an outer bound for the vector gaussian ceo problem we study the vector gaussian ceo problem where there are arbitrary number of agents each having a noisy observation of a vector gaussian source the goal of the agents is to describe the source to a central unit which wants to reconstruct the source within a given distortion the rate distortion region of the vector gaussian ceo problem is unknown in general here we provide an outer bound for the rate distortion region of the vector gaussian ceo problem we obtain our outer bound by evaluating an outer bound for the multiterminal source coding problem by means of a technique relying on the de bruijn identity and properties of the fisher information next we investigate the tightness of our outer bound although our outer bound is tight for certain cases we show that our outer bound does not provide the exact rate distortion region in general to this end we provide an example and show that the rate distortion region is strictly contained in our outer bound for this example

linear precoding bounds for wyner type cellular networks with limited base station cooperation and dynamic clustering this work studies the achievable average data rate in the downlink of a wyner type linear cellular network with limited cooperation and linear precoders we derive upper and lower bounds on the achievable average data rate subject to an average power constraint the bounds show that even a small number of cooperating base stations applying suboptimal linear precoding can approach optimal performance and significantly increase the average user data rates as compared to those achievable with noncooperating cellular systems we highlight the importance of dynamic clustering and of base station bs silencing dynamic clustering allows the system to build clusters that benefit some users at the expense of others and then shifts the priority between the users such a scheme results in higher average rates for all users while meeting some level of fairness bs silencing is shown to be important for limited cooperation networks in the high snr regime silencing is a simple and efficient way to reduce the interference and hence increase the user rates without increasing the number of cooperating bss the theoretical analysis is accompanied by several numerical examples in selected scenarios

an efficient greedy scheduler for zero forcing dirty paper coding in this paper an efficient greedy scheduler for zero forcing dirty paper coding zf dpc which can be incorporated in complex householder qr factorization of the channel matrix is proposed the ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by zf dpc is o m 1 while such ratio for the original greedy scheduler is o m where m is the number of transmitters therefore the new scheduler reduces the overhead of scheduling from being the bottleneck of zf dpc to being negligible

derivation of the bias of the normalized sample covariance matrix in a heterogeneous noise with application to low rank stap filter in a previous work we have developed a low rank lr spatio temporal adaptive processing stap filter when the disturbance is modeled as the sum of a low rank spherically invariant random vector sirv clutter and a zero mean white gaussian noise this lr stap filter is built from the normalized sample covariance matrix nscm and exhibits good robustness properties to secondary data contamination by target components in this correspondence we derive the bias of the nscm with this noise model we show that the eigenvectors estimated from the nscm are unbiased the new expressions of the expectation of nscm eigenvalues are also given from these results we also show that the estimate of the clutter subspace projector based on the nscm used in our lr stap is a consistent estimate of the true one results on numerical data validates the theoretical approach

user selection with zero forcing beamforming achieves the asymptotically optimal sum rate in this paper we propose a generalized greedy g greedy algorithm based on zero forcing beamforming zfbf for the multiple input multiple output mimo broadcast channel this algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations as previous results only give the scaling law of the sum rate of dirty paper coding dpc with the help of the g greedy structure we are able to obtain the exact limit of the dpc sum rate for a large number of users we also prove that the difference between the sum rates obtained by g greedy user selection and by dpc goes to zero as the number of users increases in addition to this we investigate one particular greedy user selection scheme called sequential water filling swf for this algorithm a complexity reduction is achieved by an iterative procedure based on an lq decomposition which converts the calculation of the moore penrose matrix inverse to one vector matrix multiplication a sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction with the help of the g greedy algorithm we prove that swf achieves the full dpc sum rate for a large number of users for a moderate number of users simulation demonstrates that compared with other user selection algorithms swf achieves a higher sum rate that is close to the maximal sum rate achievable by zfbf with the same order of complexity

robust lattice alignment for k user mimo interference channels with imperfect channel knowledge in this paper we consider a robust lattice alignment design for k user quasi static multiple input multiple output mimo interference channels with imperfect channel knowledge with random gaussian inputs the conventional interference alignment ia method has the feasibility problem when the channel is quasi static on the other hand structured lattices can create structured interference as opposed to the random interference caused by random gaussian symbols the structured interference space can be exploited to transmit the desired signals over the gaps however the existing alignment methods on the lattice codes for quasi static channels either require infinite signal to noise ratio snr or symmetric interference channel coefficients furthermore perfect channel state information csi is required for these alignment methods which is difficult to achieve in practice in this paper we propose a robust lattice alignment method for quasi static mimo interference channels with imperfect csi at all snr regimes and a two stage decoding algorithm to decode the desired signal from the structured interference space we derive the achievable data rate based on the proposed robust lattice alignment method where the design of the precoders decorrelators scaling coefficients and interference quantization coefficients is jointly formulated as a mixed integer and continuous optimization problem the effect of imperfect csi is also accommodated in the optimization formulation and hence the derived solution is robust to imperfect csi we also design a low complex iterative optimization algorithm for our robust lattice alignment method by using the existing iterative ia algorithm that was designed for the conventional ia method numerical results verify the advantages of the proposed robust lattice alignment method compared with the time division multiple access tdma two stage maximum likelihood ml decoding generalized han kobayashi hk distributive ia and conventional ia methods in the literature

performance analysis of covariance matrix estimates in impulsive noise this paper deals with covariance matrix estimates in impulsive noise environments physical models based on compound noise modeling spherically invariant random vectors sirv compound gaussian processes allow to correctly describe reality e g range power variations or clutter transitions areas in radar problems however these models depend on several unknown parameters covariance matrix statistical distribution of the texture disturbance parameters that have to be estimated based on these noise models this paper presents a complete analysis of the main covariance matrix estimates used in the literature four estimates are studied the well known sample covariance matrix mscm and a normalized version mn the fixed point fp estimate mfp and a theoretical benchmark mtfp among these estimates the only one of practical interest in impulsive noise is the fp the three others which could be used in a gaussian context are in this paper only of academic interest i e for comparison with the fp a statistical study of these estimates is performed through bias analysis consistency and asymptotic distribution this study allows to compare the performance of the estimates and to establish simple relationships between them finally theoretical results are emphasized by several simulations corresponding to real situations

performance of two low rank stap filters in a heterogeneous noise this paper considers the space time adaptive processing stap problem where the disturbance is modeled as the sum of a low rank lr spherically invariant random vector sirv clutter and a zero mean white gaussian noise to derive our adaptive lr stap filters the estimation of the projector onto the clutter subspace is performed from the sample covariance matrix scm and the normalized sample covariance matrix nscm we compute the theoretical performance of both corresponding lr stap filters through the analysis of the signal to interference plus noise ratio sinr loss based on a perturbation analysis numerical simulations validate the theoretical formula and allow to show that the lr stap filter built from the scm performance does not depend on the heterogeneity of the sirv clutter whereas the lr stap filter built from the nscm performance does

