improved estimation of eigenvalues and eigenvectors of covariance matrices using their sample estimates the problem of estimating the eigenvalues and eigenvectors of the covariance matrix associated with a multivariate stochastic process is considered the focus is on finite sample size situations whereby the number of observations is limited and comparable in magnitude to the observation dimension using tools from random matrix theory and assuming a certain eigenvalue splitting condition new estimators of the eigenvalues and eigenvectors of the covariance matrix are derived that are shown to be consistent in a more general asymptotic setting than the traditional one indeed these estimators are proven to be consistent not only when the sample size increases without bound for a fixed observation dimension but also when the observation dimension increases to infinity at the same rate as the sample size numerical evaluations indicate that the estimators have an excellent performance in small sample size scenarios where the observation dimension and the sample size are comparable in magnitude

on the pareto optimal beam structure and design for multi user mimo interference channels in this paper the pareto optimal beam structure for multi user multiple input multiple output mimo interference channels is investigated and a necessary condition for any pareto optimal transmit signal covariance matrix is presented for the k pair gaussian mimo interference channel it is shown that any pareto optimal transmit signal covariance matrix at a transmitter should have its column space contained in the union of the signal spaces of the channel matrices from the transmitter to all receivers based on this necessary condition an efficient parameterization for the beam search space is proposed the proposed parameterization is given by the product manifold of a stiefel manifold and a subset of a hyperplane and enables us to construct an efficient beam design algorithm by exploiting its rich geometrical structure and existing tools for optimization on stiefel manifolds reduction in the beam search space dimension and computational complexity by the proposed parameterization and the proposed beam design approach is significant when the number of transmit antennas is much larger than the sum of the numbers of receive antennas as in upcoming cellular networks adopting massive mimo technologies numerical results validate the proposed parameterization and the proposed cooperative beam design method based on the proposed parameterization for mimo interference channels

joint fronthaul link selection and transmit precoding for energy efficiency maximization of multiuser mimo aided distributed antenna systems we jointly select the fronthaul links and optimize the transmit precoding matrices for maximizing the energy efficiency ee of a multiuser multiple input multiple output aided distributed antenna system the fronthaul link s power consumption is taken into consideration which is assumed to be proportional to the number of active fronthaul links quantified by using indicator functions both the rate requirements and the power constraints of the remote access units are considered under realistic power constraints some of the users cannot be admitted hence we formulate a two stage optimization problem in stage i a novel user selection method is proposed for determining the maximum number of admitted users in stage ii we deal with the ee optimization problem first the indicator function is approximated by a smooth concave logarithmic function second a triple layer iterative algorithm is proposed for solving the approximated ee optimization problem which is proved to converge to the karush kuhn tucker conditions of the smoothened ee optimization problem to further reduce the complexity a single layer iterative algorithm is conceived which guarantees convergence our simulation results show that the proposed user selection algorithm approaches the performance of the exhaustive search method finally the proposed algorithms are capable of achieving an order of magnitude higher ee than its conventional counterpart operating without considering link selection

a deterministic equivalent for the analysis of correlated mimo multiple access channels in this article novel deterministic equivalents for the stieltjes transform and the shannon transform of a class of large dimensional random matrices are provided these results are used to characterize the ergodic rate region of multiple antenna multiple access channels when each point to point propagation channel is modelled according to the kronecker model specifically an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water filling algorithm to obtain these precoders are provided an original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides the above results are validated by monte carlo simulations

unitary beamformer designs for mimo interference broadcast channels interference broadcast channel ibc is a generalized scenario for interference channel ic where each base station bs transmits to multiple users in its own cell while sharing same time frequency resources with other adjacent bss in this case it has been shown that by using interference alignment ia and under the availability of perfect channel state information csi the achievable degrees of freedom dofs can be linearly scaled up with the number of users however in the presence of imperfect csi the sum rate becomes degraded and the achievability of full dof can not be guaranteed in this paper considering a multiple input multiple output mimo ibc with constant channel coefficients we propose ia algorithms that result in unitary beamformers first we consider two improved beamformer designs based on minimizing the weighted leakage interference min wli and maximizing the signal to interference plus noise ratio max sinr second we propose a novel minimum mean square error mmse based ia algorithm both the improved max sinr and the mmse based ia schemes are optimized upon the knowledge of the channel estimation error variance so as to achieve better performance under csi mismatch we then demonstrate that these two schemes outperform min wli and the conventional max sinr ia under perfect and imperfect csi furthermore it is shown that the mmse based ia achieves the same performance trend as the improved max sinr ia does however the former needs less csi to be available and has less computational complexity compared to the latter moreover it is established that the mmse based ia can result in diagonalized decoupled subchannels under perfect csi the superiority of the proposed algorithms over the conventional schemes is corroborated by numerical simulations

sum rate maximization in the multicell mimo broadcast channel with interference coordination this paper studies the precoding designs to maximize the weighted sum rate wsr in a multicell multiple input multiple output mimo broadcast channel bc we consider a multicell network under universal frequency reuse with multiple mobile stations ms per cell with interference coordination ic between the multiple cells the base station bs at each cell only transmits information signals to the mss within its cell using the dirty paper coding dpc technique while coordinating the inter cell interference ici induced to other cells the main focus of this work is to jointly optimize the encoding covariance matrices across the bss in order to maximize the network wide wsr since this optimization problem is shown to be nonconvex obtaining its globally optimal solution is highly complicated to address this problem we consider two low complexity solution approaches with distributed implementation to obtain at least locally optimal solutions in the first approach by applying a successive convex approximation technique the original nonconvex problem is decomposed into a sequence of simpler problems which can be solved optimally and separately at each bs in the second approach the wsr problem is solved via an equivalent problem of weighted sum mean squared error minimization both solution approaches will unfold the control signaling among the coordinated bss to allow their distributed implementation simulation results confirm the convergence of the proposed algorithms as well as their superior performances over schemes with linear precoding or no interference coordination among the bss

comparison of distributed beamforming algorithms for mimo interference networks this paper presents a comparative study of algorithms for jointly optimizing beamformers and receive filters in an interference network where each node may have multiple antennas each user transmits at most one data stream and interference is treated as noise we focus on techniques that seek good suboptimal solutions by means of iterative and distributed updates those include forward backward iterative algorithms max signal to interference plus noise ratio sinr and interference leakage weighted sum mean squared error mse algorithms and interference pricing with incremental signal to noise ratio snr adjustments we compare their properties in terms of convergence and information exchange requirements and then numerically evaluate their sum rate performance averaged over random stationary channel realizations the numerical results show that the max sinr algorithm achieves the maximum degrees of freedom i e supports the maximum number of users with near zero interference and exhibits better convergence behavior at high snrs than the weighted sum mse algorithms however it assumes fixed power per user and achieves only a single point in the rate region whereas the weighted sum mse criterion gives different points in contrast the incremental snr algorithm adjusts the beam powers and deactivates users when interference alignment is infeasible furthermore that algorithm can provide a slight increase in sum rate relative to max sinr at the cost of additional iterations

