joint source channel coding with side information using hybrid digital analog codes we study the joint source channel coding problem of transmitting a gaussian source over a gaussian channel in two cases i the presence of interference known only to the transmitter and ii in the presence of side information about the source known only to the receiver we introduce hybrid digital analog forms of the costa and wyner ziv coding schemes we present the random coding counterpart of schemes based on lattices proposed by kochman and zamir then we discuss applications of the hybrid digital analog schemes in the case of channel signal to noise ratio mismatch and for lossy multicasting of a common source with bandwidth compression

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

duality between channel capacity and rate distortion with two sided state information we show that the duality between channel capacity and data compression is retained when state information is available to the sender to the receiver to both or to neither we present a unified theory for eight special cases of channel capacity and rate distortion with state information which also extends existing results to arbitrary pairs of independent and identically distributed i i d correlated state information s sub 1 s sub 2 available at the sender and at the receiver respectively in particular the resulting general formula for channel capacity c max sub p u x s sub 1 i u s sub 2 y i u s sub 1 assumes the same form as the generalized wyner ziv 1976 rate distortion function r d min sub p u x s sub 1 p x spl i cap u s sub 2 i u s sub 1 x 1 u s sub 2

an efficient kernel matrix evaluation measure we study the problem of evaluating the goodness of a kernel matrix for a classification task as kernel matrix evaluation is usually used in other expensive procedures like feature and model selections the goodness measure must be calculated efficiently most previous approaches are not efficient except for kernel target alignment kta that can be calculated in o n 2 time complexity although kta is widely used we show that it has some serious drawbacks we propose an efficient surrogate measure to evaluate the goodness of a kernel matrix based on the data distributions of classes in the feature space the measure not only overcomes the limitations of kta but also possesses other properties like invariance efficiency and an error bound guarantee comparative experiments show that the measure is a good indication of the goodness of a kernel matrix

minimization of csi feedback dimension for interference alignment in mimo interference multicast networks it is well known that interference alignment ia can achieve substantial theoretical gains in multiple input multiple output mimo networks however the conventional works usually assume the full channel state information csi is available at the transmitter side which would create a overwhelming csi feedback overhead for practical frequency division duplexing fdd wireless systems to implement ia in practice it is highly desirable to reduce the amount of required csi feedback overhead in this paper we consider ia in mimo interference multicast networks under partial csi feedback and we attempt to minimize the csi feedback cost subject to ia feasibility constraints with a given degree of freedom dof requirements first we propose a csi feedback profile to embrace two important csi feedback reduction strategies and we use the metric of csi feedback dimension to quantify the associated csi feedback cost we then formulate the ia conditions under partial csi feedback in mimo interference multicast networks and we derive new ia feasibility conditions under the proposed partial csi feedback framework based on these results we consider the csi feedback dimension minimization subject to the ia feasibility constraints with a given dof requirements in mimo interference multicast networks which is formulated as a combinatorial optimization problem based on the specific problem structure we derive an asymptotically optimal solution for a category of network topologies and we further obtain closed form tradeoff results between dofs and the csi feedback cost for mimo interference multicast networks

spatial frequency signal alignment for opportunistic transmission in this paper we investigate opportunistic transmission based on signal alignment for multiple input multiple output mimo orthogonal frequency division multiplexing ofdm cognitive radio cr systems where both primary and secondary users have multiple antennas in the studied scenario primary users are transmitting based on ofdm and secondary users generate interference free transmission to the primary users by using both the spatial and frequency space leftover by the primary system moreover inter and intra interference among secondary users are considered as well the number of symbols that can be transmitted by each secondary user satisfying all interference free constraints is obtained precoding matrix design will be discussed for perfectly and partially aligned transmission two chordal distance based schemes called as exhaustive search algorithm and heuristic algorithm will be developed for each case compared to the traditional time division multiple access tdma scheme the proposed scheme can support more interference free symbols to be transmitted by secondary users simultaneously

efficient learning of supervised kernels with a graph based loss function this paper presents our study of the problems associated with learning supervised kernels from a large amount of side information we propose a new loss function derived from the laplacian matrix of a special complete graph that is generated from the side information we analyze the relationship between the proposed loss function and the kernel alignment our theoretical analysis shows that the proposed loss function has a close relationship with kernel alignment that is they both make use of side information that is fused in a matrix in addition to a similar regularization strategy moreover the proposed loss function has a linear form and thus it is more efficient in learning side information than kernel alignment that has to be performed nonlinearly the proposed loss function is used to generate new kernels as low cost alternatives of kernels learned by certain state of the art methods the empirical results demonstrate the superiority of the proposed method over state of the art methods in terms of classification accuracy and computational cost

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

gaussian kernel optimization for pattern classification this paper presents a novel algorithm to optimize the gaussian kernel for pattern classification tasks where it is desirable to have well separated samples in the kernel feature space we propose to optimize the gaussian kernel parameters by maximizing a classical class separability criterion and the problem is solved through a quasi newton algorithm by making use of a recently proposed decomposition of the objective criterion the proposed method is evaluated on five data sets with two kernel based learning algorithms the experimental results indicate that it achieves the best overall classification performance compared with three competing solutions in particular the proposed method provides a valuable kernel optimization solution in the severe small sample size scenario

centered kernel alignment inspired fuzzy support vector machine abstract support vector machine svm is a theoretically well motivated algorithm developed from statistical learning theory which has shown impressive performance in many fields in spite of its success it still suffers from the noise sensitivity problem originating from the assumption that each training point has equal importance or weight in the training process to relax this problem the svm was extended to the fuzzy svm fsvm by applying a fuzzy membership to each training point such that different training points can make different contributions to the learning of the decision surface although well determined fuzzy memberships can improve classification performance there are no general guidelines for their construction in this paper inspired by the centered kernel alignment cka which measures the degree of similarity between two kernels or kernel matrices we propose a new fuzzy membership function calculation method in which a heuristic function derived from the cka is used to calculate the dependence between a data point and its associated label although the cka induced fsvm is similar to the kernel target alignment kta induced fsvm there is actually a critical difference without that centering the definition of alignment does not correlate well with the performance of learning machines extensive experiments are performed on real world data sets from the uci benchmark repository and the application domain of computational biology which validate the superiority of the proposed fsvm model in terms of several classification performance measures

quantization based methods additive attacks performance analysis the main goal of this study consists in the development of the worst case additive attack wcaa for ary quantization based data hiding methods using as design criteria the error probability and the maximum achievable rate of reliable communications our analysis focuses on the practical scheme known as distortion compensated dither modulation dc dm from the mathematical point of view the problem of the worst case attack wca design using probability of error as a cost function is formulated as the maximization of the average probability of error subject to the introduced distortion for a given decoding rule when mutual information is selected as a cost function a solution of the minimization problem should provide such an attacking noise probability density function pdf that will maximally decrease the rate of reliable communications for an arbitrary decoder structure the obtained results demonstrate that within the class of additive attacks the developed attack leads to a stronger performance decrease for the considered class of embedding techniques than the additive white gaussian or uniform noise attacks