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

stable standing waves of nonlinear klein gordon equations in this paper we give sufficient conditions for the stability of the standing waves of least energy for nonlinear klein gordon equations

high snr analysis for mimo broadcast channels dirty paper coding versus linear precoding in this correspondence we compare the achievable throughput for the optimal strategy of dirty paper coding dpc to that achieved with suboptimal and lower complexity linear precoding techniques zero forcing and block diagonalization both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain but an absolute difference in terms of throughput does exist the sum rate difference between the two strategies is analytically computed at asymptotically high snr furthermore the difference is not affected by asymmetric channel behavior when each user has a different average snr weighted sum rate maximization is also considered in the process it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate

near capacity dirty paper code design a source channel coding approach this paper examines near capacity dirty paper code designs based on source channel coding we first point out that the performance loss in signal to noise ratio snr in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss which is a function of the granular loss from source coding and the target dirty paper coding rate or snr we then examine practical designs by combining trellis coded quantization tcq with both systematic and nonsystematic irregular repeat accumulate ira codes like previous approaches we exploit the extrinsic information transfer exit chart technique for capacity approaching ira code design but unlike previous approaches we emphasize the role of strong source coding to achieve as much granular gain as possible using tcq instead of systematic doping we employ two relatively shifted tcq codebooks where the shift is optimized via tuning the exit charts to facilitate the ira code design our designs synergistically combine tcq with ira codes so that they work together as well as they do individually by bringing together tcq the best quantizer from the source coding community and exit chart based ira code designs the best from the channel coding community we are able to approach the theoretical limit of dirty paper coding for example at 0 25 bit per symbol b s our best code design with 2048 state tcq performs only 0 630 db away from the shannon capacity

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

rate balancing in multiuser mimo ofdm systems recently the capacity region of the gaussian broadcast channel has been characterized for a given transmit power constraint those points on the boundary of the capacity region can be regarded as the set of optimal operational points the present work addresses the problem of selecting the point within this set that satisfies given constraints on the ratios between rates achieved by the different users in the network this problem is usually known as rate balancing to this end the optimum iterative approach for general mimo channels is revisited and adapted to an ofdm transmission scheme specifically an algorithm is proposed that exploits the structure of the ofdm channel and whose convergence speed is essentially insensitive to the number of subcarriers this is in contrast to a straightforward extension of the general mimo algorithm to an ofdm scheme still relatively high complexity and the need of a time sharing policy to reach certain rates are at least two obstacles for a practical implementation of the optimum solution based on a novel decomposition technique for broadcast channels a suboptimum non iterative algorithm is introduced that does not require time sharing and very closely approaches the optimum solution

k user symmetric m times n mimo interference channel under finite precision csit a gdof perspective generalized degrees of freedom gdof are characterized for the symmetric k user multiple input multiple output interference channel under the assumption that the channel state information at the transmitters csits is limited to finite precision in this symmetric setting each transmitter is equipped with m antennas each receiver is equipped with n antennas each desired channel i e a channel between a transmit antenna and a receive antenna belonging to the same user has strength sim p while each undesired channel has strength sim p alpha where p is a nominal snr parameter the result generalizes a previous gdof characterization for the siso setting m n 1 and is enabled by a significant extension of the aligned image sets bound that is broadly useful gdof per user take the form of a w curve with respect to alpha for fixed values of m and n under finite precision csit in spite of the presence of multiple antennas all the benefits of interference alignment are lost

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

on vector perturbation precoding for the mimo gaussian broadcast channel precoding schemes in the framework of vector perturbation vp for the multiple input multiple output mimo gaussian broadcast channel gbc are investigated the vp scheme originally a one shot technique is generalized to encompass processing over multiple time instances using lattice based extended alphabets perturbations and considering the infinite time span extension limit a lower bound on the achievable sum rate using the generalized vp scheme is analytically obtained the lower bound is shown to asymptotically achieve the optimum sum rate in the high signal to noise ratio snr regime both in terms of degrees of freedom and power offset for any number of users and transmit antennas for the two user cases it is shown that the lower bound coincides with the sum capacity for low snr the above lower bound is constructively obtained by means of an efficient practically oriented suboptimal transmit energy minimization algorithm which exhibits a polynomial complexity in the number of users the proposed precoding scheme demonstrates that the shaping gain is achievable for vp schemes when employing good multidimensional lattices it is also shown that the suboptimum algorithm has its merits even when processing over multiple time instances is not employed for the 2 times 2 mimo gbc the vp scheme is generalized further and an inner bound for the entire achievable rate region is obtained by which an interesting correspondence is identified with the ultimate capacity region as obtained by dirty paper coding

tomlinson harashima precoding for multiuser mimo systems with quantized csi feedback and user scheduling this paper studies the sum rate performance of a low complexity quantized csi based tomlinson harashima th precoding scheme for downlink multiuser mimo transmission employing greedy user selection the asymptotic distribution of the output signal to interference plus noise ratio of each selected user and the asymptotic sum rate as the number of users k grows large are derived by using extreme value theory for fixed finite signal to noise ratios and a finite number of transmit antennas n t we prove that as k grows large the proposed approach can achieve the optimal sum rate scaling of the mimo broadcast channel we also prove that if we ignore the precoding loss the average sum rate of this approach converges to the average sum capacity of the mimo broadcast channel our results provide insights into the effect of multiuser interference caused by quantized csi on the multiuser diversity gain

