transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

a criterion for the existence of common invariant subspaces of matrices it is shown that square matrices a and b have a common invariant subspace w of dimension k 1 if and only if for some scalar s a c si and b c si are invertible and their kth compounds have a common eigenvector which is a grassmann representative for w t he applicability of this criterion and its ability to yield a basis for the common invariant subspace are investigated 2001 elsevier science inc all rights reserved

admissibility and dissipativity analysis for discrete time singular systems with mixed time varying delays abstract the problems of admissibility and dissipativity are studied for discrete time singular systems with mixed time varying delays the mixed time delays consist of both discrete and distributed delays by taking advantage of the delay partitioning technique a criterion that warrants the admissibility of the considered systems is established based on the criterion a dissipativity condition is also given all the results presented depend upon not only discrete delay and distributed delay but also depend upon the number of delay partitions some numerical examples are included to demonstrate the improvement and effectiveness of the proposed methods

dead beat functional observers for discrete time lpv systems with unknown inputs this technical note deals with functional observers for discrete time linear parameter varying lpv systems more specifically dead beat observers for reconstructing linear combinations of the state are proposed the system inputs are assumed to be unknown and the observers reduce to functions of the output over a finite number of time steps the existence of such observers is proven by resorting to the notion of inverse system together with the concepts of maximal robust invariant subspaces and nilpotent semigroups a constructive approach to derive the explicit equations of the observer is provided an example illustrates the efficiency and the computational aspects of the method

novel robust stability criteria for uncertain systems with time varying delay this paper is concerned with the delay dependent stability and robust stability criteria for linear systems with time varying delay and norm bounded uncertainties through constructing a general form of lyapunov krasovskii functional and using integral inequalities some slack matrices and newly established convex combination condition in the calculation the delay dependent stability criteria are derived in terms of linear matrix inequalities numerical examples are given to illustrate the improvement on the conservatism of the delay bound over some reported results in the literature

linear precoding via conic optimization for fixed mimo receivers in this paper the problem of designing linear precoders for fixed multiple input multiple output mimo receivers is considered two different design criteria are considered in the first the transmitted power is minimized subject to signal to interference plus noise ratio sinr constraints in the second the worst case sinr is maximized subject to a power constraint it is shown that both problems can be solved using standard conic optimization packages in addition conditions are developed for the optimal precoder for both of these problems and two simple fixed point iterations are proposed to find the solutions that satisfy these conditions the relation to the well known uplink downlink duality in the context of joint transmit beamforming and power control is also explored the proposed precoder design is general and as a special case it solves the transmit rank one beamforming problem simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders

common eigenvectors of two matrices abstract a computable criterion is given for two square matrices to possess a common eigenvector as well as a criterion for one matrix to have an eigenvector lying in a given subspace some applications are discussed

duality gap estimation and polynomial time approximation for optimal spectrum management consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectra jointly in response to physical channel conditions including the effects of interference the goal of the users is to maximize a system wide utility function e g weighted sum rate of all users subject to individual power constraints a popular approach to solve the discretized version of this nonconvex problem is by lagrangian dual relaxation unfortunately the discretized spectrum management problem is np hard and its lagrangian dual is in general not equivalent to the primal formulation due to a positive duality gap in this paper we use a convexity result of lyapunov to estimate the size of duality gap for the discretized spectrum management problem and show that the duality gap vanishes asymptotically at the rate o 1 radicn where n is the size of the uniform discretization of the shared spectrum if the channels are frequency flat the duality gap estimate improves to o 1 n moreover when restricted to the fdma spectrum sharing strategies we show that the lagrangian dual relaxation combined with a linear programming scheme can generate an epsiv optimal solution for the continuous formulation of the spectrum management problem in polynomial time for any epsiv 0

multiuser transmit optimization for multicarrier broadcast channels asymptotic fdma capacity region and algorithms we derive optimal and suboptimal multiuser transmit optimization methods for a multicarrier broadcast channel with intersymbol interference under the frequency division multiple access fdma restriction the general fdma based multicarrier broadcast problem is formulated as a maximum weighted rate sum problem given each user s subchannel assignment the optimal transmit strategy is achieved by multilevel waterfilling unfortunately the problem of finding the optimal subchannel assignments is combinatorial however by relaxing the fdma restriction we obtain a convex reformulation that allows for efficient computation of the optimal solution and therefore a characterization of the fdma capacity region for a broadcast channel if all users share the same transmission medium we prove that the optimal frequency partitioning among the users has an ordered structure that can be exploited to significantly reduce the computational complexity to make multiuser transmit optimization schemes practical for applications with relatively fast time varying user data rate requirements or priorities further reduction in computational complexity is necessary this is achieved by restricting the energy distribution to be constant across the used subchannels simulations indicate the low complexity constant energy methods presented are very robust and suffer from negligible performance loss