a unified convergence analysis of block successive minimization methods for nonsmooth optimization the block coordinate descent bcd method is widely used for minimizing a continuous function f of several block variables at each iteration of this method a single block of variables is optimized while the remaining variables are held fixed to ensure the convergence of the bcd method the subproblem of each block variable needs to be solved to its unique global optimal unfortunately this requirement is often too restrictive for many practical scenarios in this paper we study an alternative inexact bcd approach which updates the variable blocks by successively minimizing a sequence of approximations of f which are either locally tight upper bounds of f or strictly convex local approximations of f the main contributions of this work include the characterizations of the convergence conditions for a fairly wide class of such methods especially for the cases where the objective functions are either nondifferentiable or nonconvex our results unify and extend the existing convergence results

the determinant of a fuzzy matrix with respect to t and co t norms abstract we study determinants of square matrices over the interval 0 1 when ordinary multiplication is replaced by a triangular norm and ordinary addition is replaced by a triangular conorm

the determinant and adjoint of a square fuzzy matrix abstract the theory of the determinant and adjoint of a square fuzzy matrix will be studied also we define the circular fuzzy matrices and show that some properties of a square fuzzy matrix such as reeflexivity transitivity circularity are carried over to the adjoint of the matrix finally we show how to construct a transitive fuuzzy matrix from a given one through the adjoint matrix

laplace maps and constraints for a class of third order partial differential operators we explore the existence of a class of generalised laplace maps for third order partial differential operators of the form 1 2 3 a1 2 3 a2 1 3 a3 1 2 a12 3 a23 1 a13 2 a123 and related first order 3 systems and show that they require the satisfaction of constraints on the invariants for such operators

cell edge aware precoding for downlink massive mimo cellular networks we propose a cell edge aware cea zero forcing zf precoder that exploits the excess spatial degrees of freedom provided by a large number of base station bs antennas to suppress inter cell interference at the most vulnerable user equipments ues we evaluate the downlink performance of cea zf as well as that of a conventional cell edge unaware ceu zf precoder in a network with a random bs topology our analysis and simulations show that the proposed cea zf precoder outperforms ceu zf precoding in terms of i aggregate per cell data rate ii coverage probability and iii 95 likely or edge user rate in particular when both perfect channel state information and a large number of antennas n are available at the bss we demonstrate that the outage probability under cea zf and ceu zf decay as 1 n 2 and 1 n respectively this result identifies cea zf as a more effective precoding scheme for massive multiple input multiple output mimo cellular networks our framework also reveals the importance of scheduling the optimal number of ues per bs and confirms the necessity to control the amount of pilot contamination received during the channel estimation phase

distributed low overhead schemes for multi stream mimo interference channels our aim in this paper is to propose fully distributed schemes for transmit and receive filter optimization the novelty of the proposed schemes is that they only require a few forward backward iterations thus causing minimal communication overhead for that purpose we relax the well known leakage minimization problem and then propose two different filter update structures to solve the resulting nonconvex problem though one leads to conventional full rank filters the other results in rank deficient filters that we exploit to gradually reduce the transmit and receive filter rank and greatly speed up the convergence furthermore inspired from the decoding of turbo codes we propose a turbo like structure to the algorithms where a separate inner optimization loop is run at each receiver in addition to the main forward backward iteration in that sense the introduction of this turbo like structure converts the communication overhead required by conventional methods to computational overhead at each receiver a cheap resource allowing us to achieve the desired performance under a minimal overhead constraint finally we show through comprehensive simulations that both proposed schemes hugely outperform the relevant benchmarks especially for large system dimensions

operators that preserve semiring matrix functions abstract characterizations are obtained of those linear operators over certain semirings that preserve 1 the rth coefficient of the rook polynomial those that preserve 2 the term rank of matrices with term rank r and those that preserve 3 the rth elementary symmetric permanental function our results apply to many algebraic systems of combinatorial interest including the nonnegative integer matrices boolean matrices and fuzzy matrices

optimal energy efficient transmit beamforming for multi user miso downlink this paper studies beamforming techniques for energy efficiency maximization eemax in multiuser multiple input single output miso downlink system for this challenging nonconvex problem we first derive an optimal solution using branch and reduce and bound brb approach we also propose two low complexity approximate designs the first one uses the well known zero forcing beamforming zfbf to eliminate inter user interference so that the eemax problem reduces to a concave convex fractional program particularly the problem is then efficiently solved by closed form expressions in combination with the dinkelbach s approach in the second design we aim at finding a stationary point using the sequential convex approximation sca method by proper transformations we arrive at a fast converging iterative algorithm where a convex program is solved in each iteration we further show that the problem in each iteration can also be approximated as a second order cone program socp allowing for exploiting computationally efficient state of the art socp solvers numerical experiments demonstrate that the second design converges quickly and achieves a near optimal performance to further increase the energy efficiency we also consider the joint beamforming and antenna selection jbas problem for which two designs are proposed in the first approach we capitalize on the perspective reformulation in combination with continuous relaxation to solve the jbas problem in the second one sparsity inducing regularization is introduced to approximate the jbas problem which is then solved by the sca method numerical results show that joint beamforming and antenna selection offers significant energy efficiency improvement for large numbers of transmit antennas

per stream mse based linear transceiver design for mimo interference channels with csi error this paper studies the linear transceiver design for multi stream multiple input multiple output mimo interference channels with imperfect channel state information csi two csi error models are considered the same coding and modulation scheme is assumed for all users and data streams in the first model where the csi error is statistical we minimize the average maximum per stream mean square error mse in the second model where the csi error is norm bounded the worst case maximum per stream mse is optimized since the problems are not jointly convex the alternate optimization approach is adopted to obtain suboptimal transceivers for the statistical csi error a low complexity algorithm utilizing lagrangian duality is proposed which has a semi closed form solution and can be implemented distributively compared with the classical algorithm using the second order cone programming the proposed algorithm significantly reduces the computational complexity without sacrificing the performance for the bounded csi error we present two approaches one uses s procedure to obtain an equivalent problem and the other one solves an approximated problem simulation results demonstrate the robustness of the proposed algorithms and their improved performance over the sum mse and the maximum per user mse based methods the lower complexity of the lagrangian duality based algorithm is also verified numerically

traffic aware resource allocation schemes for multi cell mimo ofdm systems we consider a downlink multi cell multiple input multiple output mimo interference broadcast channel ibc using orthogonal frequency division multiplexing ofdm with multiple users contending for space frequency resources in a given scheduling instant the problem is to design precoders efficiently to minimize the number of backlogged packets queuing in the coordinating base stations bss conventionally the queue weighted sum rate maximization q wsrm formulation with the number of backlogged packets as the corresponding weights is used to design the precoders in contrast we propose joint space frequency resource allocation jsfra formulation in which the precoders are designed jointly across the space frequency resources for all users by minimizing the total number of backlogged packets in each transmission instant thereby performing user scheduling implicitly since the problem is nonconvex we use the combination of successive convex approximation sca and alternating optimization ao to handle nonconvex constraints in the jsfra formulation in the first method we approximate the signal to interference plus noise ratio sinr by convex relaxations while in the second approach the equivalence between the sinr and the mean squared error mse is exploited we then discuss the distributed approaches for the centralized algorithms using primal decomposition and alternating directions method of multipliers finally we propose a more practical iterative precoder design by solving the karush kuhn tucker expressions for the mse reformulation that requires minimal information exchange for each update numerical results are used to compare the proposed algorithms to the existing solutions

