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

automorphisms of b h with respect to minus partial order abstract let h be an infinite dimensional hilbert space and b h the algebra of all bounded linear operators on h we discuss possible extensions of the concept of the minus partial order from matrix to operator algebras in particular we show that mitra s unified theory of matrix partial orders based on generalized inverses can be modified in such a way that we get a unified approach to partial orders on b h or even more general algebras and rings then we choose the most natural among possible definitions of minus partial order on b h and describe the structure of corresponding automorphisms

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

beam division multiple access transmission for massive mimo communications we study multicarrier multiuser multiple input multiple output mu mimo systems in which the base station employs an asymptotically large number of antennas we analyze a fully correlated channel matrix and provide a beam domain channel model where the channel gains are independent of sub carriers for this model we first derive a closed form upper bound on the achievable ergodic sum rate based on which we develop asymptotically necessary and sufficient conditions for optimal downlink transmission that require only statistical channel state information at the transmitter furthermore we propose a beam division multiple access bdma transmission scheme that simultaneously serves multiple users via different beams by selecting users within non overlapping beams the mu mimo channels can be equivalently decomposed into multiple single user mimo channels this scheme significantly reduces the overhead of channel estimation as well as the processing complexity at transceivers for bdma transmission we work out an optimal pilot design criterion to minimize the mean square error mse and provide optimal pilot sequences by utilizing the zadoff chu sequences simulations demonstrate the near optimal performance of bdma transmission and the advantages of the proposed pilot sequences

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

star partial order on b h abstract let h be an infinite dimensional complex hilbert space and let b h be the algebra of all bounded linear operators on h in the paper the equivalent definition of the star partial order on b h using selfadjoint idempotent operators is introduced also some properties of the generalized concept of order relations on b h defined with the help of idempotent operators are investigated

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

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

the effect of diversity on a burst mode carrier frequency estimator in the frequency selective multipath channel this paper describes a carrier frequency offset estimator derived using maximum likelihood techniques the estimator is designed for a digital space diversity receiver operating in a wide band frequency selective multipath fading channel the estimator is suited to a burst mode time division multiple access system because the estimate is formed in an open loop manner and relies on a training sequence normally used in burst mode systems the main advantage is that it does not require channel state information rather it only requires knowledge of the auto correlation of the channel simulation results show the estimator to be unbiased over a wide frequency range the normalized error standard deviation is shown to be 0 0015 across the frequency offset range for a receiver with four diversity branches when the normalized channel delay spread is 0 1 the signal to noise ratio snr is 10 db and the training sequence length is 23 symbols it is found that for most parameter configurations there is approximately a factor of two improvement in the estimate error standard deviation when the antenna diversity is doubled

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

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

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

on mappings preserving the sharp and star orders abstract the present paper is devoted to the study of linear maps preserving certain relations such as the sharp partial order and the star partial order in semisimple banach algebras and c algebras

maps preserving the diamond partial order the present paper is devoted to the study of the diamond partial order in c algebras we characterize linear maps preserving this partial order

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

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

estimation of sensor gain and phase the problem of estimating the direction independent gain and phase characteristics of an array of sensors using knowledge of the true field covariance at the sensor locations is considered a concise expression for the log likelihood function is derived and several mathematical properties of this objective function are given the cramer rao c r lower bounds on the variances of gain and phase estimates are derived with the plane wave in isotropic noise considered as a special case the maximum likelihood estimates are shown to be consistent asymptotically efficient and asymptotically normal a simple estimator is proposed which is consistent and which gives good initial estimates for a newton algorithm for finding the maximum likelihood solution comparison of the maximum likelihood estimates and the c r bounds is given for the plane wave in isotropic noise example

no eigenvalues outside the limiting support of generally correlated gaussian matrices this paper investigates the behaviour of the spectrum of generally correlated gaussian random matrices whose columns are zero mean independent vectors but have different correlations under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace following the approach proposed by vallet et al we prove that under some mild conditions there is no eigenvalue outside the limiting support of generally correlated gaussian matrices as an outcome of this result we establish that the smallest singular value of these matrices is almost surely greater than zero from a practical perspective this control of the smallest singular value is paramount to applications from statistical signal processing and wireless communication in which this kind of matrices naturally arise

