on 2 d pole placement the problem of characteristic polynomial assignment by dynamic output feedback in 2 d systems is solved via 2 d polynomial methods a simple necessary and sufficient condition is given the class of all assignable characteristic polynomials is described in a parametric form stable and causal solutions are treated

stochastic precoding for miso interference channels with channel mean feedback this work considers linear precoding strategies for multiple input single out miso interference channels with channel mean feedback at transmitters where the interference at each receiver is treated as additive noise the challenge here is that previous precoder designs with perfect channel state information csi at transmitters do not apply and new approaches are required based on the laplace transform order an altruistic non equilibrium strategy i e the stochastic zero forcing is first proposed under practical assumptions generalizing the traditional zero forcing which requires perfect csi interestingly the precoding matrices here are all rank one beamformers as in the traditional zero forcing the competitive use of the common physical media in miso interference channels is also formulated as a strategic noncooperative game in contrast to the perfect csi case with a unique rank one nash equilibrium with channel mean feedback the nash equilibria here are not necessarily rank one in general nevertheless when achieved by the rank one beamforming the equilibrium is unique and convenient for implementation accordingly the condition for beamforming to achieve the equilibrium is derived comparisons of the above two strategies reveal no overall dominance of one over the other thereby establishing stochastic zero forcing as an alternative to the nash equilibrium designs

coefficient assignment of 2 d systems by periodic feedback the coefficient assignment problem by periodic feedback for 2 d linear systems described by the roesser model is considered sufficient conditions for the existence of a solution to the problem are established a procedure for finding a sequence of feedback gain matrices is presented and illustrated by a numerical example

minimal representation of convex regions defined by analytic functions in this paper we are concerned with characterizing minimal representation of feasible regions defined by both linear and convex analytic constraints we say that a representation is minimal if every other representation has either more analytic nonlinear constraints or has the same number of analytic constraints and at least as many linear constraints we prove necessary and sufficient conditions for the representation to be minimal these are expressed in terms of the redundant constraints pseudo analytic constraints and implicit equality constraints in order to prove the minimal representation theorem we present results on the facets of the convex regions defined by analytic constraints finally we outline the steps of the procedure that could be used to determine a minimal representation

n k user interference channels degrees of freedom this paper analyzes the gains of opportunistic communication in multiuser interference channels consider a fully connected n user gaussian interference channel at each time instance only k n transmitters are allowed to be communicating with their respective receivers and the remaining n k transmitter receiver pairs remain inactive for finite n if the transmitters can acquire the instantaneous channel realizations and if all channel gains are bounded away from zero and infinity the seminal results on interference alignment establish that for any k arbitrary active pairs the total number of spatial degrees of freedom per orthogonal time and frequency domain is k 2 in dense networks n however as the size of the network increases it becomes less likely to sustain the bounding conditions on the channel gains by exploiting this fact we show that when n obeys certain scaling laws by opportunistically and dynamically selecting the k active pairs at each time instance the number of degrees of freedom can exceed k 2 and in fact can be made arbitrarily close to k more specifically for single antenna transmitters and receivers the network size scaling as n snrd d 1 when power allocation is allowed and scaling as n snrd k 1 without power allocation are sufficient conditions for achieving d 1 k degrees of freedom moreover for achieving these degrees of freedom the transmitters do not require the knowledge of the instantaneous channel realizations hence invoking opportunistic communication in the context of interference channels leads to achieving higher degrees of freedom that are not achievable otherwise we extend the results for multi antenna gaussian interference channels

some results concerning post infeasibility analysis abstract linear constraints are used to model diverse phenomena the number of constraints is large in many practical applications often running into several thousands a system of linear constraints is quite often inconsistent especially at the stage of model formulation a number of different approaches are possible when a system of linear constraints turns out to be inconsistent we prove some results on some plausible approaches and their limitations

separability assignment problem for q dimensional linear discrete time systems separability assignment problem for q dimensional system is formulated sufficient conditions for the existence of a solution to the problem are presented an algorithm for finding the feedback gain matrix is given and illustrated by an example of a 4 d system

