stochastic precoding for miso interference channels with channel mean feedback this work considers linear precoding strategies for multiple input single out miso interference channels with channel mean feedback at transmitters where the interference at each receiver is treated as additive noise the challenge here is that previous precoder designs with perfect channel state information csi at transmitters do not apply and new approaches are required based on the laplace transform order an altruistic non equilibrium strategy i e the stochastic zero forcing is first proposed under practical assumptions generalizing the traditional zero forcing which requires perfect csi interestingly the precoding matrices here are all rank one beamformers as in the traditional zero forcing the competitive use of the common physical media in miso interference channels is also formulated as a strategic noncooperative game in contrast to the perfect csi case with a unique rank one nash equilibrium with channel mean feedback the nash equilibria here are not necessarily rank one in general nevertheless when achieved by the rank one beamforming the equilibrium is unique and convenient for implementation accordingly the condition for beamforming to achieve the equilibrium is derived comparisons of the above two strategies reveal no overall dominance of one over the other thereby establishing stochastic zero forcing as an alternative to the nash equilibrium designs

cooperative resource allocation games under spectral mask and total power constraints resource allocation problems in multi user systems modeled as nash bargaining nb cooperative games are investigated under different constraints using the joint time division multiplexing and frequency division multiplexing tdm fdm scheme as a manner of cooperation in the nb resource allocation game with only spectrum mask constraints smcs it is shown that the efficiency of the corresponding solution depends on both the interference to signal and interference to noise ratios of the users sufficient conditions under which the joint tdm fdm based nb solution outperforms a noncooperative nash equilibrium solution are derived and shown to be mild a semi distributed algorithm is proposed for finding the nb solution of the corresponding game with smcs only the nb based resource allocation game with both smcs and total power constraints tpcs is shown to be a nonconvex optimization problem of high complexity for such a game a classification of two user systems into bandwidth and power dominant systems is proposed based on the concept of pareto optimality this classification gives insights to the resource allocation problem by showing that the benefits of both users are guaranteed to increase simultaneously only when the dominant resource in the system increases using this classification efficient suboptimal algorithms of low complexity are derived based on the idea of optimally allocating the dominant resource and suboptimally allocating the other resource simulation results demonstrate the efficiency of the proposed cooperative nb resource allocation strategies

energy efficient subcarrier assignment and power allocation in ofdma systems with max min fairness guarantees in next generation wireless networks energy efficiency optimization needs to take individual link fairness into account in this paper we investigate a max min energy efficiency optimal problem mep to ensure fairness among links in terms of energy efficiency in ofdma systems in particular we maximize the energy efficiency of the worst case link subject to the rate requirements transmit power and subcarrier assignment constraints due to the nonsmooth and mixed combinatorial features of the formulation we focus on low complexity suboptimal algorithms design using a generalized fractional programming theory and the lagrangian dual decomposition we first propose an iterative algorithm to solve the problem we then devise algorithms to separate the subcarrier assignment and power allocation to further reduce the computational cost our simulation results verify the convergence performance and the fairness achieved among links and particularly reveal a new tradeoff between the network energy efficiency and fairness by comparing the mep with the existing algorithms

optimal spectrum management in multiuser interference channels in this paper we study the problem of continuous frequency optimal spectrum management in multiuser frequency selective interference channels we assume that interference is treated as noise by the decoders and separate encoding is applied first a simple pair wise channel condition for frequency division multiple access schemes to achieve all pareto optimal points of the rate region is derived it enables fully distributed global optimal decision making on whether any two users should use orthogonal channels next we present an analytical solution to finding the maximum sum rate in two user symmetric frequency flat channels generalizing this solution to frequency selective channels a convex optimization is established that yields the global optimum finally we show that our method generalizes to k user k 2 weighted sum rate maximization in asymmetric frequency selective channels and we transform this classic nonconvex optimization to an equivalent convex optimization in the primal domain