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

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

on some characterizations of the star partial ordering for matrices and rank subtractivity abstract the main result is that drazin s star partial ordering a b holds if and only if a b and b a b a where a b is defined by a a a b and aa ba and where a b denotes rank subtractivity here a and b are m n complex matrices and the superscript denotes the moore penrose inverse several other characterizations of a b are given with particular emphasis on what extra condition must be added in order that rank subtractivity becomes the stronger star order a key tool is a new canonical form for rank subtractivity connections with simultaneous singular value decompositions schur complements and idempotent matrices are also mentioned

numerically stable and efficient algorithm for vector channel parameter and frequency offset estimation in this paper we present a novel and numerically efficient algorithm for vector channel and calibration vector estimation which works when frequency offset error caused by either unstable oscillator or doppler effect is present in spread spectrum antenna system we propose an estimation algorithm based on gauss seidal algorithm rather than using eigen decomposition or svd in computing eigenvalues and eigenvectors at each iteration the algorithm is based on the two step procedures one for estimating both channel and frequency offset and the other for estimating the unknown array gain and phase consequently estimates of the doas the multi path impulse response of the reference signal source and the carrier frequency offset as well as the calibration of antenna array are provided the analytic performance improvement in multiplications number is presented the performance of the proposed algorithm is investigated by means of computer simulations throughout the analytic and computer simulation we show that the proposed algorithm reduces the number of multiplications by order of one

matrix partial orders through generalized inverses unified theory the unified theory presented here covers as special cases the star order of drazin the minus order of hartwig and nambooripad the sharp order and other partial orders introduced by the author

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

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

a subspace method for estimating sensor gains and phases the problem of array signal processing under model errors is studied a signal subspace constraint is used to obtain a simple way for computing a set of sensor gains and phases consistent with a given set of doa angles then the issue of uniqueness of the set of sensor gains and phases and doa angles is addressed

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

carrier frequency estimation for transmissions over selective channels this paper deals with carrier frequency estimation for burst transmissions over frequency selective channels three estimation schemes are proposed all based on the use of known training sequences the first scheme employs an arbitrary sequence and provides joint maximum likelihood ml estimates of the carrier frequency and the channel response its implementation complexity is relatively high but its accuracy achieves the cramer rao bound the second scheme is still based on the ml criterion but the training sequence is periodic which helps to reduce the computational load the third scheme also employs periodic sequences but its structure comes from heuristic reasoning theoretical analysis and simulations are employed to assess the performance of the three schemes

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

orthogonality preserving linear maps on c algebras with non zero socles abstract we study orthogonality preserving surjective linear maps from a unital c algebra with non zero socle a to a c algebra in particular we prove that when a has essential socle every biorthogonality preserving surjective linear map t a b is automatically bounded and a jordan isomorphism multiplied by an invertible element

automatic continuity of biorthogonality preservers between compact c algebras and von neumann algebras abstract we prove that every biorthogonality preserving linear surjection between two dual or compact c algebras or between two von neumann algebras is automatically continuous

on group inverses and the sharp order abstract in this work the group inverse of a matrix is used to define the order on square matrices of index 1 the order is similar to the order of drazin 2 and the minus order of hartwig 6 10 and nambooripad 17 the order and the order are compared and contrasted many conditions are given which assure the equivalence of the various partial orders studied

automatic continuity of m norms on c algebras abstract elements a and b of a c algebra are called orthogonal a b if a b a b 0 we say that vectors x and y in a banach space x are semi m orthogonal x sm y if x y max x y we prove that every linear bijection t a x where x is a banach space a is either a von neumann algebra or a compact c algebra and t a sm t b whenever a b must be continuous consequently every complete semi m norm on a von neumann algebra or on a compact c algebra is automatically continuous

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

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

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

left star and right star partial orderings abstract two partial orderings in the set of complex matrices are introduced by combining each of the conditions a a a b and aa ba which define the star partial ordering with one of the conditions m a m b and m a m b which define the space preordering several properties of these orderings are examined with main emphasis on comparing the new orderings with the star ordering the minus ordering and other related partial orderings moreover some further characterizations of partial orderings in terms of inclusions of appropriate classes of generalized inverses are derived with the main emphasis on characterizations involving reflexive generalized inverses