feasibility in reverse convex mixed integer programming abstract in this paper we address the problem of the infeasibility of systems defined by reverse convex inequality constraints where some or all of the variables are integer in particular we provide a polynomial algorithm that identifies a set of all constraints critical to feasibility cf that is constraints that may affect a feasibility status of the system after some perturbation of the right hand sides furthermore we will investigate properties of the irreducible infeasible sets and infeasibility sets showing in particular that every irreducible infeasible set as well as infeasibility sets in the considered system are subsets of the set cf of constraints critical to feasibility

capacity regions and sum rate capacities of vector gaussian interference channels the capacity regions of vector or multiple input multiple output gaussian interference channels are established for very strong interference and aligned strong interference furthermore the sum rate capacities are established for z interference noisy interference and mixed aligned weak intermediate and aligned strong interference these results generalize known results for scalar gaussian interference channels

note on the pole assignment of q dimensional linear systems the method in chu 1986 for the solution of the pole assignment problem of separable 2 d linear discrete systems with state feedback is improved and extended to q d linear discrete systems and systems with output feedback

asynchronous iterative water filling for gaussian frequency selective interference channels this paper considers the maximization of information rates for the gaussian frequency selective interference channel subject to power and spectral mask constraints on each link to derive decentralized solutions that do not require any cooperation among the users the optimization problem is formulated as a static noncooperative game of complete information to achieve the so called nash equilibria of the game we propose a new distributed algorithm called asynchronous iterative water filling algorithm in this algorithm the users update their power spectral density psd in a completely distributed and asynchronous way some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference the proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water filling algorithms e g sequential and simultaneous versions the main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the unique nash equilibrium of the game

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

superposition signaling in broadcast interference networks it is known that superposition signaling in gaussian interference networks is capable of improving the achievable rate region however the problem of maximizing the rate gain offered by superposition signaling is computationally prohibitive even in the simplest case of two user single input single output interference networks this paper examines superposition signaling for the general multiple input multiple output broadcast gaussian interference networks the problem of maximizing either the sum rate or the minimal user s rate under superposition signaling and dirty paper coding is solved by a computationally efficient path following procedure which requires only a convex quadratic program for each iteration but ensures convergence at least to a locally optimal solution numerical results demonstrate the substantial performance advantage of the proposed approach

fixed rate transmission over fading interference channels using point to point gaussian codes this paper investigates transmission schemes for fixed rate communications over a rayleigh block fading interference channel there are two source destination pairs where each source in the presence of a short term power constraint intends to communicate with its dedicated destination at a fixed data rate it encodes its messages using a point to point gaussian codebook the two users transmissions can be conducted orthogonally or non orthogonally in the latter case each destination performs either direct decoding by treating the interference as noise or successive interference cancellation sic to recover its desired message for each scheme we seek solutions of a power control problem to efficiently assign power to the sources such that the codewords can be successfully decoded at destinations however because of the random nature of fading the power control problem for some channel realizations may not have any feasible solution and the transmission will be in outage thus for each transmission scheme we first compute a lower bound and an upper bound on the outage probability next we use these results to find an outer bound and an inner bound on the epsilon outage achievable rate region i e the rate region in which the outage probability is below a certain value epsilon

mmse of bad codes we examine codes over the additive gaussian noise channel designed for reliable communication at some specific signal to noise ratio snr and constrained by the permitted minimum mean square error mmse at lower snrs the maximum possible rate is below point to point capacity and hence these are nonoptimal codes alternatively referred to as bad codes we show that the maximum possible rate is the one attained by superposition codebooks moreover the mmse and mutual information behavior as a function of snr for any code attaining the maximum rate under the mmse constraint is known for all snr we also provide a lower bound on the mmse for finite length codes as a function of the error probability of the code

