the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

quadratically saturated regulator for constrained linear systems the problem of stabilization and null controllability of open loop unstable discrete time multi input systems with constraints on the inputs and the controls is addressed in this paper first necessary and sufficient conditions for solvability of the problem are derived they guarantee the existence of a linear controller leaving the state constraint set for the closed loop system positively invariant an optimal control law is computed and the admissible set of initial conditions is given such that along trajectories of the closed loop system the state and input constraints are satisfied then the domain of feasible initial conditions is enlarged using a saturating control if such is feasible

global predictive regulation of null controllable input saturated linear systems a predictive regulator is described for stabilizing linear plants subject to polyhedral input constraints while the asymptotic stability of general linear plants is ensured subject to a set membership condition on the initial state global asymptotic and semiglobal exponential regulation is achieved for input saturated plants which are asymptotically null controllable with bounded inputs the design knobs of the regulator can be chosen off line so as to compromise between nonconservative regulation performance and computational complexity and an online optimization problem of prequantifiable numerical burden results

a new approach for mutual information analysis of large dimensional multi antenna channels this paper adresses the behavior of the mutual information of correlated multiple input multiple output mimo rayleigh channels when the numbers of transmit and receive antennas converge to infin at the same rate using a new and simple approach based on poincare nash inequality and on an integration by parts formula it is rigorously established that the mutual information when properly centered and rescaled converges to a standard gaussian random variable simple expressions for the centering and scaling parameters are provided these results confirm previous evaluations based on the powerful but nonrigorous replica method it is believed that the tools that are used in this paper are simple robust and of interest for the communications engineering community

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

fulfilling hard constraints in uncertain linear systems by reference managing a method based on conceptual tools of predictive control is described for tackling tracking problems of uncertain linear systems wherein pointwise in time input and or state inequality constraints are present the method consists of adding to a primal compensated system a nonlinear device called predictive reference filter which manipulates the desired reference in order to fulfill the prescribed constraints provided that an admissibility condition on the initial state is satisfied the control scheme is proved to fulfill the constraints as well as stability and set point tracking requirements for all systems whose impulse step responses lie within given uncertainty ranges

on the sublinear behavior of massive multi user mimo sum rates for deterministic channel models this paper studies the behavior of the sum rate of outdoor multi user multiple input multiple output systems where a uniform linear array is utilized at the base station bs as the number of bs antennas and the number of users increase two schemes are studied for the downlink the zero forcing and the maximum ratio transmission mrt to begin with the channel matrix is described deterministically using direct scattering theory its matrix elements are the fourier coefficients of functions that have a physical significance being connected to the geometry of the environment for the case when the energy is not arriving at the bs from every spatial direction we prove for the zf scheme that the achievable sum rate behavior is sublinear in the number of antennas at the bs for the mrt scheme we prove that there is a link between the sum rate and the distribution of the users in the city to numerically evaluate the sum rate for a given city schematically described by its streets and its buildings we introduce a model for the fourier coefficients of the aforementioned functions which mixes geometrical and statistical ingredients we randomly distribute high buildings that will act as strong scatterers and look at the influence of their number on the sum rate with the zf scheme we perform the calculations for the case where the number of bs antennas m t is equal to the number of users m r and for the case where m t is larger than m r we observe that the sum rate first increases linearly with the number of bs antennas and becomes sublinear after m t reaches a certain value the threshold depends on the number of high buildings with the mrt scheme the calculations confirm the theoretical predictions and the sum rate is greater if the users are spread over all of the city

capacity scaling in mimo wireless systems under correlated fading previous studies have shown that single user systems employing n element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to n assuming independent rayleigh fading between antenna pairs we explore the capacity of dual antenna array systems under correlated fading via theoretical analysis and ray tracing simulations we derive and compare expressions for the asymptotic growth rate of capacity with n antennas for both independent and correlated fading cases the latter is derived under some assumptions about the scaling of the fading correlation structure in both cases the theoretic capacity growth is linear in n but the growth rate is 10 20 smaller in the presence of correlated fading we analyze our assumption of separable transmit receive correlations via simulations based on a ray tracing propagation model results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n 16 we present results for both the cases when the transmitter does and does not know the channel realization

optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information we study the optimal transmission strategy of a multiple input single output miso wireless communication link the receiver has perfect channel state information csi while the transmitter has different types of csi i e either perfect csi or no csi or long term knowledge of the channel covariance matrix for the case in which the transmitter knows the channel covariance matrix it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix however the optimal eigenvalues are difficult to compute we derive a characterization of the optimum power allocation furthermore we apply this result to provide an efficient algorithm which computes the optimum power allocation in addition to this we analyze the impact of correlation on the ergodic capacity of the miso system with different csi schemes at first we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated next we show that the ergodic capacity with perfect csi and without csi at the transmitter is schur concave i e the more correlated the transmit antennas are the less capacity is achievable in addition we show that the ergodic capacity with covariance knowledge at the transmitter is schur convex with respect to the correlation properties these results completely characterize the impact of correlation on the ergodic capacity in miso systems furthermore the capacity loss or gain due to correlation is quantified for no csi and perfect csi at the transmitter the capacity loss due to correlation is bounded by some small constant whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix finally we illustrate all theoretical results by numerical simulations

piecewise affinity of min max mpc with bounded additive uncertainties and a quadratic criterion this brief shows how a min max mpc with bounded additive uncertainties and a quadratic cost function results in a piecewise affine and continuous control law proofs based on properties of the cost function and the optimization problem are given the boundaries of the regions in which the state space can be partitioned are also treated the results are illustrated by an example

influence of environment richness on the increase of mimo capacity with number of antennas we study the capacity of mimo systems with uniform linear arrays in complex media as the number of antennas increases the distance between adjacent antennas is kept constant the transfer matrix describing the channel is expressed in terms of the antennas and the physical characteristics of the environment using direct scattering theory we prove that the capacity increases logarithmically when the number of antennas in the system belongs to a large interval of intermediate values we then take the case where the number of antennas is large and we study the effects on the capacity of adding a new scatterer using a city model with buildings of different sizes randomly distributed in space we show numerically that initially the capacity increases at a nearly linear rate as the number of antennas increases after a certain threshold the capacity growth becomes logarithmic we show that the number of antennas where this transition occurs increases as the number of buildings increases

techniques for mimo channel covariance matrix quantization in this correspondence we develop techniques to efficiently quantize channel covariance matrices in multiple input multiple output mimo rayleigh fading environments while these covariance matrices change less frequently than the channel matrices themselves this information needs to be updated when it does change furthermore these covariance matrices have significantly more parameters to quantize than their channel matrix counterparts since many applications focus on utilizing the strongest eigenmodes of the channel covariance matrix and since these matrices tend to be low rank we focus on efficiently quantizing the dominant eigenvectors of these matrices we develop lloyd type algorithms based on training data from the environment to develop our codebooks we also develop an algorithm based on the reduced parameter kronecker and weichselberger models to generate codebooks with reduced real time codeword search

efficient robust constrained model predictive control with a time varying terminal constraint set abstract an efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints the approach is novel in that it off line constructs a continuum of terminal constraint sets and on line achieves robust stability by using a relatively short control horizon even n 0 with a time varying terminal constraint set this algorithm not only dramatically reduces the on line computation but also significantly enlarges the size of the allowable set of initial conditions moreover this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium the controller design is illustrated through a benchmark problem

on the trade off between feasibility and performance in bilinear and state affine model based predictive control closed loop stabilizing model based predictive control mpc algorithms for discrete time bilinear and state affine models are presented stability of the closed loop is obtained through the use of an appropriate end point weighting and end point inequality constraint in this way the infinite horizon performance index is bounded from above by the objective function that is minimized in the mpc algorithm this paper presents an algorithm that aims at obtaining a large feasibility region by maximizing off line the region that is defined by the end point inequality constraint in order to improve the performance of the mpc algorithm the conservatism of the upper bound on the infinite horizon performance index is reduced in the on line computations