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

on the equivalence between stein and de bruijn identities this paper focuses on illustrating 1 the equivalence between stein s identity and de bruijn s identity and 2 two extensions of de bruijn s identity first it is shown that stein s identity is equivalent to de bruijn s identity under additive noise channels with specific conditions second for arbitrary but fixed input and noise distributions under additive noise channels the first derivative of the differential entropy is expressed by a function of the posterior mean and the second derivative of the differential entropy is expressed in terms of a function of fisher information several applications over a number of fields such as signal processing and information theory are presented to support the usefulness of the developed results in this paper

how much does transmit correlation affect the sum rate scaling of mimo gaussian broadcast channels this paper considers the effect of spatial correlation between transmit antennas on the sum rate capacity of the mimo gaussian broadcast channel i e downlink of a cellular system specifically for a system with a large number of users n we analyze the scaling laws of the sum rate for the dirty paper coding and for different types of beamforming transmission schemes when the channel is i i d it has been shown that for large n the sum rate is equal to m log log n m log p m o 1 where m is the number of transmit antennas p is the average signal to noise ratio and o 1 refers to terms that go to zero as n rarr infin when the channel exhibits some spatial correlation with a covariance matrix r non singular with tr r m we prove that the sum rate of dirty paper coding is m log log n m log p m log det r o 1 we further show that the sum rate of various beamforming schemes achieves m log log n m log p m m log c o 1 where c les 1 depends on the type of beamforming we can in fact compute c for random beamforming proposed in and more generally for random beamforming with preceding in which beams are pre multiplied by a fixed matrix simulation results are presented at the end of the paper

transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

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

toward a practical scheme for binary broadcast channels with varying channel quality using dirty paper coding we consider practical schemes for binary dirty paper channels and broadcast channels bcs with two receivers and varying channel quality with the bc application in mind this paper proposes a new design for binary dirty paper coding dpc by exploiting the concept of coset binning the complexity of the system is greatly reduced when compared to the existing works some design challenges of the coset binning approach are identified and addressed the proposed binary dpc system achieves similar performance to the state of the art superposition coding based system while demonstrating significant advantages in terms of complexity and flexibility of system design for binary bcs achieving the capacity generally requires the superposition of a normal channel code and a carefully designed channel code with non uniform bit distribution the non uniform bit distribution is chosen according to the channel conditions therefore to achieve the capacity for binary bcs with varying channel quality it is necessary to use quantization codes of different rates which significantly increases the implementation complexity in this paper we also propose a broadcast scheme that generalizes the concept of binary dpc which we term soft dpc by combining soft dpc with time sharing we achieve a large percentage of the capacity for a wide range of channel quality with little complexity overhead our scheme uses only one fixed pair of codes for users 1 and 2 and a single quantization code which possesses many practical advantages over traditional time sharing and superposition coding solutions and provides strictly better performance

a new entropy power inequality for integer valued random variables the entropy power inequality epi yields lower bounds on the differential entropy of the sum of two independent real valued random variables in terms of the individual entropies versions of the epi for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy but no universal inequality is known beyond trivial ones more recently the sumset theory for the entropy function yields a sharp inequality h x x prime h x geq 1 over 2 o 1 when x x prime are independent identically distributed i i d with high entropy this paper provides the inequality h x x prime h x geq g h x where x x prime are arbitrary i i d integer valued random variables and where g is a universal strictly positive function on bbr satisfying g 0 0 extensions to nonidentically distributed random variables and to conditional entropies are also obtained

aligned image sets under channel uncertainty settling conjectures on the collapse of degrees of freedom under finite precision csit a conjecture made by lapidoth et al at allerton 2005 also an open problem presented at ita 2006 states that the degrees of freedom dof of a two user broadcast channel where the transmitter is equipped with two antennas and each user is equipped with one antenna must collapse under finite precision channel state information at the transmitter csit that this conjecture which predates interference alignment has remained unresolved is emblematic of a pervasive lack of understanding of the dof of wireless networks including interference and x networks under channel uncertainty at the transmitter s in this paper we prove that the conjecture is true in all non degenerate settings e g where the probability density function of unknown channel coefficients exists and is bounded the dof collapse even when perfect channel knowledge for one user is available to the transmitter this also settles a related recent conjecture by tandon et al the key to our proof is a bound on the number of codewords that can cast the same image within noise distortion at the undesired receiver whose channel is subject to finite precision csit while remaining resolvable at the desired receiver whose channel is precisely known by the transmitter we are also able to generalize the result along two directions first if the peak of the probability density function is allowed to scale as o sqrt p alpha representing the concentration of probability density improving csit due to e g quantized feedback at rate alpha 2 log p then the dof is bounded above by 1 alpha which is also achievable under quantized feedback second we generalize the result to arbitrary number of antennas at the transmitter arbitrary number of single antenna users and complex channels the generalization directly implies a collapse of dof to unity under non degenerate channel uncertainty for the general k user interference and m times n user x networks as well

on the user selection for mimo broadcast channels in this paper a downlink communication system in which a base station bs equipped with antennas communicates with users each equipped with receive antennas is considered an efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum rate throughput of the system in a rayleigh fading environment for the asymptotic case when tends to infinity the necessary and sufficient conditions in order to achieve the maximum sum rate throughput such that the difference between the achievable sum rate and the maximum value approaches zero is derived the complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the bs as well as the number of searches required for selecting the users it is shown that the proposed method is capable of achieving a large portion of the sum rate capacity with a very low complexity

recursive estimation of the covariance matrix of a compound gaussian process and its application to adaptive cfar detection adaptive detection of signals embedded in gaussian or non gaussian noise is a problem of primary concern among radar engineers we propose a recursive algorithm to estimate the structure of the covariance matrix of either a set of gaussian vectors that share the spectral properties up to a multiplicative factor or a set of spherically invariant random vectors sirvs with the same covariance matrix and possibly correlated texture components we also assess the performance of an adaptive implementation of the normalized matched filter nmf relying on the newly introduced estimate in the presence of compound gaussian clutter dominated disturbance in particular it is shown that a proper initialization of the recursive procedure leads to an adaptive nmf with the constant false alarm rate cfar property and that it is very effective to operate in heterogeneous environments of relevant practical interest

degrees of freedom region of the m n n mimo broadcast channel with partial csit an application of sum set inequalities based on aligned image sets the degrees of freedom dof region is characterized for the 2 user multiple input multiple output mimo broadcast channel bc where the transmitter is equipped with m antennas the two receivers are equipped with n 1 and n 2 antennas and the levels of channel state information at the transmitter csit for the two users are parameterized by beta 1 beta 2 respectively the achievability of the dof region was established by hao rassouli and clerckx but no proof of optimality was heretofore available the proof of optimality is provided in this work with the aid of sum set inequalities based on the aligned image sets ais approach

