optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

bifurcation analysis of a stochastically driven limit cycle we establish the existence of a bifurcation from an attractive random equilibrium to shear induced chaos for a stochastically driven limit cycle indicated by a change of sign of the first lyapunov exponent this relates to an open problem posed by lin and young nonlinearity 21 899 922 2008 and young nonlinearity 21 245 252 2008 extending results by wang and young commun math phys 240 3 509 529 2003 on periodically kicked limit cycles to the stochastic context

isomorphic copies in the lattice e and its symmetrization e with applications to orlicz lorentz spaces the paper is devoted to the isomorphic structure of symmetrizations of quasi banach ideal function or sequence lattices the symmetrization e of a quasi banach ideal lattice e of measurable functions on i 0 a 0 a or i n consists of all functions with decreasing rearrangement belonging to e for an order continuous e we show that every subsymmetric basic sequence in e which converges to zero in measure is equivalent to another one in the cone of positive decreasing elements in e and conversely among several consequences we show that provided e is order continuous with fatou property e contains an order isomorphic copy of lp if and only if either e contains a normalized lp basic sequence which converges to zero in measure or e contains the function t 1 p we apply these results to the family of two weighted orlicz lorentz spaces w v i defined on i n or i 0 a 0 a this family contains usual orlicz lorentz spaces w i when v 1 and orlicz marcinkiewicz spaces m w i when v 1 w we show that for a large class of weights w v it is equivalent for the space w v 0 1 and for the non weighted orlicz space l 0 1 to contain a given sequential orlicz space h isomorphically as a sublattice in their respective order continuous parts we provide a complete characterization of order isomorphic copies of lp in these spaces over 0 1 or n exclusively in terms of the indices of if i 0 we show that the set of exponents p for which lp lattice embeds in the order continuous part of w v i is the union of three intervals determined respectively by the indices of and by the condition that the function t 1 p belongs to the space

noncooperative eigencoding for mimo ad hoc networks a new noncooperative eigencoding algorithm is introduced for multiple input multiple output mimo ad hoc networks the algorithm performs generalized waterfilling with respect to its transmit covariance matrix and the receive node covariance matrix both of which can be estimated locally a cooperative algorithm is also developed as a benchmark in simulations simulation results show that the noncooperative algorithm performance is close to that of the cooperative method and is much better than greedy optimization a game theoretic interpretation of the algorithm is also provided

asymptotic analysis of the lyapunov exponent and rotation number of the random oscillator and application we construct asymptotic expansions for the exponential growth rate lyapunov exponent and rotation number of the random oscillator when the noise is large small rapidly varying or slowly varying we then apply our results to problems in the stability of the random oscillator the spectrum of the one dimensional random schr6dinger operator and wave propagation in a one dimensional random medium

minimum ber linear transceivers for mimo channels via primal decomposition this paper considers the employment of linear transceivers for communication through multiple input multiple output mimo channels with channel state information csi at both sides of the link the design of linear mimo transceivers has been studied since the 1970s by optimizing simple measures of the quality of the system such as the trace of the mean square error matrix subject to a power constraint recent results showed how to solve the problem in an optimal way for the family of schur concave and schur convex cost functions in particular when the constellations used on the different transmit dimensions are equal the bit error rate ber averaged over these dimensions happens to be a schur convex function and therefore it can be optimally solved in a more general case however when different constellations are used the average ber is not a schur convex function and the optimal design in terms of minimum ber is an open problem this paper solves the minimum ber problem with arbitrary constellations by first reformulating the problem in convex form and then proposing two solutions one is a heuristic and suboptimal solution which performs remarkably well in practice the other one is the optimal solution obtained by decomposing the convex problem into several subproblems controlled by a master problem a technique borrowed from optimization theory for which extremely simple algorithms exist thus the minimum ber problem can be optimally solved in practice with very simple algorithms

globally optimal linear precoders for finite alphabet signals over complex vector gaussian channels we study the design optimization of linear precoders for maximizing the mutual information between finite alphabet input and the corresponding output over complex valued vector channels this mutual information is a nonlinear and non concave function of the precoder parameters posing a major obstacle to precoder design optimization our work presents three main contributions first we prove that the mutual information is a concave function of a matrix which itself is a quadratic function of the precoder matrix second we propose a parameterized iterative algorithm for finding optimal linear precoders to achieve the global maximum of the mutual information the proposed iterative algorithm is numerically robust computationally efficient and globally convergent third we demonstrate that maximizing the mutual information between a discrete constellation input and the corresponding output of a vector channel not only provides the highest practically achievable rate but also serves as an excellent criterion for minimizing the coded bit error rate our numerical examples show that the proposed algorithm achieves mutual information very close to the channel capacity for channel coding rate under 0 75 and also exhibits a large gain over existing linear precoding and or power allocation algorithms moreover our examples show that certain existing methods are susceptible to being trapped at locally optimal precoders

statistical precoding with decision feedback equalization over a correlated mimo channel the decision feedback df transceiver combining linear precoding and df equalization can establish point to point communication over a wireless multiple input multiple output channel matching the df transceiver design parameters to the channel characteristics can improve system performance but requires channel knowledge we consider the fast fading channel scenario with a receiver capable of tracking the channel state variations accurately while the transmitter only has long term channel distribution information the receiver design problem given channel state information is well studied in the literature we focus on transmitter optimization which amounts to designing a statistical precoder to assist the channel tailored df equalizer we develop a design framework that encompasses a wide range of performance metrics common cost functions for precoder optimization are analyzed thereby identifying a structure of typical cost functions transmitter design is approached for typical cost functions in general and we derive a precoder design formulation as a convex optimization problem two important subclasses of cost functions are considered in more detail first we explore a symmetry of df transceivers with a uniform subchannel rate allocation and derive a simplified convex optimization problem which can be efficiently solved even as system dimensions grow second we explore the tractability of a certain class of mean square error based cost functions and solve the transmitter design problem with a simple algorithm that identifies the convex hull of a set of points in r2 the behavior of df transceivers with optimal precoders is investigated by numerical means