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

minimum ber linear transceivers for mimo channels via primal decomposition this paper considers the employment of linear transceivers for communication through multiple input multiple output mimo channels with channel state information csi at both sides of the link the design of linear mimo transceivers has been studied since the 1970s by optimizing simple measures of the quality of the system such as the trace of the mean square error matrix subject to a power constraint recent results showed how to solve the problem in an optimal way for the family of schur concave and schur convex cost functions in particular when the constellations used on the different transmit dimensions are equal the bit error rate ber averaged over these dimensions happens to be a schur convex function and therefore it can be optimally solved in a more general case however when different constellations are used the average ber is not a schur convex function and the optimal design in terms of minimum ber is an open problem this paper solves the minimum ber problem with arbitrary constellations by first reformulating the problem in convex form and then proposing two solutions one is a heuristic and suboptimal solution which performs remarkably well in practice the other one is the optimal solution obtained by decomposing the convex problem into several subproblems controlled by a master problem a technique borrowed from optimization theory for which extremely simple algorithms exist thus the minimum ber problem can be optimally solved in practice with very simple algorithms

asynchronous iterative water filling for gaussian frequency selective interference channels this paper considers the maximization of information rates for the gaussian frequency selective interference channel subject to power and spectral mask constraints on each link to derive decentralized solutions that do not require any cooperation among the users the optimization problem is formulated as a static noncooperative game of complete information to achieve the so called nash equilibria of the game we propose a new distributed algorithm called asynchronous iterative water filling algorithm in this algorithm the users update their power spectral density psd in a completely distributed and asynchronous way some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference the proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water filling algorithms e g sequential and simultaneous versions the main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the unique nash equilibrium of the game

globally optimal linear precoders for finite alphabet signals over complex vector gaussian channels we study the design optimization of linear precoders for maximizing the mutual information between finite alphabet input and the corresponding output over complex valued vector channels this mutual information is a nonlinear and non concave function of the precoder parameters posing a major obstacle to precoder design optimization our work presents three main contributions first we prove that the mutual information is a concave function of a matrix which itself is a quadratic function of the precoder matrix second we propose a parameterized iterative algorithm for finding optimal linear precoders to achieve the global maximum of the mutual information the proposed iterative algorithm is numerically robust computationally efficient and globally convergent third we demonstrate that maximizing the mutual information between a discrete constellation input and the corresponding output of a vector channel not only provides the highest practically achievable rate but also serves as an excellent criterion for minimizing the coded bit error rate our numerical examples show that the proposed algorithm achieves mutual information very close to the channel capacity for channel coding rate under 0 75 and also exhibits a large gain over existing linear precoding and or power allocation algorithms moreover our examples show that certain existing methods are susceptible to being trapped at locally optimal precoders

hecke theory of series formed with modular symbols and relations among convolution l functions in g1 g2 the distribution of modular symbols is studied and a new class of functions which satisfy a transformation law involving these objects is introduced the goal of goldfeld s program is to prove szpiro s conjecture which states that for elliptic curves with minimal discriminant d and conductor n there is an absolute constant such that d n to do this an equivalent conjecture involving modular symbols is established in g4 using the now proven conjecture of shimura taniyama and weil it seems that a sufficiently good understanding of the new series proposed by goldfeld should yield a resolution of these conjectures we repeat here their definition in a somewhat more general form to include period polynomials rather than modular symbols only for positive integers m n such that m n let m k be non negative integers such that m k 2 0 and let be a dirichlet character modulo n first for each f sk m holomorphic cusp forms of weight k and level m we denote by rf the map which sends 0 m the hecke congruence group of level m to the polynomial function

capacity of the discrete time gaussian channel with intersymbol interference the discrete time gaussian channel with intersymbol interference isi where the inputs are subject to a per symbol average energy constraint is considered the capacity of this channel is derived by means of a hypothetical channel model called the n circular gaussian channel ncgc whose capacity is readily derived using the theory of the discrete fourier transform the results obtained for the ncgc are used further to prove that in the limit of increasing block length n the capacity of the discrete time gaussian channel dtgc with isi using a per block average energy input constraint n block dtgc is indeed also the capacity when using the per symbol average energy constraint

game theoretic opportunistic spectrum sharing strategy selection for cognitive mimo multiple access channels this paper studies opportunistic spectrum sharing strategy i e quantized precoding strategy selection for cognitive multiple input multiple output multiple access channels with limited feedback under interference power constraint and maximum transmission stream number constraint we put forward a game theoretic framework to model the precoding strategy selection behaviors of the secondary users under the specified constraints first we prove the formulated discrete game is a potential game which possesses at least one feasible pure strategy nash equilibrium the feasibility and optimality of the nash equilibrium are also analyzed then we prove that the solution to the sum rate maximization problem constitutes a feasible pure strategy nash equilibrium of our formulated game furthermore we design two algorithms the iterative precoding strategy selection algorithm based on the best response rule is designed to attain a feasible nash equilibrium the modified algorithm is designed to improve the sum rate performance simulation results show that our designed algorithms can achieve optimal or near optimal sum rate performance with low complexity