is non unique decoding necessary in multiterminal communication systems signals carrying messages meant for different destinations are often observed together at any given destination receiver han and kobayashi proposed a receiving strategy which performs a joint unique decoding of messages of interest along with a subset of messages which are not of interest it is now well known that this provides an achievable region which is in general larger than if the receiver treats all messages not of interest as noise nair and el gamal and chong motani garg and el gamal independently proposed a generalization called indirect or nonunique decoding where the receiver uses the codebook structure of the messages to uniquely decode only its messages of interest nonunique decoding has since been used in various scenarios the main result in this paper is to provide an interpretation and a systematic proof technique for why nonunique decoding in all known cases where it has been employed can be replaced by a particularly designed joint unique decoding strategy without any penalty from a rate region viewpoint

the discrete memoryless interference channel with one sided generalized feedback and secrecy we study the interference channel with one sided generalized feedback and secrecy requirement in our model message 1 that is known just to encoder 1 should be decoded by both receivers message 2 known only to encoder 2 should be decoded by decoder 2 and kept as secret as possible from decoder 1 the uncertainty of decoder 1 about message 2 is measured by means of the equivocation rate in addition a noisy feedback is provided to encoder 2 we derive an outer bound on the capacity equivocation region for this model that is valid for the noisy cribbing regime the gap between this upper bound and the inner bound reported before is just in the markov conditions satisfied by one of the auxiliary random variables furthermore we consider a simplified causal cognitive interference model the interference channel with a cribbing encoder we show that when conditioned on the input of encoder 1 the interference channel is degraded our outer bound is tight thereby establishing the capacity equivocation region for this case

on the capacity of the k user cyclic gaussian interference channel this paper studies the capacity region of a k user cyclic gaussian interference channel where the kth user interferes with only the k 1 th user mod k in the network inspired by the work of etkin tse and wang who derived a capacity region outer bound for the two user gaussian interference channel and proved that a simple han kobayashi power splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters this paper shows that a similar strategy also achieves the capacity region of the k user cyclic interference channel to within a constant gap in the weak interference regime specifically for the k user cyclic gaussian interference channel a compact representation of the han kobayashi achievable rate region using fourier motzkin elimination is first derived a capacity region outer bound is then established it is shown that the etkin tse wang power splitting strategy gives a constant gap of at most 2 bits in the weak interference regime for the special three user case this gap can be sharpened to 1 bits by time sharing of several different strategies the capacity result of the k user cyclic gaussian interference channel in the strong interference regime is also given further based on the capacity results this paper studies the generalized degrees of freedom gdof of the symmetric cyclic interference channel it is shown that the gdof of the symmetric capacity is the same as that of the classic two user interference channel no matter how many users are in the network

matrix assignment for 2 d systems with periodically variable coefficients by periodic feedback abstract the matrix assignment problem by periodic state feedback for 2 d linear systems with periodically variable coefficients is considered it is shown that an arbitrary matrix can be assigned by periodic state feedback if the system is locally controllable a procedure for finding a sequence of feedback gain matrices is presented and illustrated by a numerical example

system utility maximization with interference processing for cognitive radio networks in spectrum underlay cognitive radio networks secondary users sus are allowed to reuse the spectrum allocated to a primary system the interference between sus actually carries information and can potentially be exploited to improve the network performance through information theoretic interference processing in this paper we design an optimal joint power and rate control algorithm that maximizes the secondary system utility subject to the interference temperature constraints of primary users based on the capacity approaching interference processing scheme called as the han kobayashi scheme the optimal solution is difficult to achieve because the optimization problem is in general non convex to make the optimization problem tractable this paper first transforms the problem into a monotonic optimization problem through exploiting its hidden monotonicity we then devise an effective algorithm to obtain the global optimal solution to the joint power and rate control problem in the han kobayashi scheme the key idea behind the proposed algorithm is to construct a sequence of shrinking polyblocks that approximate the upper boundary of the feasible region with increasing precision numerical results further show that the achieved utility of our scheme significantly outperforms the utility of conventional schemes which treat the interference between sus as the noise

