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

a quantization of conjugacy classes of matrices abstract we construct a generator system of the annihilator of the generalized verma module of g l n c induced from any character of any parabolic subalgebra as an analogue of minors and elementary divisors the generator system has a quantization parameter e and it generates the defining ideal of the conjugacy class of square matrices at the classical limit e 0

asymptotic capacity and optimal precoding in mimo multi hop relay networks a multihop relaying system is analyzed where data sent by a multi antenna source is relayed by successive multi antenna relays until it reaches a multi antenna destination assuming correlated fading at each hop each relay receives a faded version of the signal from the previous level performs linear precoding and retransmits it to the next level using free probability theory and assuming that the noise power at relays but not at destination is negligible the closed form expression of the asymptotic instantaneous end to end mutual information is derived as the number of antennas at all levels grows large the so obtained deterministic expression is independent from the channel realizations while depending only on channel statistics this expression is also shown to be equal to the asymptotic average end to end mutual information the singular vectors of the optimal precoding matrices maximizing the average mutual information with finite number of antennas at all levels are also obtained it turns out that these vectors are aligned to the eigenvectors of the channel correlation matrices thus they can be determined using only the channel statistics as the structure of the singular vectors of the optimal precoders is independent from the system size it is also optimal in the asymptotic regime

hua operators poisson transform and relative discrete series on line bundles over bounded symmetric domains let d g k be a bounded symmetric domain and s k l be its shilov boundary we consider the action of g with weight nu in mathbb z on functions on d viewed as sections the line bundle and the corresponding eigenspace of g invariant di erential operators the poisson transform maps hyperfunctions on the s to the eigenspaces we characterize the image in terms of hua operators on the sections of the line bundle for some special parameter the poisson transform is of szego type mapping into the relative discrete series we compute the corresponding elements in the discrete series

complex valued matrix differentiation techniques and key results a systematic theory is introduced for finding the derivatives of complex valued matrix functions with respect to a complex valued matrix variable and the complex conjugate of this variable in the framework introduced the differential of the complex valued matrix function is used to identify the derivatives of this function matrix differentiation results are derived and summarized in tables which can be exploited in a wide range of signal processing related situations

sum rate optimal precoding for multi cell large scale mimo uplink based on statistical csi we investigate the sum rate optimal precoding for the uplink of the multi cell large scale mimo systems specifically we focus on transmitter precoder design based only on the statistical channel state information csi we first consider the partial cooperation system where only the csi is shared among cells and its base station bs decodes its in cell users by treating out cell signals as colored gaussian noise we derive the ergodic sum rate and its deterministic approximation for the regime where both the number of total user antennas and the number of bs antennas are large we obtain the necessary conditions to maximize the deterministic approximation of the sum rate under the transmit power constraint based on which a gradient search algorithm is proposed to find the local optimal precoders furthermore a super cell system is also considered where users from all cells are jointly decoded the deterministic approximation to the sum rate and optimal precoder design for such systems are given numerical experiments show that the proposed precoders achieve significant performance gains over systems with no precoding compared with the existing precoding methods that require perfect csi the proposed precoders achieve similar sum rates and require only the statistical csi

