interference alignment with asymmetric complex signaling settling the host madsen nosratinia conjecture it has been conjectured by ho madsen and nosratinia that complex gaussian interference channels with constant channel coefficients have only one degree of freedom regardless of the number of users while several examples are known of constant channels that achieve more than 1 degree of freedom these special cases only span a subset of measure zero in other words for almost all channel coefficient values it is not known if more than 1 degree of freedom is achievable in this paper we settle the host madsen nosratinia conjecture in the negative we show that at least 1 2 degrees of freedom are achievable for all values of complex channel coefficients except for a subset of measure zero for the class of linear beamforming and interference alignment schemes considered in this paper it is also shown that 1 2 is the maximum number of degrees of freedom achievable on the complex gaussian 3 user interference channel with constant channel coefficients for almost all values of channel coefficients to establish the achievability of 1 2 degrees of freedom we use the novel idea of asymmetric complex signaling i e the inputs are chosen to be complex but not circularly symmetric it is shown that unlike gaussian point to point multiple access and broadcast channels where circularly symmetric complex gaussian inputs are optimal for interference channels optimal inputs are in general asymmetric with asymmetric complex signaling we also show that the 2 user complex gaussian x channel with constant channel coefficients achieves the outer bound of 4 3 degrees of freedom i e the assumption of time variations frequency selectivity used in prior work to establish the same result is not needed

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

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

replication based outer bounds on the optimality of half the cake for rank deficient mimo interference networks in order to gain new insights into multiple input multiple output mimo interference networks the optimality of sum k 1 k m k 2 half the cake per user degrees of freedom is explored for a k user mimo interference channel where the cross channels have arbitrary rank constraints and the k th transmitter and receiver are equipped with m k antennas each the result consolidates and significantly generalizes results from prior studies by krishnamurthy et al of rank deficient interference channels where all users have m antennas and by tang et al of full rank interference channels where the k th user pair has m k antennas the broader outcome of this paper is a novel class of replication based outer bounds for arbitrary rank constrained mimo interference networks where replicas of existing users are added as auxiliary users and the network connectivity is chosen to ensure that any achievable scheme for the original network also works in the new network the replicated network creates a new perspective of the problem so that even simple arguments such as user cooperation become quite powerful when applied in the replicated network giving rise to stronger outer bounds than when applied directly in the original network remarkably the replication based bounds are broadly applicable not only to mimo interference channels with arbitrary rank constraints but much more broadly even beyond gaussian settings

degrees of freedom of full duplex cellular networks effect of self interference it was recently shown that full duplex fd operation at a base station bs can provide up to twice as many degrees of freedom dof as a conventional half duplex hd cellular network in the absence of self interference in practice however self interference in an fd bs may not be eliminated completely due to imperfect cancellation and it is not yet known whether fd operation can improve the sum dof of cellular networks in the presence of residual self interference in this paper we provide a complete characterization of the sum dof in an fd bs cellular network with self interference where the rank of the self interference matrix is arbitrary specifically we propose a self interference cancellation scheme that maximizes the sum dof and we prove its optimality by deriving the matching upper bound our results show that even in the presence of residual self interference an fd bs network can still outperform a conventional hd bs network and furthermore the sum dof coincides with that of an fd bs network with no self interference under certain conditions we also derive an achievable sum rate under ergodic phase fading showing that not only a sum dof gain but also a sum rate gain can be obtained over the entire signal to noise ratio range even if residual self interference exists

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

brief control of nonlinear distributed parameter systems using generalized invariants a framework is presented to facilitate the formulation of control strategies for nonlinear dps the key contribution is the generalized quantitative expression of the stability condition for any nonlinear dps the methodology derives from the use of symmetry groups that determine the group invariant solutions of a differential system an invariance condition in the prolonged space of the differential system provides the framework for the distributed control law

distributed sliding mode control in systems described by linear and quasilinear partial differential equations abstract the theory of variable structure systems and their associated sliding regimes is extended to controlled dynamical systems described by first order quasilinear partial differential equations