on the capacity of symmetric m user gaussian interference channels with feedback a general time varying feedback coding scheme is proposed for m user fully connected symmetric gaussian interference channels based on the analysis of the general coding scheme we prove a theorem which gives a criterion for designing good time varying feedback codes for gaussian interference channels the proposed scheme improves the suh tse and kramer inner bounds of the channel capacity for the cases of weak and not very strong interference when m 2 this capacity improvement is more significant when the signal to noise ratio snr is not very high in addition our coding scheme can be proved mathematically and numerically to outperform the kramer code for m geq 2 when the snr is equal to the interference to noise ratio inr besides the generalized degrees of freedom gdof of our proposed coding scheme can be proved to be optimal in the all network situations very weak weak strong very strong for any m the numerical results show that our coding scheme can attain better performance than the suh tse coding scheme for m 2 or the mohajer tandon poor lattice coding scheme for m 2 furthermore the simplicity of the encoding decoding algorithms is another strong point of our proposed coding scheme compared with the suh tse coding scheme when m 2 and the mohajer tandon poor lattice coding scheme when m 2 more importantly our results show that an optimal coding scheme for the symmetric gaussian interference channels with feedback can be achieved by only using marginal posterior distributions under a better cooperation strategy between transmitters

efficient computation of pareto optimal beamforming vectors for the miso interference channel with successive interference cancellation we study the two user multiple input single output miso gaussian interference channel where the transmitters have perfect channel state information and employ single stream beamforming the receivers are capable of performing successive interference cancellation so when the interfering signal is strong enough it can be decoded treating the desired signal as noise and subtracted from the received signal before the desired signal is decoded we propose efficient methods to compute the pareto optimal rate points and corresponding beamforming vector pairs by maximizing the rate of one link given the rate of the other link we do so by splitting the original problem into four subproblems corresponding to the combinations of the receivers decoding strategies either decode the interference or treat it as additive noise we utilize recently proposed parameterizations of the optimal beamforming vectors to equivalently reformulate each subproblem as a quasi concave problem which we solve very efficiently either analytically or via scalar numerical optimization the computational complexity of the proposed methods is several orders of magnitude less than the complexity of the state of the art methods we use the proposed methods to illustrate the effect of the strength and spatial correlation of the channels on the shape of the rate region

pole assignment problem in two dimensional linear systems sufficient conditions for existence of a solution to the pole assignment problem in a class of 2 d linear systems using state feedback are given an algorithm for finding the feedback gain matrix for a class of 2 d linear systems is presented and illustrated by simple numerical example

the discrete memoryless interference channel with one sided generalized feedback we study the interference channel with one sided generalized feedback and secrecy requirements in our model message 1 that is known just to encoder 1 should be decoded by both receivers message 2 known only to encoder 2 should be decoded by decoder 2 and kept as secret as possible from decoder 1 the uncertainty of decoder 1 about message 2 is measured by means of the equivocation rate in addition a noisy feedback is provided to encoder 2 we derive an achievable rate equivocation region for this model and an outer bound for the noisy cribbing regime without secrecy the gap being the markov conditions satisfied by one of the auxiliary random variables furthermore we consider a simplified causal cognitive interference model the interference channel with a cribbing encoder we derive an inner bound on the rate region for this model and prove that when the interference channel is degraded conditionally on the input of encoder 1 our inner bound is tight

state amplification we consider the problem of transmitting data at rate over a state dependent channel with state information available at the sender and at the same time conveying the information about the channel state itself to the receiver the amount of state information that can be learned at the receiver is captured by the mutual information between the state sequence and the channel output the optimal tradeoff is characterized between the information transmission rate and the state uncertainty reduction rate when the state information is either causally or noncausally available at the sender in particular when state transmission is the only goal the maximum uncertainty reduction rate is given by this result is closely related and in a sense dual to a recent study by merhav and shamai which solves the problem of masking the state information from the receiver rather than conveying it