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

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

cooperative multicell zero forcing beamforming in cellular downlink channels in this work a multicell cooperative zero forcing beamforming zfbf scheme combined with a simple user selection procedure is considered for the wyner cellular downlink channel the approach is to transmit to the user with the ldquobestrdquo local channel in each cell the performance of this suboptimal scheme is investigated in terms of the conventional sum rate scaling law and the sum rate offset for an increasing number of users per cell we term this characterization of the sum rate for large number of users as high load regime characterization and point out the similarity of this approach to the standard affine approximation used in the high signal to noise ratio snr regime it is shown that under an overall power constraint the suboptimal cooperative multicell zfbf scheme achieves the same sum rate growth rate and slightly degraded offset law when compared to an optimal scheme deploying joint multicell dirty paper coding dpc asymptotically with the number of users per cell moreover the overall power constraint is shown to ensure in probability equal per cell power constraints when the number of users per cell increases

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

determinant theory for fuzzy matrices abstract we study determinant theory for fuzzy square matrices including some boolean matrices and consider the cayley hamilton theorem for these matrices we prove that det a adj a det a det adj a a where adj a denotes the adjoint matrix of a fuzzy matrix a

multicell coordinated beamforming with rate outage constraint part i complexity analysis this paper studies the coordinated beamforming cobf design in the multiple input single output interference channel assuming only channel distribution information given a priori at the transmitters the cobf design is formulated as an optimization problem that maximizes a predefined system utility e g the weighted sum rate or the weighted max min fairness mmf rate subject to constraints on the individual probability of rate outage and power budget while the problem is non convex and appears difficult to handle due to the intricate outage probability constraints so far it is still unknown if this outage constrained problem is computationally tractable to answer this we conduct a computational complexity analysis of the outage constrained cobf problem specifically we show that the outage constrained cobf problem with the weighted sum rate utility is intrinsically difficult i e np hard moreover the outage constrained cobf problem with the weighted mmf rate utility is also np hard except the case when all the transmitters are equipped with single antenna the presented analysis results confirm that efficient approximation methods are indispensable to the outage constrained cobf problem

the capacity and optimal signaling for gaussian mimo channels under interference constraints gaussian mimo channel under the joint transmit tx and interference power constraints tpc and ipc is studied a closed form solution for the optimal tx covariance matrix in the general case is obtained using the kkt based approach up to dual variables a number of more explicit closed form solutions are given with optimal dual variables including full rank and rank 1 beamforming cases as well as the case of identical eigenvectors typical for massive mimo settings which differer significantly from the standard water filling solution a whitening filter is shown to be an important part of optimal precoding under interference constraints sufficient and necessary conditions for each constraint to be redundant are given capacity scaling with the snr is shown to be determined by a natural linear algebraic structure of sub spaces induced by channel matrices of multiple users a number of unusual properties of optimal tx covariance matrix under the joint tpc and ipc are pointed out and a bound on its rank is established an interplay between the tpc and ipc is studied including the transition from power limited to interference limited regimes as the tx power increases while closed from solutions for optimal dual variables are given in some special cases an iterative bisection algorithm iba is proposed to find optimal dual variables in the general case and its convergence is proved for some special cases numerical experiments illustrate its efficient performance bounds for the optimal dual variables are given

no eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices let b n 1 n t n 1 2 x n x n t n 1 2 where x n is n times n with i i d complex standardized entries having finite fourth moment and t n 1 2 is a hermitian square root of the nonnegative definite hermitian matrix t n it is known that as n to infty if n n converges to a positive number and the empirical distribution of the eigenvalues of t n converges to a proper probability distribution then the empirical distribution of the eigenvalues of b n converges a s to a nonrandom limit in this paper we prove that under certain conditions on the eigenvalues of t n for any closed interval outside the support of the limit with probability 1 there will be no eigenvalues in this interval for all n sufficiently large

asymptotic analysis of rzf in large scale mu mimo systems over rician channels in this paper we focus on the downlink ergodic sum rate of a single cell large scale multiuser mimo system in which the base station employs n antennas to communicate with k single antenna user equipments ues a regularized zero forcing rzf scheme is used for precoding under the assumption that each ue uses a specific power and each link forms a spatially correlated mimo rician fading channel the analysis is conducted assuming that n and k grow large with a given ratio and perfect channel state information is available at the base station new results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal to interference plus noise ratio as a function of system parameters spatial correlation matrix and rician factor numerical results are used to validate the accuracy of asymptotic approximations in the finite system regime and to evaluate the performance under different operating conditions it turns out that the asymptotic expressions provide accurate approximations even for relatively small values of n and k

maximization of worst case weighted sum rate for miso downlink systems with imperfect channel knowledge the problem of robust weighted sum rate maximization wsrmax in multicell downlink multi input single output systems is considered we assume that channel state information csi of all users is imperfectly known at the base stations the problem is known to be np hard even in the case of perfect csi we propose optimal and suboptimal but fast converging algorithms for wsrmax problem with csi errors assuming bounded ellipsoidal model for the csi errors we optimize the worst case weighted sum rate the proposed optimal algorithm is based on branch and bound bb technique and it globally solves the worst case wsrmax problem with an optimality certificate as the convergence speed of the bb method can be slow for large networks we also provide a fast but possibly suboptimal algorithm based on alternating optimization technique and sequential convex programming the optimal bb based algorithm can be used to provide performance benchmarks for any suboptimal algorithm numerical results show that the convergence speed of the suboptimal algorithm is fast and it finds a close to optimal solution in only a few iterations