output feedback model predictive control for lpv systems based on quasi min max algorithm this paper proposes a robust output feedback model predictive control mpc scheme for linear parameter varying lpv systems based on a quasi min max algorithm this approach involves an off line design of a robust state observer for lpv systems using linear matrix inequality lmi and an on line robust output feedback mpc algorithm using the estimated state the proposed mpc method for lpv systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems a numerical example for an lpv system subject to input constraints is given to demonstrate its effectiveness

ensemble properties of rvq based limited feedback beamforming codebooks the ensemble properties of random vector quantization rvq codebooks for limited feedback beamforming in multiinput multioutput mimo systems are studied with the metrics of interest being the received ssr snr loss and mutual information loss both relative to a perfect channel state information csi benchmark the simplest case of unskewed codebooks is first studied in the correlated mimo setting and these loss metrics are computed as a function of the number of bits of feedback b transmit antenna dimension nt and spatial correlation in particular it is established that 1 the loss metrics are a product of two components a quantization component and a channel dependent component 2 the quantization component which is also common to analysis of channels with i i d fading decays as b increases at the rate 2 b nt 1 3 the channel dependent component reflects the condition number of the channel further the precise connection between the received ssr snr loss and the squared singular values of the channel is shown to be a schur convex majorization relationship finally the ensemble properties of skewed codebooks that are generated by skewing rvq codebooks with an appropriately designed fixed skewing matrix are studied based on an estimate of the loss expression for skewed codebooks it is established that the structure of a good skewing matrix is critically dependent on the condition numbers of the effective channel product of the true channel and the skewing matrix and the skewing matrix

information capacity of a random signature multiple input multiple output channel a closed form expression for information capacity of the random signature multiple input multiple output channel is given a direct calculation of the capacity is provided additional to the proof involving the capacity of minimum mean square error systems provided by verdu and shamai see ieee trans inform theory vol 45 p 622 40 1999

robust constrained predictive control of uncertain norm bounded linear systems a novel robust predictive control algorithm is presented for uncertain discrete time input saturated linear systems described by structured norm bounded model uncertainties the solution is based on the minimization at each time instant of a semi definite convex optimization problem subject to a number of lmi feasibility constraints which grows up only linearly with the control horizon length n the general case of arbitrary n is considered closed loop stability and feasibility retention over the time are proved and comparisons with robust multi model polytopic mpc algorithms are reported

resolution adaptive hybrid mimo architectures for millimeter wave communications in this paper we propose a hybrid analog digital beamforming architecture with resolution adaptive adcs for millimeter wave mmwave receivers with large antenna arrays we adopt array response vectors for the analog combiners and derive adc bit allocation ba solutions in closed form the ba solutions reveal that the optimal number of adc bits is logarithmically proportional to the rf chain s signal to noise ratio raised to the 1 3 power using the solutions two proposed ba algorithms minimize the mean square quantization error of received analog signals under a total adc power constraint contributions of this paper include 1 adc bit allocation algorithms to improve communication performance of a hybrid mimo receiver 2 approximation of the capacity with the ba algorithm as a function of channels and 3 a worst case analysis of the ergodic rate of the proposed mimo receiver that quantifies system tradeoffs and serves as the lower bound simulation results demonstrate that the ba algorithms outperform a fixed adc approach in both spectral and energy efficiency and validate the capacity and ergodic rate formula for a power constraint equivalent to that of fixed 4 bit adcs the revised ba algorithm makes the quantization error negligible while achieving 22 better energy efficiency having negligible quantization error allows existing state of the art digital beamformers to be readily applied to the proposed system

