gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

rate region boundary of the siso z interference channel with improper signaling this paper provides a complete characterization of the boundary of an achievable rate region called the pareto boundary of the single antenna z interference channel z ic when interference is treated as noise and users transmit complex gaussian signals that are allowed to be improper by considering the augmented complex formulation we derive a necessary and sufficient condition for improper signaling to be optimal this condition is stated as a threshold on the interference channel coefficient which is a function of the interfered user rate and which allows insightful interpretations into the behavior of the achievable rates in terms of the circularity coefficient i e degree of impropriety furthermore the optimal circularity coefficient is provided in closed form the simplicity of the obtained characterization permits interesting insights into when and how improper signaling outperforms proper signaling in the single antenna z ic we also provide an in depth discussion on the optimal strategies and the properties of the pareto boundary

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

capacity theorems for the z channel we consider the two user z channel zc where there are two senders and two receivers one of the senders transmits information to its intended receiver without interfering with the unintended receiver while the other sender transmits information to both receivers the complete characterization of the discrete memoryless zc remains unknown to date for the gaussian zc the capacity has only been established for a crossover link gain of 1 in this work we study both the discrete memoryless zc and the gaussian zc we first establish achievable rates for the general discrete memoryless zc the coding strategy uses rate splitting and superposition coding at the sender with information for both receivers at the receivers we use joint decoding we then specialize the rates obtained to two different types of degraded discrete memoryless zcs and also derive respective outer bounds to their capacity regions we show that as long as a certain condition is satisfied the achievable rate region is the capacity region for one type of degraded discrete memoryless zc the results are then extended to the two user gaussian zc with different crossover link gains we determine an outer bound to the capacity region of the gaussian zc with strong crossover link gain and establish the capacity region for moderately strong crossover link gain

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

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

outer bounds on the sum rate of the k user mimo gaussian interference channel this paper derives outer bounds on the sum rate of the k user mimo gaussian interference channel gic three outer bounds are derived under different assumptions of cooperation and providing side information to receivers the novelty in the derivation lies in the careful selection of side information which results in the cancellation of the negative differential entropy terms containing signal components leading to a tractable outer bound the overall outer bound is obtained by taking the minimum of the three outer bounds the derived bounds are simplified for the mimo gaussian symmetric ic to obtain outer bounds on the generalized degrees of freedom gdof the relative performance of the bounds yields insight into the performance limits of multiuser mimo gics and the relative merits of different schemes for interference management these insights are confirmed by establishing the optimality of the bounds in specific cases using an inner bound on the gdof derived by the authors in a previous work it is also shown that many of the existing results on the gdof of the gic can be obtained as special cases of the bounds e g by setting k 2 or the number of antennas at each user to 1

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

space time processing for x channels using precoders in this paper we investigate how to send space time codes with full diversity and low decoding complexity for x channels using precoders first we assume that we have 2 transmitters and 2 receivers each transmitter sends different codewords to each receiver at the same time we propose an orthogonal transmission scheme that combines space time block coding and array processing to achieve low complexity decoding and full diversity for transmitted signals to our best knowledge this is the first scheme which can achieve low complexity decoding and full diversity for any transmitted codeword in x channel when all the users transmit at the same time finally we show that under certain conditions our proposed scheme can be extended to a general case with any number of transmitters and receivers each with any number of antennas simulation results validate our theoretical analysis

capacity bounds for the gaussian interference channel the capacity region of the two user gaussian interference channel ic is studied three classes of channels are considered weak one sided and mixed gaussian ics for the weak gaussian ic a new outer bound on the capacity region is obtained that outperforms previously known outer bounds the sum capacity for a certain range of channel parameters is derived for this range it is proved that using gaussian codebooks and treating interference as noise are optimal it is shown that when gaussian codebooks are used the full han kobayashi achievable rate region can be obtained by using the naive han kobayashi achievable scheme over three frequency bands equivalently three subspaces for the one sided gaussian ic an alternative proof for the sato s outer bound is presented we derive the full han kobayashi achievable rate region when gaussian codebooks are utilized for the mixed gaussian ic a new outer bound is obtained that outperforms previously known outer bounds for this case the sum capacity for the entire range of channel parameters is derived it is proved that the full han kobayashi achievable rate region using gaussian codebooks is equivalent to that of the one sided gaussian ic for a particular range of channel parameters

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

outer bounds on the capacity of gaussian interference channels two outer bounds on the capacity region of the two user gaussian interference channel ifc are derived the idea of the first bound is to let a genie give each receiver just enough information to decode both messages this bound unifies and improves the best known outer bounds of sato and carleial furthermore the bound extends to discrete memoryless ifcs and is shown to be equivalent to another bound of carleial the second bound follows directly from existing results of costa and sato and possesses certain optimality properties for weak interference