linear precoding via conic optimization for fixed mimo receivers in this paper the problem of designing linear precoders for fixed multiple input multiple output mimo receivers is considered two different design criteria are considered in the first the transmitted power is minimized subject to signal to interference plus noise ratio sinr constraints in the second the worst case sinr is maximized subject to a power constraint it is shown that both problems can be solved using standard conic optimization packages in addition conditions are developed for the optimal precoder for both of these problems and two simple fixed point iterations are proposed to find the solutions that satisfy these conditions the relation to the well known uplink downlink duality in the context of joint transmit beamforming and power control is also explored the proposed precoder design is general and as a special case it solves the transmit rank one beamforming problem simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders

semiunitary precoding for spatially correlated mimo channels the focus of this paper is on spatial precoding in correlated multiantenna channels where the number of data streams is adapted independent of the number of transmit antennas towards the goal of a low complexity implementation a statistical semiunitary precoder is studied where the precoder matrix evolves fairly slowly with respect to the channel evolution while prior work on statistical precoding has focussed on information theoretic limits most of these computations result in complicated functional dependencies of the mutual information with the channel statistics that do not explicitly reveal the impact of statistics on performance in contrast estimates that are directly in terms of the channel statistics are obtained here for the relative mutual information loss of a semiunitary precoder with respect to a perfect channel information benchmark based on these estimates matching metrics are developed that capture the degree of matching of a channel to the precoder structure continuously and allow ordering two matrix channels in terms of their mutual information performance while these metrics are based on bounds numerical studies are used to show that the proposed metrics capture the performance tradeoffs accurately the main conclusion of this work is a simple to state fundamental principle in the context of signaling design for single user mimo systems the best channel for the statistical precoder is the channel that is matched to it

progressive linear precoder optimization for mimo packet retransmissions exploiting channel covariance information this work investigates the design of linear precoders for arq packet retransmissions in multi input multi output mimo systems we consider transmitter precoder design based on partial mimo channel information in the form of their covariance feedback our objective is to maximize the ergodic mutual information provided by multiple re transmissions of a packet subject to transmission power constraint we propose a set of near optimal successive linear arq precoders for flat fading mimo channels this progressive linear arq precoder combines the appropriate power loading and the reverse order pairing of singular values in the current retransmission with previous transmissions this reverse order pairing is a special feature unique to our sequential arq preceding approach with demonstrated performance gains

banach saks property in marcinkiewicz spaces abstract we catalogue all marcinkiewicz function and sequence spaces with the banach saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p banach saks property 1 p we apply our results to several open problems

optimal sequences and sum capacity of synchronous cdma systems the sum capacity of a multiuser synchronous cdma system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed by rupf and massey see ibid vol 40 p 1261 6 1994 which had solved the equal power constraint case we identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them

optimal linear precoders for mimo wireless correlated channels with nonzero mean in space time coded systems this paper proposes linear precoder designs exploiting statistical channel knowledge at the transmitter in a multiple input multiple output mimo wireless system the paper focuses on channel statistics since obtaining real time channel state information at the transmitter can be difficult due to channel dynamics the considered channel statistics consist of the channel mean and transmit antenna correlation the receiver is assumed to know the instantaneous channel precisely the precoder operates along with a space time block code stbc and aims to minimize the chernoff bound on the pairwise error probability pep between a pair of block codewords averaged over channel fading statistics two pep design criteria are studied minimum distance and average distance the optimal precoder with an orthogonal stbc is established using a convex optimization framework different relaxations then extend the solution to systems with nonorthogonal stbcs in both cases the precoder is a function of both the channel mean and the transmit correlation a linear precoder acts as a combination of a multimode beamformer and an input shaping matrix matching each side to the channel and to the input signal structure respectively both the optimal beam direction and the power of each mode obtained via a dynamic water filling process depend on the signal to noise ratio snr asymptotic analyses of the results reveal that for all stbcs the precoder approaches a single mode beamformer on the dominant right singular vector of the channel mean as the channel k factor increases on the other hand as the snr increases it approaches an equipower multiple mode beamformer matched to the eigenvectors of the transmit correlation design examples and numerical simulation results for both orthogonal and nonorthogonal stbc precoding solutions are provided illustrating the precoding array gain

robust beamforming for cognitive multi antenna relay networks with bounded channel uncertainties in cognitive relay networks the interferences from secondary users sus and relays to primary users are constrained to be lower than a threshold the interference constraints are difficult to satisfy when the channel state information csi is imperfect in this paper we propose a robust beamforming scheme for the multi antenna non regenerative cognitive relay network where the multi antenna relay with imperfect csis helps the communication of single antenna su our objective is to design a robust beamforming scheme which maximizes the system capacity subject to transmit power constraint and interference constraints the bounded channel uncertainties are modeled using the worst case model the robust beamforming problem neglecting the correlation of channel uncertainties is reformulated as a convex semidefinite programming sdp by rank one relaxation this convex sdp is related with the worst case relay transmit power minimization problem which is further reformulated as a convex sdp whose rank one solution is proved to exist thus we propose the suboptimal solution to the robust beamforming problem which is found effectively by solving two convex sdps simulation results are provided to demonstrate the effectiveness of the proposed scheme

generalized linear precoder and decoder design for mimo channels using the weighted mmse criterion we address the problem of designing jointly optimum linear precoder and decoder for a mimo channel possibly with delay spread using a weighted minimum mean squared error mmse criterion subject to a transmit power constraint we show that the optimum linear precoder and decoder diagonalize the mimo channel into eigen subchannels for any set of error weights furthermore we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights we show how to obtain 1 the maximum information rate design 2 qos based design we show how to achieve any set of relative snrs across the subchannels and 3 the unweighted mmse and equal error design for fixed rate systems