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

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

power control in networks with heterogeneous users a quasi variational inequality approach this paper deals with the power allocation problem in a multipoint to multipoint network which is heterogenous in the sense that each transmit and receiver pair can arbitrarily choose whether to selfishly maximize its own rate or energy efficiency this is achieved by modeling the transmit and receiver pairs as rational players that engage in a noncooperative game in which the utility function changes according to each player s nature the underlying game is reformulated as a quasi variational inequality qvi problem using convex fractional program theory the equivalence between the qvi and the noncooperative game provides us with all the mathematical tools to study the uniqueness of its nash equilibrium points and to derive novel algorithms that allow the network to converge to these points in an iterative manner both with and without the need for a centralized processing numerical results are used to validate the proposed solutions in different operating conditions

achieving the maximum sum rate using d c programming in cellular networks intercell interference is the major limitation to the performance of future cellular systems despite the joint detection and joint transmission techniques aiming at interference cancellation which suffer from the limited possible cooperation among the nodes power allocation is a promising approach for optimizing the system performance if the interference is treated as noise the power allocation optimization problem aiming at maximizing the sum rate with a total power constraint is nonconvex and up to now an open problem in the present paper the solution is found by reformulating the nonconvex objective function of the sum rate as a difference of two concave functions a globally optimum power allocation is found by applying a branch and bound algorithm to the new formulation in principle the algorithm partitions the feasible region recursively into subregions where for every subregion the objective function is upper and lower bounded for each subregion a linear program is applied for estimating the upper bound of the sum rate which is derived from a convex maximization formulation of the problem with piecewise linearly approximated constraints the performance is investigated by system level simulations the results show that the proposed algorithm outperforms the known conventional suboptimum schemes furthermore it is shown that the algorithm asymptotically converges to a globally optimum power allocation

convergence of iterative water filling with quantized feedback a sufficient condition in this paper the iterative water filling iwf algorithm is considered when the noise plus interference levels fed back from the receivers are quantized a sufficient condition for this algorithm to have a unique nash equilibrium is derived this condition is shown to approach the corresponding condition for standard iwf when the quantization resolution or the transmission power are sufficiently high

novel cloning machine with supplementary information probabilistic cloning was first proposed by duan and guo then pati established a novel cloning machine ncm for copying superposition of multiple clones simultaneously in this paper we deal with the novel cloning machine with supplementary information ncmsi for the case of cloning two states we demonstrate that the optimal efficiency of the ncmsi in which the original party and the supplementary party can perform quantum communication equals that achieved by a two step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties from this equivalence it follows that ncmsi may increase the success probabilities for copying also an upper bound on the unambiguous discrimination of two nonorthogonal pure product states is derived our investigation generalizes and completes the results in the literature

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

pareto region characterization for rate control in mimo interference systems and nash bargaining in this note the problem of rate control in multiuser multiple input multiple output mimo interference systems is formulated as a multicriteria optimization mco problem the pareto rate region of the mco problem is first characterized by giving a sufficient condition for the convexity of the pareto rate region second various rate region convexification approaches including a multistage interference cancellation and a full projection fp based interference avoidance scheme are analyzed an achievable rate region based on fp is also given for mimo interference systems third nash bargaining nb is applied to transform the mco problem into a single objective problem the characteristics of the nb over mimo interference systems such as the uniqueness and optimality of different type nb solutions are investigated a method to determine the optimality of fp and time division multiplexing based nb solutions is presented as well finally the convexity of the rate region and the existence of the fp based nb solution for mimo interference systems are examined numerically