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

a strong entropy power inequality when one of the random summands is gaussian we sharpen the entropy power inequality epi in terms of the strong data processing function for gaussian channels among other consequences this strong epi generalizes the vector extension of costa s epi to non gaussian channels in a precise sense this leads to a new reverse epi and as a corollary sharpens stam s uncertainty principle relating entropy power and fisher information or equivalently gross logarithmic sobolev inequality applications to network information theory are also given including a short self contained proof of the rate region for the two encoder quadratic gaussian source coding problem and a new outer bound for the one sided gaussian interference channel

on the evaluation of marton s inner bound for two receiver broadcast channels marton s inner bound is the best known achievable rate region for a general two receiver discrete memoryless broadcast channel in this paper we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region we combine a perturbation technique along with a representation using concave envelopes of information theoretic functions that involve the use of auxiliary random variables to achieve this improvement the new cardinality bounds lead to a proof that a randomized time division strategy achieves every rate triple in marton s region for binary input broadcast channels this extends the result by hajek and pursley which showed that the cover van der muelen region was exhausted by the randomized time division strategy

partial interference alignment for k user mimo interference channels in this paper we consider a partial interference alignment and interference detection piaid design for k user quasi static mimo interference channels with discrete constellation inputs each transmitter has m antennas and transmits l independent data streams to the desired receiver with n receive antennas we focus on the case where not all k 1 interfering transmitters can be aligned at every receiver as a result there will be residual interference at each receiver that cannot be aligned each receiver detects and cancels the residual interference based on the constellation map however there is a window of unfavorable interference profile at the receiver for interference detection id in this paper we propose a low complexity partial interference alignment scheme in which we dynamically select the user set for ia so as to create a favorable interference profile for id at each receiver we first derive the average symbol error rate ser by taking into account of the non guassian residual interference due to discrete constellation using graph theory we then devise a low complexity user set selection algorithm for the piaid scheme which minimizes the asymptotically tight bound for the average end to end ser performance moreover we substantially simplify interference detection at the receiver using semi definite relaxation sdr techniques it is shown that the ser performance of the proposed piaid scheme has significant gain compared with various conventional baseline solutions

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

on the equivalence of two achievable regions for the broadcast channel a recent inner bound on the capacity region of the two receiver discrete memoryless broadcast channel is shown to be equivalent to the marton gelfand pinsker region the proof method is based on a result of gelfand and pinsker concerning channel input distributions

on gaussian mimo bc mac duality with multiple transmit covariance constraints owing to the special structure of the gaussian multiple input multiple output mimo broadcast channel bc the associated capacity region computation and beamforming optimization problems are typically non convex and thus cannot be solved directly one feasible approach is to consider the respective dual multiple access channel mac problems which are easier to deal with due to their convexity properties the conventional bc mac duality has been established via bc mac signal transformation and is applicable only for the case in which the mimo bc is subject to a single transmit sum power constraint an alternative approach is based on minimax duality which can be applied to the case of the sum power constraint or per antenna power constraint in this paper the conventional bc mac duality is extended to the general linear transmit covariance constraint ltcc case which includes sum power and per antenna power constraints as special cases the obtained general bc mac duality is applied to solve the capacity region computation for the mimo bc and beamforming optimization for the multiple input single output miso bc respectively with multiple ltccs the relationship between this new general bc mac duality and the minimax duality is also discussed and it is shown that the general bc mac duality leads to simpler problem formulations moreover the general bc mac duality is extended to deal with the case of nonlinear transmit covariance constraints in the mimo bc

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

robust covariance matrix estimation in heterogeneous low rank context this paper addresses the problem of robust covariance matrix cm estimation in the context of a disturbance composed of a low rank lr heterogeneous clutter plus an additive white gaussian noise the lr clutter is modeled by a spherically invariant random vector with assumed high clutter to noise ratio in such a context adaptive process should require less training samples than classical methods to reach equivalent performance as in a full rank clutter configuration the main issue is that classical robust estimators of the cm cannot be computed in the undersampled configuration to overcome this issue the current approach is based on regularization methods nevertheless most of these solutions are enforcing the estimate to be well conditioned while in our context it should be lr structured this paper therefore addresses this issue and derives an algorithm to compute the maximum likelihood estimator of the cm for the considered disturbance model several relaxations and robust generalizations of the result are discussed performance is finally illustrated on numerical simulations and on a space time adaptive processing for airborne radar application

eigen based transceivers for the mimo broadcast channel with semi orthogonal user selection this paper studies the sum rate performance of two low complexity eigenmode based transmission techniques for the mimo broadcast channel employing greedy semi orthogonal user selection sus the first approach termed zfdpc sus is based on zero forcing dirty paper coding the second approach termed zfbf sus is based on zero forcing beamforming we first employ new analytical methods to prove that as the number of users k grows large the zfdpc sus approach can achieve the optimal sum rate scaling of the mimo broadcast channel we also prove that the average sum rates of both techniques converge to the average sum capacity of the mimo broadcast channel for large k in addition to the asymptotic analysis we investigate the sum rates achieved by zfdpc sus and zfbf sus for finite k and show that zfdpc sus has significant performance advantages our results also provide key insights into the benefit of multiple receive antennas and the effect of the sus algorithm in particular we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second order behavior of the multi user diversity gain for finite k the benefit can be very significant we also show the interesting result that the semi orthogonality constraint imposed by sus whilst facilitating a very low complexity user selection procedure asymptotically does not reduce the multi user diversity gain in either first k or second order k terms

full rank solutions for the mimo gaussian wiretap channel with an average power constraint this paper considers a multiple input multiple output mimo gaussian wiretap channel with a transmitter a legitimate receiver and an eavesdropper each equipped with multiple antennas we first study the rank of the optimal input covariance matrix that achieves the secrecy capacity of the mimo gaussian wiretap channel under an average power constraint the rank and other properties of the optimal solution are derived based on certain relationships between the channel matrices for the legitimate receiver and eavesdropper next by obtaining necessary and sufficient conditions on the mimo wiretap channel parameters we determine the conditions under which the optimal input covariance matrix is full rank or rank deficient for the case that the optimal input covariance is full rank we fully characterize the solution when the optimal input covariance is rank deficient we show that the given mimo wiretap channel can be modeled by an equivalent wiretap channel whose optimal input covariance is full rank and achieves the same secrecy capacity as the original system numerical results are presented to illustrate the proposed theoretical findings

