on the capacity achieving distribution of the discrete time noncoherent and partially coherent awgn channels we investigate the communication limits over rapid phase varying channels and consider the capacity of a discrete time noncoherent additive white gaussian noise ncawgn channel under the average power constraint we obtain necessary and sufficient conditions for the capacity achieving input distribution and show that this distribution is discrete and possesses an infinite number of mass points using this characterization of the capacity achieving distribution we compute a tight lower bound on the capacity of the channel based on examining suboptimal input distributions in addition we provide some easily computable lower and upper bounds on the channel capacity finally we extend some of these results to the partially coherent channel where it is assumed that a phase locked loop pll is used to track the carrier phase at the receiver and that an ideal interleaver and de interleaver are employed rendering the tikhonov distributed residual phase errors statistically independent from one symbol interval to another

mitigation of loopback self interference in full duplex mimo relays full duplex relaying is more spectrally efficient than half duplex relaying as only one channel use is needed per two hops however it is crucial to minimize relay self interference to render full duplex feasible for this purpose we analyze a broad range of multiple input multiple output mimo mitigation schemes natural isolation time domain cancellation and spatial suppression cancellation subtracts replicated interference signal from the relay input while suppression reserves spatial dimensions for receive and transmit filtering spatial suppression can be achieved by antenna subset selection null space projection i e receiving and transmitting in orthogonal subspaces or joint transmit and receive beam selection to support more spatial streams by choosing the minimum eigenmodes for overlapping subspaces in addition minimum mean square error mmse filtering can be employed to maintain the desired signal quality which is inherent for cancellation and the combination of time and spatial domain processing may be better than either alone targeting at minimal interference power we solve optimal filters for each scheme in the cases of joint separate and independent design the performance of mitigation schemes is evaluated and compared by simulations the results confirm that self interference can be mitigated effectively also in the presence of imperfect side information

stepsize selection in the rigorous defect control of taylor series methods abstract modern numerical methods for initial value problems ivps in ordinary differential equations ode produce a piecewise differentiable numerical solution the defect or residual evaluated at it induces a perturbed ode that is satisfied exactly by this solution defect control methods try to ensure that a norm of the defect is bounded by a user specified tolerance this paper justifies and implements a simple and effective stepsize selection strategy and an overall method for both validated and non validated defect control of an explicit taylor series method for ivp odes in validated mode this method guarantees that the defect is bounded by a user specified tolerance

on taylor model based integration of odes interval methods for verified integration of initial value problems ivps for odes have been used for more than 40 years for many classes of ivps these methods are able to compute guaranteed error bounds for the flow of an ode where traditional methods provide only approximations to a solution overestimation however is a potential drawback of verified methods for some problems the computed error bounds become overly pessimistic or the integration even breaks down the dependency problem and the wrapping effect are particular sources of overestimations in interval computations berz and his coworkers have developed taylor model methods which extend interval arithmetic with symbolic computations the latter is an effective tool for reducing both the dependency problem and the wrapping effect by construction taylor model methods appear particularly suitable for integrating nonlinear odes we analyze taylor model based integration of odes and compare taylor model methods with traditional enclosure methods for ivps for odes

primal dual aggregation and disaggregation for stochastic linear programs a multistage stochastic linear program can be approximated by replacing the underlying information structure by a coarser structure given the ordinary lagrangian for the original problem this amounts to restricting both the primal and dual variables to be adapted to the coarser information structure the resulting primal problem has the same form as the original but with aggregated constraints and decisions mutual upper and lower bounds on the optimal values of the original and aggregated problems are obtained via partially aggregated problems formed by restricting only the primal variables or only the dual variables to the coarser structure the introduction of the partially aggregated problems leads to a general disaggregation framework for developing heuristic approaches to solving the original problem

capacity of the discrete time gaussian channel with intersymbol interference the discrete time gaussian channel with intersymbol interference isi where the inputs are subject to a per symbol average energy constraint is considered the capacity of this channel is derived by means of a hypothetical channel model called the n circular gaussian channel ncgc whose capacity is readily derived using the theory of the discrete fourier transform the results obtained for the ncgc are used further to prove that in the limit of increasing block length n the capacity of the discrete time gaussian channel dtgc with isi using a per block average energy input constraint n block dtgc is indeed also the capacity when using the per symbol average energy constraint

aggregation and discretization in multistage stochastic programming multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen negative events in order to ensure computational tractability continuous state stochastic programs are usually discretized and frequently the curse of dimensionality dictates that decision stages must be aggregated in this article we construct two discrete stage aggregated stochastic programs which provide upper and lower bounds on the optimal value of the original problem the approximate problems involve finitely many decisions and constraints thus principally allowing for numerical solution