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

the mimo iterative waterfilling algorithm this paper considers the noncooperative maximization of mutual information in the vector gaussian interference channel in a fully distributed fashion via game theory this problem has been widely studied in a number of works during the past decade for frequency selective channels and recently for the more general multiple input multiple output mimo case for which the state of the art results are valid only for nonsingular square channel matrices surprisingly these results do not hold true when the channel matrices are rectangular and or rank deficient matrices the goal of this paper is to provide a complete characterization of the mimo game for arbitrary channel matrices in terms of conditions guaranteeing both the uniqueness of the nash equilibrium and the convergence of asynchronous distributed iterative waterfilling algorithms our analysis hinges on new technical intermediate results such as a new expression for the mimo waterfilling projection valid also for singular matrices a mean value theorem for complex matrix valued functions and a general contraction theorem for the multiuser mimo watefilling mapping valid for arbitrary channel matrices the quite surprising result is that uniqueness convergence conditions in the case of tall possibly singular channel matrices are more restrictive than those required in the case of full rank fat channel matrices we also propose a modified game and algorithm with milder conditions for the uniqueness of the equilibrium and convergence and virtually the same performance in terms of nash equilibria of the original game

a generalized iterative water filling algorithm for distributed power control in the presence of a jammer consider a scenario in which k users and a jammer share a common spectrum of n orthogonal tones both the users and the jammer have limited power budgets the goal of each user is to allocate its power across the n tones in such a way that maximizes the total sum rate that he she can achieve while treating the interference of other users and the jammer s signal as additive gaussian noise the jammer on the other hand wishes to allocate its power in such a way that minimizes the utility of the whole system that being the total sum of the rates communicated over the network for this noncooperative game we propose a generalized version of the existing iterative water filling algorithm whereby the users and the jammer update their power allocations in a greedy manner we study the existence of a nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative water filling algorithm converges to a nash equilibrium of the game the conditions that we derive in this paper depend only on the system parameters and hence can be checked a priori simulations show that when the convergence conditions are violated the presence of a jammer can cause the otherwise convergent iterative water filling algorithm to oscillate

distributed power allocation with rate constraints in gaussian parallel interference channels this paper considers the minimization of transmit power in gaussian parallel interference channels subject to a rate constraint for each user to derive decentralized solutions that do not require any cooperation among the users we formulate this power control problem as a generalized nash equilibrium ne game we obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem then to compute the solutions of the game we propose two distributed algorithms based on the single user water filling solution the sequential and the simultaneous iterative water filling algorithms wherein the users update their own strategies sequentially and simultaneously respectively we derive a unified set of sufficient conditions that guarantee the uniqueness of the solution and global convergence of both algorithms our results are applicable to all practical distributed multipoint to multipoint interference systems either wired or wireless where a quality of service in qos terms of information rate must be guaranteed for each link

optimum linear joint transmit receive processing for mimo channels with qos constraints this paper considers vector communications through multiple input multiple output mimo channels with a set of quality of service qos requirements for the simultaneously established substreams linear transmit receive processing also termed linear precoder at the transmitter and linear equalizer at the receiver is designed to satisfy the qos constraints with minimum transmitted power the exact conditions under which the problem becomes unfeasible are given although the original problem is a complicated nonconvex problem with matrix valued variables with the aid of majorization theory we reformulate it as a simple convex optimization problem with scalar variables we then propose a practical and efficient multilevel water filling algorithm to optimally solve the problem for the general case of different qos requirements the optimal transmit receive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols for situations in which the resulting transmit power is too large we give the precise way to relax the qos constraints in order to reduce the required power based on a perturbation analysis we also propose a robust design under channel estimation errors that has an important interest for practical systems numerical results from simulations are given to support the mathematical development of the problem

gaussian multiaccess channels with isi capacity region and multiuser water filling the capacity region of a two user gaussian multiaccess channel with intersymbol interference isi in which the inputs pass through respective linear systems and are superimposed before being corrupted by an additive gaussian noise process is discussed a geometrical method for obtaining the optimal input power spectral densities and the capacity region is presented this method can be viewed as a nontrivial generalization of the single user water filling argument it is shown that as in the traditional memoryless multiaccess channel frequency division multiaccess fdma with optimally selected frequency bands for each user achieves the total capacity of the multiuser gaussian multiaccess channel with isi however the capacity region of the two user channel with memory is in general not a pentagon unless the channel transfer functions for both users are identical