ergodic interference alignment this paper develops a new communication strategy ergodic interference alignment for the k user interference channel with time varying fading at any particular time each receiver will see a superposition of the transmitted signals plus noise the standard approach to such a scenario results in each transmitter receiver pair achieving a rate proportional to 1 k its interference free ergodic capacity however given two well chosen time indices the channel coefficients from interfering users can be made to exactly cancel by adding up these two observations each receiver can obtain its desired signal without any interference if the channel gains have independent uniform phases this technique allows each user to achieve at least 1 2 its interference free ergodic capacity at any signal to noise ratio prior interference alignment techniques were only able to attain this performance as the signal to noise ratio tended to infinity extensions are given for the case where each receiver wants a message from more than one transmitter as well as the x channel case with two receivers where each transmitter has an independent message for each receiver finally it is shown how to generalize this strategy beyond gaussian channel models for a class of finite field interference channels this approach yields the ergodic capacity region

linear interference alignment in full duplex mimo networks with imperfect csi in this paper we consider a system where full duplex fd base stations bss communicate with half duplex hd downlink dl and uplink ul users in a multi user multi cell network where all nodes are equipped with multiple antennas the introduction of fd bss offers potential to increase spectral efficiency however it also causes a surge in the number of interference links compared with the hd network counterpart here we apply linear interference alignment ia to manage interference in this network under imperfect channel state information csi first we characterize the performance losses incurred with respect to the achievable sum rate and degrees of freedom dofs results show that the general trend in performance loss is mainly determined by how the error scales with the signal to noise ratio snr in particular full ul and dl dof can be achieved even under imperfect csi when the channel error is at least inversely proportional to snr moreover in such cases the sum rate loss is always finite and either goes to zero or is upper bounded by a derived value second we design two linear ia algorithms applicable to the system under consideration these are based on minimizing the mean square error mmse and maximizing the signal to interference plus noise ratio and consider statistical knowledge of the csi error for added robustness the proposed algorithms follow specific design principles that distribute the different interference components amongst the various beamformers and result in unitary receivers and precoders in addition we show that under certain conditions both designs result in identical beamforming solutions even though the mmse algorithm has lower computational complexity finally we also derive the proper condition for ia feasibility in the multi cell system under consideration

sum capacity computation for the gaussian vector broadcast channel via dual decomposition a numerical algorithm for the computation of sum capacity for the gaussian vector broadcast channel is proposed the sum capacity computation relies on a duality between the gaussian vector broadcast channel and the sum power constrained gaussian multiple access channel the numerical algorithm is based on a lagrangian dual decomposition technique and it uses a modified iterative water filling approach for the gaussian multiple access channel the algorithm converges to the sum capacity globally and efficiently

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

joint uplink downlink cooperative interference management with flexible cell associations we study information theoretic models of interference networks that consist of k base station bs mobile terminal mt pairs bs i is connected to the mts with indices in the set i i 1 ldots i l we fix the value of l and study the per user degrees of freedom pudof in large networks we assume that each mt can be associated with n c bss and these associations are determined by a cloud based controller that has a global view of the network an mt has to be associated with a bs for the bs to transmit its message in the downlink or have its decoded message in the uplink we propose pudof inner bounds for arbitrary values of l for the uplink and prove their optimality when only zero forcing schemes are allowed we then introduce new achievable average uplink downlink pudof values and show their optimality for the range when n c leq frac l 2 and when we restrict our attention to zero forcing schemes additionally for the remaining range we characterize the optimal downlink scheme when the uplink optimal associations are used finally we show that the proposed scheme is information theoretically optimal for wyner s linear interference network

face recognition using kernel direct discriminant analysis algorithms techniques that can introduce low dimensional feature representation with enhanced discriminatory power is of paramount importance in face recognition fr systems it is well known that the distribution of face images under a perceivable variation in viewpoint illumination or facial expression is highly nonlinear and complex it is therefore not surprising that linear techniques such as those based on principle component analysis pca or linear discriminant analysis lda cannot provide reliable and robust solutions to those fr problems with complex face variations in this paper we propose a kernel machine based discriminant analysis method which deals with the nonlinearity of the face patterns distribution the proposed method also effectively solves the so called small sample size sss problem which exists in most fr tasks the new algorithm has been tested in terms of classification error rate performance on the multiview umist face database results indicate that the proposed methodology is able to achieve excellent performance with only a very small set of features being used and its error rate is approximately 34 and 48 of those of two other commonly used kernel fr approaches the kernel pca kpca and the generalized discriminant analysis gda respectively

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

generalized discriminant analysis using a kernel approach we present a new method that we call generalized discriminant analysis gda to deal with nonlinear discriminant analysis using kernel function operator the underlying theory is close to the support vector machines svm insofar as the gda method provides a mapping of the input vectors into high dimensional feature space in the transformed space linear properties make it easy to extend and generalize the classical linear discriminant analysis lda to nonlinear discriminant analysis the formulation is expressed as an eigenvalue problem resolution using a different kernel one can cover a wide class of nonlinearities for both simulated data and alternate kernels we give classification results as well as the shape of the decision function the results are confirmed using real data to perform seed classification

a diversity analysis for distributed interference alignment using the max sinr algorithm gomadam recently proposed two distributed interference alignment algorithms namely the zero forcing and the maximal signal to interference plus noise ratio max sinr algorithms both of them only require local channel state information and no symbol extension is needed then ning showed that when only one stream of information symbols is sent by each user interference alignment may achieve receive diversity using the max sinr algorithm this result was however derived only based on an assumption in this paper using a different approach we prove that interference alignment using the max sinr algorithm indeed achieves receive diversity without the assumption used by ning the result in this paper not only completes the proof of the result by ning but also generalizes it by allowing more than one stream of information symbols to be sent by each user

a feasibility test for linear interference alignment in mimo channels with constant coefficients in this paper we consider the feasibility of linear interference alignment ia for multiple input multiple output mimo channels with constant coefficients for any number of users antennas and streams per user and propose a polynomial time test for this problem combining algebraic geometry techniques with differential topology ones we first prove a result that generalizes those previously published on this topic in particular we consider the input set complex projective space of mimo interference channels the output set precoder and decoder grassmannians and the solution set channels decoders and precoders satisfying the ia polynomial equations not only as algebraic sets but also as smooth compact manifolds using this mathematical framework we prove that the linear alignment problem is feasible when the algebraic dimension of the solution variety is larger than or equal to the dimension of the input space and the linear mapping between the tangent spaces of both smooth manifolds given by the first projection is generically surjective if that mapping is not surjective then the solution variety projects into the input space in a singular way and the projection is a zero measure set this result naturally yields a simple feasibility test which amounts to checking the rank of a matrix we also provide an exact arithmetic version of the test which proves that testing the feasibility of ia for generic mimo channels belongs to the bounded error probabilistic polynomial complexity class

feasibility of single beam interference alignment in multi carrier interference channels sun and luo recently showed that if the vector space single beam interference alignment problem for a k user l carrier interference channel is feasible then k leq 2l 2 we prove the converse that if k leq 2l 2 then the problem is feasible i e that the requisite beamformers do exist