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

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

variational collocation on finite intervals in this paper we study a set of functions defined on an interval of finite width which are orthogonal and which reduce to the sinc functions when the appropriate limit is taken we show that these functions can be used within a variational approach to obtain accurate results for a variety of problems we have applied them to the interpolation of functions on finite domains and to the solution of the schrodinger equation and we have compared the performance of the present approach with others

interference alignment and the generalized degrees of freedom of the x channel we explore the capacity and generalized degrees of freedom gdof of the two user gaussian x channel i e a generalization of the two user interference channel where there is an independent message from each transmitter to each receiver there are three main results in this paper first we characterize the sum capacity of the deterministic x channel under a symmetric setting second we characterize the gdof of the gaussian x channel under a similar symmetric model third we extend the sum capacity characterization previously obtained for the gaussian interference channel in the noisy interference regime to the gaussian x channel specifically we show that the gaussian x channel has the same sum capacity as the underlying gaussian interference channel in this regime

interference alignment from degrees of freedom to constant gap capacity approximations interference alignment is a key technique for communication scenarios with multiple interfering links in several such scenarios interference alignment was used to characterize the degrees of freedom of the channel however these degree of freedom capacity approximations are often too weak to make accurate predictions about the behavior of channel capacity at finite signal to noise ratios snrs the aim of this paper is to significantly strengthen these results by showing that interference alignment can be used to characterize capacity to within a constant gap we focus on real time invariant frequency flat x channels the only known solutions achieving the degrees of freedom of this channel are either based on real interference alignment or on layer selection schemes neither of these solutions seems sufficient for a constant gap capacity approximation in this paper we propose a new communication scheme and show that it achieves the capacity of the gaussian x channel to within a constant gap to aid in this process we develop a novel deterministic channel model this deterministic model depends on the 1 2 log snr most significant bits of the channel coefficients rather than only the single most significant bit used in conventional deterministic models the proposed deterministic model admits a wider range of achievable schemes that can be translated to the gaussian channel for this deterministic model we find an approximately optimal communication scheme we then translate this scheme for the deterministic channel to the original gaussian x channel and show that it achieves capacity to within a constant gap this is the first constant gap result for a general fully connected network requiring interference alignment

noisy interference sum rate capacity for vector gaussian interference channels new sufficient conditions for a vector gaussian interference channel to achieve the sum rate capacity by treating interference as noise are derived which generalize and extend the existing results more concise conditions for multiple input single output and single input multiple output scenarios are obtained

on the sum rate of the gaussian mimo z channel and the gaussian mimo x channel in this paper we study the gaussian mimo z channel and the gaussian mimo x channel the mimo x channel xc consists of two multiple antenna transmit receive pairs where each transmitter communicates with both receivers the mimo z channel zc is obtained from the mimo x channel by eliminating one of the links and its corresponding message first we derive a sum rate upper bound for the mimo z channel and compare it with an existing bound in literature next we consider the mimo x channel and propose a new sum rate upper bound by utilizing the sum rate upper bound for the mimo zc subsequently we derive another upper bound for the mimo xc by assuming receiver cooperation and deriving the worst noise covariance matrix for the resulting two user mac we compare the above two upper bounds for the mimo xc with the maddahali motahari khandani mmk scheme then we consider some consequences of the above results for the mimo interference channel finally we present some numerical results the numerical results suggest that the proposed sum rate capacity upper bounds are tighter than existing bounds

existence and convergence theorems for doubly nonlinear partial differential equations of elliptic parabolic type here t 0 v u ax au ax au ax and b is a map from rn x 0 t x r x rn into r for each i 1 n satisfying certain conditions to be specified at a later time a precise formulation of 1 1 is given in section 3 for given u0 and f we study the existence of weak solutions of 1 1 although doubly nonlinear equations of the type 1 1 are of mathematical interest in their own right they arise as a model for a variety of diffusion problems in particular they comprise in a unifying scheme free boundary problems of different natures an example situation is nonstationary saturated unsaturated flow of an incompressible fluid through a porous medium in the case of time dependent water levels a weak formulation of this problem leads to equations of the type 1 1 see 2 however a large held of application for our results is the diffusion problem involving a solid liquid phase change of the stefan type an architypical example is heat transfer during solidification in a nonhomogeneous 205

the capacity region of the mimo interference channel and its reciprocity to within a constant gap the capacity region of the two user multi input multioutput mimo gaussian interference channel ic is characterized to within a constant gap that is independent of the channel matrices for the general case of the mimo ic with an arbitrary number of antennas at each node an achievable rate region and an outer bound to the capacity region of a class of interference channels were obtained in previous work by telatar and tse as unions over all possible input distributions in contrast to that previous work on the mimo ic a simple and an explicit achievable coding scheme are obtained here and shown to have the constantgap to capacity property and in which the sub rates of the common and private messages of each user are explicitly specified for each achievable rate pair the constant gap to capacity results are thus proved in this work by first establishing explicit upper and lower bounds to the capacity region a reciprocity result is also proved which is that the capacity of the reciprocal mimo ic is within a constant gap of the capacity region of the forward mimo ic