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

joint sensing and power allocation in nonconvex cognitive radio games quasi nash equilibria in this paper we propose a novel class of nash problems for cognitive radio cr networks composed of multiple primary users pus and secondary users sus wherein each su player competes against the others to maximize his own opportunistic throughput by choosing jointly the sensing duration the detection thresholds and the vector power allocation over a multichannel link in addition to power budget constraints several deterministic or probabilistic interference constraints can be accommodated in the proposed general formulation such as constraints on the maximum individual aggregate probabilistic interference tolerable from the pus to keep the optimization as decentralized as possible global interference constraints when present are imposed via pricing the prices are thus additional variables to be optimized the resulting players optimization problems are nonconvex and there are price clearance conditions associated with the nonconvex global interference constraints to be satisfied by the equilibria of the game which make the analysis of the proposed game a challenging task none of classical results in the game theory literature can be successfully applied to deal with the nonconvexity of the game we introduce a relaxed equilibrium concept the quasi nash equilibrium qne and study its main properties performance and connection with local nash equilibria quite interestingly the proposed game theoretical formulations yield a considerable performance improvement with respect to current centralized and decentralized designs of cr systems which validates the concept of qne

inefficiency of nash equilibria it is shown that nash equilibria of smooth games generally tend to be inefficient in the pareto sense

practical algorithms for a family of waterfilling solutions many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure the classical example is the capacity achieving solution for a frequency selective channel for simple waterfilling solutions with a single waterlevel and a single constraint typically a power constraint some algorithms have been proposed in the literature to compute the solutions numerically however some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints for such cases it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure in addition a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing the purpose of this paper is twofold on the one hand it overviews the waterfilling results existing in the literature from a unified viewpoint on the other hand it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice to be more precise it provides a practical algorithm to evaluate numerically a general waterfilling solution which includes the currently existing waterfilling solutions and others that may possibly appear in future problems

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

distributed power control for one to many transmissions in gaussian interference channels in this paper we extend the distributed power control problem for one to one transmissions in gaussian interference channels to one to many transmission scenarios we assume a user centric wireless network where the end users play the roles of decision makers we formulate the power control problem as a noncooperative game new challenges arise due to the coupling issues among power strategy spaces of distributed end users which make standard nash equilibrium based noncooperative game approach inapplicable indeed our problem turns out to be a generalized nash equilibrium problem gnep resorting to variational inequality theory we show several fundamental properties of the gnep then we propose a penalty based distributed algorithm ip 2ja which possesses favorable properties for practical implementation numerical results are provided to verify our arguments and proposed algorithm

properties of eisenstein series formed with modular symbols in this work a new kind of non holomorphic eisenstein series first introduced by goldfeld is studied for an arbitrary fuchsian group of the first kind we fix a holomorphic cusp form and consider eisenstein series constructed with the modular symbol associated with this cusp form we develop the theory analogously with that of the usual eisenstein series starting with its meromorphic continuation to the entire complex plane a functional equation is then obtained relating the values at s to those at 1 s introduction let h z c im z 0 be the upper half plane and let sl2 r be a fixed non co compact fuchsian group of the first kind for example n 0 n acting on h for simplicity assume that has a unique cusp at infinity with stability group 1 m 0 1 m z for each in we shall label its matrix elements a b c d let f z be an element of s2 the space holomorphic cusp forms of weight 2 for following go we define a modified eisenstein series 0 1 e z s f im z s z h where for the modular symbol is given by f 2 i w w f d the definition being independent of w h note that since 1 2 f 1 f 2 f the series is not automorphic the transformation rule is e z s e z s f e z s for all where e z s is the usual eisenstein series for this new type of non holomorphic eisenstein series was introduced by goldfeld in order to study the distribution properties of modular symbols f as ranges over the group the series 0 1 converges for re s 2 and goldfeld hypothesised that it should have an analytic continuation and a functional equation in this paper selberg s method described in iw he is extended to establish the following results typeset by ams tex 1