mse balancing in the mimo bc unequal targets and probabilistic interference constraints second order cone soc restrictions have been widely employed in the design of wireless communication systems to recast precoding optimizations in convex form this paper highlights the flexibility of this framework to handle various transmit power and interference limitations also in the multistream multiple input multiple output broadcast channel with imperfect channel state information at the transmitter in particular we propose an iterative solution for mean square error mse balancing with such constraints via the lagrangian dual formulation the mse balancing criteria contrary to signal to interference plus noise ratio and rate criteria exhibit an interesting property when considering different targets for the receivers users with low target values are strictly prioritized in comparison to users with large mse targets that can even be switched off therefore only a subset of the receivers is served at the solution with stringent limitations for the precoders an example of such stringent limitations are small power constraints and probabilistic interference temperature constraints that set a measurable threshold on the generated interference in a cognitive radio system we provide four different approaches to approximate these probabilistic constraints with deterministic soc constraints and compare their accuracy

robust power allocation algorithms for mimo ofdm systems with imperfect csi this paper presents a bayesian approach to the design of transmit prefiltering matrices in closed loop schemes robust to channel estimation errors the algorithms are derived for a multiple input multiple output mimo orthogonal frequency division multiplexing ofdm system two different optimization criteria are analyzed the minimization of the mean square error and the minimization of the bit error rate in both cases the transmitter design is based on the singular value decomposition svd of the conditional mean of the channel response given the channel estimate the performance of the proposed algorithms is analyzed and their relationship with existing algorithms is indicated as with other previously proposed solutions the minimum bit error rate algorithm converges to the open loop transmission scheme for very poor csi estimates

a general robust linear transceiver design for multi hop amplify and forward mimo relaying systems in this paper linear transceiver design for multi hop amplify and forward af multi input multi output mimo relaying systems with gaussian distributed channel estimation errors is investigated commonly used transceiver design criteria including weighted mean square error mse minimization capacity maximization worst mse max mse minimization and weighted sum rate maximization are considered and unified into a single matrix variate optimization problem a general robust design algorithm is proposed to solve the unified problem specifically by exploiting majorization theory and properties of matrix variate functions the optimal structure of the robust transceiver is derived when either the covariance matrix of channel estimation errors seen from the transmitter side or the corresponding covariance matrix seen from the receiver side is proportional to an identity matrix based on the optimal structure the original transceiver design problems are reduced to much simpler problems with only scalar variables whose solutions are readily obtained by an iterative water filling algorithm a number of existing transceiver design algorithms are found to be special cases of the proposed solution the differences between our work and the existing related work are also discussed in detail the performance advantages of the proposed robust designs are demonstrated by simulation results

asymptotic performance analysis of coded blast architectures with statistical rate and power allocations in this paper we first analyze some mathematical properties of ergodic capacity and outage capacity functions of the layers in bell labs layered space time blast architectures employing successive decoding and interference cancellation we then present statistical rate allocation and power allocation methods that optimize the asymptotic performance of blast architectures since the methods are developed by using ergodic capacity and outage capacity functions of the layers the allocated rates and powers depend only on a given channel statistic finally we prove that the rate allocation yields a better asymptotic performance than the power allocation numerical results show that blast architectures with the rate and power allocation perform better by 4 db and 3 db respectively than a blast architecture with the same rate and power in all layers

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

maximization of worst case weighted sum rate for miso downlink systems with imperfect channel knowledge the problem of robust weighted sum rate maximization wsrmax in multicell downlink multi input single output systems is considered we assume that channel state information csi of all users is imperfectly known at the base stations the problem is known to be np hard even in the case of perfect csi we propose optimal and suboptimal but fast converging algorithms for wsrmax problem with csi errors assuming bounded ellipsoidal model for the csi errors we optimize the worst case weighted sum rate the proposed optimal algorithm is based on branch and bound bb technique and it globally solves the worst case wsrmax problem with an optimality certificate as the convergence speed of the bb method can be slow for large networks we also provide a fast but possibly suboptimal algorithm based on alternating optimization technique and sequential convex programming the optimal bb based algorithm can be used to provide performance benchmarks for any suboptimal algorithm numerical results show that the convergence speed of the suboptimal algorithm is fast and it finds a close to optimal solution in only a few iterations

extrapolation methods and rubio de francia s extrapolation theorem we develop a general framework to study extrapolation of inequalities 2005 elsevier inc all rights reserved msc primary 47b38 46m35 secondary 42b25 42b20

stability of a stochastic two dimensional non hamiltonian system we study the top lyapunov exponent of the response of a two dimensional non hamiltonian system driven by additive white noise the origin is not a fixed point for the system however there is an invariant measure for the one point motion of the system in this paper we consider the stability of the two point motion by khasminskii s method of linearization along trajectories the specific system we consider is the third order truncated normal form of the unfolding of a hopf bifurcation we show that in the small noise limit the top lyapunov exponent always approaches zero from below and is thus negative for noise sufficiently small we also show that there exist open sets of parameters for which the top lyapunov exponent is positive thus the two point motion can be either stable or unstable while the stationary density that describes the one point motion always exists

improved linear transmit processing for single user and multi user mimo communications systems in this paper we propose a novel linear transmit precoding strategy for multiple input multiple output mimo systems employing improper signal constellations in particular improved zero forcing zf and minimum mean square error mmse precoders are derived based on modified cost functions and are shown to achieve a superior performance without loss of spectrum efficiency compared to the conventional linear and nonlinear precoders the superiority of the proposed precoders over the conventional solutions are verified by both simulation and analytical results the novel approach to precoding design is also applied to the case of an imperfect channel estimate with a known error covariance as well as to the multi user scenario where precoding based on the nullspace of channel transmission matrix is employed to decouple multi user channels in both cases the improved precoding schemes yield significant performance gain compared to the conventional counterparts