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

on the role of the number of degrees of freedom of the field in mimo channels the aim of this paper is to investigate the relationship between the effective number of degrees of freedom endf of a multiple input multiple output mimo channel and the number of degrees of freedom ndf of the field in particular the ndf of the field represents an upperbound for the endf of a mimo channel consequently the evaluation of the maximum endf can be carried out by adopting the literature on the ndf based on the spatial bandlimitation properties of the field this approach allows a simple and intuitive explanation of the maximum endf in a mimo channel based on a geometrical interpretation of the spatial channel in terms of spatial nyquist intervals

model predictive control for linear parameter varying constrained systems using ellipsoidal set prediction this paper proposes a new model predictive control mpc method for linear parameter varying systems with bounded parameter variation subject to input constraints the method adopts closed loop prediction and constructs ellipsoidal sets to predict the future states with reasonable computational effort then the information on the parameter variation rate is exploited to improve the accuracy of the prediction furthermore a relaxed terminal condition which guarantees the stability for infinite horizon is introduced to enlarge the stabilizable region it is shown that the feasibility of the mpc problem at the initial step ensures the stability of the closed loop system finally a simulation result illustrates the effectiveness of the proposed method

worst case formulations of model predictive control for systems with bounded parameters two different predictive control formulations are developed based on minimization of the worst case quadratic cost for systems with bounded parameters the two formulations differ on the assumptions made about the future inputs in optimizing the current input one assumes open loop control while the other considers closed loop control their closed loop properties such as asymptotic stability are examined we then focus on a moving average model with an integrator and derive computationally simpler suboptimal algorithms

isotropic fading vector broadcast channels the scalar upper bound and loss in degrees of freedom we propose a scalar upper bound on the capacity region of the isotropic fading vector broadcast channel in terms of the capacity region of a scalar fading broadcast channel the scalar upper bound is applicable to the broad class of isotropic fading broadcast channels regardless of the distribution of the users channel magnitudes the distribution of the additive noise experienced by each user or the amount of channel knowledge available at the receiver using this upper bound we prove the optimality of the alamouti scheme in a broadcast setting extend the recent results on the capacity of nondegraded fading scalar broadcast channels to nondegraded fading vector broadcast channels and determine the capacity region of a fading vector gaussian broadcast channel with channel magnitude feedback we also provide an example of a rayleigh fading broadcast channel with no channel state information available to the receiver csir where the bound on the capacity region obtained by a naive application of the scalar upper bound is provably loose because it fails to account for the additional loss in degrees of freedom due to lack of channel knowledge at the receiver a tighter upper bound is obtained by separately accounting for the loss in degrees of freedom due to lack of csir before applying the scalar upper bound

balancing domain decomposition for problems with large jumps in coefficients the balancing domain decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent the abstract theory introduced recently by the first named author is used to develop condition number bounds for conforming linear elements in two and three dimensions the bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains and grow only as the squared logarithm of the mesh size h computational experiments for two and three dimensional problems confirm the theory

mimo channels in the low snr regime communication rate error exponent and signal peakiness we consider multiple input multiple output mimo fading channels and characterize the reliability function in the low signal to noise snr regime as a function of the number of transmit and receive antennas for the case when the fading matrix h has independent entries we show that the number of transmit antennas plays a key role in reducing the peakiness in the input signal required to achieve the optimal error exponent for a given communication rate further by considering a correlated channel model we show that the maximum performance gain in terms of the error exponent and communication rate is achieved when the entries of the channel fading matrix are fully correlated the results we presented in this work in the low snr regime can also be applied to the infinite bandwidth regime

analysis of preconditioners for domain decomposition domain decomposition is a class of techniques that are designed to solve elliptic problems on irregular domains and on multiprocessor systems typically a domain is decomposed into many smaller regular subdomains and the capacitance system governing the interface unknowns is solved by some version of the preconditioned conjugate gradient method in this paper we show that for a simple model problem poisson s equation on a rectangle decomposed into two smaller rectangles the capacitance system can be inverted exactly by fast fourier transform an exact eigen decomposition of the capacitance matrix also makes it possible to relate and compare the various preconditioners that have been proposed in the literature for example we show that in the limit as the aspect ratio of the two rectangles tend to infinity the preconditioner proposed by golub and mayers becomes exact but the one proposed by dryja does not both preconditioners however are poor when the aspect ratio is small

