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

geometrical relations between space time block code designs and complexity reduction in this work the geometric relation between space time block code design for the coherent channel and its noncoherent counterpart is exploited to get an analog of the information theoretic inequality i x s lesi x h s in terms of diversity it provides a lower bound on the performance of noncoherent codes when used in coherent scenarios this leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced subtasks moreover a geometrical criterion for high performance space time code design is derived

some 2 spl times 2 unitary space time codes from sphere packing theory with optimal diversity product of code size 6 in this correspondence we propose some new designs of 2 spl times 2 unitary space time codes of sizes 6 32 48 64 with best known diversity products or product distances by partially using sphere packing theory in particular we present an optimal 2 spl times 2 unitary space time code of size 6 in the sense that it reaches the maximal possible diversity product for 2 spl times 2 unitary space time codes of size 6 the construction and the optimality of the code of size 6 provide the precise value of the maximal diversity product of a 2 spl times 2 unitary space time code of size 6

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

a unified snr dependent analysis of space time codes in fading channels the pairwise error probability pep for multiple input multiple output mimo radio interfaces is investigated by means of a novel formulation based on compound matrices the proposed approach is suitable for any mimo system having average upper bounded pep written as det i gamma a zeta where a is a hermitian matrix zeta an integer number and gamma the signal to noise ratio snr that bound frequently results in mimo single and multicarrier transmissions it is shown that the minimization of the bounded pep should consider the whole set of nonzero compound matrices of a in particular the snr of interest marks the compound matrix that mainly drives the system performance both diversity advantage and coding gain are given as continuous functions of the variable gamma hence their asymptotic behaviors are taken as important case of studies the interaction effects between channel code and propagation environment are also discussed it is shown how the eigenvectors and eigenvalues of the autocorrelation channel matrix may be considered for code design it is also proved the maximization of the code rank is not always a necessary requirement for performance improvement being its optimal value fixed by the channel structure and snr of interest finally the analysis is applied to space time trellis coded transmissions over spatially correlated slow rayleigh fading channels

multiple voting location and single voting location on trees abstract we examine voting location problems in which the goal is to place based on an election amongst the users a given number of facilities in a graph the user preference is modeled by shortest path distances in the graph a condorcet solution is a set of facilities to which there does not exist an alternative set preferred by a majority of the users recent works generalize the model to additive indifference and replaced user majority by proportion we show that for multiple voting location condorcet and simpson decision problems are 2 p complete and investigate the approximability of the simpson and the simpson score optimization problem further we contribute a result towards lower bounds on the complexity of the single voting location problem on the positive side we develop algorithms for the optimization problems on tree networks which are substantially faster than the existing algorithms for general graphs finally we suggest a generalization of the indifference notion to threshold functions

unitary space time constellation analysis an upper bound for the diversity the diversity product and the diversity sum are two very important parameters for a good performing unitary space time constellation a basic question is what the maximal diversity product or sum is in this correspondence we are going to derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension n and any size m using packing techniques on the compact lie group u n

representation theory for high rate multiple antenna code design multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment but the practical success of using multiple antennas depends crucially on our ability to design high rate space time constellations with low encoding and decoding complexity it has been shown that full transmitter diversity where the constellation is a set of unitary matrices whose differences have nonzero determinant is a desirable property for good performance we use the powerful theory of fixed point free groups and their representations to design high rate constellations with full diversity furthermore we thereby classify all full diversity constellations that form a group for all rates and numbers of transmitter antennas the group structure makes the constellations especially suitable for differential modulation and low complexity decoding algorithms the classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd we therefore also consider extensions of the constellation designs to nongroups we conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

integer programming formulations for three sequential discrete competitive location problems with foresight abstract we deal with three competitive location problems based on the classical maximal covering location problem the environment of these problems consists of an open market with two firms leader and follower several customers and locations where facilities can be located in order to capture the demand of the customers the leader enters the market by locating a set of facilities knowing the potential locations where the follower can locate her facilities after the leader s decision we consider here three pairs of objective functions for the leader follower previously studied in the literature maximizing minimizing the demand captured by the leader minimizing maximizing the regret of the leader maximizing the demand captured by each firm also known as stackelberg for each model we propose an integer linear programming formulation with a polynomial number of variables and an exponential number of constraints the formulations are solved by branch and cut algorithms where the constraints are generated on demand by solving appropriate separation problems we report extensive computational experiments realized on instances inspired by those from the literature comparing our algorithms with the exact and heuristic algorithms previously published for these problems

a branch and cut algorithm for the discrete r p centroid problem abstract the environment of the r p centroid problem is composed of two noncooperative firms a leader and a follower competing to serve the demand of customers from a given market the demand of each customer is totally served by a facility of the leader or follower according to a customer choice rule the goal of both the leader and the follower is to maximize its own market share the r p centroid problem consists of deciding where the leader should place p facilities knowing that the follower will react by placing r facilities the discrete version of the problem is a 2 p hard one where both the applicant facilities and the customers are nodes on a graph in spite of it we present an integer programming formulation with polynomially many variables and exponentially many constraints moreover we report several experiments with different number of customers and applicant facilities and different values of p and r our results show that our method requires less computational time than the two exact algorithms found in the literature being able to optimally solve 29 previously open instances with up to 100 customers 100 applicant facilities and p r 15