robust optimization for amplify and forward mimo relaying from a worst case perspective in this paper we consider robust optimization of amplify and forward af multiple input multiple output mimo relay precoders in presence of deterministic imperfect channel state information csi when the csi uncertainty lies in a norm bounded region two widely used performance metrics mutual information mi and mean square error mse are adopted as design objectives according to the philosophy of worst case robustness the robust optimization problems with respect to maximizing the worst case mi and minimizing the worst case mse are formulated as maximin and minimax problems respectively due to the fact that these two problems do not have a concave convex or convex concave structure we cannot rely on the conventional saddle point theory to find the robust solutions nevertheless by exploiting majorization theory we show that the formulated maximin and minimax problems both admit saddle points we further analytically characterize the saddle points and provide closed form solutions to robust relay precoder designs interestingly we find that under both mi and mse metrics the robust relay optimization leads to a channel diagonalizing structure meaning that eigenmode transmission is optimal from the worst case robustness perspective the proposed robust designs can improve the spectral efficiency and reliability of af mimo relaying against csi uncertainties at the similar cost of computational complexity as the existing non robust schemes

optimum linear joint transmit receive processing for mimo channels with qos constraints this paper considers vector communications through multiple input multiple output mimo channels with a set of quality of service qos requirements for the simultaneously established substreams linear transmit receive processing also termed linear precoder at the transmitter and linear equalizer at the receiver is designed to satisfy the qos constraints with minimum transmitted power the exact conditions under which the problem becomes unfeasible are given although the original problem is a complicated nonconvex problem with matrix valued variables with the aid of majorization theory we reformulate it as a simple convex optimization problem with scalar variables we then propose a practical and efficient multilevel water filling algorithm to optimally solve the problem for the general case of different qos requirements the optimal transmit receive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols for situations in which the resulting transmit power is too large we give the precise way to relax the qos constraints in order to reduce the required power based on a perturbation analysis we also propose a robust design under channel estimation errors that has an important interest for practical systems numerical results from simulations are given to support the mathematical development of the problem

gaussian multiaccess channels with isi capacity region and multiuser water filling the capacity region of a two user gaussian multiaccess channel with intersymbol interference isi in which the inputs pass through respective linear systems and are superimposed before being corrupted by an additive gaussian noise process is discussed a geometrical method for obtaining the optimal input power spectral densities and the capacity region is presented this method can be viewed as a nontrivial generalization of the single user water filling argument it is shown that as in the traditional memoryless multiaccess channel frequency division multiaccess fdma with optimally selected frequency bands for each user achieves the total capacity of the multiuser gaussian multiaccess channel with isi however the capacity region of the two user channel with memory is in general not a pentagon unless the channel transfer functions for both users are identical

an efficient approximation of spatial correlation based on gauss hermite quadrature an efficient spatial correlation approximation for clustered multiple input multiple output channels based on a hierarchical angle structure is presented to avoid complicated numerical integrations different approximations have been proposed in the literature one approximation is expressed in a high order series expansion of bessel functions while the other suffers low accuracy for large angle spread an approximation based on gauss hermite quadrature ghq is proposed whose values are shown to match well with theoretical results when the antenna spacing is within a critical range by exploring the properties of the abscissas and the weights of the ghq the proposed approximation can be effectively computed with only a few expansion terms and its validity can be maintained over a large range of angle spread the approximation errors of the proposed and existing methods are analyzed simulation results verify the accuracy of the analysis and the efficiency of the proposed approximation

maximum mutual information design for mimo systems with imperfect channel knowledge new results on maximum mutual information design for multiple input multiple output mimo systems are presented assuming that both transmitter and receiver know only an estimate of the channel state as well as the transmit and receive correlation since an exact capacity expression is difficult to obtain for this case a tight lower bound on the mutual information between the input and the output of a mimo channel has been previously formulated as a design criterion however in the previous literature there has been no analytical expression of the optimum transmit covariance matrix for this lower bound here it is shown that for the general case with channel correlation at both ends there exists a unique and globally optimum transmit covariance matrix whose explicit expression can be conveniently determined for the special case with transmit correlation only the closed form optimum transmit covariance matrix is presented interestingly the optimal transmitters for the maximum mutual information design and the minimum total mean square error design share the same structure as they do in the case with perfect channel state information simulation results are provided to demonstrate the effects of channel estimation errors and channel correlation on the mutual information

on the inseparability of parallel mimo broadcast channels with linear transceivers parallel multiple input multiple output mimo broadcast channels have been shown to be separable from an information theoretic point of view i e capacity can be achieved with a strategy that performs separate encoding and decoding on each subchannel subject to a power allocation across subchannels in this paper we show that separability does not necessarily hold if the transmit strategy is restricted to linear transceivers the proof will be done by identifying a rate tuple that is achievable in a certain set of channels with joint treatment of the subchannels but lies outside the achievable rate region of separate linear precoding the implications of this result are that any algorithm to optimize transmit strategies in parallel mimo broadcast channels that is based on both linear transceivers and separate encoding on each subchannel does in fact introduce two suboptimalities aandnd not only one

the optimum combination of block codes and receivers for arbitrary channels a determination is made of the combinations of transmitted block codewords and matching receiver filters that maximize the signal to noise ratio at the detector with arbitrary channel impulse response and arbitrary noise spectrum this permits representing the channel as a set of parallel uncoupled subchannels with uncorrelated noise the representation is used to calculate the capacity of an arbitrary block coded time discrete channel it is shown that substantial coding gains compared to symbol by symbol processing can be achieved the block code used can be concatenated with trellis coded modulation so that the two coding gains are additive