ergodic channel capacities for the amplify and forward half duplex cooperative systems in this paper the ergodic channel capacities are established for the amplify and forward af half duplex cooperative systems which consist of a source node a destination and multiple relay nodes the relay nodes assist the transmission from the source node to the destination since the channel matrices for the cooperative systems involve product of gaussian random variables which are no longer gaussian the approach in obtaining the ergodic channel capacity for conventional multiple input multiple output mimo gaussian channels telatar 1999 is not applicable by using a novel approach we have arrived at the following conclusions about the ergodic channel capacities for the af cooperative systems for the single antenna af relay systems in which all nodes are equipped with one antenna the optimal covariance matrix of the input signals to achieve the ergodic channel capacity is diagonal and the diagonal elements are obtained by solving optimization problems of multidimensional integrals these diagonal entries are not all equal even if all the channel gains in the cooperative systems are independent and identically distributed i i d gaussian with unit variance therefore a white input signal for the af cooperative system may not achieve the ergodic channel capacity of the system this is in direct contrast to the case of conventional multiple input single output miso systems having i i d gaussian channel gains of unit variance in which case the ergodic capacity is achieved if the input covariance matrix is a scaled identity matrix for the mimo relay system in which the nodes have multiple antennas the input covariance matrix to achieve the ergodic capacity is block diagonal and each block diagonalizes the autocorrelation of channel matrix from the source to the destination this is different from the case of conventional mimo systems where the input covariance matrix to achieve the ergodic channel capacity diagonalizes the channel autocorrelation matrix of the mimo system tulina lozano and verdu 2006 if the channel gains in conventional mimo systems are correlated gaussian random variables the input covariance matrix is a full matrix not block diagonal and if the channel gains are i i d gaussians the optimal input covariance matrix is a scaled identity the observations obtained in this paper reveal useful insights of how the af cooperative systems ldquomimicrdquo the conventional miso and mimo systems from the ergodic channel capacity perspective

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

rate of channel hardening of antenna selection diversity schemes and its implication on scheduling for a multiple antenna system we find a simple and accurate expression for the asymptotic distribution of the antenna selection gain when the transmitter selects the transmit antenna with the strongest channel we use this to estimate the underlying channel capacity distributions and obtain the approximate ergodic capacity this estimate is compared with upper and lower bounds this analysis demonstrates that unlike multiple input multiple output mimo systems the channel for antenna selection systems hardens at a slower rate and thus a significant multiuser scheduling gain can exist theta 1 logm for channel selection as opposed to theta 1 radicm for mimo where m is the number of transmit antennas

stochastic gradient algorithms for design of minimum error rate linear dispersion codes in mimo wireless systems linear dispersion ld codes are a good candidate for high data rate multiple input multiple ouput mimo signaling traditionally ld codes were designed by maximizing the average mutual information which cannot guarantee good error performance this paper presents a new design scheme for ld codes that directly minimizes the block error rate bler in mimo channels with arbitrary fading statistics and various detection algorithms for mimo systems employing ld codes the error rate does not admit an explicit form therefore we cannot use deterministic optimization methods to design the minimum error rate ld codes in this paper we propose a simulation based optimization methodology for the design of ld codes through stochastic approximation and simulation based gradient estimation the gradient estimation is done using the score function method originally developed in the discrete event system community the proposed method can be applied to design the minimum error rate ld codes for a variety of detector structures including the maximum likelihood ml detector and several suboptimal detectors it can also design optimal codes under arbitrary fading channel statistics in particular it can take into account the knowledge of spatial fading correlation at the transmitter and receiver ends simulation results show that codes generated by the proposed new design paradigm generally outperform the codes designed based on algebraic number theory

on the precoder design of flat fading mimo systems equipped with mmse receivers a large system approach this paper is devoted to the design of precoders maximizing the ergodic mutual information emi of bi correlated flat fading mimo systems equipped with mmse receivers the channel state information and the second order statistics of the channel are assumed available at the receiver side and at the transmitter side respectively as the direct maximization of the emi needs the use of nonattractive algorithms it is proposed to optimize an approximation of the emi introduced recently obtained when the number of transmit and receive antennas t and converge to at the same rate it is established that the relative error between the actual emi and its approximation is a o 1 t2 term it is shown that the left singular eigenvectors of the optimum precoder coincide with the eigenvectors of the transmit covariance matrix and its singular values are solution of a certain maximization problem numerical experiments show that the mutual information provided by this precoder is close from what is obtained by maximizing the true emi but that the algorithm maximizing the approximation is much less computationally intensive