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

interference alignment with finite extensions in partially connected networks in this paper we investigate the interference alignment ia for a class of partially connected multi input multi output heterogeneous networks which consist of l fully connected pico cells j partially connected pico cells and one macro cell in particular we investigate the feasibility of ia conditions with no channel extensions t independent channel extensions and t dependent channel extensions respectively for the single beam case we present three theorems to characterize some necessary conditions which l j t and the channel diversity order overline l must jointly satisfy when ia conditions are feasible these necessary conditions also implicitly impose the constraints on the upper bounds of achievable degrees of freedom with different channel extensions

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

brief paper geometric properties of partial least squares for process monitoring projection to latent structures or partial least squares pls produces output supervised decomposition on input x while principal component analysis pca produces unsupervised decomposition of input x in this paper the effect of output y on the x space decomposition in pls is analyzed and geometric properties of the pls structure are revealed several pls algorithms are compared in a geometric way for the purpose of process monitoring a numerical example and a case study are given to illustrate the analysis results

a proof of marton s coding theorem for the discrete memoryless broadcast channel corresp a simple proof using random partitions and typicality is given for marton s coding theorem for broadcast channels

degrees of freedom of cache aided wireless cellular networks this work investigates the degrees of freedom dof of a downlink cache aided cellular network where the locations of base stations bss are modeled as a grid topology and users within a grid cell can only communicate with four nearby bss we adopt a cache placement method with uncoded prefetching tailored for the network with partial connectivity according to the overlapped degree of cached contents among bss we propose transmission schemes with no bs cooperation partial bs cooperation and full bs cooperation respectively for different cache sizes in specific the common cached contents among bss are utilized to cancel some undesired signals by interference neutralization while interference alignment is used to coordinate signals of distinct cached contents our achievable results indicate that the reciprocal of per user dof of the cellular network decreases piecewise linearly with the normalized cache size mu at each bs and the gain of bs caching is more significant for the small cache region under the given cache placement scheme we also provide an upper bound of per user dof and show that our achievable dof is optimal when mu in left frac 1 2 1 right and within an additive gap of frac 4 39 to the optimum when mu in left frac 1 4 frac 1 2 right

information theoretic upper bounds on the capacity of large extended ad hoc wireless networks we derive an information theoretic upper bound on the rate per communication pair in a large ad hoc wireless network we show that under minimal conditions on the attenuation due to the environment and for networks with a constant density of users this rate tends to zero as the number of users gets large

degrees of freedom of mimo cellular networks decomposition and linear beamforming design this paper investigates the symmetric degrees of freedom dof of multiple input multiple output mimo cellular networks with g cells and k users per cell having n antennas at each base station and m antennas at each user in particular we investigate techniques for achievability that are based on either decomposition with asymptotic interference alignment or linear beamforming schemes and show that there are distinct regimes of g k m n where one outperforms the other we first note that both one sided and two sided decomposition with asymptotic interference alignment achieve the same dof we then establish specific antenna configurations under which the dof achieved using decomposition based schemes is optimal by deriving a set of outer bounds on the symmetric dof using these results we completely characterize the optimal dof of any g cell network with single antenna users for linear beamforming schemes we first focus on small networks and propose a structured approach to linear beamforming based on a notion called packing ratios packing ratio describes the interference footprint or shadow cast by a set of transmit beamformers and enables us to identify the underlying structures for aligning interference such a structured beamforming design can be shown to achieve the optimal spatially normalized dof sdof of two cell two user cell network and the two cell three user cell network for larger networks we develop an unstructured approach to linear interference alignment where transmit beamformers are designed to satisfy conditions for interference alignment without explicitly identifying the underlying structures for interference alignment the main numerical insight of this paper is that such an approach appears to be capable of achieving the optimal sdof for mimo cellular networks in regimes where linear beamforming dominates asymptotic decomposition and a significant portion of sdof elsewhere remarkably polynomial identity test appears to play a key role in identifying the boundary of the achievable sdof region in the former case

cellular interference alignment interference alignment promises that in gaussian interference channels each link can support half of a degree of freedom dof per pair of transmit receive antennas however in general this result requires to precode the data bearing signals over a signal space of asymptotically large diversity e g over an infinite number of dimensions for time frequency varying fading channels or over an infinite number of rationally independent signal levels in the case of time frequency invariant channels in this paper we consider a wireless cellular system scenario where the promised optimal dofs are achieved with linear precoding in one shot i e over a single time frequency slot we focus on the uplink of a symmetric cellular system where each cell is split into three sectors with orthogonal intrasector multiple access in our model interference is local i e it is due to transmitters in neighboring cells only we consider a noniterative local cooperation scheme where base stations pass to their neighbors their decoded messages such that interference from already decoded messages can be canceled therefore for a given decoding order the interference between sectors is described by a directed locally connected graph the problem consists of maximizing the per sector dofs over all possible decoding orders and precoding schemes in particular we provide a decoding order and a one shot interference alignment scheme able to achieve optimal per sector dofs up to an additive gap due to boundary effects that vanishes as the size of the network becomes large then we extend our treatment by considering the case of intersector interference with joint processing of the three sector at each cell site in order to avoid signaling schemes relying on the strength of interference we further introduce the notion of topologically robust schemes which are able to guarantee a minimum rate or dofs irrespectively of the strength of the interfering links toward this end we design a different decoding order and alignment scheme which is topologically robust and still achieves the same optimum dofs finally we provide a new scheme for the downlink based on local base station cooperation where base stations pass to their neighbors a quantized version of their dirty paper coded signals for the proposed downlink scheme we can prove a dofs duality result showing that for an appropriate choice of the precoding order and of the alignment beamforming vectors it can achieve the same per sector dofs of the corresponding uplink schemes

a deterministic equivalent for the analysis of non gaussian correlated mimo multiple access channels using large dimensional random matrix theory rmt we conduct mutual information analysis of a multiple input multiple output mimo multiple access channel mac our channel model reflects the characteristics in small cell networks where antenna correlations line of sight components and general type of fading distributions have to be included the mutual information expression can be expressed as functionals of the stieltjes transform through the so called shannon transform ideally if the stieltjes transform is known in the context of the large dimensional rmt then the problem is solved however it is difficult to derive the stieltjes transform of the considered channel models directly especially when the transmit correlation matrices are generally nonnegative definite and the channel entries are non gaussian to overcome this we use the generalized lindeberg principle to show that the stieltjes transforms of this class of random matrices with gaussian or non gaussian independent entries coincide in the large dimensional regime this result permits to derive the deterministic equivalents e g the stieltjes transform and the ergodic mutual information for non gaussian mimo channels from the known results developed for gaussian mimo channels as an application we determine the capacity achieving input covariance matrices for the mimo macs and prove that the capacity achieving input covariance matrices are asymptotically independent of the fading distribution