robust mimo cognitive radio via game theory cognitive radio cr systems improve the spectral efficiency by allowing the coexistence in harmony of primary users pus the legacy users with secondary users sus this coexistence is built on the premises that no su can generate interference higher than some prescribed limits against pus the system design based on perfect channel state information csi can easily end up violating the interference limits in a realistic situation where csi may be imperfect in this paper we propose a robust design of cr systems composed of multiple pus and multiple noncooperative sus in either single input single output siso frequency selective channels or more general multiple input multiple output mimo channels we formulate the design of the su network as a noncooperative game where the sus compete with each other over the resources made available by the pus by maximizing their own information rates subject to the transmit power and robust interference constraints following the philosophy of the worst case robustness we take explicitly into account the imperfectness of su to pu csi by adopting proper interference constraints that are robust with respect to the worst channel errors relying on the variational inequality theory we study the existence and uniqueness properties of the nash equilibria of the resulting robust games and devise totally asynchronous and distributed algorithms along with their convergency properties we also propose efficient numerical methods based on decomposition techniques to compute the robust transmit strategy for each su

no local broadcasting theorem for multipartite quantum correlations we prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled as long as it does not simply encode a multipartite classical probability distribution said quantumness is revealed by the new task of local broadcasting i e of locally sharing preestablished correlations which is feasible if and only if correlations are stricly classical our operational approach leads to natural definitions of measures for quantumness of correlations it also reproduces the standard no broadcasting theorem as a special case

separation principles in wireless networking a general wireless networking problem is formulated whereby end to end user rates routes link capacities transmit power frequency and power resources are jointly optimized across fading states even though the resultant optimization problem is generally nonconvex it is proved that the gap with its lagrange dual problem is zero so long as the underlying fading distribution function is continuous the major implication is that separating the design of wireless networks in layers and per fading state subproblems can be optimal subgradient descent algorithms are further developed to effect an optimal separation in layers and layer interfaces

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

arithmetic statistics of modular symbols mazur rubin and stein have recently formulated a series of conjectures about statistical properties of modular symbols in order to understand central values of twists of elliptic curve l functions two of these conjectures relate to the asymptotic growth of the first and second moments of the modular symbols we prove these on average by using analytic properties of eisenstein series twisted by modular symbols another of their conjectures predicts the gaussian distribution of normalized modular symbols ordered according to the size of the denominator of the cusps we prove this conjecture in a refined version that also allows restrictions on the location of the cusps

optimal linear precoding strategies for wideband non cooperative systems based on game theory part ii algorithms in this two part paper we address the problem of finding the optimal precoding multiplexing scheme for a set of noncooperative links sharing the same physical resources e g time and bandwidth we consider two alternative optimization problems p l the maximization of mutual information on each link given constraints on the transmit power and spectral mask and p 2 the maximization of the transmission rate on each link using finite order constellations under the same constraints as in p l plus a constraint on the maximum average error probability on each link aiming at finding decentralized strategies we adopted as optimality criterion the achievement of a nash equilibrium and thus we formulated both problems p l and p 2 as strategic noncooperative matrix valued games in part i of this two part paper after deriving the optimal structure of the linear transceivers for both games we provided a unified set of sufficient conditions that guarantee the uniqueness of the nash equilibrium in this part ii of the paper we focus on the achievement of the equilibrium and propose alternative distributed iterative algorithms that solve both games specifically the new proposed algorithms are the following 1 the sequential and simultaneous iterative waterfilling based algorithms incorporating spectral mask constraints and 2 the sequential and simultaneous gradient projection based algorithms establishing an interesting link with variational inequality problems our main contribution is to provide sufficient conditions for the global convergence of all the proposed algorithms which although derived under stronger constraints incorporating for example spectral mask constraints have a broader validity than the convergence conditions known in the current literature for the sequential iterative waterfilling algorithm

probabilistic broadcasting of mixed states it is well known that the non broadcasting theorem proved by barnum et al is a fundamental principle of quantum communication as we are aware optimal broadcasting ob is the only method to broadcast noncommuting mixed states approximately in this paper motivated by the probabilistic cloning of quantum states proposed by duan and guo we propose a new way for broadcasting noncommuting mixed states probabilistic broadcasting pb and we present a sufficient condition for pb of mixed states to a certain extent we generalize the probabilistic cloning theorem from pure states to mixed states and in particular we generalize the non broadcasting theorem since the case that commuting mixed states can be exactly broadcast can be thought of as a special instance of pb where the success ratio is 1 moreover we discuss probabilistic local broadcasting plb of separable bipartite states