capacity of the gaussian two hop full duplex relay channel with residual self interference in this paper we investigate the capacity of the gaussian two hop full duplex fd relay channel with residual self interference this channel is comprised of a source an fd relay and a destination where a direct source destination link does not exist and the fd relay is impaired by residual self interference we adopt the worst case linear self interference model with respect to the channel capacity and model the residual self interference as a gaussian random variable whose variance depends on the amplitude of the transmit symbol of the relay for this channel we derive the capacity and propose an explicit capacity achieving coding scheme thereby we show that the optimal input distribution at the source is gaussian and its variance depends on the amplitude of the transmit symbol of the relay on the other hand the optimal input distribution at the relay is discrete or gaussian where the latter case occurs only when the relay destination link is the bottleneck link the derived capacity converges to the capacity of the two hop ideal fd relay channel without self interference and to the capacity of the two hop half duplex hd relay channel in the limiting cases when the residual self interference is zero and infinite respectively our numerical results show that significant performance gains are achieved with the proposed capacity achieving coding scheme compared with the achievable rates of conventional hd relaying and or conventional fd relaying

validated solutions of initial value problems for ordinary differential equations compared to standard numerical methods for initial value problems ivps for ordinary differential equations odes validated methods for ivps for odes have two important advantages if they return a solution to a problem then 1 the problem is guaranteed to have a unique solution and 2 an enclosure of the true solution is produced the authors survey taylor series methods for validated solutions of ivps for odes describe several such methods in a common framework and identify areas for future research

multi stage stochastic optimization applied to energy planning this paper presents a methodology for the solution of multistage stochastic optimization problems based on the approximation of the expected cost to go functions of stochastic dynamic programming by piecewise linear functions no state discretization is necessary and the combinatorial explosion with the number of states the well known curse of dimensionality of dynamic programming is avoided the piecewise functions are obtained from the dual solutions of the optimization problem at each stage and correspond to benders cuts in a stochastic multistage decomposition framework a case study of optimal stochastic scheduling for a 39 reservoir system is presented and discussed

on the discreteness of capacity achieving distributions we consider a scalar additive channel x spl rarr x n whose input is amplitude constrained by extending smith s 1969 argument we derive a sufficient condition on noise probability density functions pdf that guarantee finite support for the associated capacity achieving distribution s

an iterative procedure for constructing subsolutions of discrete time optimal control problems an iterative procedure for constructing subsolutions of deterministic or stochastic optimal control problems in discrete time with continuous state space is introduced the procedure generates a nondecreasing sequence of subsolutions giving true lower bounds on the minimal costs convergence of the values at any fixed initial state is shown

aggregation bounds in stochastic linear programming stochastic linear programs become extremely large and complex as additional uncertainties and possible future outcomes are included in their formulation row and column aggregation can significantly reduce this complexity but the solutions of the aggregated problem only provide an approximation of the true solution in this paper error bounds on the value of the optimal solution of the original problem are obtained from the solution of the aggregated problem these bounds apply for aggregation of both random variables and time periods

using hermite bases in studying capacity achieving distributions over awgn channels this paper studies classes of generic deterministic discrete time memoryless and nonlinear additive white gaussian noise awgn channels subject to multiple types of constraints such as the even moment and compact support constraints or a mixture the optimal input is proved to be discrete with finite number of mass points in the vast majority of the cases only under the even moment constraint and for special cases that emulate the average power constrained linear channel capacity is found to be achieved by an absolutely continuous input the results are extended to channels where the distortion is generally piecewise nonlinear where the discrete nature of the optimal input is conserved these results are reached through the development of methodology and tools that are based on standard decompositions in a hilbert space with the hermite polynomials as a basis and it is showcased how these bases are natural candidates for general information theoretic studies of the capacity of channels affected by awgn intermediately novel results regarding the output rate of decay of gaussian channels are derived namely the output probability distribution of any channel subjected to additive gaussian noise decays necessarily slower than the gaussian itself finally numerical computations are provided for some sample cases optimal inputs are determined and capacity curves are drawn these results put into question the accuracy of adopting the widely used expression 1 1 snr for computing capacities of gaussian deterministic channels

the scenario generation algorithm for multistage stochastic linear programming a multistage stochastic linear program mslp is a model of sequential stochastic optimization where the objective and constraints are linear when any of the random variables used in the mslp are continuous the problem is infinite dimensional to numerically tackle such a problem we usually replace it with a finite dimensional approximation even when all the random variables have finite support the problem is often computationally intractable and must be approximated by a problem of smaller dimension one of the primary challenges in the field of stochastic programming deals with discovering effective ways to evaluate the importance of scenarios and to use that information to trim the scenario tree in such a way that the solution to the smaller optimization problem is not much different from the problem stated with the original tree the scenario generation sg algorithm proposed in this paper is a finite element method that addresses this problem for the class of mslp with random right hand sides