shannon theoretic approach to a gaussian cellular multiple access channel with fading shannon theoretic limits on the achievable throughput for a simple infinite cellular multiple access channel mac model wyner 1994 in the presence of fading are presented in this model which is modified to account for flat fading the received signal at a given cell site s antenna is the sum of the faded signals transmitted from all users within that cell plus an attenuation factor spl alpha spl isin 0 1 times the sum of the faded signals received from the adjacent cells accompanied by gaussian additive noise this model serves as a tractable model providing considerable insight into complex and analytically intractable real world cellular communications both linear and planar cellular arrays are considered with exactly k active users in each cell we assume a hyper receiver jointly decoding all of the users incorporating the received signals from all of the active cell sites the hyper receiver is assumed to be aware of the codebooks and realizations of the fading processes of all the users in the system in this work we consider the intracell time division multiple access tdma and the wideband wb protocols we focus on the maximum reliably transmitted equal rate bounds to this rate are found for the intracell tdma protocol by incorporating information theoretic inequalities and the chebyshev markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices we demonstrate our results for the special case where the amplitudes of the fading coefficients are drawn from a rayleigh distribution i e rayleigh fading for this special case we observe the rather surprising result that fading may increase the maximum equal rate for a certain range of spl alpha as compared to the nonfaded case in this setting the wb strategy which achieves the maximum reliable equal rate of the model is proved to be superior to the tdma scheme an upper bound to the maximum equal rate of the wb scheme is also obtained this bound is asymptotically tight when the number of users is large k spl gt 1 the asymptotic bound shows that the maximum equal rate of the wb scheme in the presence of fading is higher than the rate which corresponds to the nonfaded case for any intercell interference factor spl alpha spl isin 0 1 signal to noise ratio snr values this result is found to be independent of the statistics of the fading coefficients

linear beamformer design for interference alignment via rank minimization this paper proposes a new framework for the design of transmit and receive beamformers for interference alignment ia without symbol extensions in multi antenna cellular networks we consider ia in a g cell network with k users cell n antennas at each base station bs and m antennas at each user the proposed framework is developed by recasting the conditions for ia as two sets of rank constraints one on the rank of interference matrices and the other on the transmit beamformers in the uplink the interference matrix consists of all the interfering vectors received at a bs from the out of cell users in the uplink using these conditions and the crucial observation that the rank of interference matrices under alignment can be determined beforehand this paper develops two sets of algorithms for ia the first part of this paper develops rank minimization algorithms for ia by iteratively minimizing a weighted matrix norm of the interference matrix different choices of matrix norms lead to reweighted nuclear norm minimization rnnm or reweighted frobenius norm minimization rfnm algorithms with significantly different per iteration complexities alternately the second part of this paper devises an alternating minimization am algorithm where the rank deficient interference matrices are expressed as a product of two lower dimensional matrices that are then alternately optimized simulation results indicate that rnnm which has a per iteration complexity of a semidefinite program is effective in designing aligned beamformers for proper feasible systems with or without redundant antennas while rfnm and am which have a per iteration complexity of a quadratic program are better suited for systems with redundant antennas

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

superposition coding for side information channels we present simple practical codes designed for the binary and gaussian dirty paper channels we show that the dirty paper decoding problem can be transformed into an equivalent multiple access decoding problem for which we apply superposition coding our concept is a generalization of the nested lattices approach of zamir shamai and erez in a theoretical setting our constructions are capable of achieving capacity using random component codes and maximum likelihood decoding we also present practical implementations of the constructions and simulation results for both dirty paper channels our results for the gaussian dirty paper channel are on par with the best known results for nested lattices we discuss the binary dirty tape channel for which we present a simple effective coding technique finally we propose a framework for extending our approach to general gel fand pinsker channels

vector perturbation based on symbol scaling for limited feedback miso downlinks we propose a low complexity vector precoding vp scheme for the downlink of multi user multiple input single output mu miso systems with limited feedback conventional vp requires the use of modulo operation and knowledge of the scaling factor used at the transmitter in order to remove the perturbation quantity at the receiver the latter may be problematic in certain limited feedback scenarios where only quantized versions of the scaling factor can be made available at the receiver to circumvent this shortcoming we propose a modified vp technique where the search of perturbing vectors is limited to the area in the symbol constellation which is constrictive to the information symbols i e the area where the distances from the decision thresholds are increased with respect to a distance threshold by doing this the perturbation quantities can only enhance detection and need not be removed at the receiver successful detection can therefore be done without the use of the modulo operation and the scaling factor which makes the proposed vp scheme applicable to limited feedback scenarios analytical and simulation results show that the performance of the proposed scheme is free of the error floor typically encountered with conventional vp in the presence of limited feedback

on the number of interference alignment solutions for the k user mimo channel with constant coefficients in this paper we study the number of different interference alignment ia solutions in a k user multiple input multiple output mimo interference channel when the alignment is performed via beamforming and no symbol extensions are allowed we focus on the case where the number of ia equations matches the number of variables in this situation the number of ia solutions is finite and constant for any channel realization out of a zero measure set and as we prove in this paper it is given by an integral formula that can be numerically approximated using monte carlo integration methods more precisely the number of alignment solutions is the scaled average of the determinant of a certain hermitian matrix related to the geometry of the problem interestingly while the value of this determinant at an arbitrary point can be used to check the feasibility of the ia problem its average properly scaled gives the number of solutions for single beam systems the asymptotic growth rate of the number of solutions is analyzed and some connections with classical combinatorial problems are presented nonetheless our results can be applied to arbitrary interference mimo networks with any number of users antennas and streams per user

on the feasibility of linear interference alignment for mimo interference broadcast channels with constant coefficients in this paper we analyze the feasibility of linear interference alignment ia for multi input multi output mimo interference broadcast channel mimo ibc with constant coefficients we pose and prove the necessary conditions of linear ia feasibility for general mimo ibc except for the proper condition we find another necessary condition to ensure a kind of irreducible interference to be eliminated we then prove the necessary and sufficient conditions for a special class of mimo ibc where the numbers of antennas are divisible by the number of data streams per user since finding an invertible jacobian matrix is crucial for the sufficiency proof we first analyze the impact of sparse structure and repeated structure of the jacobian matrix considering that for the mimo ibc the sub matrices of the jacobian matrix corresponding to the transmit and receive matrices have different repeated structure we find an invertible jacobian matrix by constructing the two sub matrices separately we show that for the mimo ibc where each user has one desired data stream a proper system is feasible for symmetric mimo ibc we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear ia feasibility

the feasibility conditions for interference alignment in mimo networks interference alignment ia has attracted great attention in the last few years for its breakthrough performance in interference networks however despite the numerous works dedicated to ia the feasibility conditions of ia remains unclear for most network topologies the ia feasibility analysis is challenging as the ia constraints are sets of high degree polynomials for which no systematic tool to analyze the solvability conditions exists in this work by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first order terms we propose a sufficient condition that applies to mimo interference networks with general configurations we have further proved that this sufficient condition coincides with the necessary conditions under a wide range of configurations these results further consolidate the theoretical basis of ia