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

degrees of freedom for mutually interfering broadcast channels in this paper we study spatial degree of freedom dof for two mutually interfering broadcast channels ibc as the demand for space division multiple access sdma increases the ibc where each link has a single transmit node and multiple receive nodes becomes important this paper presents the results of the lower and upper bounds on the dof of the ibc from the derived results it is shown that for most cases zero forcing zf beamforming can achieve the optimal dof of the ibc except for some special cases also we identify a condition that disabling receive cooperation in the multiple input multiple output interference channels causes no dof loss it is confirmed that we cannot expect a dof improvement by enabling in cell receive cooperation if in at least one of two bss the number of antennas is greater than or equal to that of users per cell furthermore we observe a positive result that as the number of users goes to infinity the total dof of the ibc converges to the interference free dof which is the maximum achievable dof in the absence of the inter cell interference

decentralized delay optimal control for interference networks with limited renewable energy storage in this paper we consider delay minimization for interference networks with renewable energy source where the transmission power of a node comes from both the conventional utility power ac power and the renewable energy source we assume the transmission power of each node is a function of the local channel state local data queue state and local energy queue state only we consider two delay optimization formulations namely the decentralized partially observable markov decision process dec pomdp and noncooperative partially observable stochastic game posg in dec pomdp formulation we derive a decentralized online learning algorithm to determine the control actions and lagrangian multipliers lms simultaneously based on the policy gradient approach under some mild technical conditions the proposed decentralized policy gradient algorithm converges almost surely to a local optimal solution in the noncooperative posg formulation the transmitter nodes are noncooperative we extend the decentralized policy gradient solution and establish the technical proof for almost sure convergence of the learning algorithms in both cases the solutions are very robust to model variations

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

on brauer s second main theorem and characters in blocks with nilpotent coefficient extensions 1 1 in 1 j alperin and m broue introduced a local structure in any block of a finite group with the structure m broue and l puig in 2 modified a frobenius condition for finite p nilpotent groups to introduce nilpotent blocks and showed how the characters of a nilpotent block are determined by the characters of its defect group after l puig came to the theory on pointed groups and extended brauer s second main theorem see 9 then in 11 puig determined the precise structure of nilpotent blocks with the structure theorem and brauer s second main theorem in 9 he reproved in 11 the formula on characters in nilpotent blocks these works are done by assuming that the ground fields are large enough later the first author considered the case of arbitrary ground fields and defined nilpotent blocks with the so called local control condition see 1 8 4 below which is no longer equivalent to the frobenius condition though the two conditions are equivalent for large enough ground fields and extended the structure theorem on nilpotent blocks in 4 inspired by a consideration of the frobenius condition puig and the first author in 8 introduced the blocks with nilpotent coefficient extensions see 1 8 5 below and characterized the structure of such blocks precisely the formula on characters in nilpotent blocks was extended to arbitrary ground fields in 6 but the arguments were based on the formula of puig because the author did not know what is the correct version of brauer s second main theorem over small ground fields here a suitable version we were looking for is presented i e theorem 1 6 below which will be proved in section 2 applying it we show a formula on characters in blocks

inner bound on the gdof of the k user mimo gaussian symmetric interference channel the k user multiple input multiple output mimo gaussian symmetric interference channel where each transmitter has m antennas and each receiver has n antennas is studied from a generalized degrees of freedom gdof perspective an inner bound on the gdof is derived using a combination of techniques such as treating interference as noise zero forcing zf at the receivers interference alignment ia and extending the han kobayashi hk scheme to k users as a function of the number of antennas and the log inr log snr level several interesting conclusions are drawn from the derived bounds it is shown that when k n m 1 a combination of the hk and ia schemes performs the best among the schemes considered when n m k n m 1 the hk scheme outperforms other schemes and is found to be gdof optimal in many cases in addition when the snr and inr are at the same level zf receiving and the hk scheme have the same gdof performance

degrees of freedom of interference channels with comp transmission and reception we study the degrees of freedom dof of the k user interference channel with coordinated multipoint comp transmission and reception each message is jointly transmitted by m t successive transmitters and is jointly received by m r successive receivers we refer to this channel as the comp channel with a transmit cooperation order of m t and receive cooperation order of m r since the channel has a total of k transmit antennas and k receive antennas the maximum possible dof is equal to k we show that the comp channel has k dof if and only if m t m r geq k 1 the key idea is that the zero forcing of the interference corresponding to the i rm th message at the decoder of the j rm th message where j ne i can be viewed as a shared responsibility between the m t transmitters carrying the i rm th message and the m r receivers decoding the j rm th message for the general case we derive an outer bound that states that the dof is bounded above by left lceil k m t m r 2 2 right rceil for the special case with only comp transmission i e m r 1 we propose a scheme that can achieve k m t 1 2 dof for all k and conjecture that the result holds true for all k in the proposed coding scheme the m t transmitters carrying each message are used to cancel the interference introduced by this message at the first m t 1 receivers thereby allowing each of these receivers to enjoy 1 dof and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space the achievability proofs are based on the notion of algebraic independence from algebraic geometry