instability of nonlinear bound states we establish a sharp instability theorem for the bound states of lowest energy of the nonlinear klein gordon equation utt u f u 0 and the nonlinear schrodinger equation iut u f u 0

asymptotic analysis of the amount of csi feedback in mimo broadcast channels in this paper we consider a downlink communication system in which a base station bs equipped with m antennas and power constraint p communicates with n users each equipped with k receive antennas it is assumed that the users have perfect channel state information csi of their own channels while the bs only knows the partial csi provided by the receivers via a feedback channel we study the fundamental limits on the amount of feedback required at the bs to achieve the sum rate capacity of the system when bs has perfect csi for all users in the asymptotic case of n considering various signal to noise ratio snr regimes the main results of this paper can be expressed as follows 1 in the fixed snr regime where the snr does not scale with n and low snr regime where the snr is much smaller than 1 in n to achieve the 1 e portion of the sum rate capacity the total amount of feedback should scale at least with e 1 in the fixed snr regime to reduce the gap between the achievable sum rate and the sum rate capacity of the system which is defined as the sum rate gap to zero the amount of feedback should scale at least logarithmically with the sum rate capacity which is achievable by using the random beam forming rbf scheme proposed by sharif and hassibi in the low snr regime we propose an opportunistic beam forming obf scheme which is shown to be asymptotically feedback optimal 2 in the high snr regime where the snr grows to infinity as n the total amount of feedback depends on the number of receive antennas in particular to reduce the sum rate gap to zero in the case of k 1 m 1 should scale at least logarithmically with the snr in the case of k m the amount of feedback does not need to scale with the snr moreover we show that rbf is asymptotically feedback optimal in the high snr regime

on mmse vector perturbation precoding for mimo broadcast channels with per antenna group power constraints recently studies on suboptimal precoding techniques for multiple input multiple output broadcast channels mimo bc which achieve performance near to that of the dirty paper coding dpc have drawn attention to vector perturbation vp precoding in practice each antenna or more generally each antenna group has its own limit on the transmitted power which makes per antenna group power constraints more meaningful than the sum power constraint in this paper we introduce an optimization technique for vp precoding employing the minimum mean square error mmse criterion with per antenna group power constraints this technique is inspired by the p sphere encoding in a sense that it involves finding the node with the lowest mean square error mse over a lattice we demonstrate that the mse metric as well as the p norm one can be enclosed in a proper frobenius norm ball this frobenius norm ball shrinks until it captures the perturbing vector minimizing the mse numerical results show that the proposed algorithm outperforms conventional vp precoding and the p sphere encoding but at higher complexity consequently we investigate a couple of simplified techniques employing the mmse criterion which perform almost as well as the proposed precoding technique but are less complex

exact sum rate analysis of mimo broadcast channels with random unitary beamforming random unitary beamforming rub is an attractive transmission scheme for mimo broadcast channels because of its ability to achieve high sum rate capacity with limited feedback in this letter we derive the exact analytical expressions for the ergodic sum rate of mimo broadcast channels with rub the analysis is facilitated by the development of the complete statistical characterization of ordered beam sinrs for a user which can find their application in many related problems

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 vector perturbation with user selection for multiuser mimo downlink recent works on multiuser mimo study have shown that the linear growth of capacity in single user mimo system can be translated to the multiuser mimo scenario as well in this paper we propose a method pursuing performance gain of vector perturbation in multiuser downlink systems instead of employing the maximum number of mobile users for communication we use small part of them as virtual users for improving reliability of users participating communication by controlling parameters of the virtual users including information and perturbation vector we obtain considerable improvement in the effective snr simulation results on the realistic multiuser miso and mimo downlink systems show that the proposed method brings substantial performance gain over the standard vector perturbation with marginal overhead in computations

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

an extremal inequality motivated by multiterminal information theoretic problems we prove a new extremal inequality motivated by the vector gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems as a corollary this inequality yields a generalization of the classical entropy power inequality epi as another corollary this inequality sheds insight into maximizing the differential entropy of the sum of two dependent random variables

the capacity region of the degraded multiple input multiple output compound broadcast channel the capacity region of a compound multiple antenna broadcast channel is characterized when the users exhibit a certain degradedness order the channel under consideration has two users each user has a finite set of possible realizations the transmitter transmits two messages one for each user in such a manner that regardless of the actual realizations both users will be able to decode their messages correctly an alternative view of this channel is that of a broadcast channel with two common messages each common message is intended to a different set of users the degradedness order between the two sets of realizations users is defined through an additional fictitious user whose channel is degraded with respect to all realizations users from one set while all realizations users from the other set are degraded with respect to him

blow up near higher modes of nonlinear wave equations etude des proprietes d instabilite des modes superieurs de l equation des ondes non lineaire u tt u f u 0 definie sur un domaine a frontiere reguliere avec des conditions aux limites de dirichlet

information theoretic proofs of entropy power inequalities while most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information up to now shannon s entropy power inequality epi is an exception existing information theoretic proofs of the epi hinge on representations of differential entropy using either fisher information or minimum mean square error mmse which are derived from de bruijn s identity in this paper we first present an unified view of these proofs showing that they share two essential ingredients 1 a data processing argument applied to a covariance preserving linear transformation 2 an integration over a path of a continuous gaussian perturbation using these ingredients we develop a new and brief proof of the epi through a mutual information inequality which replaces stam and blachman s fisher information inequality fii and an inequality for mmse by guo shamai and verdu used in earlier proofs the result has the advantage of being very simple in that it relies only on the basic properties of mutual information these ideas are then generalized to various extended versions of the epi zamir and feder s generalized epi for linear transformations of the random variables takano and johnson s epi for dependent variables liu and viswanath s covariance constrained epi and costa s concavity inequality for the entropy power

onset of chaos in differential delay equations abstract in the present paper we study the onset of chaos in the differential delay equation x dot t x t bx t 2 1 x 10 t 2 b 0 we develop a new numerical technique and apply it to study the global behavior of the flow on the attractor using this technique we find unstable periodic orbits connections between different periodic orbits transverse homoclinic orbits and try to explain the underlying reason for chaos

