coverage probability and achievable rate analysis of ffr aided multi user ofdm based mimo and simo systems expressions are derived for the coverage probability and average rate of both multi user multiple input multiple output mu mimo and single input multiple output simo systems in the context of a fractional frequency reuse ffr scheme in particular given a reuse region of frac 1 3 fr3 and a reuse region of 1 fr1 as well as a signal to interference plus noise ratio sinr threshold s th which decides the user assignment to either the fr1 or fr3 regions we theoretically show that 1 the optimal choice of s th which maximizes the coverage probability is s th t where t is the target sinr required for ensuring adequate coverage and 2 the optimal choice of s th which maximizes the average rate is given by s th t prime where t prime is a function of the path loss exponent the number of antennas and of the fading parameters the impact of frequency domain correlation amongst the ofdm sub bands allocated to the fr1 and fr3 cell regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the ffr network furthermore the performance of our ffr aided mu mimo and simo systems is compared our analysis shows that the 2 times 2 mu mimo system achieves 22 5 higher rate than the 1 times 3 simo system and for lower target sinrs the coverage probability of a 2 times 2 mu mimo system is comparable to a 1 times 3 simo system hence the former one may be preferred over the latter our simulation results closely match the analytical results

limited feedback low encoding complexity precoder design for downlink of fdd multi user massive mimo systems we investigate a limited feedback precoder based on symbol pairwise error probability pep for a block faded k times n t downlink multiple input multiple output mimo channel in the considered system k lfloor n t alpha rfloor single antenna users feedback quantized channel state information to the n t antenna transmitter using b bits per transmit antenna per user we analytically show that for alpha b geq 1 and n t rightarrow infty both symbol pep and achievable rate of each of the k downlink users almost surely converge to the symbol pep and achievable rate of k parallel additive white gaussian noise awgn channels respectively we show that the encoding complexity of the precoder is o n t k we also show that if channel coefficients estimated by the user are corrupted by awgn noise the symbol pep and achievable rate of each user almost surely converge to the symbol pep and achievable rate in a scaled awgn channel with b 1 and n t rightarrow infty for correlated channels we derive a condition which enables the proposed precoder almost surely to cancel multi user interference for large n t values finally we numerically compare the bit error rate encoding complexity and per user achievable rate of the proposed scheme with the existing designs

user selection with zero forcing beamforming achieves the asymptotically optimal sum rate in this paper we propose a generalized greedy g greedy algorithm based on zero forcing beamforming zfbf for the multiple input multiple output mimo broadcast channel this algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations as previous results only give the scaling law of the sum rate of dirty paper coding dpc with the help of the g greedy structure we are able to obtain the exact limit of the dpc sum rate for a large number of users we also prove that the difference between the sum rates obtained by g greedy user selection and by dpc goes to zero as the number of users increases in addition to this we investigate one particular greedy user selection scheme called sequential water filling swf for this algorithm a complexity reduction is achieved by an iterative procedure based on an lq decomposition which converts the calculation of the moore penrose matrix inverse to one vector matrix multiplication a sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction with the help of the g greedy algorithm we prove that swf achieves the full dpc sum rate for a large number of users for a moderate number of users simulation demonstrates that compared with other user selection algorithms swf achieves a higher sum rate that is close to the maximal sum rate achievable by zfbf with the same order of complexity

use of logrank tests and group sequential methods at fixed calendar times this paper presents simulations to determine the operating characteristics of several group sequential boundaries when applied to the repeated analysis of survival data at equal intervals of calendar time because the group sequential boundaries of pocock 1977 biometrika 64 191 199 and o brien and fleming 1979 biometrics 35 549 556 were constructed on the assumption that each interim analysis provides an equal increment of statistical information these boundaries are not theoretically appropriate for interim analysis at prescheduled calendar times nonetheless our simulations show that these boundaries yield size and power near nominal levels for repeated logrank analyses at equal intervals of calendar time

constant q curvature metrics in arbitrary dimension working in a given conformal class we prove existence of constant q curvature metrics on compact manifolds of arbitrary dimension under generic assumptions the problem is equivalent to solving a nth order non linear elliptic differential or integral equation with variational structure where n is the dimension of the manifold since the corresponding euler functional is in general unbounded from above and below we use critical point theory jointly with a compactness result for the above equation

low complexity user selection algorithms for multiuser mimo systems with block diagonalization block diagonalization bd is a precoding technique that eliminates interuser interference in downlink multiuser multiple input multiple output mimo systems with the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission the number of simultaneously supportable users with bd is limited by the ratio of the number of base station transmit antennas to the number of user receive antennas in a downlink mimo system with a large number of users the base station may select a subset of users to serve in order to maximize the total throughput the brute force search for the optimal user set however is computationally prohibitive we propose two low complexity suboptimal user selection algorithms for multiuser mimo systems with bd both algorithms aim to select a subset of users such that the total throughput is nearly maximized the first user selection algorithm greedily maximizes the total throughput whereas the criterion of the second algorithm is based on the channel energy we show that both algorithms have linear complexity in the total number of users and achieve around 95 of the total throughput of the complete search method in simulations