spectrum management for interference limited multiuser communication systems consider a multiuser communication system in a frequency selective environment whereby users share a common spectrum and can interfere with each other assuming gaussian signaling and no interference cancelation we study optimal spectrum sharing strategies for the maximization of sum rate under separate power constraints for individual users since the sum rate function is nonconcave in terms of the users power allocations there can be multiple local maxima for the sum rate maximization problem in general in this paper we show that if the normalized crosstalk coefficients are larger than a given threshold roughly equal to 1 2 then the optimal spectrum sharing strategy is frequency division multiple access fdma in case of arbitrary positive crosstalk coefficients if each user s power budget exceeds a given threshold then fdma is again sum rate optimal at least in a local sense in addition we show that the problem of finding the optimal fdma spectrum allocation is np hard implying that the general problem of maximizing sum rate is also np hard even in the case of two users we also propose several simple distributed spectrum allocation algorithms that can approximately maximize sum rates numerical results indicate that these algorithms are efficient and can achieve substantially larger sum rates than the existing iterative waterfilling solutions either in an interference rich environment or when the users power budgets are sufficiently high

an algorithmic approach to simultaneous triangularization abstract we present and prove the validity of an algorithm constructing a simultaneous triangularization of a set on n matrices in c n n to do so we first prove that if a set of matrices has a common block decomposition then the set of matrices has a simultaneous triangularization if and only if the blocks on the diagonal have a simultaneous triangularization

on the complexity of joint subcarrier and power allocation for multi user ofdma systems consider a multi user orthogonal frequency division multiple access ofdma system where multiple users share multiple discrete subcarriers but at most one user is allowed to transmit power on each subcarrier to adapt fast traffic and channel fluctuations and improve the spectrum efficiency the system should have the ability to dynamically allocate subcarriers and power resources to users assuming perfect channel knowledge two formulations for the joint subcarrier and power allocation problem are considered in this paper the first is to minimize the total transmission power subject to the quality of service constraints and the ofdma constraint and the second is to maximize some system utility function subject to the total transmission power constraint per user and the ofdma constraint in spite of the existence of various heuristics approaches little is known about the computational complexity status of the above problem this paper aims at filling this theoretical gap i e characterizing the complexity of the joint subcarrier and power allocation problem for the multi user ofdma system it is shown in this paper that both formulations of the joint subcarrier and power allocation problem are strongly np hard several subclasses of the problem which can be solved efficiently in polynomial time are also identified these complexity results suggest that there are not polynomial time algorithms that are able to solve the general joint subcarrier and power allocation problem to global optimality unless p np and determining an approximately optimal subcarrier and power allocation strategy is more realistic in practice

dual methods for nonconvex spectrum optimization of multicarrier systems the design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints the optimization problem is numerically difficult to solve when the problem does not have a convexity structure this paper makes progress toward solving optimization problems of this type by showing that under a certain condition called the time sharing condition the duality gap of the optimization problem is always zero regardless of the convexity of the objective function further we show that the time sharing condition is satisfied for practical multiuser spectrum optimization problems in multicarrier systems in the limit as the number of carriers goes to infinity this result leads to efficient numerical algorithms that solve the nonconvex problem in the dual domain we show that the recently proposed optimal spectrum balancing algorithm for digital subscriber lines can be interpreted as a dual algorithm this new interpretation gives rise to more efficient dual update methods it also suggests ways in which the dual objective may be evaluated approximately further improving the numerical efficiency of the algorithm we propose a low complexity iterative spectrum balancing algorithm based on these ideas and show that the new algorithm achieves near optimal performance in many practical situations