achievable sum dof of the k user mimo interference channel with delayed csit this paper considers a k user multiple input multiple output mimo interference channel ic where 1 the channel state information obtained by the transmitters csit is completely outdated and 2 the number of transmit antennas at each transmitter i e m is greater than the number of receive antennas at each user i e n the usefulness of the delayed csit was first identified in a k phase retrospective interference alignment ria scheme proposed by maddah ali and tse for the multiple input single output broadcast channel but the extension to the mimo ic is a non trivial step as each transmitter only has the message intended for the corresponding user recently abdoli et al focused on a single input single output ic and solved such bottleneck by inventing a k phase ria with distributed overheard interference retransmission in this paper we propose two k phase ria schemes suitable for the mimo ic by generalizing and integrating some key features of both abdoli s and maddah ali s works the two schemes jointly yield the best known sum degrees of freedom dof performance so far for the case m n geq k the achieved sum dof is asymptotically given by 64 15 n when k to infty

the approximate capacity region of the symmetric k user gaussian interference channel with strong interference the symmetric k user interference channel ic is studied with the goal of characterizing its capacity region in the strong interference regime within a constant gap the achievable rate region of a scheme combining rate splitting at the transmitters and interference alignment and successive decoding computation at the receivers is derived next it is shown that this scheme achieves the so called greedy max corner points of the capacity region within a constant gap by combining this result with previous results by ordentlich et al on the sum capacity of the symmetric ic a constant gap characterization of the capacity region for the strong interference regime is obtained this leads to the first approximate characterization of the capacity region of the symmetric k user ic furthermore a new scheme that achieves the sum capacity of the channel in the strong interference regime within a constant gap is also proposed and the corresponding gap is calculated the advantage of the new scheme is that it leads to a characterization within a constant gap without leaving an outage set contrary to the scheme by ordentlich et al

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

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

use of symmetry groups in sliding mode control of nonlinear distributed parameter systems sliding mode control theory is applied to a class of distributed parameter systems the viability of using symmetry groups to aid in feedback control of such systems is discussed a conjecture is presented that leads to the calculation of the control law to support the conjecture the method is applied to the control of a chemical reactor

degrees of freedom of the k user m times n mimo interference channel we provide inner bound and outer bound for the total number of degrees of freedom of the k user multiple input multiple output mimo gaussian interference channel with m antennas at each transmitter and n antennas at each receiver if the channel coefficients are time varying and drawn from a continuous distribution the bounds are tight when the ratio max m n min m n r is equal to an integer for this case we show that the total number of degrees of freedom is equal to min m n k if k r and min m n r r 1 k if k r achievability is based on interference alignment we also provide examples where using interference alignment combined with zero forcing can achieve more degrees of freedom than merely zero forcing for some mimo interference channels with constant channel coefficients

mimo interference alignment in random access networks in this paper we analyze a multiple input multiple output mimo interference channel where nodes are randomly distributed on a plane as a spatial poisson cluster point process a poisson cluster point process consists of clusters with fixed number of points randomly distributed as with the cluster centers distributed randomly on the plane the nodes in each cluster use interference alignment ia to suppress intra cluster interference but unlike most work on ia we do not neglect inter cluster interference we also connect the accuracy of channel state information to the distance between the nodes i e the quality of csi degrades with increasing distance accounting for the training and feedback overhead we derive the transmission capacity of this mimo ia ad hoc network and then compare it to open loop interference blind spatial multiplexing finally we present exemplary system setups where spatial multiplexing outperforms ia due to the imperfect channel state information or the non aligned inter cluster interference