high snr analysis for mimo broadcast channels dirty paper coding versus linear precoding in this correspondence we compare the achievable throughput for the optimal strategy of dirty paper coding dpc to that achieved with suboptimal and lower complexity linear precoding techniques zero forcing and block diagonalization both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain but an absolute difference in terms of throughput does exist the sum rate difference between the two strategies is analytically computed at asymptotically high snr furthermore the difference is not affected by asymmetric channel behavior when each user has a different average snr weighted sum rate maximization is also considered in the process it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate

compactness of solutions to some geometric fourth order equations we prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds the proof is based on a refined bubbling analysis for which the main estimates are given in integral form our result is used in a subsequent paper to find critical points via minimax arguments of some geometric functional which give rise to conformal metrics of constant q curvature as a byproduct of our method we also obtain compactness of such metrics

simple space time symmetries generalizing conformal field theory we study simple space time symmetry groups g which act on a space time manifold m g h which admits a g invariant global causal structure we classify pairs g m which share the following additional properties of conformal field theory 1 the stability subgroup h of o m is the identity component of a parabolic subgroup of g implying factorization h man where m generalizes lorentz transformations a dilatations and n special conformal transformations 2 special conformal transformations n act trivially on tangent vectors v tom the allowed simple lie groups g are the universal coverings of su m m so 2 d sp l r so 4n and e7 25 and h are particular maximal parabolic subgroups they coincide with the groups of fractional linear transformations of euclidean jordan algebras whose use as generalizations of minkowski space time was advocated by gunaydin mod phys lett a 8 1407 1993 all these groups g admit positive energy representations it will also be shown that the classical confor

energy efficient zero forcing precoding design for small cell networks we consider small cell networks with multiple antenna transceivers and base stations bss cooperating to jointly design linear precoders to maximize the network energy efficiency subject to a sum power and per antenna power constraints at individual bss as well as user specific quality of service qos requirements assuming zero forcing precoding we formulate the problem of interest as a concave convex fractional program to which we proposed a centralized optimal solution based on the prevailing dinkelbach algorithm to facilitate distributed implementations we transform the design problem into an equivalent convex program using charnes cooper s transformation then based on the framework of alternative direction method of multipliers admm we develop a decentralized algorithm which is numerically shown to achieve fast convergence since bss are generally power hungry it may be more energy efficient if some bss can be shut down while still satisfying the qos constraints toward this end we investigate the problem of joint precoder design and bs selection which is a mixed boolean nonlinear program and then provide an optimal solution by customizing the branch and bound method for real time applications we propose a greedy algorithm which achieves near optimal performance in polynomial time numerical results are provided to demonstrate the effectiveness of the proposed algorithms

discrete sequential boundaries for clinical trials summary pocock 1977 o brien fleming 1979 and slud wei 1982 have proposed different methods to construct discrete sequential boundaries for clinical trials these methods require that the total number of decision times be specified in advance in the present paper we propose a more flexible way to construct discrete sequential boundaries the method is based on the choice of a function a t which characterizes the rate at which the error level ac is spent the boundary at a decision time is determined by a t and by past and current decision times but does not depend on the future decision times or the total number of decision times

parametrization of causal actions of universal covering groups and global hyperbolicity abstract the transformation group of the universal covering of the real projective line obtained by lifting ordinary projective transformations is given explicitly in terms of canonical coordinates a similar formulation is given of the action of the universal covering of su 2 2 upon the universal covering of the shilov boundary of its associated bounded hermitian symmetric domain structured as r1 su 2 the former group g isomorphic to s u 1 1 has a unique and continuous bi invariant global partial ordering similar to that expressing space time causality relations corresponding to its bivariant lorentzian metric the partial ordering is the same as that induced by the ordering of the real line which the transformation group preserves as an application the compactness of the intervals g 1 g 2 g g g 1 g g 2 for g 1 g 2 g necessary for global hyperbolicity of the metric is studied it is shown that g1 g2 is compact if and only if g g1 for all g in a neighborhood of g2 where is the generator of the center of g satisfying e in particular the interior of e is a maximal open global hyperbolic submanifold s u 1 1 is not globally hyperbolic

repeated significance testing for a general class of statistics used in censored survival analysis abstract the asymptotic joint distribution of a class of sequentially computed statistics used in survival analysis is derived when the individuals under study enter serially and are subject to random loss to follow up these results are used for constructing repeated significance tests over real time

existence of conformal metrics with constant q curvature given a compact four dimensional manifold we prove existence of conformal metrics with constant q curvature under generic assumptions the problem amounts to solving a fourth order nonlinear elliptic equation with variational structure since the corresponding euler functional is in general unbounded from above and from below we employ topological methods and min max schemes jointly with the compactness result of 35