decentralized sum rate maximization with qos constraints for interfering broadcast channel via successive convex approximation weighted sum rate maximization wsrmax with user specific quality of service qos constraints and general convex transmit power constraints is considered in multi cell multi user multiple input multiple output system the particular focus in the proposed joint transmitter receiver design is on tractability in terms of implementation and moderately fast changing time correlated channel conditions the non convex transmit precoder design problem is formulated as a difference of convex functions program for which a locally optimal solution is achieved by successive convex approximation sca to achieve practically realizable designs two decentralized approaches with low signaling overhead are proposed primal decomposition based solution provides better compliance of the provided qos constraints in slowly fading channel conditions on the other hand solution based on lagrangian relaxation of the coupling rate constraints is proposed for relaxed feasibility conditions and improved convergence properties as a special case an iterative solution via the karush kuhn tucker conditions of the precoder design problem with per base station transmit power constraints is also proposed finally we propose a heuristic extension of the sca method which is shown to significantly improve the rate of convergence while achieving comparable sum rate with recently published methods

mimo interference alignment over correlated channels with imperfect csi interference alignment ia given uncorrelated channel components and perfect channel state information obtains the maximum degrees of freedom in an interference channel little is known however about how the sum rate of ia behaves at finite transmit power with imperfect channel state information or antenna correlation this paper provides an approximate closed form signal to interference plus noise ratio sinr expression for ia over multiple input multiple output mimo channels with imperfect channel state information and transmit antenna correlation assuming linear processing at the transmitters and zero forcing receivers random matrix theory tools are utilized to derive an approximation for the postprocessing sinr distribution of each stream for each user perfect channel knowledge and i i d channel coefficients constitute special cases this sinr distribution not only allows easy calculation of useful performance metrics like sum rate and symbol error rate but also permits a realistic comparison of ia with other transmission techniques more specifically ia is compared with spatial multiplexing and beamforming and it is shown that ia may not be optimal for some performance criteria

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

an iteratively weighted mmse approach to distributed sum utility maximization for a mimo interfering broadcast channel consider the multiple input multiple output mimo interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to each other the basic problem is to design linear beamformers that can maximize the system throughput in this paper we propose a linear transceiver design algorithm for weighted sum rate maximization that is based on iterative minimization of weighted mean square error mse the proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum rate maximization problem furthermore the algorithm and its convergence can be extended to a general class of sum utility maximization problem the effectiveness of the proposed algorithm is validated by numerical experiments

invariants of hyperbolic partial differential operators we present a construction of a large class of laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order

coordinated multicell multiuser precoding for maximizing weighted sum energy efficiency energy efficiency optimization of wireless systems has become urgently important due to its impact on the global carbon footprint in this paper we investigate energy efficient multicell multiuser precoding design and consider a new criterion of weighted sum energy efficiency which is defined as the weighted sum of the energy efficiencies of multiple cells this objective is more general than the existing methods and can satisfy heterogeneous requirements from different kinds of cells but it is hard to tackle due to its sum of ratio form in order to address this non convex problem the user rate is first formulated as a polynomial optimization problem with the test conditional probabilities to be optimized based on that the sum of ratio form of the energy efficient precoding problem is transformed into a parameterized polynomial form optimization problem by which a solution in closed form is achieved through a two layer optimization we also show that the proposed iterative algorithm is guaranteed to converge numerical results are finally provided to confirm the effectiveness of our energy efficient beamforming algorithm it is observed that in the low signal to noise ratio snr region the optimal energy efficiency and the optimal sum rate are simultaneously achieved by our algorithm while in the middle high snr region a certain performance loss in terms of the sum rate is suffered to guarantee the weighed sum energy efficiency

discrete sum rate maximization for miso interference broadcast channels convex approximations and efficient algorithms this paper considers the discrete sum rate maximization dsrm problem for beamformer optimization in multi input single output interference broadcast channels in this problem the achievable rates of the receivers are restricted to be taken from a set of finite discrete rate values and such constraints arise from practical limitations with the modulation and coding schemes many existing studies consider sum rate maximization without the discrete rate constraints and that may result in performance loss in this paper the dsrm problem is tackled via a convex approximation approach due to the discrete rate constraints dsrm is a mixed integer program the idea of the proposed approach is to reformulate dsrm as a continuous but still nonconvex optimization problem then appropriate convex approximations are applied the advantage of the proposed approach is that the resulting approximate problems can be easily decomposed from a first order optimization viewpoint utilizing this special feature low complexity and decentralized algorithms based on projected gradient are derived numerical results are used to show the efficiencies of the proposed algorithms in a multicell coordinated beamforming scenario also this paper provides a proof for the convergence guarantee of one decentralized optimization strategy namely inexact maximum block improvement

a stochastic successive minimization method for nonsmooth nonconvex optimization with applications to transceiver design in wireless communication networks consider the problem of minimizing the expected value of a cost function parameterized by a random variable the classical sample average approximation method for solving this problem requires minimization of an ensemble average of the objective at each step which can be expensive in this paper we propose a stochastic successive upper bound minimization method ssum which minimizes an approximate ensemble average at each iteration to ensure convergence and to facilitate computation we require the approximate ensemble average to be a locally tight upper bound of the expected cost function and be easily optimized the main contributions of this work include the development and analysis of the ssum method as well as its applications in linear transceiver design for wireless communication networks and online dictionary learning moreover using the ssum framework we extend the classical stochastic sub gradient method to the case of minimizing a nonsmooth nonconvex objective function and establish its convergence

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

joint spatial division and multiplexing the large scale array regime we propose joint spatial division and multiplexing jsdm an approach to multiuser mimo downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced dimensional channel state information at the transmitter csit jsdm achieves significant savings both in the downlink training and in the csit uplink feedback thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing fdd systems for which uplink downlink channel reciprocity cannot be exploited in the proposed scheme the multiuser mimo downlink precoder is obtained by concatenating a prebeamforming matrix which depends only on the channel second order statistics with a classical multiuser precoder based on the instantaneous knowledge of the resulting reduced dimensional effective channel matrix we prove a simple condition under which jsdm incurs no loss of optimality with respect to the full csit case for linear uniformly spaced arrays we show that such condition is approached in the large number of antennas limit for this case we use szego s asymptotic theory of toeplitz matrices to show that a dft based prebeamforming matrix is near optimal requiring only coarse information about the users angles of arrival and angular spread finally we extend these ideas to the case of a 2 d base station antenna array with 3 d beamforming including multiple beams in the elevation angle direction we provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max min fairness criteria showing extremely attractive performance our numerical results are obtained via asymptotic random matrix theory avoiding lengthy monte carlo simulations and providing accurate results for realistic finite number of antennas and users

optimized signaling for mimo interference systems with feedback the system mutual information of a multiple input multiple output mimo system with multiple users which mutually interfere is considered perfect channel state information is assumed to be known to both transmitters and receivers asymptotic performance analysis shows that the system mutual information changes behavior as the interference becomes sufficiently strong in particular beamforming is the optimum signaling for all users when the interference is large we propose several numerical approaches to decide the covariance matrices of the transmitted signals and compare their performance in terms of the system mutual information we model the system as a noncooperative game and perform iterative water filling to find the nash equilibrium distributively a centralized global approach and a distributed iterative approach based on the gradient projection method are also proposed numerical results show that all proposed approaches give better performance than the standard signaling which is optimum for the case without interference both the global and the iterative gradient projection methods are shown to outperform the nash equilibrium significantly