an information based approximation scheme for stochastic optimization problems in continuous time dynamic stochastic optimization problems with a large possibly infinite number of decision stages and high dimensional state vectors are inherently difficult to solve in fact scenario tree based algorithms are unsuitable for problems with many stages while dynamic programming type techniques are unsuitable for problems with many state variables this paper proposes a stage aggregation scheme for stochastic optimization problems in continuous time thus having an extremely large i e uncountable number of decision stages by perturbing the underlying data and information processes we construct two approximate problems that provide bounds on the optimal value of the original problem moreover we prove that the gap between the bounds converges to zero as the stage aggregation is refined if massive aggregation of stages is possible without sacrificing too much accuracy the aggregate approximate problems can be addressed by means of scenario tree based methods the suggested approach applies to problems that exhibit randomness in the objective and the constraints while the constraint functions are required to be additively separable in the decision variables and random parameters

continuous numerical methods for odes with defect control abstract over the last decade several general purpose numerical methods for ordinary differential equations odes have been developed which generate a continuous piecewise polynomial approximation that is defined for all values of the independent variable in the range of interest for such methods it is possible to introduce measures of the quality of the approximate solution based on how well the piecewise polynomial satisfies the ode this leads naturally to the notion of defect control numerical methods that adopt error estimation and stepsize selection strategies in order to control the magnitude of the associated defect can be very effective and such methods are now being widely used in this paper we will review the advantages of this class of numerical methods and present examples of how they can be effectively applied we will focus on numerical methods for initial value problems ivps and boundary value problems bvps where most of the developments have been introduced but we will also discuss the implications and related developments for other classes of odes such as delay differential equations ddes and differential algebraic equations daes

existence results and finite horizon approximates for infinite horizon optimization problems the paper deals with infinite horizon optimization problems the existence of optimal solutions is obtained as a consequence of an asymptotic growth condition we also exhibit finite horizon approximates that yield upper and lower bounds for the optimal values and whose optimal solutions converge to the long term optimal trajectories

the capacity of discrete time memoryless rayleigh fading channels we consider transmission over a discrete time rayleigh fading channel in which successive symbols face independent fading and where neither the transmitter nor the receiver has channel state information subject to an average power constraint we study the capacity achieving distribution of this channel and prove it to be discrete with a finite number of mass points one of them located at the origin we numerically compute the capacity and the corresponding optimal distribution as a function of the signal to noise ratio snr the behavior of the channel at low snr is studied and finally a comparison is drawn with the ideal additive white gaussian noise channel

bounds and approximations for multistage stochastic programs consider typically large multistage stochastic programs which are defined on scenario trees as the basic data structure it is well known that the computational complexity of the solution depends on the size of the tree which itself increases typically exponentially fast with its height i e the number of decision stages for this reason approximations which replace the problem by a simpler one and allow bounding the optimal value are of great importance in this paper we study several methods to obtain lower and upper bounds for multistage stochastic programs and we demonstrate their use in a multistage inventory problem

a gaussian input is not too bad we consider the problem of choosing a robust input for communicating over an input constrained additive noise channel where the noise distribution is arbitrary we show that the mutual information rate achievable using a white gaussian input never incurs a loss of more than half a bit per sample with respect to the power constrained capacity for comparison for the family of colored gaussian noise channels a white gaussian input loses at most log e 2e spl ap 0 265 bit per sample with respect to the optimum water pouring solution for general input constraints we derive a formula for choosing the best input in the min max capacity loss bound sense the bound on the capacity loss is tight for pulse position modulation ppm in the presence of a bursty jammer

primal and dual linear decision rules in stochastic and robust optimization linear stochastic programming provides a flexible toolbox for analyzing real life decision situations but it can become computationally cumbersome when recourse decisions are involved the latter are usually modeled as decision rules i e functions of the uncertain problem data it has recently been argued that stochastic programs can quite generally be made tractable by restricting the space of decision rules to those that exhibit a linear data dependence in this paper we propose an efficient method to estimate the approximation error introduced by this rather drastic means of complexity reduction we apply the linear decision rule restriction not only to the primal but also to a dual version of the stochastic program by employing techniques that are commonly used in modern robust optimization we show that both arising approximate problems are equivalent to tractable linear or semidefinite programs of moderate sizes the gap between their optimal values estimates the loss of optimality incurred by the linear decision rule approximation our method remains applicable if the stochastic program has random recourse and multiple decision stages it also extends to cases involving ambiguous probability distributions