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

electromagnetic degrees of freedom in 2 d scattering environments the electromagnetic em degrees of freedom dof of a noise limited system in two dimensions with random multiple scattering is evaluated numerically following a rigorous dof theory first developed by miller and piestun for optical systems the received em fields are efficiently calculated by fast multipole method fmm and the ensemble average of the dof number is obtained through monte carlo simulation technique the results show that the average em dof number is strongly dependent on the sizes of the transmit volume the receive volume and the scattering region in particular the average number of dof generally increases with both the transmit and receive volumes however this increase is a non linear process and will not continue indefinitely as the transmit volume or the receive volume expands an upper bound of the average dof number is expected due to noise effects due to the lack of criteria for choosing a critical parameter involved in miller and piestun s original dof definition a modified definition is also considered even though the modified definition is snr dependent it provides a clearer physical meaning of the dof in addition the simulations also suggest that it might not be appropriate to ignore the influence of the snr on the dof number when the system concerned is of general form and relative small where no critical point of the channel quality can be identified a logarithmic dependence of the dof number on the total source power is demonstrated for such systems

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

a feedback min max mpc algorithm for lpv systems subject to bounded rates of change of parameters a novel closed loop model based predictive control mpc strategy for input saturated polytopic linear parameter varying lpv discrete time systems is proposed it is postulated that the plant belongs to a polytopic family of linear systems each member of which being parameterized by the value that a parameter vector assumes in the unit simplex such a parameter can be measured online and used for feedback while a bound on its rate of change is known and exploited for predictions the paper extends the mpc scheme presented by lu et al 2000 for the restricting case of 1 step long control horizons to the general case of control horizons of arbitrary length n this is done by suitably modifying the robust mpc scheme presented by casavola et al 2000 for uncertain polytopic systems the feasibility and closed loop stability of this strategy are proved and a numerical example is also presented in order to show how the freedom of extending the control horizon and knowledge of the parameter is significant in order to improve the performance of the control strategy

robustly asymptotically stable finite horizon mpc this paper presents a robustly stable finite horizon model predictive control mpc scheme for linear uncertain systems in which the uncertainty is not restricted to some specific uncertainty class polytopic affine lft etc the only requirement is that the state space matrices remain bounded over the uncertainty set suitable constraints are added to the mpc cost function to impose robust asymptotic stability and to deal with input output constraints the resulting optimization problem is solved at each time instant in a probabilistic framework using an iterative randomized ellipsoid algorithm rea the method is compared in simulation to the existing approach of kothare balakrishnan and morari 1996 robust constrained model predictive control using linear matrix inequalities automatica 32 10 1361 1379

on the limit of the largest eigenvalue of the large dimensional sample covariance matrix in this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tend to infinity the above result is proved under the mild restriction that the fourth moment of the elements of the sample sums of squares and cross products sp matrix exist

degrees of freedom in multiple antenna channels a signal space approach multiple antenna systems that are limited by the area and geometry of antenna arrays are considered given these physical constraints the limit on the available number of spatial degrees of freedom is derived the commonly used statistical multiple input multiple output mimo model is inadequate antenna theory is applied to take into account the area and geometry constraints and to define the spatial signal space so as to interpret experimental channel measurements in an array independent but manageable description of the physical environment based on these modeling strategies for a spherical array of effective aperture a in a physical environment of angular spread spl omega in solid angle the number of spatial degrees of freedom is shown to be a spl omega for uni polarized antennas and 2a spl omega for tri polarized antennas together with the 2wt degrees of freedom for a system of bandwidth w transmitting in an interval t the total degrees of freedom of a multiple antenna channel is therefore 4wta spl omega