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

joint design of tx rx beamformers in mimo downlink channel we consider a single cell multiple input multiple output mimo downlink channel where linear transmission and reception strategy is employed the base station bs transmitter is equipped with a scheduler using a simple opportunistic beamforming strategy which associates an intended user for each of the transmitted data streams for the case when the channel of the scheduled users is available at the bs we propose a general method for joint design of the transmit and the receive beamformers according to different optimization criteria including weighted sum rate maximization weighted sum mean square error minimization minimum signal to interference plus noise ratio sinr maximization and sum power minimization under a minimum sinr constraint the proposed method can handle multiple antennas at the bs and at the mobile user with single and or multiple data streams per scheduled user the optimization problems encountered in the beamformer design e g covariance rank constraint are not convex in general therefore the problem of finding the global optimum is intrinsically nontractable however by exploiting the uplink downlink sinr duality we decompose the original optimization problem as a series of simpler optimization problems which can be efficiently solved by using standard convex optimization tools even though each subproblem is optimally solved there is no guarantee that the global optimum has been found due to the nonconvexity of the problem however the simulations show that the algorithms converge fast to a solution which can be a local optimum but is still efficient

lie semialgebras are real phenomena in recent year there has been considerable interest in local semigroups in lie groups partly from the view point of geometric control theory partly from the view point of differential geometry for the former aspect see br hi js l for the latter lo o11 and 2 pa ro vi lie theory relates local subgroups of a lie group with subalgebras of its lie algebra in just the same spirit it relates certain local subsemigroups with lie semialgebras in its lie algebra here a lie semialgebra in a finite dimensional real lie algebra is a wedge i e a topologically closed subset which is stable under addition and multiplication by non negative scalars for which there is a neighborhood b of 0 in l such that for all x y b the campbellhausdorff product x y x y 89 y l is well defined and in addition stays in w for x ye w if w is a lie semialgebra in l then w w is a lie subalgebra hl 2 l if w is any wedge in l and if w contains the lie algebra w w generated by all commutators w w with w w w then w is a lie semialgebra lie semialgebras arising in this fashion we will call trivial we shall prove the following

asymptotically optimal water filling in vector multiple access channels dynamic resource allocation is an important means to increase the sum capacity of fading multiple access channels macs in this paper we consider vector multi access channels channels where each user has multiple degrees of freedom and study the effect of power allocation as a function of the channel state on the sum capacity or spectral efficiency defined as the maximum sum of rates of users per unit degree of freedom at which the users can jointly transmit reliably in an information theoretic sense assuming random directions of received signal direct sequence code division multiple access ds cdma channels and macs with multiple antennas at the receiver are two systems that fall under the model our main result is the identification of a simple dynamic power allocation scheme that is optimal in a large system i e with a large number of users and a correspondingly large number of degrees of freedom a key feature of this policy is that for any user it depends on the instantaneous amplitude of channel state of that user alone and the structure of the policy is water filling in the contest of ds cdma and in the special case of no fading the asymptotically optimal power policy of water filling simplifies to constant power allocation over all realizations of signature sequences this result verifies the conjecture made in verdu and shamai 1999 we study the behavior of the asymptotically optimal water filling policy in various regimes of number of users per unit degree of freedom and signal to noise ratio snr we also generalize this result to multiple classes i e the situation when users in different classes have different average power constraints

geodesical refinement of mimo limited feedback in this paper we investigate a codeword refinement technique called double codeword coding in the context of mimo feedback in the proposed method the second codeword is fed back in addition to the best codeword as their interpolation at the transmitter improves the channel knowledge the derivation of the optimal interpolation parameter is presented together with the derivation of an upper bound to the interpolation parameter based on channel quality feedback available at the transmitter we show that double codeword feedback refinement has slightly lower complexity than alternative techniques and still achieves similar performance furthermore double codeword coding can be generalized to higher transmission ranks using extended multiuser mimo link simulations we verify that the double codeword feedback is able to provide significant gains in 3gpp lte context