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

channel diversity needed for vector space interference alignment we consider vector space interference alignment strategies over the k user interference channel and derive an upper bound on the achievable degrees of freedom as a function of the channel diversity l where the channel diversity is modeled by l real valued parallel channels with coefficients drawn from a nondegenerate joint distribution the seminal work of cadambe and jafar shows that when l is unbounded vector space interference alignment can achieve 1 2 degrees of freedom per user independent of the number of users k however wireless channels have limited diversity in practice dictated by their coherence time and bandwidth and an important question is the number of degrees of freedom achievable at finite l when k 3 and if l is finite bresler et al show that the number of degrees of freedom achievable with vector space interference alignment is bounded away from 1 2 and the gap decreases inversely proportional to l in this paper we show that when k geq 4 the gap is significantly larger in particular the gap to the optimal 1 2 degrees of freedom per user can decrease at most like 1 sqrt l and when l is smaller than the order of 2 k 2 k 3 it decays at most like 1 sqrt 4 l

a network information theory for wireless communication scaling laws and optimal operation how much information can be carried over a wireless network with a multiplicity of nodes and how should the nodes cooperate to transfer information to study these questions we formulate a model of wireless networks that particularly takes into account the distances between nodes and the resulting attenuation of radio signals and study a performance measure that weights information by the distance over which it is transported consider a network with the following features i n nodes located on a plane with minimum separation distance spl rho sub min 0 ii a simplistic model of signal attenuation e sup spl gamma spl rho spl rho sup spl delta over a distance spl rho where spl gamma spl ges 0 is the absorption constant usually positive unless over a vacuum and spl delta 0 is the path loss exponent iii all receptions subject to additive gaussian noise of variance spl sigma sup 2 the performance measure we mainly but not exclusively study is the transport capacity c sub t sup spl sigma on sub spl lscr 1 sup m r sub spl lscr spl middot spl rho sub spl lscr where the supremum is taken over m and vectors r sub 1 r sub 2 r sub m of feasible rates for m source destination pairs and spl rho sub spl lscr is the distance between the spl lscr th source and its destination it is the supremum distance weighted sum of rates that the wireless network can deliver we show that there is a dichotomy between the cases of relatively high and relatively low attenuation when spl gamma 0 or spl delta 3 the relatively high attenuation case the transport capacity is bounded by a constant multiple of the sum of the transmit powers of the nodes in the network however when spl gamma 0 and spl delta 3 2 the low attenuation case we show that there exist networks that can provide unbounded transport capacity for fixed total power yielding zero energy priced communication examples show that nodes can profitably cooperate over large distances using coherence and multiuser estimation when the attenuation is low these results are established by developing a coding scheme and an achievable rate for gaussian multiple relay channels a result that may be of interest in its own right

multiple kernel clustering based on centered kernel alignment multiple kernel clustering mkc which performs kernel based data fusion for data clustering is an emerging topic it aims at solving clustering problems with multiple cues most mkc methods usually extend existing clustering methods with a multiple kernel learning mkl setting in this paper we propose a novel mkc method that is different from those popular approaches centered kernel alignment an effective kernel evaluation measure is employed in order to unify the two tasks of clustering and mkl into a single optimization framework to solve the formulated optimization problem an efficient two step iterative algorithm is developed experiments on several uci datasets and face image datasets validate the effectiveness and efficiency of our mkc algorithm

communication over mimo x channels interference alignment decomposition and performance analysis in a multiple antenna system with two transmitters and two receivers a scenario of data communication known as the x channel is studied in which each receiver receives data from both transmitters in this scenario it is assumed that each transmitter is unaware of the other transmitter s data noncooperative scenario this system can be considered as a combination of two broadcast channels from the transmitters points of view and two multiple access channels from the receivers points of view taking advantage of both perspectives two signaling schemes for such a scenario are developed in these schemes some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple antenna broadcast subchannels or two noninterfering multiple antenna multiple access subchannels the main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain mg it is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable mg in particular it is shown that in some specific cases the achieved mg is the same as the mg of the system if full cooperation is provided either between the transmitters or between the receivers in the second part of the paper it is shown that by using mixed design schemes rather than decomposition schemes and taking the statistical properties of the interference terms into account the power offset of the system can be improved the power offset represents the horizontal shift in the curve of the sum rate versus the total power in decibels

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

optimizing the kernel in the empirical feature space in this paper we present a method of kernel optimization by maximizing a measure of class separability in the empirical feature space an euclidean space in which the training data are embedded in such a way that the geometrical structure of the data in the feature space is preserved employing a data dependent kernel we derive an effective kernel optimization algorithm that maximizes the class separability of the data in the empirical feature space it is shown that there exists a close relationship between the class separability measure introduced here and the alignment measure defined recently by cristianini extensive simulations are carried out which show that the optimized kernel is more adaptive to the input data and leads to a substantial sometimes significant improvement in the performance of various data classification algorithms

subspace alignment chains and the degrees of freedom of the three user mimo interference channel we show that the three user mt mr multiple input multiple output mimo interference channel where each transmitter is equipped with mt antennas and each receiver is equipped with mr antennas has m d m n min m 2 1 n 2 1 degrees of freedom dof normalized by time frequency and space dimensions where min mt mr n max mt mr m n m while the dof outer bound of d m n is established for every mt mr value the achievability of d m n dof is established in general subject to a normalization with respect to spatial extensions i e the scaling of the number of antennas at all nodes in particular we show that qd m n dof are achievable for the three user qmt qmr mimo interference channel for some positive integer q which may be seen as a spatial extension factor q is the scaling factor needed to make the value qd m n an integer given spatial extensions the achievability relies only on linear beamforming based interference alignment schemes and requires neither channel extensions nor channel variations in time or frequency in the absence of spatial extensions it is shown through examples how essentially the same interference alignment scheme may be applied over time extensions over either constant or time varying channels the central new insight to emerge from this paper is the notion of subspace alignment chains as the dof bottlenecks the subspace alignment chains are instrumental both in identifying the extra dimensions to be provided by a genie to a receiver for the dof outer bound as well as in the construction of the optimal interference alignment schemes the dof value d m n is a piecewise linear function of m n with either m or n being the bottleneck within each linear segment whereas the other value contains some redundancy i e it can be reduced without reducing the dof the corner points of these piecewise linear segments correspond to two sets a 1 2 2 3 3 4 and b 1 3 3 5 5 7 the set a contains all those values of m n and only those values of m n for which there is redundancy in both m and n i e either can be reduced without reducing the dof the set b contains all those values of m n and only those values of m n for which there is no redundancy in either m or n i e neither can be reduced without reducing the dof because a and b represent settings with maximum and minimum redundancy essentially they are the basis for the dof outer bounds and inner bounds respectively our results settle the question of feasibility of linear interference alignment introduced previously by cenk et al for the three user mt mr mimo interference channel completely for all values of mt mr in particular we show that the linear interference alignment problem mt mr d 3 as defined in previous paper by cenk et al is feasible if and only if d d m n with the exception of the values m n b and only with that exception we show that for every m n value there are proper systems as defined by cenk et al that are not feasible evidently the redundancy contained in all other values of m n manifests itself as superfluous variables that are not discounted in the definition of proper systems thus creating a discrepancy between proper and feasible systems our results show that m n a are the only values for which there is no dof benefit of joint processing among co located antennas at the transmitters or receivers this may also be seen as a consequence of the maximum redundancy in the m n a settings