averaged iterative water filling algorithm robustness and convergence the convergence properties of the iterative water filling iwf based algorithms have been derived in the ideal situation where the transmitters in the network are able to obtain the exact value of the interference plus noise ipn experienced at the corresponding receivers in each iteration of the algorithm however these algorithms are not robust because they diverge when there is time varying estimation error of the ipn a situation that arises in real communication system in this correspondence we propose an algorithm that possesses convergence guarantees in the presence of various forms of such time varying error moreover we also show by simulation that in scenarios where the interference is strong the conventional iwf diverges while our proposed algorithm still converges

vi constrained hemivariational inequalities distributed algorithms and power control in ad hoc networks we consider centralized and distributed algorithms for the numerical solution of a hemivariational inequality hvi where the feasible set is given by the intersection of a closed convex set with the solution set of a lower level monotone variational inequality vi the algorithms consist of a main loop wherein a sequence of one level strongly monotone hvis are solved that involve the penalization of the non vi constraint and a combination of proximal and tikhonov regularization to handle the lower level vi constraints minimization problems possibly with nonconvex objective functions over implicitly defined vi constraints are discussed in detail the methods developed in the paper are then used to successfully solve a new power control problem in ad hoc networks

quantum state separation unambiguous discrimination and exact cloning unambiguous discrimination and exact cloning reduce the square overlap between quantum states exemplifying the more general type of procedure we term state separation we obtain the maximum probability with which two equiprobable quantum states can be separated by an arbitrary degree and find that the established bounds on the success probabilities for discrimination and cloning are special cases of this general bound the latter also gives the maximum probability of successfully producing n exact copies of a quantum system whose state is chosen secretly from a known pair given m initial realizations of the state where n m we also discuss the relationship between this bound and that on unambiguous state discrimination

real and complex monotone communication games noncooperative game theoretic tools have been increasingly used to study many important resource allocation problems in communications networking smart grids and portfolio optimization in this paper we consider a general class of convex nash equilibrium problems neps where each player aims at solving an arbitrary smooth convex optimization problem differently from most of current works we do not assume any specific structure for the players problems and we allow the optimization variables of the players to be matrices in the complex domain our main contribution is the design of a novel class of distributed asynchronous best response algorithms suitable for solving the proposed neps even in the presence of multiple solutions the new methods whose convergence analysis is based on variational inequality vi techniques can select among all the equilibria of a game those that optimize a given performance criterion at the cost of limited signaling among the players this is a major departure from existing best response algorithms whose convergence conditions imply the uniqueness of the ne some of our results hinge on the use of vi problems directly in the complex domain the study of these new kind of vis also represents a noteworthy innovative contribution we then apply the developed methods to solve some new generalizations of single input single output siso and multiple input multiple output mimo games in cognitive radio systems showing a considerable performance improvement over classical pure noncooperative schemes

convex primal decomposition for multicarrier linear mimo transceivers the design of linear transceivers for multiple input multiple output mimo communication systems with channel state information is particularly challenging for two main reasons first since several substreams are established through the mimo channel it is not even clear how the quality of the system should be measured second once a cost function has been chosen to measure the quality the optimization of the system according to such criterion is generally difficult due to the nonconvexity of the problem recent results have solved the problem for the wide family of schur concave convex functions resulting in simple closed form solutions when the system is modeled as a single mimo channel however with several mimo channels such as in multi antenna multicarrier systems the solution is generally more involved leading in some cases to the need to employ general purpose interior point methods this problem is specifically addressed in this paper by combining the closed form solutions for single mimo channels with a primal decomposition approach resulting in a simple and efficient method for multiple mimo channels the extension to functions that are not schur concave convex is also briefly considered relating the present work with a recently proposed method to minimize the average bit error rate ber of the system