essential unitarization of symplectics and applications to field quantization abstract symplectic operators satisfying generic and group invariant spectral positivity conditions are studied the theory developed is applied and illustrated to determine the unique invariant frequency decomposition equivalently linear quantization with invariant vacuum state of the klein gordon equation in non static spacetimes let h be any linear topological symplectic space such that there exists a real linear and topological isomorphism of h with some complex hilbert space carrying into the imaginary part of the scalar product then any bounded invertible symplectic s sp h resp bounded infinitesimally symplectic a sp h which satisfies sv v 0 resp av v 0 for all nonzero v h where s i is invertible is realized uniquely and constructively as a unitary resp skewadjoint operator in a complex hilbert space which depends in general on the operator and typically only densely intersects h the essentially unique weakly and uniformly closed invariant convex cones in sp h are determined extending previously known results in the finite dimensional case a notion of skew adjoint extension of a closed semi bounded infinitesimally symplectic operator is defined strictly including the usual notion of positive self adjoint extension in a complex hilbert space all such skew adjoint extensions are parametrized as in the von neumann or birman krein vishik theories finally the unique complex hilbertian structure formulated on the space of solutions of the covariant klein gordon equation in generic conformal perturbations of flat space is uniquely determined by invariance under the scattering operator the invariant hilbert structure is explicitly calculated to first order for an infinite dimensional class of purely time dependent metric perturbations and higher order contributions are rigorously estimated

spatial reuse precoding for scalable downlink networks in this paper we develop linear precoding schemes for mimo downlink networks with quasi static channels that are scalable in the sense that they can be implemented with moderate complexity in networks with increasing numbers of cells and users the principle that underlies the proposed precoding scheme is to exploit the decomposable structure of the equivalent channel matrix by designing the precoders at the base stations to be decomposable as well thus the channel matrices and the designed precoders can be expressed as the kronecker product of constituent matrices for networks with a finite number of cells the proposed structured precoding schemes enable inter cell interference cancellation without the need for inter cell feedback and provide more degrees of freedom than conventional interference avoidance schemes while incurring a latency that grows only linearly in the number of cells the proposed structured precoding schemes also enable a scaling approach for unbounded networks that we have called spatial reuse precoding srp srp is based on the observation that at each receiver the signals from interfering sources that employ the same precoder arrive in the same subspace regardless of the particular channel matrices between the interfering sources and the receiver in some typical cellular architectures we show how an srp scheme based on the proposed structured precoders can be designed to eliminate the dominant sources of interference without requiring cooperation between cells in addition we show that srp can provide substantial performance gains in certain heterogeneous networks

time domain differential feedback for massive miso ofdm systems in correlated channels massive multiple input multiple output mimo orthogonal frequency division multiplexing ofdm is a promising technology for next generation wireless communications however when channel state information csi at the transmitter is obtained using channel feedback the benefits of this system are severely limited by the tradeoff between downlink capacity and feedback overhead to solve this problem we propose a time domain differential feedback scheme for massive multiple input single output miso ofdm systems the proposed scheme exploits channel correlations in time frequency and space domains simultaneously by considering differential channel impulse response cir to simplify the codebook design and to reduce codeword search complexity we partition and then quantize the differential cir using a number of subcodebooks because the total feedback bits are shared by the subcodebooks we further optimize the bit allocation for them to minimize the total quantization error for this we analyze the quantization error of the proposed scheme and then use the analysis results for the bit allocation optimization in simulations the proposed scheme efficiently exploits all correlations and achieves significant spectral efficiency gain compared to conventional feedback schemes

generalized design of low complexity block diagonalization type precoding algorithms for multiuser mimo systems block diagonalization bd based precoding techniques are well known linear transmit strategies for multiuser mimo mu mimo systems by employing bd type precoding algorithms at the transmit side the mu mimo broadcast channel is decomposed into multiple independent parallel single user mimo su mimo channels and achieves the maximum diversity order at high data rates the main computational complexity of bd type precoding algorithms comes from two singular value decomposition svd operations which depend on the number of users and the dimensions of each user s channel matrix in this work low complexity precoding algorithms are proposed to reduce the computational complexity and improve the performance of bd type precoding algorithms we devise a strategy based on a common channel inversion technique qr decompositions and lattice reductions to decouple the mu mimo channel into equivalent su mimo channels analytical and simulation results show that the proposed precoding algorithms can achieve a comparable sum rate performance as bd type precoding algorithms substantial bit error rate ber performance gains and a simplified receiver structure while requiring a much lower complexity

invariant convex cones and causality in semisimple lie algebras and groups the convex cones in a simple lie algebra g invariant under the adjoint group g of g are studied using a earlier abstract classification of such cones we find explicit algebraic presentations of such cones in all the classical hermitian symmetric lie algebras nontrivial such cones exist only in these cases the g orbits in such cones are listed the notion of a temporal action of a lie group with an invariant causal orientation upon a causally oriented manifold is defined the canonical actions of such classical groups g as above on the shilov boundaries of the associated tube type hermitian symmetric spaces are shown to be temporal actions corollaries are 1 the existence of nontrivial lie semigroups s in the infinite sheeted coverings g of g which are invariant under conjugation by g and satisfy s s 1 e and 2 the global causality i e no closed time like curves of such covering groups g