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

maximal lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise asymptotic expansions for the exponential growth rate known as the lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise are constructed such systems arise naturally in the investigation of the stability of steady state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems almost sure stability or instability of dynamical systems depends on the sign of the maximal lyapunov exponent stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable the results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging where approximate ito equations in amplitudes and phases are obtained in the sense of weak convergence

johnson schechtman inequalities for noncommutative martingales abstract in this paper we study johnson schechtman inequalities for noncommutative martingales more precisely disjointification inequalities of noncommutative martingale difference sequences are proved in an arbitrary symmetric operator space e m of a finite von neumann algebra m without making any assumption on the boyd indices of e we show that we can obtain johnson schechtman inequalities for arbitrary martingale difference sequences and that in contrast with the classical case of independent random variables or the noncommutative case of freely independent random variables the inequalities are one sided except when e l 2 0 1 as an application we partly resolve a problem stated by randrianantoanina and wu in 46 we also show that we can obtain sharp moment analogues for orlicz functions satisfying p convexity and q concavity for 1 p 2 q 2 and p 2 2 q this is new even for the classical case we also extend and strengthen the noncommutative burkholder gundy inequalities in symmetric spaces and in the moment case

robust transceiver optimization in downlink multiuser mimo systems we study robust transceiver optimization in a downlink multiuser wireless system where the transmitter and the receivers are equipped with antenna arrays the robustness is defined with respect to imperfect knowledge of the channel at the transmitter the errors in the channel state information are assumed to be bounded and certain quality of service targets in terms of mean square errors mses are guaranteed for all channels from the uncertainty regions iterative algorithms are proposed for the transceiver design the iterations perform alternating optimization of the transmitter and the receivers and have equivalent semidefinite programming representations with efficient numerical solutions the framework supports robust counterparts of several mse optimization problems including transmit power minimization with per user or per stream mse constraints sum mse minimization min max fairness etc although the convergence to the global optimum cannot be claimed due to the intricacy of the problems numerical examples show good practical performance of the presented methods we also provide various possibilities for extensions in order to accommodate a broader set of scenarios regarding the precoder structure the uncertainty modeling and a multicellular setup

practical algorithms for a family of waterfilling solutions many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure the classical example is the capacity achieving solution for a frequency selective channel for simple waterfilling solutions with a single waterlevel and a single constraint typically a power constraint some algorithms have been proposed in the literature to compute the solutions numerically however some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints for such cases it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure in addition a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing the purpose of this paper is twofold on the one hand it overviews the waterfilling results existing in the literature from a unified viewpoint on the other hand it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice to be more precise it provides a practical algorithm to evaluate numerically a general waterfilling solution which includes the currently existing waterfilling solutions and others that may possibly appear in future problems

a robust maximin approach for mimo communications with imperfect channel state information based on convex optimization this paper considers a wireless communication system with multiple transmit and receive antennas i e a multiple input multiple output mimo channel the objective is to design the transmitter according to an imperfect channel estimate where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy the robust transmission scheme is composed of an orthogonal space time block code ostbc whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them at the receiver the signal is detected assuming a perfect channel knowledge the optimization problem corresponding to the design of the power allocation among the estimated eigenmodes whose goal is the maximization of the signal to noise ratio snr is transformed to a simple convex problem that can be easily solved different sources of errors are considered in the channel estimate such as the gaussian noise from the estimation process and the errors from the quantization of the channel estimate among others for the case of gaussian noise the robust power allocation admits a closed form expression finally the benefits of the proposed design are evaluated and compared with the pure ostbc and nonrobust approaches

robust mimo cognitive radio via game theory cognitive radio cr systems improve the spectral efficiency by allowing the coexistence in harmony of primary users pus the legacy users with secondary users sus this coexistence is built on the premises that no su can generate interference higher than some prescribed limits against pus the system design based on perfect channel state information csi can easily end up violating the interference limits in a realistic situation where csi may be imperfect in this paper we propose a robust design of cr systems composed of multiple pus and multiple noncooperative sus in either single input single output siso frequency selective channels or more general multiple input multiple output mimo channels we formulate the design of the su network as a noncooperative game where the sus compete with each other over the resources made available by the pus by maximizing their own information rates subject to the transmit power and robust interference constraints following the philosophy of the worst case robustness we take explicitly into account the imperfectness of su to pu csi by adopting proper interference constraints that are robust with respect to the worst channel errors relying on the variational inequality theory we study the existence and uniqueness properties of the nash equilibria of the resulting robust games and devise totally asynchronous and distributed algorithms along with their convergency properties we also propose efficient numerical methods based on decomposition techniques to compute the robust transmit strategy for each su

distributionally concave symmetric spaces and uniqueness of symmetric structure abstract we present new results concerning the uniqueness of symmetric structure of symmetric function spaces our methods are partly based on a detailed study of distributionally concave spaces and the tensor product operator

minimum ber block precoders for zero forcing equalization we determine the linear precoder that minimizes the bit error rate ber at moderate to high signal to noise ratios snrs for block transmission systems with zero forcing zf equalization and threshold detection the design is developed for the two standard schemes for eliminating inter block interference viz zero padding zp and cyclic prefix cp we show that both the zp minimum ber precoder and the cp minimum ber precoder provide substantially lower error rates than standard block transmission schemes such as orthogonal frequency division multiplexing ofdm the corresponding snr gains can be on the order of several decibels we also show that the cp minimum ber precoder can be obtained by a two stage modification of the water filling discrete multitone modulation dmt scheme in which the diagonal water filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete fourier transform dft matrix

exponential state estimation for stochastically disturbed discrete time memristive neural networks multiobjective approach the state estimation of the discrete time memristive model is studied in this article by applying the stochastic analysis technique sufficient formulas are established to ensure the exponentially mean square stability of the error model moreover the derived control gain matrix can be calculated via the linear matrix inequality lmi it should be mentioned that by extending the derived conclusion to a multiobjective optimization problem the maximum bound of the active function and the minimum bound of the disturbance attenuation are derived the corresponding simulation figures are provided in the end