hybrid mu miso scheduling with limited feedback using hierarchical codebooks the multiuser mimo mu mimo systems tend to have inter user interference in practical systems with limited feedback practical mu mimo systems with limited feedback can be divided into two classes in general one is zero forcing beamforming zfbf and the other is per user unitary rate control pu2rc which is an extended version of random beamforming rbf to improve performance zfbf needs more feedback bits and pu2rc needs a larger number of users we propose a new hybrid mu miso system which has the advantages of the two mu mimo schemes simultaneously and analyze the sum rate performance and the quantization error of the hybrid scheme the analysis shows how the number of feedback bits the number of users and the signal power affect the sum rate the throughput scaling laws are also derived in the high and the medium snr regimes simulation results show that the proposed hybrid mu miso system performs better than either of the two mu mimo systems with the same number of feedback bits another advantage is that it has lower complexity for codeword search since it has a hierarchical codebook structure

interference alignment with asymmetric complex signaling on mimo x channels it is known that with conventional spatial interference alignment i e linear interference alignment without symbol extension the achievable degrees of freedom dof of mimo x channels is no more than lfloor d outer rfloor where d outer denotes the outer bound of dof of mimo x channels in this paper we propose a spatial interference alignment and zero forcing framework in combination with asymmetric complex signaling which can achieve the dof of 1 2 lfloor 2d outer rfloor for arbitrary number of antennas on each terminal note that 1 2 lfloor 2d outer rfloor is equal to or larger than lfloor d outer rfloor the result shows that the technique of asymmetric complex signaling which was originally proposed for single antenna systems can be useful for mimo channels in particular when symbol extensions are not allowed

analog matching of colored sources to colored channels analog uncoded transmission provides a simple and robust scheme for communicating a gaussian source over a gaussian channel under the mean squared error mse distortion measure unfortunately its performance is usually inferior to the all digital separation based source channel coding solution which requires exact knowledge of the channel at the encoder the loss comes from the fact that except for very special cases e g white source and channel of matching bandwidth bw it is impossible to achieve perfect matching of source to channel and channel to source by linear means we show that by combining prediction and modulo lattice operations it is possible to match any colored gaussian source to any colored gaussian noise channel of possibly different bw hence achieve shannon s optimum attainable performance r d c furthermore when the source and channel bws are equal but otherwise their spectra are arbitrary this scheme is asymptotically robust in the sense that for high signal to noise ratio snr a single encoder independent of the noise variance achieves the optimum performance the derivation is based upon a recent modulo lattice modulation scheme for transmitting a wyner ziv source over a dirty paper channel

degrees of freedom for the mimo interference channel in this correspondence we show that the exact number of spatial degrees of freedom dof for a two user nondegenerate full rank channel matrices multiple input multiple output mimo gaussian interference channel with m1 m2 antennas at transmitters 1 2 and n1 n2 antennas at the corresponding receivers and perfect channel knowledge at all transmitters and receivers is min m1 m2 n1 m2 max m1 n2 max m2 n1 a constructive achievability proof shows that zero forcing is sufficient to achieve all the available dof on the two user mimo interference channel we also show through an example of a share and transmit scheme how the gains of transmitter cooperation may be entirely offset by the cost of enabling that cooperation so that the available dof are not increased

in defense of one vs all classification we consider the problem of multiclass classification our main thesis is that a simple one vs all scheme is as accurate as any other approach assuming that the underlying binary classifiers are well tuned regularized classifiers such as support vector machines this thesis is interesting in that it disagrees with a large body of recent published work on multiclass classification we support our position by means of a critical review of the existing literature a substantial collection of carefully controlled experimental work and theoretical arguments

multiple description quantization via gram schmidt orthogonalization the multiple description md problem has received considerable attention as a model of information transmission over unreliable channels a general framework for designing efficient md quantization schemes is proposed in this paper we provide a systematic treatment of the el gamal cover egc achievable md rate distortion region and show it can be decomposed into a simplified egc segc region and a superimposed refinement operation furthermore any point in the segc region can be achieved via a successive quantization scheme along with quantization splitting for the quadratic gaussian case the proposed scheme has an intrinsic connection with the gram schmidt orthogonalization which implies that the whole gaussian md rate distortion region is achievable with a sequential dithered lattice based quantization scheme as the dimension of the optimal lattice quantizers becomes large moreover this scheme is shown to be universal for all independent and identically distributed i i d smooth sources with performance no worse than that for an i i d gaussian source with the same variance and asymptotically optimal at high resolution a class of md scalar quantizers in the proposed general framework is also constructed and is illustrated geometrically the performance is analyzed in the high resolution regime which exhibits a noticeable improvement over the existing md scalar quantization schemes

joint space decomposition and synthesis approach and achievable dof regions for k user mimo interference channels the paper proposes a new approach of joint space decomposition and synthesis jsds for deriving achievable degree of freedom dof region by interference alignment without symbol extension for k user mimo interference channel solving the interference alignment problem is to find the precoders that align desired signal and interference with disjoint subspaces at receivers a related property of these precoders is that the solution range for each one of them is a union of linear spaces termed transmit spaces based on this property the jsds approach is developed to derive transmit spaces that fulfill alignment conditions from this approach achievable dof regions for 2 and 3 user interference channels are obtained the region for the 2 user channel is shown to coincide with the existing result of the dof capacity of the channel for the k user k 3 case inner as well as outer bounds are given

achievable rates for multiple descriptions consider a sequence of independent identically distributed i i d random variables x l x 2 cdots x n and a distortion measure d x i x i on the estimates x i of x i two descriptions i x in 1 2 cdots 2 nr 1 and j x in 1 2 cdots 2 nr 2 are given of the sequence x x 1 x 2 cdots x n from these two descriptions three estimates i x x2 j x and hat x o i x j x are formed with resulting expected distortions e frac 1 n sum n k 1 d x k hat x mk d m m 0 1 2 we find that the distortion constraints d 0 d 1 d 2 are achievable if there exists a probability mass distribution p x p hat x 1 hat x 2 hat x 0 x with ed x hat x m leq d m such that r 1 i x hat x 1 r 2 i x hat x 2 where i cdot denotes shannon mutual information these rates are shown to be optimal for deterministic distortion measures