withdrawal censoring and the sequential logrank procedure the effects of withdrawal censoring on the power of the group sequential logrank procedure are examined in the context of survival studies special attention is given to an assumption that the withdrawal censoring mechanism is only conditionally independent of survival time simulation studies of two sample fixed duration trials under random right censoring staggered entry and exponential life times reveal a general decrease in statistical power that is most pronounced when the withdrawals are unbalanced the majority occurring in the group with the higher hazard rate generally this decrease in power is not of practical concern under typical withdrawal rates except when conditional independence is present in which case large fluctuations in power and type i error rates can occur

joint spatial division and multiplexing the large scale array regime we propose joint spatial division and multiplexing jsdm an approach to multiuser mimo downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced dimensional channel state information at the transmitter csit jsdm achieves significant savings both in the downlink training and in the csit uplink feedback thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing fdd systems for which uplink downlink channel reciprocity cannot be exploited in the proposed scheme the multiuser mimo downlink precoder is obtained by concatenating a prebeamforming matrix which depends only on the channel second order statistics with a classical multiuser precoder based on the instantaneous knowledge of the resulting reduced dimensional effective channel matrix we prove a simple condition under which jsdm incurs no loss of optimality with respect to the full csit case for linear uniformly spaced arrays we show that such condition is approached in the large number of antennas limit for this case we use szego s asymptotic theory of toeplitz matrices to show that a dft based prebeamforming matrix is near optimal requiring only coarse information about the users angles of arrival and angular spread finally we extend these ideas to the case of a 2 d base station antenna array with 3 d beamforming including multiple beams in the elevation angle direction we provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max min fairness criteria showing extremely attractive performance our numerical results are obtained via asymptotic random matrix theory avoiding lengthy monte carlo simulations and providing accurate results for realistic finite number of antennas and users

zero forcing methods for downlink spatial multiplexing in multiuser mimo channels the use of space division multiple access sdma in the downlink of a multiuser multiple input multiple output mimo wireless communications network can provide a substantial gain in system throughput the challenge in such multiuser systems is designing transmit vectors while considering the co channel interference of other users typical optimization problems of interest include the capacity problem maximizing the sum information rate subject to a power constraint or the power control problem minimizing transmitted power such that a certain quality of service metric for each user is met neither of these problems possess closed form solutions for the general multiuser mimo channel but the imposition of certain constraints can lead to closed form solutions this paper presents two such constrained solutions the first referred to as block diagonalization is a generalization of channel inversion when there are multiple antennas at each receiver it is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high snr the second known as successive optimization is an alternative method for solving the power minimization problem one user at a time and it yields superior results in some e g low snr situations both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined in order to accommodate more general scenarios we also propose a framework for coordinated transmitter receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas while the proposed algorithms are suboptimal they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity

constructive multiuser interference in symbol level precoding for the miso downlink channel this paper investigates the problem of interference among the simultaneous multiuser transmissions in the downlink of multiple antenna systems using symbol level precoding a new approach to exploit the multiuser interference is discussed the concept of exploiting the interference between spatial multiuser transmissions by jointly utilizing data information di and channel state information csi in order to design symbol level precoders is proposed to this end the interference between data streams is transformed under certain conditions into useful signal that can improve the signal to interference noise ratio sinr of the downlink transmissions we propose a maximum ratio transmission mrt based algorithm that jointly exploits di and csi to glean the benefits from constructive multiuser interference subsequently a relation between the constructive interference downlink transmission and physical layer multicasting is established in this context novel constructive interference precoding techniques that tackle the transmit power minimization min power with individual sinr constraints at each user s receivers is proposed furthermore fairness through maximizing the weighted minimum sinr max min sinr of the users is addressed by finding the link between the min power and max min sinr problems moreover heuristic precoding techniques are proposed to tackle the weighted sum rate problem finally extensive numerical results show that the proposed schemes outperform other state of the art techniques

transmit selection diversity for unitary precoded multiuser spatial multiplexing systems with linear receivers multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference in such a system the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain this paper proposes two precoding methods that use extra transmit antennas beyond the minimum required to provide additional degrees of diversity the approach taken is to solve for a unitary transmit precoder under a zero interuser interference constraint that minimizes an upper bound on the symbol error rate ser for each user solutions where all transmit antennas are employed as well as subsets of antennas to reduce analog components are described numerical results confirm a dramatic improvement in terms of ser and mutual information over single user multiple input multiple output mimo methods and static allocation methods for example the proposed techniques achieve a signal to noise ratio snr improvement of 6 10 db at an uncoded ser of 10 3 with only one extra transmit antenna