capacity scaling and spectral efficiency in wide band correlated mimo channels the dramatic linear increase in ergodic capacity with the number of antennas promised by multiple input multiple output mimo wireless communication systems is based on idealized channel models representing a rich scattering environment is such scaling sustainable in realistic scattering scenarios existing physical models although realistic are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters such as the angles of arrival and delays in this paper we leverage a recently introduced virtual representation of physical models that is essentially a fourier series representation of wide band mimo channels in terms of fixed virtual angles and delays motivated by physical considerations we propose a d connected model for correlated channels defined by a virtual spatial channel matrix consisting of d nonvanishing diagonals with independent and identically distributed i i d gaussian entries the parameter d provides a meaningful and tractable measure of the richness of scattering we derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth in the large antenna regime we show that linear capacity scaling is possible if d scales linearly with the number of antennas this in turn is possible if the number of resolvable paths grows quadratically with the number of antennas the capacity saturates for linear growth in the number of paths fixed d the ergodic capacity does not depend on frequency selectivity of the channel in the wide band case increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior for large bandwidth the capacity scales linearly with the signal to noise ratio snr as well we also provide an explicit characterization of the wide band slope recently proposed by verdu numerical results are presented to illustrate the key theoretical results

stochastic model predictive control of lpv systems via scenario optimization a stochastic receding horizon control approach for constrained linear parameter varying discrete time systems is proposed in this paper it is assumed that the time varying parameters have stochastic nature and that the system s matrices are bounded but otherwise arbitrary nonlinear functions of these parameters no specific assumption on the statistics of the parameters is required by using a randomization approach a scenario based finite horizon optimal control problem is formulated where only a finite number m of sampled predicted parameter trajectories scenarios are considered this problem is convex and its solution is a priori guaranteed to be probabilistically robust up to a user defined probability level p the p level is linked to m by an analytic relationship which establishes a tradeoff between computational complexity and robustness of the solution then a receding horizon strategy is presented involving the iterated solution of a scenario based finite horizon control problem at each time step our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time either deterministically or with probability no smaller than p the features of the approach are illustrated by a numerical example

brief optimizing the end point state weighting matrix in model based predictive control in this paper a linear model based predictive control mpc algorithm is presented for which nominal closed loop stability is guaranteed the input is obtained by minimizing a quadratic performance index over a finite horizon plus an end point state eps penalty subject to input state and output constraints under certain conditions the weighting matrix in the eps penalty enables one to specify an invariant ellipsoid in which the input state and output constraints are satisfied in existing mpc algorithms this weighting matrix is calculated off line the main contribution of this paper is to incorporate the calculation of the eps weighting matrix into the on line optimization problem of the controller the main advantage of this approach is that a natural and automatic trade off between feasibility and optimality is obtained this is demonstrated in a simulation example

correlated mimo wireless channels capacity optimal signaling and asymptotics the capacity of the multiple input multiple output mimo wireless channel with uniform linear arrays ulas of antennas at the transmitter and receiver is investigated it is assumed that the receiver knows the channel perfectly but that the transmitter knows only the channel statistics the analysis is carried out using an equivalent virtual representation of the channel that is obtained via a spatial discrete fourier transform a key property of the virtual representation that is exploited is that the components of virtual channel matrix are approximately independent with this approximation the virtual representation allows for a general capacity analysis without the common simplifying assumptions of gaussian statistics and product form correlation kronecker model for the channel matrix elements a deterministic line of sight los component in the channel is also easily incorporated in much of the analysis it is shown that in the virtual domain the capacity achieving input vector consists of independent zero mean proper complex gaussian entries whose variances can be computed numerically using standard convex programming algorithms based on the channel statistics furthermore in the asymptotic regime of low signal to noise ratio snr it is shown that beamforming along one virtual transmit angle is asymptotically optimal necessary and sufficient conditions for the optimality of beamforming and the value of the corresponding optimal virtual angle are also derived based on only the second moments of the virtual channel coefficients numerical results indicate that beamforming may be close to optimum even at moderate values of snr for sparse scattering environments finally the capacity is investigated in the asymptotic regime where the numbers of receive and transmit antennas go to infinity with their ratio being kept constant using a result of girko an expression for the asymptotic capacity scaling with the number of antennas is obtained in terms