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

nilpotent semigroups for the characterization of flat outputs of switched linear and lpv discrete time systems abstract this paper addresses the problem of flat output characterization for switched linear systems the characterization is also extended to lpv systems the characterization is based on the notion of nilpotent semigroups a complete corresponding recursive algorithm is provided it stops after a finite number of steps bounded by the dimension of the system illustrative examples for the respective class of switched linear and lpv systems highlight the efficiency of the characterization

improvement on delay dependent absolute stability of lurie control systems with multiple time delays absolute stability of lurie control systems with multiple time delays is studied in this paper by using extended lyapunov functionals we avoid the use of the stability assumption on the main operator and derive improved stability criteria which are strictly less conservative than the criteria in 2 3

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

joint power and admission control non convex l_ q approximation and an effective polynomial time deflation approach in an interference limited network joint power and admission control jpac aims at supporting a maximum number of links at their specified signal to interference plus noise ratio sinr targets while using minimum total transmission power various convex approximation deflation approaches have been developed for the jpac problem in this paper we propose an effective polynomial time non convex approximation deflation approach for solving the problem the approach is based on the non convex ell q 0 approximation of an equivalent sparse ell 0 reformulation of the jpac problem we show that for any instance of the jpac problem there exists a bar q in 0 1 such that it can be exactly solved by solving its ell q approximation problem with any q in 0 bar q we also show that finding the global solution of the ell q approximation problem is np hard then we propose a potential reduction interior point algorithm which can return an epsilon kkt solution of the np hard ell q approximation problem in polynomial time the returned solution can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure resulting in the polynomial time non convex approximation deflation approach for the jpac problem numerical simulations show that the proposed approach outperforms the existing convex approximation approaches in terms of the number of supported links and the total transmission power particularly exhibiting a quite good performance in selecting which subset of links to support

asymptotic and exponential stability of uncertain system with interval delay abstract this paper considers the problem of asymptotic and exponential stability analysis of the continuous system with interval time varying delay and uncertainties by constructing a new lyapunov krasovskii functional several delay range dependent conditions are derived in terms of the linear matrix inequalities lmis two novel integral equalities are employed to overcome the disadvantages of the methods in existing references the merits of the proposed criteria lie in the exponential stability being a free value and the less conservativeness finally some numerical examples are included to illustrate the effectiveness and the improvement of the proposed method

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

simultaneous reduction of matrices in the presence of a nonderogatory matrix abstract some known results on the question when are two matrices simultaneously similar to matrices in upper triangular form are simplified in the case when one of the matrices is nonderogatory

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

bi perspective functions for mixed integer fractional programs with indicator variables perspective functions have long been used to convert fractional programs into convex programs more recently they have been used to form tight relaxations of mixed integer nonlinear programs with so called indicator variables motivated by a practical application maximising energy efficiency in an ofdma system we consider problems that have a fractional objective and indicator variables simultaneously to obtain a tight relaxation of such problems one must consider what we call a bi perspective bi p function an analysis of bi p functions leads to the derivation of a new kind of cutting planes which we call bi p cuts computational results indicate that bi p cuts typically close a substantial proportion of the integrality gap

improved delay dependent robust stability criteria for uncertain time delay systems abstract this paper deals with the robust stability analysis for uncertain systems with time varying delay new delay dependent robust stability criteria of uncertain time delay systems are proposed by exploiting appropriate lyapunov functional candidate these developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism due to the introduction of a method to estimate the upper bound of the derivative of lyapunov functional candidate without ignoring the additional useful terms numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method

the common invariant subspace problem an approach via grobner bases let a be an n n matrix it is a relatively simple process to construct a homogeneous ideal generated by quadrics whose associated projective variety parametrizes the one dimensional invariant subspaces of a given a finite collection of n n matrices one can similarly construct a homogeneous ideal again generated by quadrics whose associated projective variety parametrizes the one dimensional subspaces which are invariant subspaces for every member of the collection grobner basis techniques then provide a finite rational algorithm to determine how many points are on this variety in other words a finite rational algorithm is given to determine both the existence and quantity of common one dimensional invariant subspaces to a set of matrices this is then extended for each d to an algorithm to determine both the existence and quantity of common d dimensional invariant subspaces to a set of matrices 2004 published by elsevier inc

technical communique delay dependent robust stability for uncertain linear systems with interval time varying delay this paper is concerned with the delay dependent robust stability problem for uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and no restriction on the derivative of the time varying delay is needed which allows the delay to be a fast time varying function the uncertainty under consideration is norm bounded and possibly time varying uncertainty based on the lyapunov krasovskii functional approach a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria numerical examples are given to demonstrate effectiveness of the proposed method