on the duality of mimo transceiver designs with bit allocation bit rate and power are two commonly used optimality criteria for mimo transceiver design in the literature bit rate maximization and power minimization problems are viewed as different problems and solved independently in this paper we derive the duality between these two problems for both the cases with and without integer constraint on bit allocation we will show that if a transceiver is optimal for the power minimizing problem it is also optimal for the rate maximizing problem and the converse is true such a duality has not been stated and proved in the literature to the best of our knowledge the derivation does not involve any existing optimal solution and we can establish duality result even for the rate maximization problem with integer bit constraint which the optimal solution is not known the duality also allows us to develop an algorithm for finding the rate maximizing transceiver with integer bit allocation using the solution of power minimizing system we will also consider some possible generalizations of the problem for example when there is a constraint on the maximal constellation size and when the subchannel bit error rates bers are constrained for each of these cases we will see that the duality between the two problems continued to hold in the simulations we will compute the optimal solutions for these two problems and demonstrate the duality between these two

robust transceiver optimization for downlink multiuser mimo systems this correspondence addresses the joint transceiver design for downlink multiuser multiple input multiple output mimo systems with imperfect channel state information csi at the base station bs and mobile stations mss by incorporating antenna correlation at both ends of the channel and taking channel estimation errors into account we solve two robust design problems minimization of the weighted sum mean square error mse and minimization of the maximum weighted mse these problems are solved as follows first we establish three kinds of mse uplink downlink duality by transforming only the power allocation matrices from uplink channel to downlink channel and vice versa second in the uplink channel we formulate the power allocation part of each problem ensuring global optimality finally based on the solution of the uplink power allocation and the mse duality results for each problem we propose an iterative algorithm that performs optimization alternatively between the uplink and downlink channels computer simulations verify the robustness of the proposed design compared to the nonrobust naive design

multihop nonregenerative mimo relays qos considerations for nonregenerative multihop multiple input multiple output mimo relay communication systems the optimal source precoding matrix and the optimal relay amplifying matrices have been recently established for a broad class of objective functions subjecting to the transmission power constraint at each node however existing works do not consider any quality of service qos constraints which are important in practical communication systems in this paper we derive the optimal source and relay matrices of a multihop mimo relay system that guarantee the predetermined qos criteria be attained with the minimal total transmission power in particular we consider two types of receivers at the destination node the linear minimal mean squared error mmse receiver and the nonlinear decision feedback equalizer dfe based on the mmse criterion we show that for both types of receivers the solution to the original optimization problem can be upper bounded by using a successive geometric programming gp approach and lower bounded by utilizing a dual decomposition technique simulation results show that both bounds are tight and to obtain the same qos the mimo relay system using the nonlinear mmse dfe receiver requires substantially less total transmission power than the linear mmse receiver based system

the asymptotic stability of a noisy non linear oscillator abstract the purpose of this work is to obtain an approximation for the top lyapunov exponent the exponential growth rate of the response of a single well kramers oscillator driven by either a multiplicative or an additive white noise process to this end we consider the equations of motion as dissipative and noisy perturbations of a two dimensional hamiltonian system a perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation we show analytically that the top lyapunov exponent is positive and for small values of noise intensity e and dissipation e the exponent grows in proportion with e1 3

statistically robust design of linear mimo transceivers the treatment of channel state information csi is critical in the design of mimo systems accurate csi at the transmitter is often not possible or may require high feedback rates herein we consider the robust design of linear mimo transceivers with perfect csi either at the transmitter or at both sides of the link the framework considers the design problem where the imperfect csi consists of the channel mean and covariance matrix or equivalently the channel estimate and the estimation error covariance matrix the robust transceiver design is based on a general cost function of the average mses as well as a design with individual mse based constraints in particular a lower bound of the average mse matrix is explored for the design when only the csi at the transmitter is imperfect under different csi conditions the proposed robust transceivers exhibit a similar structure to the transceiver designs for perfect csi but with a different equivalent channel and or noise covariance matrix

worst case mse precoder design for imperfectly known mimo communications channels this paper considers a worst case precoder design problem for multiple input multiple output mimo wireless communication systems with imperfect channel knowledge at the transmitter when the mimo channel is a full row rank matrix which arises generically when the number n sub t of transmit antennas is greater or equal to the number n sub r of receive antennas and when channel state information is known perfectly at the transmitter the channel can be equalized exactly by employing a precoder equal to the channel pseudo inverse however in actual systems it is necessary to take into account the channel estimation error we consider here a worst case precoder design problem where the goal is to find the precoder minimizing the equalization mean square error for the least favorable channel located in a ball centered about the estimated channel lagrangian optimization is used to convert this min max problem into a min min convex minimization problem over a convex domain which can be solved in closed form the robust precoder and associated least favorable channel have an intuitive interpretation since the least favorable channel zeroes out the weakest subchannels and the robust precoder implements a pseudo inverse only for the remaining subchannels

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

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

robust joint design of linear relay precoder and destination equalizer for dual hop amplify and forward mimo relay systems this paper addresses the problem of robust linear relay precoder and destination equalizer design for a dual hop amplify and forward af multiple input multiple output mimo relay system with gaussian random channel uncertainties in both hops by taking the channel uncertainties into account two robust design algorithms are proposed to minimize the mean square error mse of the output signal at the destination one is an iterative algorithm with its convergence proved analytically the other is an approximated closed form solution with much lower complexity than the iterative algorithm although the closed form solution involves a minor relaxation for the general case when the column covariance matrix of the channel estimation error at the second hop is proportional to identity matrix no relaxation is needed and the proposed closed form solution is the optimal solution simulation results show that the proposed algorithms reduce the sensitivity of the af mimo relay systems to channel estimation errors and perform better than the algorithm using estimated channels only furthermore the closed form solution provides a comparable performance to that of the iterative algorithm