a unified successive pseudoconvex approximation framework in this paper we propose a successive pseudoconvex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems the stationary points are obtained by solving a sequence of successively refined approximate problems each of which is much easier to solve than the original problem to achieve convergence the approximate problem only needs to exhibit a weak form of convexity namely pseudoconvexity we show that the proposed framework not only includes as special cases a number of existing methods for example the gradient method and the jacobi algorithm but also leads to new algorithms that enjoy easier implementation and faster convergence speed we also propose a novel line search method for nondifferentiable optimization problems which is carried out over a properly constructed differentiable function with the benefit of a simplified implementation as compared to the state of the art line search techniques that directly operate on the original nondifferentiable objective function the advantages of the proposed algorithm are shown both theoretically and numerically by several example applications namely multi input multi output mimo broadcast channel capacity computation energy efficiency maximization in massive mimo systems and ell 1 regularized least square problems in sparse signal recovery

outage constrained robust transmit optimization for multiuser miso downlinks tractable approximations by conic optimization in this paper we study a probabilistically robust transmit optimization problem under imperfect channel state information csi at the transmitter and under the multiuser multiple input single output miso downlink scenario the main issue is to keep the probability of each user s achievable rate outage as caused by csi uncertainties below a given threshold as is well known such rate outage constraints present a significant analytical and computational challenge indeed they do not admit simple closed form expressions and are unlikely to be efficiently computable in general assuming gaussian csi uncertainties we first review a traditional robust optimization based method for approximating the rate outage constraints and then develop two novel approximation methods using probabilistic techniques interestingly these three methods can be viewed as implementing different tractable analytic upper bounds on the tail probability of a complex gaussian quadratic form and they provide convex restrictions or safe tractable approximations of the original rate outage constraints in particular a feasible solution from any one of these methods will automatically satisfy the rate outage constraints and all three methods involve convex conic programs that can be solved efficiently using off the shelf solvers we then proceed to study the performance complexity tradeoffs of these methods through computational complexity and comparative approximation performance analyses finally simulation results are provided to benchmark the three convex restriction methods against the state of the art in the literature the results show that all three methods offer significantly improved solution quality and much lower complexity

coexisting linear and widely linear transceivers in the mimo interference channel recent results have shown the benefits of widely linear precoding wlp in the mimo interference channel mimo ic assuming that all transmitters can follow the same strategy motivated by a transitional scenario where legacy linear transmitters coexist with widely linear ones this work investigates the general k user mimo ic in a heterogeneous linear and widely linear transmitter deployment in particular we address the maximization of the weighted sum rate wsr for widely linear transmit filters design through the use of the complex valued formulation since the maximum wsr problem is non convex and thus difficult to be solved we formulate an equivalent minimum weighted mean square error problem that allows deriving closed form expressions for widely linear transceivers then an iterative procedure is proposed which is proven to reach a stationary point of the maximum wsr problem simulations show that the proposed procedure allows increasing the sum rate as compared to coordinated linear transceiver schemes the gains are larger and significant in two different nonexclusive conditions as the interference level increases or when the number of antennas is low

large system analysis of linear precoding in correlated miso broadcast channels under limited feedback in this paper we study the sum rate performance of zero forcing zf and regularized zf rzf precoding in large miso broadcast systems under the assumptions of imperfect channel state information at the transmitter and per user channel transmit correlation our analysis assumes that the number of transmit antennas m and the number of single antenna users k are large while their ratio remains bounded we derive deterministic approximations of the empirical signal to interference plus noise ratio sinr at the receivers which are tight as m k in the course of this derivation the per user channel correlation model requires the development of a novel deterministic equivalent of the empirical stieltjes transform of large dimensional random matrices with generalized variance profile the deterministic sinr approximations enable us to solve various practical optimization problems under sum rate maximization we derive 1 for rzf the optimal regularization parameter 2 for zf the optimal number of users 3 for zf and rzf the optimal power allocation scheme and 4 the optimal amount of feedback in large fdd tdd multiuser systems numerical simulations suggest that the deterministic approximations are accurate even for small m k

zero forcing precoding and generalized inverses we consider the problem of linear zero forcing precoding design and discuss its relation to the theory of generalized inverses in linear algebra special attention is given to a specific generalized inverse known as the pseudo inverse we begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudo inverse are optimal among the generalized inverses in this setting then we proceed to examine individual per antenna power constraints in this case the pseudo inverse is not necessarily the optimal inverse in fact finding the optimal matrix is nontrivial and depends on the specific performance measure we address two common criteria fairness and throughput and show that the optimal generalized inverses may be found using standard convex optimization methods we demonstrate the improved performance offered by our approach using computer simulations

weighted sum rate maximizing linear transceiver filters for the k user mimo interference channel this letter is concerned with transmit and receive filter optimization for the k user mimo interference channel specifically linear transmit and receive filter sets are designed which maximize the weighted sum rate while allowing each transmitter to utilize only the local channel state information our approach is based on extending the existing method of minimizing the weighted mean squared error mse for the mimo broadcast channel to the k user interference channel at hand for the case of the individual transmitter power constraint however a straightforward generalization of the existing method does not reveal a viable solution it is in fact shown that there exists no closed form solution for the transmit filter but simple one dimensional parameter search yields the desired solution compared to the direct filter optimization using gradient based search our solution requires considerably less computational complexity and a smaller amount of feedback resources while achieving essentially the same level of weighted sum rate a modified filter design is also presented which provides desired robustness in the presence of channel uncertainty

hierarchical interference mitigation for massive mimo cellular networks we propose a hierarchical interference mitigation scheme for massive mimo cellular networks the mimo precoder at each base station bs is partitioned into an inner precoder and an outer precoder the inner precoder controls the intra cell interference and is adaptive to local channel state information csi at each bs csit the outer precoder controls the inter cell interference and is adaptive to channel statistics such hierarchical precoding structure reduces the number of pilot symbols required for csi estimation in massive mimo downlink and is robust to the backhaul latency we study joint optimization of the outer precoders the user selection and the power allocation to maximize a general concave utility which has no closed form expression we first apply random matrix theory to obtain an approximated problem with closed form objective then using the hidden convexity of the problem we propose an iterative algorithm to find the optimal solution for the approximated problem we also obtain a low complexity algorithm with provable convergence simulations show that the proposed design has significant gain over various state of the art baselines