precoder design for multiuser miso systems exploiting statistical and outdated csit we propose a multiuser downlink transmission scheme exploiting both statistical and outdated channel state information csi at the transmitter based on the outdated csi aided transmission scheme introduced in denoted as mat the proposed scheme reduces the original k user mat system to a two user virtual mat system through statistical precoding in the first two transmission slots thus the proposed scheme denoted as v mat reduces efficiently the implementation complexity while increasing the achievable rate at finite signal to noise ratios snrs for the v mat scheme we derive an analytical high snr rate approximation for correlated rayleigh fading furthermore for independent and identically distributed rayleigh fading we derive an exact rate expression at high snrs as well as a tight lower bound which applies for arbitrary snrs then precoder design is investigated where an efficient near optimal solution is proposed for arbitrary number of transmit antennas and a closed form optimal solution is derived for the two antenna case it is demonstrated that the proposed v mat scheme yields higher achievable rate than the original mat scheme at practical snrs moreover by combining the v mat scheme and the generalized mat scheme of where precoding is implemented in the third transmission slot the achievable rate can be further increased

analysis in space time bundles i general considerations and the scalar bundle abstract mathematical features involved in the systematic development of elementary particle theory on an alternative cosmos space time are presented bundles representative of physical fields are studied in the unique variant of minkowski space m 0 enjoying similar properties of causality and symmetry the universal cosmos m is the universal cover of the causal compactification of m 0 the bundles studied are induced from representations of the scale extended poincare group which forms the isotropy group in m of the universal cover g s u 2 2 of the connected component of the group of all causal transformations on m discrete symmetries and higher dimensional cases are also discussed the primary focus is on the temporal evolution especially stability involving positivity of the energy wave equations implicative of finite propagation velocity and the unitarity and or composition series of associated actions of g general spin bundles on m are treated parallelized and correlated with bundles on m 0 associated covariant wave equations and the spectral resolution of fundamental quantum numbers are studied in detail in the scalar case

sequential monitoring for comparison of changes in a response variable in clinical studies the spending function approach proposed by lan and demets 1983 biometrika 70 659 663 for sequential monitoring of clinical trials is applied to situations where comparison of changes in a continuous response variable between two groups is the primary concern death loss to follow up and missed visits could cause follow up measurements to be right censored or missing for some participants furthermore the probability of being censored may be dependent on the parameter value of the response variable informative censoring we propose to compare treatment effects by comparing areas under the expected response change curves between the two groups when the response curves are linear as a function of time in both groups this comparison is equivalent to comparing the rates of change in the response variable covariances of the sequential test statistics are derived conditions for having independent increments are presented for studies designed to evaluate long term treatment effects spending functions obtained by shifting the usual spending functions kim and demets 1987 biometrika 74 149 154 to the right and then rescaling to the remaining interval are also proposed such a shifted spending function is applied to the monitoring plan for the lung health study anthonisen 1989 american review of respiratory diseases 140 871 872

weighted sum rate optimization for downlink multiuser mimo coordinated base station systems centralized and distributed algorithms this paper considers the joint linear transceiver design problem for the downlink multiuser multiple input multiple output mimo systems with coordinated base stations bss we consider maximization of the weighted sum rate with per bs antenna power constraint problem we propose novel centralized and computationally efficient distributed iterative algorithms that achieve local optimum to the latter problem these algorithms are described as follows first by introducing additional optimization variables we reformulate the original problem into a new problem second for the given precoder matrices of all users the optimal receivers are computed using minimum mean square error mmse method and the optimal introduced variables are obtained in closed form expressions third by keeping the introduced variables and receivers constant the precoder matrices of all users are optimized by using second order cone programming socp and matrix fractional minimization approaches for the centralized and distributed algorithms respectively finally the second and third steps are repeated until these algorithms converge we have shown that the proposed algorithms are guaranteed to converge we also show that the proposed algorithms require less computational cost than that of the existing linear algorithm all simulation results demonstrate that our distributed algorithm achieves the same performance as that of the centralized algorithm moreover the proposed algorithms outperform the existing linear algorithm in particular when each of the users has single antenna we have observed that the proposed algorithms achieve the global optimum

analysis in space time bundles ii the spinor and form bundles abstract the structures of the spin and form bundles over the universal cosmos m and their relations with corresponding bundles over the minkowski space m 0 canonically imbedded in m are treated wave equations covariant with respect to the causal group g of m are studied their solution manifolds and other stable essentially positive energy invariant subspaces of the section spaces of the bundles are determined and the indecomposability of relevant invariant subspace chains is shown explicit parallelizations of the bundles are applied to the dirac and maxwell equations on m a basis for spinor fields that diagonalizes a complete set of k covariant quantum numbers k maximal essentially compact subgroup of g is developed local multilinear invariants of bundles over m are treated and specialized to convergent mathematical versions of the fermi and yukawa interaction lagrangians that are g invariant for the appropriate conformal weights