convex separable problems with linear constraints in signal processing and communications in this work we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints the solution is given in closed form as a function of some lagrange multipliers that can be computed through an iterative procedure in a finite number of steps graphical interpretations are given casting valuable insights into the proposed algorithm and allowing to retain some of the intuition spelled out by the water filling policy it turns out that it is not only general enough to compute the solution to different instances of the problem at hand but also remarkably simple in the way it operates we also show how some power allocation problems in signal processing and communications can be solved with the proposed algorithm

worst case robust mimo transmission with imperfect channel knowledge in this paper we consider robust transmit strategies against the imperfectness of the channel state information at the transmitter csit for multi input multi output mimo communication systems following a worst case deterministic model the actual channel is assumed to be inside an ellipsoid centered at a nominal channel the objective is to maximize the worst case received signal to noise ratio snr or to minimize the worst case chernoff bound of the error probability thus leading to a maximin problem moreover we also consider the qos problem as a complement of the maximin design which minimizes the transmit power consumption and meanwhile keeps the received snr above a given threshold for any channel realization in the ellipsoid it is shown that for a general class of power constraints both the maximin and qos problems can be equivalently transformed into convex problems or even further into semidefinite programs sdps thus efficiently solvable by the numerical methods the most interesting result is that the optimal transmit directions i e the eigenvectors of the transmit covariance are just the right singular vectors of the nominal channel under some mild conditions this result leads to a channel diagonalizing structure as in the cases of perfect csit and statistical csit with mean or covariance feedback and reduces the complicated matrix valued problem to a scalar power allocation problem then we provide the closed form solution to the resulting power allocation problem

vector coding for partial response channels a linear technique for combining equalization and coset codes on partial response channels with additive white gaussian noise is developed the technique vector coding uses a set of transmit filters or vectors to partition the channel into an independent set of parallel intersymbol interference isi free channels for any given finite or infinite block length the optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length and the gains of the individual channels are the eigenvalues an optimal bit allocation and energy distribution are derived for the set of parallel channels under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions examples are presented that demonstrate performance advantages with respect to zero forcing decision feedback methods that use the same coset code on the same partial response channel only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system

mimo minimum total mse transceiver design with imperfect csi at both ends this paper presents new results on joint linear transceiver design under the minimum total mean square error mse criterion with channel mean as well as both transmit and receive correlation information at both ends of a multiple input multiple output mimo link the joint design is formulated into an optimization problem the optimum closed form precoder and decoder are derived compared to the case with perfect channel state information csi linear filters are added at both ends to balance the suppression of channel noise and the noise from imperfect channel estimation the impact of channel estimation error as well as channel correlation on system performance is assessed based on analytical and simulation results

positive lyapunov exponents in the kramers oscillator the maximum lyapunov exponent is computed numerically for the double well oscillator in a heat bath positive exponents are found in a wide range of friction coefficients in the low damping regime

lyapunov exponents for small random perturbations of hamiltonian systems consider the stochastic nonlinear oscillator equation ddot x x x 3 varepsilon 2 beta dot x varepsilon sigma x dot w t with beta 0 and sigma neq 0 if 4 beta sigma 2 0 then for small enough varepsilon 0 the system x dot x is positive recurrent in bf r 2 setminus 0 0 now let overline lambda varepsilon denote the top lyapunov exponent for the linearization of this equation along trajectories the main result asserts that overline lambda varepsilon varepsilon 2 3 overline lambda o varepsilon 4 3 qquad mbox as varepsilon to 0 with overline lambda 0 this result depends crucially on the fact that the system above is a small perturbation of a hamiltonian system the method of proof can be applied to a more general class of small perturbations of two dimensional hamiltonian systems the techniques used include i an extension of results of pinsky and wihstutz for perturbations of nilpotent linear systems and ii a stochastic averaging argument involving

mimo transceivers with decision feedback and bit loading theory and optimization this paper considers mimo transceivers with linear precoders and decision feedback equalizers dfes with bit allocation at the transmitter zero forcing zf is assumed considered first is the minimization of transmitted power for a given total bit rate and a specified set of error probabilities for the symbol streams the precoder and dfe matrices are optimized jointly with bit allocation it is shown that the generalized triangular decomposition gtd introduced by jiang li and hager offers an optimal family of solutions the optimal linear transceiver which has a linear equalizer rather than a dfe with optimal bit allocation is a member of this family this shows formally that under optimal bit allocation linear and dfe transceivers achieve the same minimum power the dfe transceiver using the geometric mean decomposition gmd is another member of this optimal family and is such that optimal bit allocation yields identical bits for all symbol streams no bit allocation is necessary when the specified error probabilities are identical for all streams the qr based system used in vblast is yet another member of the optimal family and is particularly well suited when limited feedback is allowed from receiver to transmitter two other optimization problems are then considered a minimization of power for specified set of bit rates and error probabilities the qos problem and b maximization of bit rate for fixed set of error probabilities and power it is shown in both cases that the gtd yields an optimal family of solutions

robust mmse precoding in mimo channels with pre fixed receivers in this paper we design robust precoders under the minimum mean square error mmse criterion for different types of channel state information csi in multiple input multiple output mimo channels we consider low complexity pre fixed receivers that may adapt to the channel but are oblivious to the existence of a precoder at the transmitter in particular three types of csi are taken into account i perfect csi ii statistical csi in the form of mean feedback and iii deterministic imperfect csi assuming that the actual channel is within the neighborhood of a nominal channel which leads to the worst case robust design that is the focus of this paper interestingly it is found that under some mild conditions the optimal transmit directions i e the left singular vectors of the precoder are equal to the right singular vectors of the channel the channel mean and the nominal channel for perfect csi statistical csi and the worst case design respectively consequently the matrix valued problems can be simplified to scalar power allocation problems that either admit closed form solutions or can be efficiently solved by the proposed algorithm