on the generalized degrees of freedom of the gaussian interference relay channel the symmetric two user gaussian interference relay channel irc is studied from a generalized degrees of freedom gdof perspective while it is known that the relay does not in crease the dof of the irc such a characterization has not been reported for the gdof yet the focus of this paper is on all cases where the interference link is stronger than the link from the source to the relay this regime basically covers half the space of all possible parameters of the irc by using genie aided approaches new sum capacity upper bounds are derived these bounds are then compared with rates achieved with a novel transmission scheme which is based on a functional decode and forward fdf strategy it is shown that the gdof of the irc is achieved by fdf in the given regime and that a relay can indeed increase the gdof of irc finally the fdf scheme is compared with other schemes like decode and forward as well as compress and forward at low moderate and high signal to noise ratios

outer bounds on the capacity of interference channels corresp new outer bounds are demonstrated for the capacity regions of discrete memoryless interference channels and gaussian interference channels the bound for discrete channels coincides with the capacity region in special cases the bound for gaussian channels improves previous knowledge when the interference is of medium strength

interference alignment based sum capacity bounds for random dense gaussian interference networks we consider a dense k user gaussian interference network formed by paired transmitters and receivers placed independently at random in a fixed spatial region under natural conditions on the node position distributions and signal attenuation we prove convergence in probability of the average per user capacity c k to 1 2e log 1 2snr the achievability result follows directly from results based on an interference alignment scheme presented in recent work of nazer et al our main contribution comes through an upper bound motivated by ideas of bottleneck capacity developed in recent work of jafar by controlling the physical location of transmitter receiver pairs we can match a large proportion of these pairs to form so called e bottleneck links with consequent control of the sum capacity

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

a logarithmic barrier function algorithm for quadratically constrained convex quadratic programming an interior point method for quadratically constrained convex quadratic programming is presented that is based on a logarithmic barrier function approach and terminates at a required accuracy of an approximate solution in polynomial time this approach generates a sequence of unconstrained optimization problems each of which is approximately solved by taking a single step in a newton direction

a large step analytic center method for a class of smooth convex programming problems in this paper a large step analytic center method for smooth convex programming is proposed the method is a natural implementation of the classical method of centers it is assumed that the objective and constraint functions fulfil the so called relative lipschitz condition with lipschitz constant m 0 a great advantage of the method over the existing path following methods is that the steps can be made long by performing linesearches in this method linesearches are performed along the newton direction with respect to a strictly convex potential function when located far away from the central path when sufficiently close to this path a lower bound for the optimal value is updated it is proven that the number of iterations required by the algorithm to converge to an epsilon optimal solution is o 1 m 2 sqrt n ln epsilon or o 1 m 2 n ln epsilon depending on the updating scheme for the lower bound

identifying redundant constraints and implicit equalities in systems of linear constraints redundant constraints are constraints that can be omitted from a system of linear constraints without changing the feasible region implicit equalities are inequality constraints that can be replaced by equalities without changing the feasible region we prove some theorems concerning the identification of both kinds of constraints based on these theorems two methods are developed that allow identification of all redundant constraints and all implicit equalities computational experience on small problems indicates a behavior at least competitive with other methods in this field

the capacity region of frequency selective gaussian interference channels under strong interference this paper presents the capacity region of frequency selective gaussian interference channels under the condition of strong interference assuming an average power constraint per user first a frequency selective gaussian interference channel is modeled as a set of independent parallel memoryless gaussian interference channels using nonfrequency selective results the capacity region of frequency selective gaussian interference channels under strong interference is expressed mathematically exploiting structures inherent in the problem a dual problem is constructed for each independent memoryless channel in which both mathematical and numerical analysis are performed furthermore three suboptimal methods are compared to the capacity achieving coding and power allocation scheme iterative waterfilling a suboptimal scheme provides close to optimum performance and has a distributed coding and power allocation scheme which are attractive in practice