decomposition by partial linearization parallel optimization of multi agent systems we propose a novel decomposition framework for the distributed optimization of general nonconvex sum utility functions arising naturally in the system design of wireless multi user interfering systems our main contributions are i the development of the first class of inexact jacobi best response algorithms with provable convergence where all the users simultaneously and iteratively solve a suitably convexified version of the original sum utility optimization problem ii the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based instead on heuristics and iii a framework that can be easily particularized to well known applications giving rise to very efficient practical jacobi or gauss seidel algorithms that outperform existing ad hoc methods proposed for very specific problems interestingly our framework contains as special cases well known gradient algorithms for nonconvex sum utility problems and many block coordinate descent schemes for convex functions

design of cognitive radio systems under temperature interference constraints a variational inequality approach the concept of cognitive radio cr has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed primary and unlicensed secondary users in the same bandwidth in this paper we propose a novel nash equilibrium ne problem to model concurrent communications of cognitive secondary users who compete against each other to maximize their information rate the formulation contains constraints on the transmit power and possibly spectral masks as well as aggregate interference tolerable at the primary users receivers the coupling among the strategies of the players due to the interference constraints presents a new challenge for the analysis of this class of nash games that cannot be addressed using the game theoretical models proposed in the literature for this purpose we need the framework given by the more advanced theory of finite dimensional variational inequalities vi this provides us with all the mathematical tools necessary to analyze the proposed ne problem e g existence and uniqueness of the solution and to devise alternative distributed algorithms along with their convergence properties

joint sensing and power allocation in nonconvex cognitive radio games nash equilibria and distributed algorithms in this paper we propose a novel class of nash problems for cognitive radio cr networks modeled as gaussian frequency selective interference channels wherein each secondary user su competes against the others to maximize his own opportunistic throughput by choosing jointly the sensing duration the detection thresholds and the vector power allocation the proposed general formulation allows us to accommodate several transmit power and deterministic probabilistic interference constraints such as constraints on the maximum individual and or aggregate probabilistic interference tolerable at the primary receivers to keep the optimization as decentralized as possible global coupling interference constraints are imposed by penalizing each su with a set of time varying prices based upon his contribution to the total interference the prices are thus additional variable to optimize the resulting players optimization problems are nonconvex moreover there are possibly price clearing conditions associated with the global constraints to be satisfied by the solution all this makes the analysis of the proposed games a challenging task none of classical results in the game theory literature can be successfully applied the main contribution of this paper is to develop a novel optimization based theory for studying the proposed nonconvex games we provide a comprehensive analysis of the existence and uniqueness of a standard nash equilibrium devise alternative best response based algorithms and establish their convergence some of the proposed algorithms are totally distributed and asynchronous whereas some others require limited signaling among the sus in the form of consensus algorithms in favor of better performance overall they are thus applicable to a variety of cr scenarios either cooperative or noncooperative which allows the sus to explore the existing tradeoff between signaling and performance

energy efficient spectrum sharing strategy selection for cognitive mimo interference channels in this paper we propose a promising discrete game theoretic framework for distributed energy efficient discrete spectrum sharing strategy selection i e joint discrete power control and multimode precoding strategy selection with limited feedback for cognitive mimo interference channels given the competitive nature the secondary users are assumed to be selfish and noncooperative each of whom attempts to maximize its individual energy efficiency under a minimum data rate constraint and an interference power constraint a mechanism for shutting down links is proposed to reduce interference and save energy a payoff function is designed to guarantee the feasibility of the pure strategy nash equilibrium with no need to know the infeasible strategy profiles a spectrum sharing strategy profile is said to be feasible if the stated constraints are satisfied otherwise the spectrum sharing strategy profile is said to be infeasible i e they may not satisfy the interference power constraint and minimum data rate constraint in advance we then investigate the existence and the feasibility of the pure strategy nash equilibrium and further devise a pricing based distributed algorithm for spectrum strategy selection the proposed algorithm is proved to converge to a feasible pure strategy nash equilibrium under specific conditions moreover by studying the relationship between our proposed game and the social optimum we find that the pricing mechanism can result in pareto improvement and lead to better convergence for the proposed distributed algorithm numerical results show that our designed algorithm significantly outperforms the random selection algorithm and the pricing mechanism has a dramatic effect in improving the system performance