optimal training design for channel estimation in decode and forward relay networks with individual and total power constraints in this paper we study the channel estimation and the optimal training design for relay networks that operate under the decode and forward df strategy with the knowledge of the interference covariance in addition to the total power constraint on all the relays we introduce individual power constraint for each relay which reflects the practical scenario where all relays are separated from one another considering the individual power constraint for the relay networks is the major difference from that in the traditional point to point communication systems where only a total power constraint exists for all colocated antennas two types of channel estimation are involved maximum likelihood ml and minimum mean square error mmse for ml channel estimation the channels are assumed as deterministic and the optimal training results from an efficient multilevel waterfilling type solution that is derived from the majorization theory for mmse channel estimation however the second order statistics of the channels are assumed known and the general optimization problem turns out to be nonconvex we instead consider three special yet reasonable scenarios the problem in the first scenario is convex and could be efficiently solved by state of the art optimization tools closed form waterfilling type solutions are found in the remaining two scenarios of which the first one has an interesting physical interpretation as pouring water into caves

carrier cooperation can reduce the transmit power in parallel mimo broadcast channels with zero forcing even though parallel multiple input multiple output mimo broadcast channels are known to be separable from an information theoretic point of view performing separate encoding and decoding on each of the parallel channels has been shown to be potentially suboptimal in broadcast channels with linear transceivers in this paper we show that suboptimality of such a carrier noncooperative transmission also occurs in broadcast channels with zero forcing and quality of service constraints if time sharing is not allowed the proof is given by constructing a minimal example and identifying a rate tuple that is achievable using carrier cooperative zero forcing with a certain sum power but requires a higher sum power with carrier noncooperative zero forcing this observation is of practical relevance since zero forcing without time sharing is a popular assumption in the design of low complexity optimization algorithms

a robust precoder design based on channel statistics for mimo ofdm systems with insufficient cyclic prefix in this paper we study the precoder design problem for mimo ofdm systems with insufficient cyclic prefix cp using statistical channel state information csi at the transmitter in our previously proposed channel independent precoding scheme an interference nulling based precoding structure is studied which can assist to either cancel interblock interference ibi or separate the subspace occupied by ibi from the subspace used for information symbols in this work we consider a robust precoder design which combines statistical csi at the transmitter and the interference nulling based precoding structure to gain a better performance compared to the channel independent precoding scheme statistical channel state information at the transmitter in the form of covariance matrix of the mimo ofdm channel matrix is utilized to perform the robust precoding the design criterion for the precoder design is to minimize the maximum average mean squared error mse of all the transmitted symbols during one ofdm block interval to achieve this goal the precoder design exhibits a similar procedure to the optimized design framework for mimo transceivers for either perfect or statistical csi with no interference effect but with a distinct equivalent channel since the average mses are set equal using this precoder the ber performance is better than our previously proposed channel independent precoder and the simulation validates this result

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

convex primal decomposition for multicarrier linear mimo transceivers the design of linear transceivers for multiple input multiple output mimo communication systems with channel state information is particularly challenging for two main reasons first since several substreams are established through the mimo channel it is not even clear how the quality of the system should be measured second once a cost function has been chosen to measure the quality the optimization of the system according to such criterion is generally difficult due to the nonconvexity of the problem recent results have solved the problem for the wide family of schur concave convex functions resulting in simple closed form solutions when the system is modeled as a single mimo channel however with several mimo channels such as in multi antenna multicarrier systems the solution is generally more involved leading in some cases to the need to employ general purpose interior point methods this problem is specifically addressed in this paper by combining the closed form solutions for single mimo channels with a primal decomposition approach resulting in a simple and efficient method for multiple mimo channels the extension to functions that are not schur concave convex is also briefly considered relating the present work with a recently proposed method to minimize the average bit error rate ber of the system

minimal transmit power in parallel vector broadcast channels with linear precoding we consider the communication over a set of parallel multiple input single output miso broadcast channels with separate linear precoding on each of them in this setup we study the problem of fulfilling per user quality of service constraints expressed in terms of rates using minimal transmit power by means of a dual decomposition approach and a branch and bound algorithm solving the arising nonconvex subproblems we find the so far unknown globally optimal solution for the case of linear precoding with time sharing although prohibitively complex for implementation in a practical system the new power minimization method is highly interesting from a theoretical point of view as it can be used to quantify the performance gap between the outcome of heuristic algorithms and the theoretical limitations of the system with linear transceivers we also extend the approach such that zero forcing constraints can be handled

multirate zero forcing tx rx design for mimo channel under ber constraints this paper is concerned with communicating parallel independent streams of data possibly of different rates through a multiple input multiple output channel each data stream is required to satisfy a bit error rate ber constraint this scenario arises in multimedia communications we find the linear zero forcing transmitter receiver tx rx matrix pair that requires the minimum transmitter power to achieve the ber constraints it is well known that the tx rx pair can be chosen to partition the matrix channel into scalar subchannels corresponding to singular values and different data streams can be transmitted through different subchannels this design is suboptimum in general the optimum design has the following structure the set of input data streams is partitioned into groups called signal groups the set of subchannels is conformably partitioned into subchannel groups each signal group is collectively transmitted through its assigned subchannel group with each signal subchannel group pair is associated a unitary matrix that mixes the signals at the transmitter and unmixes them at the receiver we derive a simple algorithm to determine the optimum signal and subchannel groups we then use a known algorithm from majorization theory to determine the unitary matrices using these we completely specify the optimum tx rx pair

joint transmitter receiver optimization for multi input multi output systems with decision feedback the joint transmit receive optimization problem for multiuser communication systems with decision feedback is investigated it is shown that minimization of the geometric mean squared error defined as the determinant of the error covariance matrix leads to a tractable transmitter optimization problem for general multi input multi output decision feedback systems several computational results are included that highlight system performance for a variety of useful transmission scenarios