why does the kronecker model result in misleading capacity estimates many recent works that study the performance of multiple input multiple output mimo systems in practice assume a kronecker model where the variances of the channel entries upon decomposition on to the transmit and the receive eigenbases admit a separable form measurement campaigns however show that the kronecker model results in poor estimates for capacity motivated by these observations a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better in this paper we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates the transmit and or the receive eigenbases using tools from random matrix theory we then establish the theoretical basis behind the kronecker mismatch at the low and the high snr extremes 1 sparsity of the dominant statistical degrees of freedom dof in the true channel at the low snr extreme and 2 nonregularity of the sparsity structure disparities in the distribution of the dof across the rows and the columns at the high snr extreme

intrinsic limits of dimensionality and richness in random multipath fields we study the dimensions or degrees of freedom of farfield multipath that is observed in a limited source free region of space the multipath fields are studied as solutions to the wave equation in an infinite dimensional vector space we prove two universal upper bounds on the truncation error of fixed and random multipath fields a direct consequence of the derived bounds is that both fixed and random multipath fields have an effective finite dimension for circular and spherical spatial regions we show that this finite dimension is proportional to the radius and area of the region respectively we use the karhunen loegraveve kl expansion of random multipath fields to quantify the notion of multipath richness the multipath richness is defined as the number of significant eigenvalues in the kl expansion that achieve 99 of the total multipath energy we establish a lower bound on the largest eigenvalue this lower bound quantifies to some extent the well known reduction of multipath richness with reducing the angular power spread of multipath angular power spectrum

sublinear capacity scaling laws for sparse mimo channels recent attention on performance analysis of single user multiple input multiple output mimo systems has been on understanding the impact of the spatial correlation model on ergodic capacity in most of these works it is assumed that the statistical degrees of freedom dof in the channel can be captured by decomposing it along a suitable eigenbasis and that the transmitter has perfect knowledge of the statistical dof with an increased interest in large antenna systems in state of the art technologies these implicit channel modeling assumptions in the literature have to be revisited in particular multiantenna measurements have showed that large antenna systems are sparse where only a few dof are dominant enough to contribute towards capacity thus in this work it is assumed that the transmitter can only afford to learn the dominant statistical dof in the channel the focus is on understanding ergodic capacity scaling laws in sparse channels unlike classical results where linear capacity scaling is implicit sparsity of mimo channels coupled with a knowledge of only the dominant dof is shown to result in a new paradigm of sublinear capacity scaling that is consistent with experimental results and physical arguments it is also shown that uniform power signaling over all the antenna dimensions is wasteful and could result in a significant penalty over optimally adapting the antenna spacings in response to the sparsity level of the channel and transmit snr

an ellipsoidal off line mpc scheme for uncertain polytopic discrete time systems an off line model predictive control mpc method based on ellipsoidal calculus and viability theory is described in order to address control problems in the presence of state and input constraints for uncertain polytopic linear plants subject to persistent disturbances in order to reduce the computational burdens and conservativeness of traditional polytopic mpc schemes the present approach carries out off line most of the computations and it makes use of closed loop predictions to improve the control performance this is done by recursively pre computing suitable ellipsoidal inner approximations of the exact controllable sets and solving on line a simple and numerically low demanding optimization problem subject to a set membership constraint comparisons with three other recent off line mpc approaches are also provided in the final example

technical communique min max predictive control strategies for input saturated polytopic uncertain systems a novel robust predictive controller for input saturated ltv discrete time systems with polytopic model uncertainties is presented the solution is based on the minimization at each time instant of an upper bound of the worst case infinite horizon quadratic cost under the constraint of steering the set valued future state evolutions emanating from the current state into a feasible and positive invariant set a condition on the initial state is given that suffices to ensure problem solvability for all subsequent time instants under the latter the proposed predictive controller is proved to robustly asymptotically stabilize the input saturated ltv polytopic system

impact of antenna correlation on the capacity of multiantenna channels this paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels the analysis is not restricted to the popular separable correlation model but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature for arbitrary signal to noise ratios snr the characterization is conducted in the regime of large numbers of antennas for the low and high snr regions in turn we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power bandwidth and rate