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

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

on infeasibility of systems of convex analytic inequalities abstract in this paper we address the problem of the infeasibility of systems defined by convex analytic inequality constraints in particular we investigate properties of irreducible infeasible sets and provide an algorithm that identifies a set of all constraints k that may affect the feasibility status of the system after some perturbation of the right hand sides we analyze properties of the irreducible sets as well as infeasibility sets in connection with the set k showing in particular that every infeasible system contains an inconsistent subsystem of cardinality not greater than the number of variables plus one the results presented in this paper are generalizations of a theory developed for the systems of quadratic and linear inequality constraints

minimal representation of quadratically constrained convex feasible regions in this paper we are concerned with characterizing minimal representations of feasible regions defined by both linear and convex quadratic constraints we say that representation is minimal if every other representation has either more quadratic constraints or has the same number of quadratic constraints and at least as many linear constraints we will prove that a representation is minimal if and only if it contains no redundant constraints no pseudo quadratic constraints and no implicit equality constraints we define a pseudo quadratic constraint as a quadratic constraint that can be replaced by a finite number of linear constraints in order to prove the minimal representation theorem we also prove that if the surfaces of two quadratic constraints match on a ball then they match everywhere in this paper we also provide algorithms that can be used to detect implicit equalities and pseudoquadratic constraints the redundant constraints can be identified using the hypersphere directions hd method

on the han kobayashi region for theinterference channel in this correspondence we derive a simplified description of the han kobayashi rate region for the general interference channel using this result we establish that the recently discovered chong motani garg rate region is a new representation of the han kobayashi region moreover a tighter bound for the cardinality of the time sharing auxiliary random variable emerges from our simplified description

the degrees of freedom of isotropic mimo interference channels without state information at the transmitters this paper fully determines the degree of freedom dof region of two user interference channels with arbitrary number of transmit and receive antennas in the case of isotropic and independent or block wise independent fading where the channel state information is available to the receivers but not to the transmitters thus the dof gap between previous upper and lower bounds due to the authors vaze and varanasi and huang jafar shamai and vishwanath is closed the dof result characterizes the capacity region to the first order of the logarithm of the signal to noise ratio snr in the high snr regime the dof region is achievable by using random gaussian codebooks independent of the channel states which implies that it is impossible to increase the dof using beamforming and interference alignment in the absence of channel state information at the transmitters

transmit optimization with improper gaussian signaling for interference channels this paper studies the achievable rates of gaussian interference channels with additive white gaussian noise awgn when improper or circularly asymmetric complex gaussian signaling is applied for the gaussian multiple input multiple output interference channel mimo ic with the interference treated as gaussian noise we show that the user s achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex gaussian signaling in terms of the users transmit covariance matrices and an additional term which is a function of both the users transmit covariance and pseudo covariance matrices the additional degrees of freedom in the pseudo covariance matrix which is conventionally set to be zero for the case of proper gaussian signaling provide an opportunity to further improve the achievable rates of gaussian mimo ics by employing improper gaussian signaling to this end this paper proposes widely linear precoding which efficiently maps proper information bearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudo covariance matrices in particular for the case of two user gaussian single input single output interference channel siso ic we propose a joint covariance and pseudo covariance optimization algorithm with improper gaussian signaling to achieve the pareto optimal rates by utilizing the separable structure of the achievable rate expression an alternative algorithm with separate covariance and pseudo covariance optimization is also proposed which guarantees the rate improvement over conventional proper gaussian signaling

an algorithm to determine boundedness of quadratically constrained convex quadratic programmes abstract in this paper we present an algorithm which can be used to determine whether or not a convex quadratic objective function is bounded from below over a feasible region defined by convex quadratic constraints if there are m constraints and n variables the algorithm terminates after at most min m 1 n 1 iterations each iteration requires the identification of implicit equality constraints in a system of homogeneous linear inequality and equality constraints and the identification can be completed by the solution of linear programmes in addition the algorithm has the advantage of providing a mechanism to reduce both the number of constraints and the dimension of the problem