an explicit expression for the newton direction on the complex grassmann manifold several important design problems in signal processing for communications can be cast as optimization problems in which the objective is a function of the subspaces spanned by tall complex matrix variables with orthonormal columns such problems can be viewed as optimization problems on the complex grassmann manifold and an effective means for performing this optimization is to use a grassmannian version of newton s method to facilitate the implementation of that method we provide an explicit expression for the grassmannian newton direction for an arbitrary twice differentiable function we also use an example in which the pairwise chordal frobenius norm between subspaces is to be optimized to outline a systematic procedure for obtaining the hessian matrix

on the geometry and quantization of manifolds of positive semi definite matrices the geometry of different spaces of positive semi definite matrices buffeted by rank and trace constraints is studied in addition to revealing their riemannian structure we derive the normalized volume of a ball over these spaces further we use the leading coefficient from the ball volume expansion to bound the quantization error incurred with finite sized sphere packing codebooks as well as random codebooks to represent sources distributed over general riemannian manifolds

relaxation of the condorcet and simpson conditions in voting location abstract a condorcet point in voting location is a location point such that there is no other closer to more than half of the users however such condorcet solution does not necessarily exist this concept is based on two assumptions first two locations are indifferent only if they are at the same distance of the voter second the number of voters needed to reject a location is more than half of them we relax the condorcet condition in two ways first by considering that two locations are indifferent for every user if the difference of the distances to them is within a positive threshold secondly by considering that the proportion of users needed to reject a location is not one half we consider the resulting new solution concepts that arise by applying both relaxations at the same time and develop algorithms for obtaining them in the finite case

multiple voting location problems the facility voting location problems arise from the application of criteria derived from the voting processes concerning the location of facilities the multiple location problems are those location problems in which the alternative solutions are sets of points this paper extends previous results and notions on single voting location problems to the location of a set of facility points the application of linear programming techniques to solve multiple facility voting location problems is analyzed we propose an algorithm to solve simpson multiple location problems from which the solution procedures for other problems are derived

bounds on packings of spheres in the grassmann manifold we derive the gilbert varshamov and hamming bounds for packings of spheres codes in the grassmann manifolds over r and c asymptotic expressions are obtained for the geodesic metric and projection frobenius chordal metric on the manifold

r p centroid problems on paths and trees an instance of the r p centroid problem is given by an edge and node weighted graph two competitors the leader and the follower are allowed to place p and r facilities respectively into the graph users at the nodes connect to the closest facility a solution of the r p centroid problem is a leader placement such that the maximum total weight of the users connecting to any follower placement is as small as possible we show that the absolute r p centroid problem is np hard even on a path which answers a long standing open question of the complexity of the problem on trees hakimi 1990 10 moreover we provide polynomial time algorithms for the discrete r p centroid on paths and the 1 p centroid on trees and complementary hardness results for more complex graph classes

direct result on exponential type operators in this paper we obtain a direct result and voronovskaya type asymptotic formula for the exponential type operators in simultaneous approximation with polynomial growth in the end we obtain the recurrence formulae for the central moments direct results and voronovskaya type asymptotic formulae for the various mixed summation integral type operators

capacity planning with competitive decision makers trilevel milp formulation degeneracy and solution approaches abstract capacity planning addresses the decision problem of an industrial producer investing on infrastructure to satisfy future demand with the highest profit traditional models neglect the rational behavior of some external decision makers by assuming either static competition or captive markets we propose a mathematical programing formulation with three levels of decision makers to capture the dynamics of duopolistic markets the trilevel model is transformed into a bilevel optimization problem with mixed integer variables in both levels by replacing the third level linear program with its optimality conditions we introduce new definitions required for the analysis of degeneracy in multilevel models and develop two novel algorithms to solve these challenging problems each algorithm is shown to converge to a different type of degenerate solution the computational experiments for capacity expansion in industrial gas markets show that no algorithm is strictly superior in terms of performance

unitary signal constellations for differential space time modulation with two transmit antennas parametric codes optimal designs and bounds we focus on the design of unitary signal constellations for differential space time modulation with double transmit antennas by using the parametric form of a two by two unitary matrix we present a class of unitary space time codes called parametric codes and show that this class of unitary space time codes leads to a five signal constellation with the largest possible diversity product and a 16 signal constellation with the largest known diversity product although the parametric code of size 16 is not a group by itself we show that it is a subset of a group of order 32 furthermore the unitary signal constellations of sizes 32 64 128 and 256 obtained by taking the subsets of the parametric codes of sizes 37 75 135 and 273 respectively have the largest known diversity products we also use large diversity sum of unitary space time signal constellations as another significant property for the signal constellations to have good performance in low snr scenarios the newly introduced unitary space time codes can lead to signal constellations with sizes of 5 and 9 through 16 that have the largest possible diversity sums subsequently we construct a few sporadic unitary signal constellations with the largest possible diversity product or diversity sum a four signal constellation which has both the largest possible diversity product and the largest possible diversity sum and three unitary signal constellations with the largest possible diversity sums for sizes of 6 7 and 8 are constructed respectively furthermore by making use of the existing results in sphere packing and spherical codes we provide several upper and lower bounds on the largest possible diversity product and the largest possible diversity sum that unitary signal constellations of any size can achieve

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

sphere packing bounds in the grassmann and stiefel manifolds applying the riemann geometric machinery of volume estimates in terms of curvature bounds for the minimal distance of packings codes in the grassmann and stiefel manifolds will be derived and analyzed in the context of space time block codes this leads to a monotonically increasing minimal distance lower bound as a function of the block length this advocates large block lengths for the code design

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold