the structure of general interference functions and applications this paper provides a theoretical framework for the analysis of interference coupled multiuser systems the fundamental behavior of such a system is modeled by interference functions defined by axioms ldquononnegativity rdquoscale invariance rdquo and ldquomonotonicity rdquo it is shown that every interference function has an interpretation as the optimum of a min max problem where the optimization is over a closed comprehensive positive coefficient set this provides new insight into the structure of general interference functions and its elementary building blocks conversely it is shown that every closed comprehensive positive set can be expressed as a level set of an interference function this shows a close connection between the analysis of interference functions and multiuser performance regions which are typically closed comprehensive the generality of this framework allows for a wide range of potential applications as an example we analyze the problem of interference balancing

strict convexity of the feasible log sir region the feasible log sir region is defined as a set of all signal to interference ratios sir expressed in logarithmic scale that can be supported in a wireless network by means of power control and with all users being active concurrently recently the feasible log sir region was shown to be a convex set which is a key ingredient in the development of some power control strategies for wireless systems in this paper under the assumption of a noiseless channel we strengthen these results by proving a necessary and sufficient condition for the feasible log sir region to be a strictly convex set the strict convexity property is of interest since it is closely related to the problem of the existence and uniqueness of a so called log sir fair power vector

a calculus for log convex interference functions the behavior of certain interference coupled multiuser systems can be modeled by means of logarithmically convex log convex interference functions in this paper we show fundamental properties of this framework a key observation is that any log convex interference function can be expressed as an optimum over elementary log convex interference functions the results also contribute to a better understanding of certain quality of service qos tradeoff regions which can be expressed as sublevel sets of log convex interference functions we analyze the structure of the qos region and provide conditions for the achievability of boundary points the proposed framework of log convex interference functions generalizes the classical linear interference model which is closely connected with the theory of irreducible nonnegative matrices perron frobenius theory we discuss some possible applications in robust communication cooperative game theory and max min fairness

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

uplink downlink duality via minimax duality the sum capacity of a gaussian vector broadcast channel is the saddle point of a minimax gaussian mutual information expression where the maximization is over the set of transmit covariance matrices subject to a power constraint and the minimization is over the set of noise covariance matrices subject to a diagonal constraint this sum capacity result has been proved using two different methods one based on decision feedback equalization and the other based on a duality between uplink and downlink channels this paper illustrates the connection between the two approaches by establishing that uplink downlink duality is equivalent to lagrangian duality in minimax optimization this minimax lagrangian duality relation allows the optimal transmit covariance and the least favorable noise covariance matrices in a gaussian vector broadcast channel to be characterized in terms of the dual variables in particular it reveals that the least favorable noise is not unique further the new lagrangian interpretation of uplink downlink duality allows the duality relation to be generalized to gaussian vector broadcast channels with arbitrary linear constraints however duality depends critically on the linearity of input constraints duality breaks down when the input constraint is an arbitrary convex constraint this shows that the minimax representation of the broadcast channel sum capacity is more general than the uplink downlink duality representation

asymptotic secrecy outage performance for tas mrc over correlated nakagami m fading channels in this paper considering both the antenna correlation and the channel correlation between the legitimate receiver and the eavesdropper we comprehensively investigate the secrecy performance for transmit antenna selection and maximal ratio combining tas mrc scheme in a multi input multi output multi antenna eavesdropper mimome system different from the existing works the correlated legitimate channels and correlated eavesdropper channels experience nakagmai m fading with distinct fading parameters and are modeled as a combination of conditionally independent channel gains and independent channel gains by this novel correlation representation the combined effect of antenna correlation and channel correlation between the legitimate receiver and the eavesdropper on secrecy performance is quantified via the secrecy outage probability sop under a more general fading circumstance in addition two special cases of correlated channels are addressed in detail finally simulations are performed to verify our analysis the analysis and simulation results show that at high signal to noise ratio snr antenna correlation at the legitimate receiver can improve the sop performance for the correlated mimome wiretap channels and this finding is contrary to the conventional wisdom that antenna correlation degrades the sop performance

combinatorial characterization of interference coupling in wireless systems we provide a combinatorial characterization of interference coupling in wireless systems with the intent of obtaining a better insight into interference coordination and management we introduce two bipartite graphs namely the power graph and interference graph we utilize these graphs and global dependency matrix containing only binary 0 and 1 entries to capture the effects of interference coupling in communication systems we show that the irreducibility of the global dependency matrix g is related to the connectivity of the power graph and the irreducibility of the matrix ggt is related to the connectivity of the interference graph we prove that for strictly positive and strictly log convex interference functions the irreducibility of the matrices g and ggt are necessary and sufficient conditions for the considered utility sets to be strictly convex in this case there exists a unique optimizer for the problem of maximizing the product of utilities we show that an interference balancing function is strictly log convex if and only if matrices g and ggt are irreducible we provide a simple yet comprehensive combinatorial characterization of interference coupled systems which abstracts away certain complexities of the physical layer

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

the kullback leibler divergence and nonnegative matrices this correspondence establishes an interesting connection between the kullback leibler divergence and the perron root of nonnegative irreducible matrices in the second part of the correspondence we apply these results to the power control problem in wireless communications networks to show a fundamental tradeoff between fairness and efficiency a power vector is said to be efficient if it maximizes the overall network efficiency expressed in terms of an aggregate network utility function parameterized by some weight vector for two widely used examples of utility functions the correspondence identifies the unique weight vector for which a power vector is both efficient and max min fair in the sense that each communication link has the same quality of service these results also give rise to new saddle point characterizations of the perron root

achievable rates of multi antenna downlink channels with peak power constraints this paper considers a gaussian multiple input single output miso broadcast channel with a per antenna peak power constraint or simply peak power constraint it is more realistic to consider the peak power constraint on each transmit antenna because in many practical implementations each antenna is equipped with its own power amplifier assuming the perfect knowledge of the channel state information csi at the transmitter we propose an achievable scheme using dirty tape coding dtc the ideal dirty paper coding dpc which is a capacity achieving scheme for the gaussian multiple input multiple output mimo broadcast channel cannot be used for our model because its optimal input distribution is gaussian and thus the peak power constraint is violated on the other hand the channel input of dtc is uniformly distributed in a fixed range which helps to control the peak power of the transmit signal easily we also present an algorithm that finds capacity achieving beamforming vectors and power allocation factors under a per antenna average power constraint and use the optimized parameters in the proposed scheme simulation results show that the proposed scheme provides gains of 2 7db over a non dtc scheme based on minimum mean square error mmse beamforming at high signal to noise ratio snr when there are three receivers and the transmitter has three antennas

a generalization of nash bargaining and proportional fairness to log convex utility sets with power constraints many solutions and concepts in resource allocation and game theory rely on the assumption of a convex utility set in this paper we show that the less restrictive assumption of a logarithmic hidden convexity is sometimes sufficient we consider the problems of nash bargaining and proportional fairness which are closely related we extend the nash bargaining framework to a broader family of log convex sets we then focus on the set of feasible signal to interference plus noise ratios sinrs for the cases of individual power constraints and a sum power constraint under the assumption of log convex interference functions we show how pareto optimality of boundary points depends on the interference coupling between the users finally we provide necessary and sufficient conditions for strict log convexity of the feasible sinr region

concave and convex interference functions general characterizations and applications many resource allocation problems can be studied within the framework of interference functions basic properties of interference functions are non negativity scale invariance and monotonicity in this paper we study interference functions with additional properties namely convexity concavity and log convexity such interference functions occur naturally in various contexts e g adaptive receive strategies robust power control or resource allocation over convex utility sets we show that every convex resp concave interference function can be expressed as a maximum resp minimum over a weighted sum of its arguments this analytical insight provides a link between the axiomatic interference framework and conventional interference models that are based on the definition of a coupling matrix we show how the results can be used to derive best possible convex concave approximations for general interference functions the results have further application in the context of feasible sets of multiuser systems convex approximations for general feasible sets are derived finally we show how convexity can be exploited to solve the problem of signal to interference plus noise ratio sinr constrained power minimization with super linear convergence

derivatives of the perron root at an essentially nonnegative matrix and the group inverse of an m matrix abstract the results of the work in this paper can be divided into two major parts in the first part we develop formulae using group inverses of irreducible m matrices for the second order partial derivatives with respect to the entries of the perron root r at an essentially nonnegative and irreducible matrix a we use these formulae to obtain explicit expressions for the matrices 2 r a ij 2 and 2 r a ii jj and examine these expressions at some special cases when for example in addition to a being essentially nonnegative and irreducible a is row stochastic or a is of rank 1 and so on in the second major part of this paper we investigate for a singular and irreducible m matrix q a certain matrix g which is a positive diagonal scaling of the group inverse q of q we show for instance that z gz 0 for all real vectors z and use this result and some of the formulae obtained in the first part of the paper to provide a matrix theoretic proof of a theorem due to j e cohen math proc cambridge philos soc 86 1979 343 350 which states that for an essentially nonnegative and irreducible matrix a the perron root is a convex function of the main diagonal of a

testing against constant factor loading matrix with large panel high frequency data abstract in this paper we introduce a nonparametric test against the constancy of the factor loading matrix of a high dimensional continuous time factor model using high frequency data the central limit theorems on the test statistics with and without perturbation are established under the null hypothesis that the factor loading matrix is constant as time evolves the tests perform well in size and power interestingly the test statistic without perturbation converges at a rate that depends not only on the sample size but also on the dimension through the cross sectional dependence of the residual process which is a distinctive feature that contrasts with the low dimensional setting extensive numerical studies including monte carlo simulations and real data analysis validate the performance of our test

capacity equivocation region of the gaussian mimo wiretap channel we study the gaussian multiple input multiple output mimo wiretap channel which consists of a transmitter a legitimate user and an eavesdropper in this channel the transmitter sends a common message to both the legitimate user and the eavesdropper in addition to this common message the legitimate user receives a private message which is desired to be kept hidden as much as possible from the eavesdropper we obtain the entire capacity equivocation region of the gaussian mimo wiretap channel this region contains all achievable common message private message and private message s equivocation secrecy rates in particular we show the sufficiency of jointly gaussian auxiliary random variables and channel input to evaluate the existing single letter description of the capacity equivocation region due to csiszar korner

on a special class of broadcast channels with confidential messages it is shown that csiszar and korner s 1978 characterization of a discrete memoryless channel dmc x spl rarr y as being less noisy than the dmc x spl rarr z is equivalent to the condition that the mutual information difference i x y i x z be a convex spl cap function of the probability distribution for x this result is used to obtain a simple determination of the capacity region of the broadcast channel with confidential messages bcc which is a dmc x spl rarr y z when the dmc x spl rarr y to the legitimate receiver is less noisy than the dmc x spl rarr z to the enemy cryptanalyst and there is a probability distribution for x having strictly positive components that achieves capacity on both these channels in particular when these dmc s are both symmetric then the secrecy capacity of the bcc is the difference of their capacities it is shown further that the less noisy condition in this result cannot be weakened to the condition that the dmc x spl rarr y be more capable than the dmc x spl rarr z in the sense of csiszar and korner

perron root minimization for interference coupled systems with adaptive receive strategies interference in multiuser systems is often characterized by a non negative and irreducible coupling matrix the maximum eigenvalue perron root of the weighted coupling matrix provides a single measure for the joint achievability of certain signal to interference ratios sir in this paper we address the more general case where the users are coupled by concave interference functions this corresponds to a system with adaptive receive strategies which minimize the interference received by each user a necessary and sufficient condition for feasibility is obtained by minimizing the perron root over the set of possible receive strategies this type of problem is directly related to the problem of weighted max min sir balancing this paper provides an analytical framework and an iterative algorithm that converges monotonically to a global optimum we also study an alternative approach based on a fixed point iteration this iteration is shown to converge to the global optimum if the sir targets lie on the boundary of the region

on the convexity of feasible qos regions the feasible quality of service qos region is the set of all qos vectors that can be provided to the users by means of power control with interference treated as noise in an interference limited scenario this set is determined by the perron root of some qos dependent nonnegative matrix in a previous work we showed that if the signal to interference ratio sir is a log convex function of the qos then the perron root is a log convex function this implies convexity of the feasible qos region in this correspondence we prove that the log convexity property is also necessary for the perron root to be convex for any choice of the path gain matrix interestingly a significantly less restrictive property is sufficient when the gain matrix is confined to be symmetric positive semidefinite

sum capacity of gaussian vector broadcast channels this paper characterizes the sum capacity of a class of potentially nondegraded gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers coordination is allowed among the transmit terminals but not among the receive terminals the sum capacity is shown to be a saddle point of a gaussian mutual information game where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information the sum capacity is achieved using a precoding strategy for gaussian channels with additive side information noncausally known at the transmitter the optimal precoding structure is shown to correspond to a decision feedback equalizer that decomposes the broadcast channel into a series of single user channels with interference pre subtracted at the transmitter

transmitter optimization for per antenna power constrained multi antenna downlinks an slnr maximization methodology in this paper we consider signal to leakage plus noise ratio slnr maximized precoding for multi antenna downlinks under per antenna power constraints papcs in contrast to the conventional sum power constraint the per antenna power constrained slnr precoder design problem no longer admits a simple closed form solution and achieving its optimal solution turns out to be much more challenging to conquer the difficulty we first propose to perform the charnes cooper transformation on the problem of interest which yields a solvable simpler second order cone program socp moving beyond this approach we are then able to obtain a semi closed form solution to the optimal slnr precoder the power allocation among users is also optimized for further performance enhancement for which we devise two numerical methods based on gradient projection and a low complexity approximation finally focusing on the imperfect channel state information csi scenario we develop a robust slnr based precoder to combat the performance degradation caused by random csi errors the superiority of all proposed precoder designs in this work is confirmed by numerical simulations

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

characterization of convex and concave resource allocation problems in interference coupled wireless systems this paper investigates the possibility of having convex or concave formulations of optimization problems for interference coupled wireless systems an axiomatic framework for interference functions proposed by yates in 1995 is used to model interference coupling in our paper the paper shows that under certain natural assumptions the exponential transformation is the unique transformation up to a positive constant for convexification of resource allocation problems for linear interference functions furthermore it is shown that under certain intuitive assumptions it is sufficient to check for the joint concavity convexity of sum of weighted functions of sinr inverse sinr with respect to s p es where p is the power vector of the users if we would like the resulting resource allocation problem to be concave convex this paper characterizes the largest class of utility functions and the largest class of interference functions respectively which allow a convex and concave formulation of a problem for interference coupled wireless systems it extends previous literature on log convex interference functions and provides boundaries on the class of problems in wireless systems which can be algorithmically tackled by convex optimization techniques

bounds on secrecy capacity over correlated ergodic fading channels at high snr we investigate the secrecy capacity of an ergodic fading wiretap channel when the main and eavesdropper channels are correlated assuming that the transmitter knows the full channel state information csi i e the channel gains from the transmitter to the legitimate receiver and eavesdropper we quantify the loss of the secrecy capacity due to the correlation and investigate the asymptotic behavior of the secrecy capacity in the high signal to noise ratio snr regime while the ergodic capacity of fading channels grows logarithmically with snr in general we have found that the secrecy capacity converges to an upper bound a closed form expression is derived that will be shown to be a function of two channel parameters the correlation coefficient and the ratio of the main to eavesdropper channel gains from this we are able to see how the two channel parameters affect the secrecy capacity and conclude that the excessively large signal power does not help to improve the secrecy capacity and the loss due to the correlation could be significant especially when the ratio of the main to eavesdropper channel gains is low

the secrecy capacity of the mimo wiretap channel we consider the mimo wiretap channel that is a mimo broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver while the other user is an eavesdropper perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate while insuring that the eavesdropper gets zero bits of information in this paper we compute the perfect secrecy capacity of the multiple antenna mimo broadcast channel where the number of antennas is arbitrary for both the transmitter and the two receivers our technique involves a careful study of a sato like upper bound via the solution of a certain algebraic riccati equation

exact bayesian moment based inference for the distribution of the small time movements of an ito semimartingale abstract we modify the gallant and tauchen 1996 efficient method of moments emm method to perform exact bayesian inference where exact means no reliance on asymptotic approximations we use this modification to evaluate the empirical plausibility of recent predictions from high frequency financial theory regarding the small time movements of an ito semimartingale the theory indicates that the probability distribution of the small moves should be locally stable around the origin it makes no predictions regarding large rare jumps which get filtered out our exact bayesian procedure imposes support conditions on parameters as implied by this theory the empirical application uses s p index options extending over a wide range of moneyness including deep out of the money puts the evidence is consistent with a locally stable distribution valid over most of the support of the observed data while mildly failing in the extreme tails about which the theory makes no prediction we undertake diagnostic checks on all aspects of the procedure in particular we evaluate the distributional assumptions regarding a semi pivotal statistic and we test by monte carlo that the posterior distribution is properly centered with short credibility intervals taken together our results suggest a more important role than previously thought for pure jump like models with diminished if not absent diffusive component

design guidelines for limited feedback in the spatially correlated broadcast channel a linear beamformer design for the broadcast channel where the base station is equipped with n t antennas and signals to m 2 users each with a single antenna and where the vector channels are spatially correlated is considered this problem is of relevance in wireless standardization efforts where two users are simultaneously scheduled instead of the theoretically feasible n t user scheduling to minimize signaling overhead the users are assumed to have perfect channel state information csi whereas the base station has statistical information of the channels in the first part of this work the role of the relevance of feedback is studied via the quantification of the gap in ergodic sum rate between the perfect csi and statistics only extremes in this direction the importance of orthogonality of the dominant eigenmodes of the two users in maximizing the gap is established in the second part of this work in scenarios with a large gap limited feedback beamforming codebooks and a codeword selection metric are designed for the low rate feedback setting the main contribution here is the proposal of a generalized eigenvector codebook and feedback of the codeword index that maximizes an estimate of the signal to interference and noise ratio textsf sinr of each user extensions of this scheme are also proposed for the general n t antenna case with m users where m le n t it is shown via numerical studies that this scheme leads to significant performance improvement across a large family of channels over schemes such as grassmannian random vector quantization single user codebooks with the channel projection metric for codeword selection

network mimo with linear zero forcing beamforming large system analysis impact of channel estimation and reduced complexity scheduling we consider the downlink of a multicell system with multiantenna base stations and single antenna user terminals arbitrary base station cooperation clusters distance dependent propagation pathloss and general fairness requirements base stations in the same cooperation cluster employ joint transmission with linear zero forcing beamforming subject to sum or per base station power constraints intercluster interference is treated as noise at the user terminals analytic expressions for the system spectral efficiency are found in the large system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio in particular for the per base station power constraint we find new results in random matrix theory yielding the squared frobenius norm of submatrices of the moore penrose pseudo inverse for the structured non i i d channel matrix resulting from the cooperation cluster user distribution and path loss coefficients the analysis is extended to the case of nonideal channel state information at the transmitters obtained through explicit downlink channel training and uplink feedback specifically our results illuminate the trade off between the benefit of a larger number of cooperating antennas and the cost of estimating higher dimensional channel vectors furthermore our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large system results depending on the desired fairness criterion the proposed scheme performs close to the optimal finite dimensional opportunistic user selection while requiring significantly less channel state feedback since only a small fraction of preselected users must feed back their channel state information