gradient based power minimization in mimo broadcast channels with linear precoding we study the problem of minimizing the sum transmit power in mutliple input multiple output mimo downlink channels with linear transceivers if per user quality of service qos constraints expressed in terms of rates have to be fulfilled to find a suboptimal solution of the arising non convex optimization problem we introduce new auxiliary variables representing the di vision of the per user rate constraints into per stream rate targets and we optimize these variables by means of gradient projection steps this new method is combined with alternating updates of the transmit and receive filters furthermore the proposed algorithm ensures that the mean square error mse matrices of all users are diagonal and in the course of the execution of the algorithm it is possible that inactive streams get activated if this leads to a decreased sum transmit power in numerical simulations the new algorithm turns out to be superior to the various existing methods since these methods either lead to a higher sum transmit power than the proposed scheme or have a higher computational complexity or make restrictive assumptions on the system parameters

design and analysis of group sequential logrank tests in maximum duration versus information trials when monitoring a clinical trial with failure time data using the logrank test and the type i error spending function approach the information time has to be estimated as a fraction of the maximum number of failures in maximum duration trials the denominator of this fraction is a random quantity and has to be estimated besides there are two candidates for the denominator one under the null hypothesis of no treatment difference and the other under the specified alternative hypothesis either way some adjustments are necessary in determining group sequential boundaries in order to maintain type i error at a desired significance level as a consequence the type i error spending function will be altered from the one chosen for the design thus affecting the operating characteristics of the subsequent group sequential logrank tests in maximum information trials however the maximum amount of information is fixed and thus the estimate of the information time is always unbiased the net effect is that computation of group sequential boundaries becomes straightforward with a potential saving in study durations as compared to maximum duration trials we will illustrate how adjustments are made in maximum duration trials to maintain type i error when the information times are estimated with the information horizons under the null and alternative hypotheses and present numerical explorations to compare robustness of two different estimates of the information times we then propose a design procedure for maximum information trials and investigate the properties of maximum information trials for different group sequential boundaries we also compare maximum information trials and maximum duration trials based on an example

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

design guidelines for limited feedback in the spatially correlated broadcast channel a linear beamformer design for the broadcast channel where the base station is equipped with n t antennas and signals to m 2 users each with a single antenna and where the vector channels are spatially correlated is considered this problem is of relevance in wireless standardization efforts where two users are simultaneously scheduled instead of the theoretically feasible n t user scheduling to minimize signaling overhead the users are assumed to have perfect channel state information csi whereas the base station has statistical information of the channels in the first part of this work the role of the relevance of feedback is studied via the quantification of the gap in ergodic sum rate between the perfect csi and statistics only extremes in this direction the importance of orthogonality of the dominant eigenmodes of the two users in maximizing the gap is established in the second part of this work in scenarios with a large gap limited feedback beamforming codebooks and a codeword selection metric are designed for the low rate feedback setting the main contribution here is the proposal of a generalized eigenvector codebook and feedback of the codeword index that maximizes an estimate of the signal to interference and noise ratio textsf sinr of each user extensions of this scheme are also proposed for the general n t antenna case with m users where m le n t it is shown via numerical studies that this scheme leads to significant performance improvement across a large family of channels over schemes such as grassmannian random vector quantization single user codebooks with the channel projection metric for codeword selection

multiuser mimo user selection based on chordal distance multiuser mimo mu mimo systems have advantages over single user mimo systems in terms of system performance in mu mimo systems inter user interference needs to be dealt with especially when linear processing is used the block diagonalization bd method is one of techniques that are widely used to eliminate the inter user interference in a cellular system where there are many users the subset of users which maximizes the system performance should be selected since the base station cannot support all the users in the cell in this paper we propose a low complexity mu mimo scheduling scheme using bd with chordal distance for a large number of users the optimal scheduling technique needs an exhaustive search which is impractical one of the key ideas of this paper is to use chordal distance as a measure of orthogonality between different users simulation results show the proposed algorithm has throughput close to the optimal scheduling scheme with lower complexity than existing low complexity scheduling algorithms

an outer bound for the gaussian mimo broadcast channel with common and private messages we consider the gaussian multiple input multiple output mimo broadcast channel with common and private messages we obtain an outer bound for the capacity region of this channel to this end we show that a parallel gaussian broadcast channel can be constructed from any given gaussian mimo broadcast channel by using the generalized singular value decomposition and a relaxation on the power constraint for the channel input due to this relaxation of the power constraint the capacity region of the constructed parallel channel which is known provides an outer bound for the capacity region of the original channel we show that this outer bound is within a finite gap of the capacity region by comparing it with an achievable rate region that can be obtained either by using dirty paper coding or by using a variation of the zero forcing scheme