the validity of the additive noise model for uniform scalar quantizers a uniform scalar quantizer with small step size large support and midpoint reconstruction levels is frequently modeled as adding orthogonal noise to the quantizer input this paper rigorously demonstrates the asymptotic validity of this model when the input probability density function pdf is continuous and satisfies several other mild conditions specifically as step size decreases the correlation between input and quantization error becomes negligible relative to the mean squared error mse the model is even valid when the input density is discontinuous at the origin but discontinuities elsewhere can prevent the correlation from being negligible though this invalidates the additive model an asymptotic formula for the correlation is found in terms of the step size and the heights and positions of the discontinuities for a finite support input density such as uniform it is shown that the support of the uniform quantizer can be matched to that of the density in ways that make the correlation approach a variety of limits the derivations in this paper are based on an analysis of the asymptotic convergence of cell centroids to cell midpoints this convergence is fast enough that the centroids and midpoints induce the same asymptotic mse but not fast enough to induce the same correlations

transmit optimization with improper gaussian signaling for interference channels this paper studies the achievable rates of gaussian interference channels with additive white gaussian noise awgn when improper or circularly asymmetric complex gaussian signaling is applied for the gaussian multiple input multiple output interference channel mimo ic with the interference treated as gaussian noise we show that the user s achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex gaussian signaling in terms of the users transmit covariance matrices and an additional term which is a function of both the users transmit covariance and pseudo covariance matrices the additional degrees of freedom in the pseudo covariance matrix which is conventionally set to be zero for the case of proper gaussian signaling provide an opportunity to further improve the achievable rates of gaussian mimo ics by employing improper gaussian signaling to this end this paper proposes widely linear precoding which efficiently maps proper information bearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudo covariance matrices in particular for the case of two user gaussian single input single output interference channel siso ic we propose a joint covariance and pseudo covariance optimization algorithm with improper gaussian signaling to achieve the pareto optimal rates by utilizing the separable structure of the achievable rate expression an alternative algorithm with separate covariance and pseudo covariance optimization is also proposed which guarantees the rate improvement over conventional proper gaussian signaling

twisted laplace maps we consider general darboux maps arising from intertwining relations on second order linear partial differential operators as deformations of the classical laplace case we present lax pairs for the corresponding relations on invariants and discuss the conditions for a lattice structure analogous to 2d toda theory

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

parallel and distributed methods for constrained nonconvex optimization part ii applications in communications and machine learning in part i of this paper we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex objective function subject to nonconvex constraints based on inner convex approximations this part ii is devoted to the nontrivial application of the framework to the following relevant large scale problems ranging from communications to machine learning 1 generalizations of the rate profile maximization in mimo interference broadcast networks 2 the max min fair multicast multigroup beamforming problem in a multicell environment and 3 a general nonconvex constrained bi criteria formulation for k sparse variable selection in statistical learning the two criteria are a nonconvex loss objective function measuring the fitness of the model to data and the latter is a nonconvex sparsity inducing constraint in the general form of difference of convex dc functions which allows to accomodate in a unified fashion convex and nonconvex surrogates of the ell 0 function the proposed algorithms outperform current state of the art schemes for 1 3 both theoretically and numerically for instance they are the first distributed schemes for the class of problems 1 and 2 and they also lead to subproblems enjoying closed form solutions

coordinated beamforming for energy efficient transmission in multicell multiuser systems in this paper we study energy efficient joint power allocation and beamforming for coordinated multicell multiuser downlink systems the considered optimization problem is in a non convex fractional form and hard to tackle we propose to first transform the original problem into an equivalent optimization problem in a parametric subtractive form by which we reach its solution through a two layer optimization scheme the outer layer only involves one dimension search for the energy efficiency parameter which can be addressed using the bi section search the key issue lies in the inner layer where a non fractional sub problem needs to tackle by exploiting the relationship between the user rate and the mean square error we then develop an iterative algorithm to solve it the convergence of this algorithm is proved and the solution is further derived in closed form our analysis also shows that the proposed algorithm can be implemented in parallel with reasonable complexity numerical results illustrate that our algorithm has a fast convergence and achieves near optimal energy efficiency it is also observed that at the low transmit power region our solution almost achieves the optimal sum rate and the optimal energy efficiency simultaneously while at the middle high transmit power region a certain sum rate loss is suffered in order to guarantee the energy efficiency

pareto boundary of the rate region for single stream mimo interference channels linear transceiver design we consider a multiple input multiple output mimo interference channel ic where a single data stream per user is transmitted and each receiver treats interference as noise the paper focuses on the open problem of computing the outermost boundary so called pareto boundary pb of the achievable rate region under linear transceiver design the pareto boundary consists of the strict pb and non strict pb for the two user case we compute the non strict pb and the two ending points of the strict pb exactly for the strict pb we formulate the problem to maximize one rate while the other rate is fixed such that a strict pb point is reached to solve this non convex optimization problem which results from the hard coupled two transmit beamformers we propose an alternating optimization algorithm furthermore we extend the algorithm to the multi user scenario and show convergence numerical simulations illustrate that the proposed algorithm computes a sequence of well distributed operating points that serve as a reasonable and complete inner bound of the strict pb compared with existing methods

cramer and cayley hamilton in the max algebra abstract cramer s rule and the cayley hamilton theorem are formulated and provided in the so called max algebra which consists of the set of reals provided with two operations maximization and addition it is surprising to see that these well known theorems carry over to the max algebra almost without any changes provided that the conventional addition and multiplication are replaced by maximization and addition respectively the definitions of determinant and eigenvalue have to be adjusted to this new formulation the role of the determinant is taken over by the permanent and a refinement of this latter concept called the dominant

rate optimization for multiuser mimo systems with linear processing this paper focuses on linear transceiver design for rate optimization in multiuser gaussian multple input multiple output mimo systems we focus on two design criteria 1 maximizing the weighted sum rate subject to a total power constraint 2 maximizing the minimum user rate subject to a total power constraint for these problems new power allocation strategies are derived which can be formulated as geometric programs gps involving mean square errors mses based on these solutions we propose iterative algorithms where each iteration contains the optimization of the uplink power uplink receive filters and downlink receive filters monotonic convergence of the algorithms is proved simulations show that the algorithms outperform existing linear schemes additionally we extend the results to other variations of the problems such as the problem of sum rate constrained or user rate constrained power minimization and the problem of sum rate maximization subject to user rate constraints and a total power constraint

wireless max min utility fairness with general monotonic constraints by perron frobenius theory this paper presents a systematic approach for solving wireless max min utility fairness optimization problems in multiuser wireless networks with general monotonic constraints these problems are often challenging to solve due to their nonconvexity by establishing a connection between this class of optimization problems and the class of conditional eigenvalue problems that can be addressed by a generalized nonlinear perron frobenius theory we show how these problems can be solved optimally using an iterative algorithm that converges geometrically fast the mathematical development in this paper unifies previous work and allows us to handle a broader class of competitive utility functions with general nonlinear monotonic constraints several representative applications illustrate the effectiveness of the proposed framework including the max min quality of service subject to robust interference temperature constraints in cognitive radio networks the min max weighted mean square error subject to signal to interference and noise ratio constraints in multiuser downlink systems the max min throughput subject to nonlinear power constraints in energyefficient wireless networks the max min sigmoid utility in multimedia wireless networks and the min max outage probability subject to outage constraints in heterogeneous wireless networks numerical results are presented to demonstrate the fast convergence behavior of the algorithms to the optimal fixed point solution characterized by our generalized nonlinear perron frobenius theoretic framework

