the skeleton we also determine the maximum degree for certain classes of trees including paths stars and caterpillars

glrt optimal noncoherent lattice decoding this paper presents new low complexity lattice decoding algorithms for noncoherent block detection of quadrature amplitude modulation qam and pulse amplitude modulation pam signals over complex valued fading channels the algorithms are optimal in terms of the generalized likelihood ratio test glrt the computational complexity is polynomial in the block length making glrt optimal noncoherent detection feasible for implementation we also provide even lower complexity suboptimal algorithms simulations show that the suboptimal algorithms have performance indistinguishable from the optimal algorithms finally we consider block based transmission and propose to use noncoherent detection as an alternative to pilot assisted transmission pat the new technique is shown to outperform pat

l rays of permutation matrices and doubly stochastic matrices abstract let m n be the space of real n n matrices we investigate a linear transformation m n r n called an l ray motivated by x ray which is defined in terms of sums of the entries in the blocks of a certain l shaped partition of the positions of a matrix a m n we find descriptions of the image of the classes of permutation matrices and doubly stochastic matrices under this map and show connections to majorization theory

tridiagonal doubly stochastic matrices abstract we study the facial structure of the polytope t n in r n n consisting of the tridiagonal doubly stochastic matrices of order n we also discuss some subclasses of t n with focus on spectral properties and rank formulas finally we discuss a connection to majorization

grassmannian beamforming for multiple input multiple output wireless systems transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple input multiple output mimo wireless systems unfortunately optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector both are hard to realize in this article a quantized maximum signal to noise ratio snr beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter by using the distribution of the optimal beamforming vector in independent and identically distributed rayleigh fading matrix channels the codebook design problem is solved and related to the problem of grassmannian line packing the proposed design criterion is flexible enough to allow for side constraints on the codebook vectors bounds on the codebook size are derived to guarantee full diversity order results on the density of grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or snr loss monte carlo simulations are presented that compare the probability of error for different quantization strategies

the diameter of the acyclic birkhoff polytope abstract in this work we give an interpretation of vertices and edges of the acyclic birkhoff polytope t n n t where t is a tree with n vertices in terms of graph theory we generalize a recent result relatively to the diameter of the graph g t n

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

faces of faces of the tridiagonal birkhoff polytope abstract the tridiagonal birkhoff polytope n t is the set of real square matrices with nonnegative entries and all rows and columns sums equal to 1 that are tridiagonal this polytope arises in many problems of enumerative combinatorics statistics combinatorial optimization etc in this paper for a given a p face of n t we determine the number of faces of lower dimension that are contained in it and we discuss its nature in fact a 2 face of n t is a triangle or a quadrilateral and the cells can only be tetrahedrons pentahedrons or hexahedrons

the monge ampere equation on almost complex manifolds we study the dirichlet problem for the monge ampere equation on almost complex manifolds we obtain the existence of the unique smooth solution in strictly pseudoconvex domains

on beamforming with finite rate feedback in multiple antenna systems we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations assuming that the transmitter uses the quantized information for beamforming we derive a universal lower bound on the outage probability for any finite set of beamformers the universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel using the bound it is shown that finite information systems approach the perfect information case as t 1 2 sup b t 1 where b is the number of feedback bits and t is the number of transmit antennas the geometrical bounding technique used in the proof of the lower bound also leads to a design criterion for good beamformers whose outage performance approaches the lower bound the design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook and is equivalent to the problem of designing unitary space time codes under certain conditions finally we show that good beamformers are good packings of two dimensional subspaces in a 2t dimensional real grassmannian manifold with chordal distance as the metric