a strong unique continuation theorem for parabolic equations the unique continuation is best understood for second order elliptic operators the classical paper by carleman 7 established the strong unique continuation theorem for second order elliptic operators which need not have analytic coefficients this was remarkable since it indicates that even a non analytic solution of an elliptic equation can behave somewhat in an analytic manner the powerful technique he used the so called carleman weighted inequality has played a central role in later developments in 1950 s aronszajn 4 and cordes 11 generalized his result to higher dimensions in recent years this classical subject caught new attention from a great number of people much efforts have been made to relax the smoothness hypotheses on the coefficients see 6 17 43 1 22 a seminal paper by jerison and kenig 26 has shown the unique continuation property for operators of the form c x with c l 2 loc where n 3 is the space dimension further improvements have been carried out in considering other classes of coefficients fefferman phong class and kato class 42 8 12 29 in extending the result to operators with first derivative terms and variable leading coefficients 46 47 51 52 and etc see 25 15 16 28 5 27 and the references therein for second order linear parabolic operators with time independent coefficients the strong unique continuation property along with detailed estimates on the hausdorff measures of nodal sets was reduced in 32 33 to the previously established elliptic counterparts the reduction from time independent parabolic

coalitional games in miso interference channels epsilon core and coalition structure stable set the multiple input single output interference channel is considered each transmitter is assumed to know the channels between itself and all receivers perfectly and the receivers are assumed to treat interference as additive noise in this setting noncooperative transmission does not take into account the interference generated at other receivers which generally leads to inefficient performance of the links to improve this situation we study cooperation between the links using coalitional games the players links in a coalition either perform zero forcing transmission or wiener filter precoding to each other the epsilon core is a solution concept for coalitional games that takes into account the overhead required in coalition deviation we provide necessary and sufficient conditions for the strong and weak epsilon core of our coalitional game not to be empty with zero forcing transmission since the epsilon core only considers the possibility of joint cooperation of all links we study coalitional games in partition form in which several distinct coalitions can form we propose a polynomial time distributed coalition formation algorithm based on coalition merging and prove that its solution lies in the coalition structure stable set of our coalition formation game simulation results reveal the cooperation gains for different coalition formation complexities and deviation overhead models

complete characterization of the pareto boundary for the miso interference channel in this correspondence we study the achievable rate region of the multiple input single output miso interference channel under the assumption that all receivers treat the interference as additive gaussian noise our main result is an explicit parametrization of the pareto boundary for an arbitrary number of users and antennas the parametrization describes the boundary in terms of a low dimensional manifold for the two user case we show that a single real valued parameter per user is sufficient to achieve all points on the pareto boundary and that any point on the pareto boundary corresponds to beamforming vectors that are linear combinations of the zero forcing zf and maximum ratio transmission mrt beamformers we further specialize the results to the miso broadcast channel bc a numerical example illustrates the result

asymptotic and non asymptotic analysis of uplink sum rate for relay assisted mimo cellular systems we consider uplink relay assisted mimo cellular systems with multiple relays deployed in each cell that perform the amplify and forward operations we are interested in obtaining deterministic expressions for the ergodic sum rate of such systems we first consider the large mimo dimension scenario and obtain two asymptotic sum rate expressions corresponding to the cases of fixed number of users and large number of users respectively we then consider the case of arbitrary mimo dimension and large number of users and obtain an upper and lower bound that the sum rate lies in between with high probability the bounds are tight when the number of users is large both single cell and multi cell systems are considered where the latter assumes full base station cooperation numerical experiments show that these deterministic sum rate expressions match well with the monte carlo simulation results therefore they can be useful tools for the design and analysis of relay assisted mimo cellular systems

distributed optimal beamformers for cognitive radios robust to channel uncertainties through spatial multiplexing and diversity multi input multi output mimo cognitive radio cr networks can markedly increase transmission rates and reliability while controlling the interference inflicted to peer nodes and primary users pus via beamforming the present paper optimizes the design of transmit and receive beamformers for ad hoc cr networks when cr to cr channels are known but cr to pu channels cannot be estimated accurately capitalizing on a norm bounded channel uncertainty model the optimal beamforming design is formulated to minimize the overall mean square error mse from all data streams while enforcing protection of the pu system when the cr to pu channels are uncertain even though the resultant optimization problem is non convex algorithms with provable convergence to stationary points are developed by resorting to block coordinate ascent iterations along with suitable convex approximation techniques enticingly the novel schemes also lend themselves naturally to distributed implementations numerical tests are reported to corroborate the analytical findings