multi cell mimo downlink with cell cooperation and fair scheduling a large system limit analysis we consider the downlink of a cellular network with multiple cells and multi antenna base stations our model includes distance dependent pathloss arbitrary clusters of cooperating cells and general fairness requirements beyond monte carlo simulation no efficient computation method to evaluate the ergodic throughput of such systems has been presented yet furthermore for systems of practical size with tens of cells and hundreds of users per cell even simulation becomes challenging we develop an analytic framework based on the combination of results from large random matrix theory and convex optimization this allows computationally efficient calculation of the system performance in the so called large system limit i e in the limit of a large number of antennas per base station and a large number of users per cell while the ratio of antennas per user is kept constant in particular the system ergodic throughput subject to per base station power constraints and to general fairness criteria is obtained via the iterative solution of a system of fixed point equations comparisons with finite dimensional simulation results show that the large system analysis provides remarkably accurate approximations for the actual finite dimensional systems even for a small number of users and base station antennas

channel state feedback over the mimo mac in order to exploit the full multiplexing gain of multi antenna multi user downlink schemes accurate channel state information at the transmitter i e at the base station is required we consider the design of a closed loop channel state information feedback scheme where user terminals feed back their channel state information simultaneously to a multi antenna base station the underlying information theoretic problem consists of lossy source channel coding of multiple independent analog sources i e the users channel coefficients over a gaussian multiple input multiple output multi access channel mimo mac unlike the classical source channel coding setting this application requires low latency otherwise the channel state information would be outdated hence source channel codewords can span only a single fading state of the uplink feedback channel furthermore the transmitters are ignorant of the realization of the uplink channel coefficients in this scenario the scaling of the maximum of the estimated downlink channel mean square errors with the snr dominates the performance of the multiuser downlink this scaling is described by the distortion snr exponent previously introduced in a single user mimo setting this paper analyzes the max min distortion snr exponent of the mimo mac for both separated source channel coding and a particular hybrid digital analog joint source channel coding scheme for the case of single antenna users we prove that the distortion snr exponent of separated source channel coding can be achieved by the concatenation of scalar quantization and uncoded quadrature amplitude modulation qam transmission with lattice decoding at the base station receiver the resulting scheme has very low encoding latency only a few symbols of the uplink slot and generally outperforms currently proposed channel state feedback schemes based on analog unquantized transmission or vector quantization with fixed codebooks

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

sum set inequalities from aligned image sets instruments for robust gdof bounds we present sum set inequalities specialized to the generalized degrees of freedom gdof framework these are information theoretic lower bounds on the entropy of bounded density linear combinations of discrete power limited dependent random variables in terms of the joint entropies of arbitrary linear combinations of new random variables that are obtained by power level partitioning of the original random variables these bounds generalize the aligned image sets approach and are useful instruments to obtain gdof characterizations for wireless networks especially with multiple antenna nodes subject to arbitrary channel strength and channel uncertainty levels to demonstrate the utility of these bounds we consider various examples of interference and broadcast channels for which we obtain tight gdof characterizations with the aid of sum set inequalities

a limited feedback joint precoding for amplify and forward relaying this paper deals with the practical precoding design for a dual hop downlink with multiple input multiple output mimo amplify and forward relaying first assuming that full channel state information csi of the two hop channels is available a suboptimal dual hop joint precoding scheme i e precoding at both the base station and relay station is investigated based on its structure a scheme of limited feedback joint precoding using joint codebooks is then proposed which uses a distributed codeword selection to concurrently choose two joint precoders such that the feedback delay is considerably decreased finally the joint codebook design for the limited feedback joint precoding system is analyzed and results reveal that independent codebook designs at the base station and relay station using the conventional grassmannian subspace packing method is able to guarantee that the overall performance of the dual hop joint precoding scheme improves with the size of each of the two codebooks simulation results show that the proposed dual hop joint precoding system using distributed codeword selection scheme exhibits a rate or ber performance close to the one using the optimal centralized codeword selection scheme while having lower computational complexity and shorter feedback delay

asymptotic achievability of the cramer rao bound for noisy compressive sampling we consider a model of the form y ax n where x isin cm is sparse with at most l nonzero coefficients in unknown locations y isin cn is the observation vector a isin cn times m is the measurement matrix and n isin cn is the gaussian noise we develop a cramer rao bound on the mean squared estimation error of the nonzero elements of x corresponding to the genie aided estimator gae which is provided with the locations of the nonzero elements of x intuitively the mean squared estimation error of any estimator without the knowledge of the locations of the nonzero elements of x is no less than that of the gae assuming that l n is fixed we establish the existence of an estimator that asymptotically achieves the cramer rao bound without any knowledge of the locations of the nonzero elements of x as n rarr infin for a a random gaussian matrix whose elements are drawn i i d according to n 0 1

vector gaussian two terminal source coding we derive a lower bound on each supporting line of the rate region of the vector gaussian two terminal ceo problem which is a special case of the indirect vector gaussian two terminal source coding problem the key technical ingredient is a new extremal inequality it is shown that the lower bound coincides with the berger tung upper bound in the high resolution regime similar results are derived for the direct vector gaussian two terminal source coding problem

a vector generalization of costa s entropy power inequality with applications this paper considers an entropy power inequality epi of costa and presents a natural vector generalization with a real positive semidefinite matrix parameter the new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean square error mmse estimate in linear vector gaussian channels as an application a new extremal entropy inequality is derived from the generalized costa epi and then used to establish the secrecy capacity regions of the degraded vector gaussian broadcast channel with layered confidential messages

the capacity region of the two receiver gaussian vector broadcast channel with private and common messages a novel method for establishing the optimality of gaussian auxiliary random variables in multiterminal information theory problems is developed this method is then employed to show that marton s inner bound achieves the capacity region of the two receiver gaussian vector broadcast channel with private and common messages

the rate distortion function for product of two sources with side information at decoders this paper investigates a lossy source coding problem in which two decoders can access their respective side information the correlated sources are a product of two component correlated sources and we exclusively investigate the case such that each component is degraded we show the rate distortion function for that case and give the following observations when the components are degraded in matched order the rate distortion function of the product sources is equal to the sum of the componentwise rate distortion functions on the other hand the former is strictly smaller than the latter when the component sources are degraded in mismatched order the converse proof for the mismatched case is motivated by the enhancement technique used for broadcast channels for binary hamming and gaussian examples we evaluate the rate distortion functions