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

choosing the kernel parameters for support vector machines by the inter cluster distance in the feature space determining the kernel and error penalty parameters for support vector machines svms is very problem dependent in practice a popular method to deciding the kernel parameters is the grid search method in the training process classifiers are trained with different kernel parameters and only one of the classifiers is required for the testing process this makes the training process time consuming in this paper we propose using the inter cluster distances in the feature spaces to choose the kernel parameters calculating such distance costs much less computation time than training the corresponding svm classifiers thus the proper kernel parameters can be chosen much faster experiment results show that the inter cluster distance can choose proper kernel parameters with which the testing accuracy of trained svms is competitive to the standard ones and the training time can be significantly shortened

regularization by truncated total least squares the total least squares tls method is a successful method for noise reduction in linear least squares problems in a number of applications the tls method is suited to problems in which both the coefficient matrix and the right hand side are not precisely known this paper focuses on the use of tls for solving problems with very ill conditioned coefficient matrices whose singular values decay gradually so called discrete ill posed problems where some regularization is necessary to stabilize the computed solution we filter the solution by truncating the small singular values of the tls matrix we express our results in terms of the singular value decomposition svd of the coefficient matrix rather than the augmented matrix this leads to insight into the filtering properties of the truncated tls method as compared to regularized least squares solutions in addition we propose and test an iterative algorithm based on lanczos bidiagonalization for computing truncated tls solutions

shannon theoretic approach to a gaussian cellular multiple access channel we obtain shannon theoretic limits for a very simple cellular multiple access system in our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor spl alpha 0 spl les spl alpha spl les 1 times the sum of the signals transmitted from the adjacent cells plus ambient gaussian noise although this simple model is scarcely realistic it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems we consider both a one dimensional linear cellular array and the familiar two dimensional hexagonal cellular pattern the discrete time channel is memoryless we assume that n contiguous cells have active transmitters in the one dimensional case and that n sup 2 contiguous cells have active transmitters in the two dimensional case there are k transmitters per cell most of our results are obtained for the limiting case as n spl rarr spl infin the results include the following 1 we define c sub n c spl circ sub n as the largest achievable rate per transmitter in the usual shannon theoretic sense in the one and two dimensional cases respectively assuming that all signals are jointly decoded we find expressions for limn spl rarr spl infin c sub n and limn spl rarr spl infin c spl circ sub n 2 as the interference parameter spl alpha increases from 0 c sub n and c spl circ sub n increase or decrease according to whether the signal to noise ratio is less than or greater than unity 3 optimal performance is attainable using tdma within the cell but using tdma for adjacent cells is distinctly suboptimal 4 we suggest a scheme which does not require joint decoding of all the users and is in many cases close to optimal

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

optimizing the gaussian kernel function with the formulated kernel target alignment criterion for two class pattern classification nowadays most of the current kernel learning approaches are showing good results in small datasets and fail to scale to large ones as such it is necessary to develop faster kernel optimization algorithms that perform better with larger datasets especially for the big data applications this paper presents a novel fast method to optimize the gaussian kernel function for two class pattern classification tasks where it is desirable for the kernel machines to use an optimized kernel that adapts well to the input data and the learning tasks we propose to optimize the gaussian kernel function by using the formulated kernel target alignment criterion by adopting the euler maclaurin formula and the local and global extremal properties of the approximate kernel separability criterion the approximate criterion function can be proved to have a determined global minimum point thus when the approximate criterion function is a sufficient approximation of the criterion function through using a newton based algorithm the proposed optimization is simply solved without being repeated the searching procedure with different starting points to locate the best local minimum the proposed method is evaluated on thirteen data sets with three gaussian kernel based learning algorithms the experimental results show that the criterion function has the determined global minimum point for the all thirteen data sets the proposed method achieves the best high time efficiency performance and the best overall classification performance

generalized interference alignment part i theoretical framework interference alignment ia has attracted enormous research interest as it achieves optimal capacity scaling with respect to signal to noise ratio on interference networks ia has also recently emerged as an effective tool in engineering interference for secrecy protection on wireless wiretap networks however despite the numerous works dedicated to ia two of its fundamental issues i e feasibility conditions and transceiver design are not completely addressed in the literature in this two part paper a generalized interference alignment gia technique is proposed to enhance the ia s capability in secrecy protection a theoretical framework is established to analyze the two fundamental issues of gia in part i and then the performance of gia in large scale stochastic networks is characterized to illustrate how gia benefits secrecy protection in part ii the theoretical framework for gia adopts methodologies from algebraic geometry determines the necessary and sufficient feasibility conditions of gia and generates a set of algorithms for solving the gia problem this framework sets up a foundation for the development and implementation of gia

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

scaling results on the sum capacity of cellular networks with mimo links scaling results for the sum capacity of the multiple access uplink channel are provided for a flat fading environment with multiple input multiple output mimo links when there is interference from other cells the classical mimo scaling regime is considered in which the number of antennas per user and per base station grow large together utilizing the known characterizations of the limiting eigenvalue distributions of large random matrices the asymptotic behavior of the sum capacity of the system is characterized for an architecture in which the base stations cooperate in the joint decoding process of all users macrodiversity this asymptotic sum capacity is compared with that of the conventional scenario in which the base stations only decode the users in their cells for the case of base station cooperation an interesting resource pooling phenomenon is observed in some cases the limiting performance of a macrodiversity multiuser network has the same asymptotic behavior as that of a single user mimo link with an equivalent amount of pooled received power this resource pooling phenomenon allows us to derive an elegant closed form expression for the sum capacity of a new version of wyner s classical model of a cellular network in which mimo links are incorporated into the model