on the capacity achieving covariance matrix for frequency selective mimo channels using the asymptotic approach in this contribution an algorithm for evaluating the capacity achieving input covariance matrices for frequency selective rayleigh mimo channels is proposed in contrast with the flat fading rayleigh case no closed form expressions for the eigenvectors of the optimum input covariance matrix are available classically both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding in this paper it is proposed to optimize w r t the input covariance matrix a large system approximation of the average mutual information derived by moustakas and simon the validity of this asymptotic approximation is clarified thanks to gaussian large random matrices methods it is shown that the approximation is a strictly concave function of the input covariance matrix and that the average mutual information evaluated at the argmax of the approximation is equal to the capacity of the channel up to a o 1 t term where t is the number of transmit antennas an algorithm based on an iterative waterfilling scheme is proposed to maximize the average mutual information approximation and its convergence studied numerical simulation results show that even for a moderate number of transmit and receive antennas the new approach provides the same results as direct maximization approaches of the average mutual information

stationary and oscillatory fronts in a two component genetic regulatory network model abstract we investigate a two component gene network model originally used to describe the spatiotemporal patterning of the gene products in early drosophila development by considering a particular mode of interaction between the two gene products denoted proteins a and b we find both stable stationary and time oscillatory fronts can occur in the reaction diffusion system we reduce the system by replacing b with its spatial average shadow system and assume an abrupt on and off switch for the genes in doing so explicit formula are obtained for all steady state solutions and their linear eigenvalues using the diffusion of a d a and the basal production rate r as bifurcation parameters we explore ranges in which a monotone stationary front is stable and show it can lose stability through a hopf bifurcation giving rise to oscillatory fronts we also discuss the existence and stability of steady state and time oscillatory solutions with multiple extrema an intuitive explanation for the occurrence of stable stationary and oscillatory front solutions is provided based on the behavior of a in the absence of b and the opposite regulation between a and b such behavior is also interpreted in terms of the biological parameters in the model including those governing the connection of the gene network

boundary value problems for various boundaries of hermitian symmetric spaces abstract the image of the poisson transform on a principal series representations on a boundary component of a hermitian symmetric space is considered we prove that the image is characterized by a covariant differential operator on a homogeneous line bundle on the symmetric space

convergence asymptotic periodicity and finite point blow up in one dimensional semilinear heat equations abstract we consider the initial value problem for the semilinear heat equation u t u xx f u t 0 x l t 0 under the dirichlet the neumann or the periodic boundary conditions we show that each solution whether it exists globally for t 0 or blows up in a finite time possesses an asymptotic profile in a certain sense and tends to this profile as time increases in the special case where f u t t f u t for some t 0 among other things the above statement is interpreted as saying that any bounded global solution converges as t to a time t periodic solution having some specific spatial structure in the case where the solution blows up in a finite time say at t t 0 assuming simply that f is a smooth function satisfying some growth conditions and that the initial data is a nonconstant bounded function we prove that the blow up set is a finite set and that lim t t 0 u x t x exists with being a smooth function having at most finitely many singular points

generalized eigenvector for decentralized transmit beamforming in the miso interference channel this paper deals with the problem of sum rate optimal transmit beamforming for the multiple input single output miso interference channel under realistic assumptions i e the beamformers are able to decrease the interference power level below the desired signal one we derive a decentralized beamformer that optimizes the sum rate this is of importance since it is known that obtaining the sum rate optimal transmit beamformer is an np hard problem the design is presented in closed form and thus it is adequate for the future wireless high data rate spectrum sharing networks due to its low complexity we evaluate its performance both analytically and numerically the results show that it behaves well in scenarios with practical level of interference and it outperforms the current decentralized designs when the channel link gains are asymmetric

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

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

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