precoding for the multiantenna downlink multiuser snr gap and optimal user ordering this paper develops a practical design method for implementing tomlinson harashima precoding thp in a downlink channel with multiple antennas at the transmitter and a single antenna at each receiver a two step design process is proposed for minimizing the total transmit power while satisfying every user s minimum data rate and maximum bit error rate ber requirements first the ber and rate requirements are converted to virtual rate requirements which account for the gap to capacity introduced by practical quadrature amplitude modulation qam and thp the second step is to determine the transmit covariance matrices which specify the entire thp system that will provide these virtual rates at the minimum total transmit power as one of the main features in the proposed scheme an algorithm for finding the optimal user encoding or presubtraction order in polynomial time is proposed in addition we also propose an algorithm that finds a near optimal order but which is much less complex the proposed method outperforms existing zero forcing based thp systems in term of power efficiency

the dirty mimo multiple access channel in the scalar dirty multiple access channel in addition to gaussian noise two additive interference signals are present each known non causally to a single transmitter it was shown by philosof et al that for strong interferences an independent identically distributed ensemble of codes does not achieve the capacity region rather a structured codes approach was presented that was shown to be optimal in the limit of high signal to noise ratios where the sum capacity is dictated by the minimal bottleneck channel gain in this paper we consider the multiple input multiple output mimo variant of this setting in order to incorporate structured codes in this case one can utilize matrix decompositions that transform the channel into effective parallel scalar dirty multiple access channels this approach however suffers from a bottleneck effect for each effective scalar channel and therefore the achievable rates strongly depend on the chosen decomposition it is shown that a recently proposed decomposition where the diagonals of the effective channel matrices are equal up to a scaling factor is optimal at high signal to noise ratios under an equal rank assumption this approach is then extended to any number of transmitters finally an application to physical layer network coding for the mimo two way relay channel is presented

a spectral method for nonlinear wave equations abstract in this paper we introduce a new integration technique to find radially symmetric solutions of nonlinear wave equations defined on a spherical domain with dirichlet boundary conditions and we use this technique to study orbital stability of the standing waves we prove analytically that the wave of lowest energy is stable and we show by numerical computations that the standing waves of higher energy are unstable

adaptive double subspace signal detection in gaussian background part i homogeneous environments in this two part paper we consider the problem of adaptive multidimensional multichannel signal detection in gaussian noise with unknown covariance matrix the test data primary data is assumed as a collection of sample vectors arranged as the columns of a rectangular data array the rows and columns of the signal matrix are both assumed to lie in known subspaces but with unknown coordinates due to this feature of the signal structure we name this kind of signal as the double subspace signal part i of this paper focuses on the adaptive detection in homogeneous environments while part ii deals with the adaptive detection in partially homogeneous environments precisely in this part we derive the generalized likelihood ratio test glrt rao test wald test as well as their two step variations in homogeneous environments three types of spectral norm tests snts are also introduced all these detectors are shown to possess the constant false alarm rate cfar property moreover we discuss the differences between them and show how they work another contribution is that we investigate various special cases of these detectors remarkably some of them are well known existing detectors while some others are still new at the stage of performance evaluation conducted by monte carlo simulations both matched and mismatched signals are dealt with for each case more than one scenario is considered

unstable ground state of nonlinear klein gordon equations on demontre l instabilite de l etat fondamental des equations de klein gordon non lineaires a n dimensions d espace n 3

an alternative proof for the capacity region of the degraded gaussian mimo broadcast channel we provide an alternative proof for the capacity region of the degraded gaussian multiple input multiple output mimo broadcast channel our proof does not use the channel enhancement technique as opposed to the original proof of weingertan and the alternative proof of liu et al our proof starts with the single letter description of the capacity region of the degraded broadcast channel and by using it obtains a tight i e achievable outer bound for the capacity region of the degraded gaussian mimo broadcast channel by using two main technical tools the first one is the generalized de bruijn identity due to palomar which provides a connection between the differential entropy and the fisher information matrix the second tool we use is an inequality due to dembo which lower bounds the differential entropy in terms of the fisher information matrix

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

gaussian state amplification with noisy observations we consider the problem of channel state amplification in a gaussian channel with additive gaussian channel states where the encoder observes noncausally a noisy version of these states a complete characterization is provided for the minimum reconstruction distortion under a transmitter power constraint and it is shown that a simple analog scheme with power control is optimal more precisely if the power available to the encoder is below certain threshold the analog scheme using full power is optimal however when the power available to the encoder is above that threshold analog transmission using only a fixed amount of the available power is optimal furthermore the problem of simultaneous message transmission and gaussian state amplification with noisy observations is studied for which an inner bound and two nontrivial outer bounds to the optimal tradeoff between the transmission rate and the state reconstruction distortion are provided the coding scheme underlying the inner bound combines analog signaling and gelfand pinsker coding where the latter deviates from the operating point of costa s dirty paper coding the first outer bound is obtained by extending the channel decomposition technique while the second outer bound requires a strategic analysis of the covariance matrix of the relevant random variables

secure communications for dual polarized mimo systems to enhance secure communications we deploy the dual polarized antenna arrays at communication nodes of the multi input multioutput mimo system where the base station communicates with multiple legitimate users in the presence of an eavesdropper we also adopt the dual structured precoding in which a preprocessing matrix based on the polarized array spatial correlation and a linear precoding based on the instantaneous channel state information csi are concatenated we design this dual structured multiuser linear precoding under three cases in the first case given perfect global csi the secrecy rate optimization problem is formulated and transformed into the weighted minimum mean square error mse problem which can be effectively solved by the block coordinate decent method in the second case where the eavesdropper s csi is unavailable an artificial noise is generated to confuse the eavesdropper by minimizing the information transmit power subject to a preset mse threshold for the recovered confidential signals which can be solved by an efficient iterative algorithm in the third case of imperfect global csi the robust optimization for secure communications is performed by minimizing the largest received mse among the users subject to the total transmit power constraint which can be reformulated into a biconvex semidefinite programming problem and solved by an efficient alternating convex optimization simulation results are included to demonstrate the excellent performance of our proposed designs over the conventional single polarized array based designs in terms of achievable secrecy rate minimum transmit power and the mse of recovered confidential signals