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

feasibility of interference alignment for the mimo interference channel we study vector space interference alignment for the multiple input multiple output interference channel with no time or frequency diversity and no symbol extensions we prove both necessary and sufficient conditions for alignment in particular we characterize the feasibility of alignment for the symmetric three user channel where all users transmit along d dimensions all transmitters have m antennas and all receivers have n antennas as well as feasibility of alignment for the fully symmetric m n channel with an arbitrary number of users an implication of our results is that the total degrees of freedom available in a k user interference channel using only spatial diversity from the multiple antennas is at most 2 this is in sharp contrast to the k 2 degrees of freedom shown to be possible by cadambe and jafar with arbitrarily large time or frequency diversity moving beyond the question of feasibility we additionally discuss computation of the number of solutions using schubert calculus in cases where there are a finite number of solutions

interference alignment with partial csi feedback in mimo cellular networks interference alignment ia is a linear precoding strategy that can achieve optimal capacity scaling at high snr in interference networks however most existing ia designs require full channel state information csi at the transmitters which could lead to significant csi signaling overhead there are two techniques namely csi quantization and csi feedback filtering that reduce csi feedback overhead in this paper we consider ia processing with csi feedback filtering in mimo cellular networks we introduce a novel metric namely the feedback dimension to quantify the first order csi feedback cost associated with the csi feedback filtering the csi feedback filtering poses several important challenges in ia processing first there is a hidden partial csi knowledge constraint in ia precoder design which cannot be handled using conventional ia design methodology furthermore existing results on the feasibility conditions of ia cannot be applied due to the partial csi knowledge finally it is very challenging to find out how much csi feedback is actually needed to support ia processing we shall address the above challenges and propose a new ia feasibility condition under partial csit knowledge in mimo cellular networks based on this we consider the csi feedback dimension minimization subject to the degrees of freedom requirements and further propose an asymptotically optimal solution and derive closed form trade off results between the csi feedback cost and ia performance in mimo cellular networks

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

an efficient gaussian kernel optimization based on centered kernel polarization criterion the formulated criterion has a defined geometrical significance the approximate criterion has a determined global minimum point with weaker constraints the influence of iteration parameters on the global optimal point is slight the proposed criterion is extended to solve multiclass problems the success of kernel based learning methods is heavily dependent on the choice of a kernel function and proper setting of its parameters in this paper we optimize the gaussian kernel for binary class problems by using centered kernel polarization criterion this criterion is an extension of kernel polarization and a simplified style of centered kernel alignment compared with formulated kernel polarization criterion the proposed criterion has a defined geometrical significance and it can locate the global optimal point with less influence of threshold selection furthermore the approximate criterion function can be proved to have a determined global minimum point by adopting the euler maclaurin formula under weaker conditions in addition taking the preservation of within class local structure into account we present an evaluation criterion named local multiclass centered kernel polarization in multiclass classification scenario comparative experiments are conducted on some benchmark examples with three gaussian kernel based learning methods and the results well demonstrate the effectiveness and efficiency of the proposed quality measures

on feasibility of interference alignment in mimo interference networks we explore the feasibility of interference alignment in signal vector space based only on beamforming for k user mimo interference channels our main contribution is to relate the feasibility issue to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry it is well known e g from bezout s theorem that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables following this intuition we classify signal space interference alignment problems as either proper or improper based on the number of equations and variables rigorous connections between feasible and proper systems are made through bernshtein s theorem for the case where each transmitter uses only one beamforming vector the multibeam case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic in the sense required by both theorems in this case we show that the connection between feasible and proper systems can be further strengthened since the equivalency between feasible and proper systems does not always hold by including standard information theoretic outer bounds in the feasibility analysis

on tikhonov regularization bias and variance in nonlinear system identification abstract regularization is a general method for solving ill posed and ill conditioned problems traditionally ill conditioning in system identification problems is approached using regularization methods such as ridge regression and principal component regression in this work it is argued that the tikhonov regularization method is a powerful alternative for regularization of nonlinear system identification problems by introducing smoothness of the model as a prior its properties is discussed in terms of an analysis of bias and variance and illustrated by a semirealistic simulation example

degrees of freedom region of the mimo x channel we provide achievability as well as converse results for the degrees of freedom region of a multiple input multiple output mimo x channel i e a system with two transmitters two receivers each equipped with multiple antennas where independent messages need to be conveyed over fixed channels from each transmitter to each receiver the inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message with m 1 antennas at each node we find that the total sum rate degrees of freedom are bounded above and below as 1 les eta x les 4 3 if m 1 and channel matrices are nondegenerate then the precise degrees of freedom eta x 4 3 m thus the mimo x channel has noninteger degrees of freedom when m is not a multiple of 3 simple zero forcing without dirty paper encoding or successive decoding suffices to achieve the 4 3 m degrees of freedom if the channels vary with time frequency then the channel with single antennas m 1 at all nodes has exactly 4 3 degrees of freedom the key idea for the achievability of the degrees of freedom is interference alignment i e signal spaces are aligned at receivers where they constitute interference while they are separable at receivers where they are desired we also explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio

a weighted view on the partial least squares algorithm in this paper it is shown that the partial least squares pls algorithm for univariate data is equivalent to using a truncated cayley hamilton polynomial expression of degree email protected email protected r for the matrix inverse x tx email protected r r x r which is used to compute the least squares ls solution furthermore the a coefficients in this polynomial are computed as the optimal ls solution minimizing parameters to the prediction error the resulting solution is non iterative the solution can be expressed in terms of a matrix inverse and is given by b p l s k a k a tx txk a 1k a tx ty where k email protected r r x a is the controllability krylov matrix for the pair x tx x ty the iterative pls algorithm for computing the orthogonal weighting matrix w a as presented in the literature is shown here to be equivalent to computing an orthonormal basis using e g the qr algorithm for the column space of k a the pls solution can equivalently be computed as b p l s w a w a tx txw a 1w a tx ty where w a is the q orthogonal matrix from the qr decomposition k a w ar furthermore we have presented an optimal and non iterative truncated cayley hamilton polynomial ls solution for multivariate data the free parameters in this solution is found as the minimizing solution of a prediction error criterion

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

causal state communication the problem of state communication over a discrete memoryless channel with discrete memoryless state is studied when the state information is available strictly causally at the encoder it is shown that block markov encoding in which the encoder communicates a description of the state sequence in the previous block by incorporating side information about the state sequence at the decoder yields the minimum state estimation error when the same channel is used to send additional independent information at the expense of a higher channel state estimation error the optimal tradeoff between the rate of the independent information and the state estimation error is characterized via the capacity distortion function it is shown that any optimal tradeoff pair can be achieved via rate splitting these coding theorems are then extended optimally to the case of causal channel state information at the encoder using the shannon strategy

csi feedback reduction for mimo interference alignment interference alignment ia is a linear precoding strategy that can achieve optimal capacity scaling at high snr in interference networks most of the existing ia designs require full channel state information csi at the transmitters which induces a huge csi signaling cost hence it is desirable to improve the feedback efficiency for ia and in this paper we propose a novel ia scheme with a significantly reduced csi feedback to quantify the csi feedback cost we introduce a novel metric namely the feedback dimension this metric serves as a first order measurement of csi feedback overhead due to the partial csi feedback constraint conventional ia schemes can not be applied and hence we develop a novel ia precoder decorrelator design and establish new ia feasibility conditions via dynamic feedback profile design the proposed ia scheme can also achieve a flexible tradeoff between the degree of freedom dof requirements for data streams the antenna resources and the csi feedback cost we show by analysis and simulations that the proposed scheme achieves substantial reductions of csi feedback overhead under the same dof requirement in mimo interference networks

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