a pole assignment problem for 2 dimensional linear discrete systems in kaczorek 1983 the pole assignment problem of a class of 2 dimensional linear discrete systems is solved in this paper an algorithm for a larger class of systems is presented if degrees of freedom permit the most robust feedback gain matrix can be found numerical examples are included

diversity multiplexing tradeoff for the interference channel with a relay we study the diversity multiplexing tradeoff dmt for the slow fading interference channel with a relay icr we derive four inner bounds on the dmt region the first is based on the compress and forward cf relaying scheme the second is based on the decode and forward df relaying scheme and the last two bounds are based on the half duplex hd and full duplex fd amplify and forward af schemes for the cf and df schemes we find conditions on the channel parameters and the multiplexing gains under which the corresponding inner bound achieves the optimal dmt region we also identify the cases in which the dmt region of the icr corresponds to that of two parallel slow fading relay channels implying that interference does not decrease the dmt for each pair and that a single relay can be dmt optimal for two pairs simultaneously for the hd af scheme we derive conditions on the channel coefficients under which the proposed scheme achieves the optimal dmt for the af based relay channel finally we identify the conditions under which adding a relay strictly enlarges the dmt region relative to the interference channel without a relay

the dispersion of nearest neighbor decoding for additive non gaussian channels we study the second order asymptotics of information transmission using random gaussian codebooks and nearest neighbor decoding over a power limited stationary memoryless additive non gaussian noise channel we show that the dispersion term depends on the non gaussian noise only through its second and fourth moments thus complementing the capacity result lapidoth 1996 which depends only on the second moment furthermore we characterize the second order asymptotics of point to point codes over k sender interference networks with non gaussian additive noise specifically we assume that each user s codebook is gaussian and that nn decoding is employed i e that interference from the k 1 unintended users gaussian interfering signals is treated as noise at each decoder we show that while the first order term in the asymptotic expansion of the maximum number of messages depends on the power of the interfering codewords only through their sum this does not hold for the second order term

outage analysis of block fading gaussian interference channels this paper considers the asymptotic behavior of the outage probability of a two source block fading single antenna gaussian interference channel in the high snr regime by means of the diversity multiplexing tradeoff a general setting where the user rates and the average channel gains are not restricted to be symmetric is investigated this asymmetric scenario allows to analyze networks with mixed interference i e when different sources are at different distance from their intended destination that are not possible under the commonly used symmetric assumption inner and outer bounds for the diversity are derived the outer bound is based on the recent to within one bit capacity result of etkin for the unfaded gaussian channel and is a re derivation of a known bound for which an error is pointed out the inner bound is based on the han and kobayashi achievable region both without rate splitting and with a rate spitting inspired by the to within one bit capacity result an analytical comparison of the diversity upper and lower bounds for a general channel seems difficult by numerical evaluations the two bounds are shown to coincide for a fairly large set of channel parameters

infeasibility analysis for systems of quadratic convex inequalities in this paper we address the problem of the infeasibility of systems defined by quadratic convex inequality constraints in particular we investigate properties of irreducible infeasible sets and provide an algorithm that identifies a set of all constraints k that may affect the feasibility status of the system after some perturbation of the right hand sides we show that all irreducible sets as well as infeasibility sets are subsets of the set k and that every infeasible system contains an inconsistent subsystem of cardinality not greater than the number of variables plus one the results presented in this paper are also applicable to linear systems

state estimation in discrete m d systems in this study observers and stochastic state estimation for m d systems are considered the analysis uses a wave advance process model in transporting the existing 1 d results to the m d setting a constrained minimization technique is used to compute the optimal state estimator which preserves quarter plane causality the optimal state estimator without the quarter plane causality constraint is also determined a comparison then yields insight into the tradeoff between quarter plane causality and estimator performance