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

generalized channel inversion methods for multiuser mimo systems block diagonalization bd is a well known precoding method in multiuser multi input multi output mimo broadcast channels this scheme can be considered as a extension of the zero forcing zf channel inversion to the case where each receiver is equipped with multiple antennas one of the limitation of the bd is that the sum rate does not grow linearly with the number of users and transmit antennas at low and medium signal to noise ratio regime since the complete suppression of multi user interference is achieved at the expense of noise enhancement also it performs poorly under imperfect channel state information in this paper we propose a generalized minimum mean squared error mmse channel inversion algorithm for users with multiple antennas to overcome the drawbacks of the bd for multiuser mimo systems we first introduce a generalized zf channel inversion algorithm as a new approach of the conventional bd applying this idea to the mmse channel inversion for identifying orthonormal basis vectors of the precoder and employing the mmse criterion for finding its combining matrix the proposed scheme increases the signal to interference plus noise ratio at each user s receiver simulation results confirm that the proposed scheme exhibits a linear growth of the sum rate as opposed to the bd scheme for block fading channels with four transmit antennas the proposed scheme provides a 3 db gain over the conventional bd scheme at 1 frame error rate also we present a modified precoding method for systems with channel estimation errors and show that the proposed algorithm is robust to channel estimation errors

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

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

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

on the characters of nilpotent blocks over small ground fields abstract i characterize how the irreducible characters of a nilpotent block over a small ground field are determined one by one by the irreducible characters of its defect groups

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

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

on group stable commutative separable semisimple subalgebras in a g algebra a of a p group g over a perfect ground field there is a commutative separable semisimple g subalgebra such that any traces on relative projectivity in a can be controlled in the subalgebra and in a residually central sense the maximal such subalgebras form exactly one a g conjugacy class applying to modules the induced module of an indecomposable module of a subnormal subgroup of p primary index is characterized

sum capacity of gaussian vector broadcast channels this paper characterizes the sum capacity of a class of potentially nondegraded gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers coordination is allowed among the transmit terminals but not among the receive terminals the sum capacity is shown to be a saddle point of a gaussian mutual information game where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information the sum capacity is achieved using a precoding strategy for gaussian channels with additive side information noncausally known at the transmitter the optimal precoding structure is shown to correspond to a decision feedback equalizer that decomposes the broadcast channel into a series of single user channels with interference pre subtracted at the transmitter

the degrees of freedom of the k user gaussian interference channel is discontinuous at rational channel coefficients the degrees of freedom of a k user gaussian interference channel gic has been defined to be the multiple of 1 2 log 2 p at which the maximum sum of achievable rates grows with increasing power p in this paper we establish that the degrees of freedom of three or more user real scalar gics viewed as a function of the channel coefficients is discontinuous at points where all of the coefficients are nonzero rational numbers more specifically for all k 2 we find a class of k user gics that is dense in the gic parameter space for which k 2 degrees of freedom are exactly achievable and we show that the degrees of freedom for any gic with nonzero rational coefficients is strictly smaller than k 2 these results are proved using new connections with number theory and additive combinatorics

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

constrained interference alignment and the spatial degrees of freedom of mimo cognitive networks an interference alignment ia scheme is presented that allows multiple opportunistic transmitters secondary users to use the same frequency band of a pre existing primary link without generating any interference the primary and secondary transmit receive pairs are equipped with multiple antennas under power constraints on the primary transmitter the rate of the primary user is maximized by water filling on the singular values of its channel matrix leaving some eigen modes unused and hence the secondary users can align their transmitted signals to produce a number of interference free dimensions at each secondary receiver without causing any interference to the primary user an outer bound is developed on the degrees of freedom dof of the secondary users in the case of a symmetric secondary network with time varying channel coefficients having m antennas at each node and operating in the presence of a primary link with d0 active eigen modes a precoding scheme is presented for the secondary transmitters that can asymptotically achieve the available m d0 2 dof per secondary user an iterative algorithm is also presented that utilizes channel reciprocity to achieve the proposed cognitive ia scheme for a cognitive 3 user secondary network with constant channel coefficients a novel closed form solution is derived for the precoding matrices of the secondary users

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

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

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

linear boundary control for a class of nonlinear pde processes abstract this paper studies the problem of output regulation via boundary feedback control for a class of nonlinear pde processes including important industrial bio chemical reactors under physically reasonable smoothness stability and steady state assumptions it is proven that a linear stable controller with integral action yields global exponential regulation of the process output

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