majorization minimization algorithms in signal processing communications and machine learning this paper gives an overview of the majorization minimization mm algorithmic framework which can provide guidance in deriving problem driven algorithms with low computational cost a general introduction of mm is presented including a description of the basic principle and its convergence results the extensions acceleration schemes and connection to other algorithmic frameworks are also covered to bridge the gap between theory and practice upperbounds for a large number of basic functions derived based on the taylor expansion convexity and special inequalities are provided as ingredients for constructing surrogate functions with the pre requisites established the way of applying mm to solving specific problems is elaborated by a wide range of applications in signal processing communications and machine learning

mimo minimum total mse transceiver design with imperfect csi at both ends this paper presents new results on joint linear transceiver design under the minimum total mean square error mse criterion with channel mean as well as both transmit and receive correlation information at both ends of a multiple input multiple output mimo link the joint design is formulated into an optimization problem the optimum closed form precoder and decoder are derived compared to the case with perfect channel state information csi linear filters are added at both ends to balance the suppression of channel noise and the noise from imperfect channel estimation the impact of channel estimation error as well as channel correlation on system performance is assessed based on analytical and simulation results

on the superiority of improper gaussian signaling in wireless interference mimo scenarios recent results have elucidated the benefits of using improper gaussian signaling igs as compared with conventional proper gaussian signaling pgs in terms of achievable rate for interference limited conditions this paper exploits majorization theory tools to formally quantify the gains of igs along with widely linear transceivers for multiple input multiple output mimo systems in interference limited scenarios the mimo point to point channel with interference is analyzed assuming that received interference can be either proper or improper and we demonstrate that the use of the optimal igs when received interference is improper strictly outperforms in terms of achievable rate and mean square error the use of the optimal pgs when interference is proper then these results are extended to two practical situations first the mimo z interference channel z ic is investigated where a trade off arises with igs we could increase the achievable rate of the interfered user while gracefully degrading the rate of the non interfered user second these concepts are applied to a two tier heterogeneous cellular network where macrocells and small cells coexist and multiple mimo z ics appear

weighted sum rate maximization in full duplex multi user multi cell mimo networks in this paper we focus on a multi user multi cell scenario with full duplex fd base stations and half duplex hd downlink dl and uplink ul users where all nodes are equipped with multiple antennas our goal is to design filters for weighted sum rate wsr maximization whilst taking into consideration the effect of transmitter and receiver distortion since wsr problems are non convex we exploit the relationship between rate and mean squared error in order to propose low complexity alternating optimization algorithms which are guaranteed to converge while the initial design assumes perfect channel state information csi we also move beyond this assumption and consider wsr problems under imperfect csi this is done using two types of error models the first is a norm bounded error model suitable for cases where the csi error is dominated by quantization issues and the second is a stochastic error model suitable for errors that occur during the channel estimation process itself results show that rates achieved in fd mode are higher than those achieved by the baseline hd schemes and demonstrate the robust performance of the proposed imperfect csi designs in addition we also extend our original wsr problem to one which maximizes the total dl rate subject to each ul user achieving a desired target rate this latter design can be used to overcome potential unfairness issues and ensure that all ul users are equally served in every time slot

phase only rf precoding for massive mimo systems with limited rf chains massive mimo systems promise high spectrum efficiency by deploying m 1 antennas at the base station bs however to achieve the full gain provided by massive mimo the bs requires m radio frequency rf chains which are expensive this motivates us to consider rf chain limited massive mimo systems with m antennas but only s m rf chains we propose a two stage precoding scheme to efficiently exploit the large spatial degree of freedom dof gain in massive mimo systems with limited rf chains and reduced channel state information csi signaling overhead in this scheme the mimo precoder is partitioned into a high dimensional phase only rf precoder followed by a low dimensional baseband precoder the rf precoder is adaptive to the spatial correlation matrices for inter cluster interference mitigation the baseband precoder is adaptive to the reduced dimensional effective csi for intra cluster spatial multiplexing we formulate the two stage precoding problem such that the minimum weighted average data rate of users is maximized under the phase only constraint on the rf precoder and the limited rf chain constraint this is a combinatorial optimization problem which is in general np hard we propose a low complexity solution based on a novel bi convex approximation approach simulations show that the proposed design has significant gain over various baselines

on the degrees of freedom achievable through interference alignment in a mimo interference channel consider a k user flat fading mimo interference channel where the kth transmitter or receiver is equipped with mk respectively nk antennas if an exponential in k number of generic channel extensions are used either across time or frequency cadambe and jafar 1 showed that the total achievable degrees of freedom dof can be maximized via interference alignment resulting in a total dof that grows linearly with a even if mk and nk are bounded in this work we consider the case where no channel extension is allowed and establish a general condition that must be satisfied by any degrees of freedom tuple d1 d2 dk achievable through linear interference alignment for a symmetric system with mk m nk n dk d for all k this condition implies that the total achievable dof cannot grow linearly with k and is in fact no more than k m n k 1 we also show that this bound is tight when the number of antennas at each transceiver is divisible by d the number of data streams per user

filter and forward relay design for mimo ofdm systems in this paper the filter and forward ff relay design for multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is investigated due to the considered mimo structure the ff relay design is investigated in the framework of joint design together with the linear mimo transceiver as the design criterion first the minimization of weighted sum mean square error mse is considered the joint design in this case is approached based on alternating optimization that iterates between the optimal design of the ff relay for given mimo precoding and decoding matrices and the optimal design of mimo precoding and decoding matrices for a given ff relay filter second a more advanced problem of joint design for rate maximization is considered the second problem is approached based on the obtained result regarding the first problem of weighted sum mse minimization and the existing result regarding the relationship between weighted mse minimization and rate maximization numerical results show the effectiveness of the proposed ff relay design method and significant performance improvement by the proposed ff relay over widely considered simple af relays for mimo ofdm systems

on the convergence of constrained parallel variable distribution algorithms we consider the parallel variable distribution pvd approach proposed by ferris and mangasarian siam j optim 4 1994 pp 815 832 for solving optimization problems the problem variables are distributed among p processors with each processor having the primary responsibility for updating its block of variables while allowing the remaining secondary variables to change in a restricted fashion along some easily computable directions for constrained nonlinear programs convergence in m c ferris and o l mangasarian siam j optim 4 1994 pp 815 832 was established in the special case of convex block separable constraints for general inseparable constraints it was suggested that a dual differentiable exact penalty function reformulation of the problem be used we propose to apply the pvd approach to problems with general convex constraints directly and show that the algorithm converges provided certain conditions are imposed on the change of secondary variables these conditions are both natural and practically implementable we also show that the original requirement of exact global solution of the parallel subproblems can be replaced by a less stringent sufficient descent condition the first rate of convergence result for the class of constrained pvd algorithms is also given