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

achievability proof of some multiuser channel coding theorems using backward decoding new and simpler achievability proofs that are based on the backward decoding technique are presented for the well known coding theorems for the multiple access channel mac with perfect feedback and the degraded relay channel a class of macs with different generalized feedback signals is also considered and achievable rate regions that are larger than those previously presented in the literature are established

monotonic optimization framework for the two user miso interference channel resource allocation and transmit optimization for the multiple antenna gaussian interference channel are important but difficult problems the spatial degrees of freedom can be exploited to avoid align or utilize the interference in recent literature the upper boundary of the achievable rate region has been characterized however the resulting programming problems for finding the sum rate proportional fair and minimax egalitarian operating points are non linear and non convex in this paper we develop a non convex optimization framework based on monotonic optimization by outer polyblock approximation first the objective functions are represented in terms of differences of monotonic increasing functions next the problems are reformulated as maximization of increasing functions over normal constraint sets finally the idea to approximate the constraint set by outer polyblocks is explained and the corresponding algorithm is derived numerical examples illustrate the advantages of the proposed framework compared to an exhaustive grid search approach

pole assignment of two dimensional systems for separable characteristic equations abstract this paper considers the problem of pole assignment of linear time invariant multivariable two dimensional systems the desirable closed loop characteristic function is considered to be separable an algorithm is presented for the solution of the problem using state feedback the necessary condition for the problem to have a solution is established and an illustrative example is given

coding schemes and asymptotic capacity for the gaussian broadcast and interference channels with feedback a coding scheme is proposed for the memoryless gaussian broadcast channel with correlated noises and feedback for all noise correlations other than 1 the gap between the sum rate that the scheme achieves and the full cooperation bound vanishes as the signal to noise ratio tends to infinity when the correlation coefficient is 1 the gains afforded by feedback are unbounded and the prelog is doubled when the correlation coefficient is 1 we demonstrate a dichotomy that if the noise variances are equal then feedback is useless and otherwise feedback affords unbounded rate gains and doubles the prelog the unbounded feedback gains however require perfect noiseless feedback when the feedback links are noisy the feedback gains are bounded unless the feedback noise decays to zero sufficiently fast with the signal to noise ratio extensions to more receivers are also discussed as is the memoryless gaussian interference channel with feedback

analysis of deterministic binary interference channels via a general outer bound we present a new outer bound for the general two user discrete memoryless interference channel ifc and use it to establish the capacity region of the binary erasure ifc whose determination was left open in we also show that there are essentially two deterministic binary ifcs in addition to the binary erasure ifc whose capacity regions are not obvious from previous results we determine the capacity region of one of these and apply the aforementioned general outer bound to obtain the best available bound on the maximum achievable sum rate for the other we also show that the new general outer bound is tight for one sided deterministic ifcs that belong to the class studied by el gamal and costa

solution to the 2 d eigenvalue assignment problem a method for eigenvalue assignment by state feedback for 2 d systems described by the roesser model is proposed an algorithm for the choice of the state feedback matrix has been provided and illustrated by a numerical example

a case where interference does not affect the channel dispersion in 1975 carleial presented a special case of an interference channel called the very strong interference regime in which the interference does not reduce the capacity of the constituent point to point gaussian channels in this paper we show that in the strictly very strong interference regime the dispersions are similarly unaffected more precisely in this paper we characterize the second order coding rates of the gaussian interference channel in the strictly very strong interference regime in other words we characterize the speed of convergence of rates of optimal block codes toward a boundary point of the rectangular capacity region these second order coding rates are expressed in terms of the average probability of error and variances of appropriately defined information densities which coincide with the dispersion of the single user gaussian channel this allows us to conclude that the dispersions are unaffected by interference in this channel model

feasible partition problem in reverse convex and convex mixed integer programming abstract in this paper we consider the consistent partition problem in reverse convex and convex mixed integer programming in particular we will show that for the considered classes of convex functions both integer and relaxed systems can be partitioned into two disjoint subsystems each of which is consistent and defines an unbounded region the polynomial time algorithm to generate the partition will be proposed and the algorithm for a maximal partition will also be provided