vector gaussian multiterminal source coding we derive an outer bound of the rate region of the vector gaussian l terminal ceo problem by establishing a lower bound on each supporting hyperplane of the rate region to this end we prove a new extremal inequality by exploiting the connection between differential entropy and fisher information as well as some fundamental estimation theoretic inequalities it is shown that the outer bound matches the berger tung inner bound in the high resolution regime we then derive a lower bound on each supporting hyperplane of the rate region of the direct vector gaussian l terminal source coding problem by coupling it with the ceo problem through a limiting argument the tightness of this lower bound in the high resolution regime and the weak dependence regime is also proved

linear multiuser mimo transceiver design with quality of service and per antenna power constraints joint design of linear multiuser multiple input multiple output mimo transceiver subject to different quality of service qos constraints per user and with per antenna or antenna group power constraints is considered solutions for two linear transceiver optimization problems are proposed i e balancing the weighted signal to interference plus noise ratio sinr per data stream and balancing the weighted rate for each scheduled user with minimum rate requirements per user the proposed joint transceiver optimization algorithms are compared to corresponding optimal nonlinear transmission methods as well as to generalized zero forcing transmission solutions unlike the optimal nonlinear schemes the optimization problems employed in the linear multiuser mimo transceiver design are not convex in general however the proposed algorithms are shown to provide very efficient solutions despite of the fact that the global optimum cannot be guaranteed due to nonconvexity of the problems

on the capacity region of the parallel degraded broadcast channel with three receivers and three degraded message sets we consider a broadcast channel with three receivers and three degraded message sets i e the transmitter has a common message intended for all three receivers a message intended for receivers 2 and 3 and a private message intended only for receiver 3 the messages are transmitted over a family of parallel degraded broadcast channels in the most general case the broadcast channel consists of the product of six parallel degraded broadcast channels each with a different order of degradedness we first consider an achievable rate region of nair and el gamal by appropriately choosing independent input random variables and auxiliary random variables for each subchannel we then show that the achievable rate region attains the capacity region for two different classes of such broadcast channels one consisting of the product of five parallel degraded broadcast channels and another consisting of the product of three parallel degraded broadcast channels to accomplish this we make use of an information theoretic inequality that may be proven using the csiszar sum identity next we extend the result to the gaussian case we consider the aligned gaussian mimo broadcast channel consisting of the product of six parallel degraded gaussian broadcast channels where the gaussian noise vectors for each of the users in each of the subchannels follow a degradedness order i e the noise covariance matrices may be ordered in a positive semi definite sense we show that the nair el gamal achievable rate region considered in this paper is maximized by gaussian inputs to prove that gaussian inputs are optimal we prove an extremal entropy inequality employing a new method recently introduced by geng and nair to prove the capacity region of the two user gaussian mimo broadcast channel with common and private messages

weighted sum rate maximization for mimo broadcast channels using dirty paper coding and zero forcing methods we consider precoder design for maximizing the weighted sum rate wsr of successive zero forcing dirty paper coding szf dpc for this problem the existing precoder designs often assume a sum power constraint spc and rely on the singular value decomposition svd the svd based designs are known to be optimal but require high complexity we first propose a low complexity optimal precoder design for szf dpc under spc using the qr decomposition then we propose an efficient numerical algorithm to find the optimal precoders subject to per antenna power constraints papcs to this end the precoder design for papcs is formulated as an optimization problem with a rank constraint on the covariance matrices a well known approach to solve this problem is to relax the rank constraints and solve the relaxed problem interestingly for szf dpc we are able to prove that the rank relaxation is tight consequently the optimal precoder design for papcs is computed by solving the relaxed problem for which we propose a customized interior point method that exhibits a superlinear convergence rate two suboptimal precoder designs are also presented and compared to the optimal ones we also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme

on the multicast capacity of the wireless broadcast channel for a multicast network in which a common source is transmitted to n users the problem of maximizing the average rate subject to a coverage constraint minimum quality of service is studied considering such a network with single antenna nodes and assuming that the channel state information is available only at the receiver side the highest expected rate achievable by a random user in the network called the expected typical rate is derived in two scenarios hard coverage constraint and soft coverage constraint in the first case the coverage is expressed in terms of the outage probability while in the second case the expected rate should satisfy a certain minimum requirement it is shown that the optimum solution achieving the highest expected typical rate for given coverage requirements in both cases is achieved by an infinite layer superposition code for which the optimal power allocation among different layers is derived the analysis is extended to a scenario with multiple transmit antennas for the miso case a suboptimal coding scheme is proposed which is shown to be asymptotically optimal when the number of transmit antennas grows at least logarithmically with the number of users in the network

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

on the capacity of the two user symmetric interference channel with transmitter cooperation and secrecy constraints this paper studies the value of limited rate cooperation between the transmitters for managing interference and simultaneously ensuring secrecy in the two user gaussian symmetric interference channel ic first the problem is studied in the symmetric linear deterministic ic sldic setting and achievable schemes are proposed based on interference cancelation relaying of the other user s data bits and transmission of random bits in the proposed achievable scheme the limited rate cooperative link is used to share a combination of data bits and random bits depending on the model parameters outer bounds on the secrecy rate are also derived using a novel partitioning of the encoded messages and outputs depending on the relative strength of the signal and the interference the partitioning helps to bound certain negative entropy terms leading to a tractable outer bound the inner and outer bounds are derived under all possible parameter settings it is found that for some parameter settings the inner and outer bounds match yielding the capacity of the sldic under transmitter cooperation and secrecy constraints in some other scenarios the achievable rate matches with the capacity region of the two user sldic without secrecy constraints derived by wang and tse thus the proposed scheme offers secrecy for free in these cases inspired by the achievable schemes and outer bounds in the deterministic case achievable schemes and outer bounds are derived in the gaussian case the proposed achievable scheme for the gaussian case is based on marton s coding scheme and stochastic encoding along with dummy message transmission one of the key techniques used in the achievable scheme for both the models is interference cancelation which simultaneously offers two seemingly conflicting benefits it cancels interference and ensures secrecy many of the results derived in this paper extend to the asymmetric case also the results show that limited transmitter cooperation can greatly facilitate secure communications over two user ics