multicell coordinated beamforming with rate outage constraint part ii efficient approximation algorithms this paper studies the coordinated beamforming cobf design for the multiple input single output interference channel provided that only channel distribution information is known to the transmitters the problem under consideration is a probabilistically constrained optimization problem which maximizes a predefined system utility subject to constraints on rate outage probability and power budget of each transmitter our recent analysis has shown that the outage constrained cobf problem is intricately difficult e g np hard therefore the focus of this paper is on suboptimal but computationally efficient algorithms specifically by leveraging on the block successive upper bound minimization bsum method in optimization we propose a gauss seidel type algorithm called distributed bsum algorithm which can handle differentiable monotone and concave system utilities by exploiting a weighted minimum mean square error wmmse reformulation we further propose a jocobi type algorithm called distributed wmmse algorithm which can optimize the weighted sum rate utility in a fully parallel manner both algorithms are shown to converge to the stationary points of the original np hard problems to further provide a performance benchmark a relaxed approximation method based on polyblock outer approximation is also proposed simulation results show that the proposed algorithms are significantly superior to the existing successive convex approximation method in both performance and computational efficiency and can yield promising approximation performance by comparing with the performance benchmark

multi cell beamforming with decentralized coordination in cognitive and cellular networks this paper considers a downlink beamforming problem in a cognitive radio network where multiple primary and secondary cells coexist each multiantenna primary and secondary transmitter serves its own set of single antenna users the optimization objective is to minimize the sum transmission power over secondary transmitters while guaranteeing the minimum sinr for each secondary user and satisfying the maximum aggregate interference power constraint for each primary user we propose a decentralized beamforming algorithm where the original centralized problem is decomposed via primal decomposition method into two levels i e transmitter level subproblems managed by a network level master problem the master problem is solved independently at each secondary transmitter using a projected subgradient method requiring limited backhaul signaling among secondary transmitters to solve the independent transmitter level subproblems we propose three alternative approaches which are based on second order cone programming semidefinite programming and uplink downlink duality special emphasis is put on the last approach which is also considered in a multi cell miso cellular network numerical results show that the proposed algorithm achieves close to optimal solution even after a few iterations in quasi static channel conditions moreover near centralized performance is demonstrated in time correlated channels

efficient solutions for weighted sum rate maximization in multicellular networks with channel uncertainties the important problem of weighted sum rate maximization wsrm in a multicellular environment is intrinsically sensitive to channel estimation errors in this paper we study ways to maximize the weighted sum rate in a linearly precoded multicellular downlink system where the receivers are equipped with a single antenna with perfect channel information available at the base stations we first present a novel fast converging algorithm that solves the wsrm problem then the assumption is relaxed to the case where the error vectors in the channel estimates are assumed to lie in an uncertainty set formed by the intersection of finite ellipsoids as our main contributions we present two procedures to solve the intractable nonconvex robust designs based on the worst case principle the proposed iterative algorithms solve semidefinite programs in each of their steps and provably converge to a locally optimal solution of the robust wsrm problem the proposed solutions are numerically compared against each other and known approaches in the literature to ascertain their robustness towards channel estimation imperfections the results clearly indicate the performance gain compared to the case when channel uncertainties are ignored in the design process for certain scenarios we also quantify the gap between the proposed approximations and exact solutions

a generalized spatial correlation model for 3d mimo channels based on the fourier coefficients of power spectrums previous studies have confirmed the adverse impact of fading correlation on the mutual information mi of two dimensional 2d multiple input multiple output mimo systems more recently the trend is to enhance the system performance by exploiting the channels degrees of freedom in the elevation which necessitates the derivation and characterization of three dimensional 3d channels in the presence of spatial correlation in this paper an exact closed form expression for the spatial correlation function scf is derived for 3d mimo channels the proposed method resorts to the spherical harmonic expansion she of plane waves and the trigonometric expansion of legendre and associated legendre polynomials the resulting expression depends on the underlying arbitrary angular distributions and antenna patterns through the fourier series fs coefficients of power azimuth and elevation spectrums the novelty of the proposed method lies in the scf being valid for any 3d propagation environment the developed scf determines the covariance matrices at the transmitter and the receiver that form the kronecker channel model in order to quantify the effects of correlation on system performance the information theoretic deterministic equivalents of the mi for the kronecker model are utilized in both mono user and multi user cases numerical results validate the proposed analytical expressions and elucidate the dependence of the system performance on azimuth and elevation angular spreads and antenna patterns some useful insights into the behavior of mi as a function of downtilt angles are provided the derived model will help evaluate the performance of correlated 3d mimo channels in the future

mean achievable rates in clustered coordinated base station transmission with block diagonalization we focus on the mean achievable rate per user of the coordinated base station downlink transmission in a clustered cellular environment with transmit power constraints at the base stations block diagonalization is employed within the cluster to remove interference among users while the interference from other clusters remains the average achievable rate per user is evaluated considering the effects of the propagation channel and the interference and a theoretical framework is presented to provide its analytical expression validated by simulation results with different power allocation schemes as an application the number of cells of the cluster that maximizes the mean achievable rate per user is investigated it can be seen that in most of the cases a reduced cluster size close to seven cells guarantees a rate very close to the maximum achievable

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

robust estimates of covariance matrices in the large dimensional regime this paper studies the limiting behavior of a class of robust population covariance matrix estimators originally due to maronna in 1976 in the regime where both the number of available samples and the population size grow large using tools from random matrix theory we prove that for sample vectors made of independent entries having some moment conditions the difference between the sample covariance matrix and a scaled version of such robust estimator tends to zero in spectral norm almost surely this result can be applied to various statistical methods arising from random matrix theory that can be made robust without altering their first order behavior

on the achievable degrees of freedom of two cell multiuser mimo interference networks in this paper we study the sum degrees of freedom dof of an uplink two cell multiuser mimo interference network with asymmetric number of users in the cells the achievable dof is devised based on a two dimensional space time spreading code framework with linear precoding decoding design and finite channel extension the derivation of the achievable dof is shown related to a rank minimization problem which corresponds to the minimization of the dimension of the interference subspace the problem is solved by the proposed grouping algorithm ga based on aligning interfering signals into a low dimensional subspace as a group and attaining the minimum number of groups the achievable sum dof derived based on the proposed ga is shown to be greater than prior arts and achieves the theoretic upper bound in several cases we also give a closed form expression of the max imum achievable sum dof when there is the maximum number of admissible users in the considered finite diversity environment