predistorter for mimo system with nonlinear power amplifiers a multiple input multiple output mimo system with nonlinear power amplifiers pas is considered the nonlinear pas distort the transmitted signal causing performance degradation the common approach for the mitigation of nonlinear distortions is the linearization of each one of the pas in the mimo system separately we propose to apply a more generic approach in the form of a global linearization of the entire nonlinear mimo channel the aim of the global linearization is to reduce the nonlinear distortions seen at the receiver an iterative technique is proposed for the implementation of such a linearization the proposed technique improves the system performance including 1 power efficiency of the pas 2 quality of the received signal measured in terms of symbol error rate and 3 spectral purity of the transmitted signals

downlink mmse transceiver optimization for multiuser mimo systems duality and sum mse minimization we address the problem of minimum mean square error mmse transceiver design for point to multipoint transmission in multiuser multiple input multiple output mimo systems we focus on the problem of minimizing the downlink sum mse under a sum power constraint it is shown that this problem can be solved efficiently by exploiting a duality between the downlink and uplink mse feasible regions we propose two different optimization frameworks for downlink mmse transceiver design the first one solves an equivalent uplink problem then the result is transferred to the original downlink problem duality ensures that any uplink mmse scheme e g linear mmse reception or mmse decision feedback equalization dfe has a downlink counterpart we propose two globally optimum algorithms based on convex optimization the basic idea of the second framework is to perform optimization in an alternating manner by switching between the virtual uplink and downlink channels this strategy exploits that the same mse can be achieved in both links for a given choice of transmit and receive filters this iteration is proven to be convergent

per stream mse based linear transceiver design for mimo interference channels with csi error this paper studies the linear transceiver design for multi stream multiple input multiple output mimo interference channels with imperfect channel state information csi two csi error models are considered the same coding and modulation scheme is assumed for all users and data streams in the first model where the csi error is statistical we minimize the average maximum per stream mean square error mse in the second model where the csi error is norm bounded the worst case maximum per stream mse is optimized since the problems are not jointly convex the alternate optimization approach is adopted to obtain suboptimal transceivers for the statistical csi error a low complexity algorithm utilizing lagrangian duality is proposed which has a semi closed form solution and can be implemented distributively compared with the classical algorithm using the second order cone programming the proposed algorithm significantly reduces the computational complexity without sacrificing the performance for the bounded csi error we present two approaches one uses s procedure to obtain an equivalent problem and the other one solves an approximated problem simulation results demonstrate the robustness of the proposed algorithms and their improved performance over the sum mse and the maximum per user mse based methods the lower complexity of the lagrangian duality based algorithm is also verified numerically

unitarization of symplectics and stability for causal differential equations in hilbert space let sp h be the symplectic group for a complex hibert space h its lie algebra sp h contains an open invariant convex cone c0 each element of c0 commutes with a unique sympletic complex structure the cayley transform c x sp h i x 1 sp h is analyzed and compared with the exponential mapping as an application we consider equations of the form ddt s a t s where t a t c0 is strongly continuous and show that if a t dt 2 and t8 a t dt c0 the scattering operator s s limt t st t where st t is the solution such that st t i is in the range of b restricted to c0 it follows that s leaves invariant a unique complex structure in particular it is conjugate in sp h to a unitary operator

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

eigen based transceivers for the mimo broadcast channel with semi orthogonal user selection this paper studies the sum rate performance of two low complexity eigenmode based transmission techniques for the mimo broadcast channel employing greedy semi orthogonal user selection sus the first approach termed zfdpc sus is based on zero forcing dirty paper coding the second approach termed zfbf sus is based on zero forcing beamforming we first employ new analytical methods to prove that as the number of users k grows large the zfdpc sus approach can achieve the optimal sum rate scaling of the mimo broadcast channel we also prove that the average sum rates of both techniques converge to the average sum capacity of the mimo broadcast channel for large k in addition to the asymptotic analysis we investigate the sum rates achieved by zfdpc sus and zfbf sus for finite k and show that zfdpc sus has significant performance advantages our results also provide key insights into the benefit of multiple receive antennas and the effect of the sus algorithm in particular we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second order behavior of the multi user diversity gain for finite k the benefit can be very significant we also show the interesting result that the semi orthogonality constraint imposed by sus whilst facilitating a very low complexity user selection procedure asymptotically does not reduce the multi user diversity gain in either first k or second order k terms

on mmse vector perturbation precoding for mimo broadcast channels with per antenna group power constraints recently studies on suboptimal precoding techniques for multiple input multiple output broadcast channels mimo bc which achieve performance near to that of the dirty paper coding dpc have drawn attention to vector perturbation vp precoding in practice each antenna or more generally each antenna group has its own limit on the transmitted power which makes per antenna group power constraints more meaningful than the sum power constraint in this paper we introduce an optimization technique for vp precoding employing the minimum mean square error mmse criterion with per antenna group power constraints this technique is inspired by the p sphere encoding in a sense that it involves finding the node with the lowest mean square error mse over a lattice we demonstrate that the mse metric as well as the p norm one can be enclosed in a proper frobenius norm ball this frobenius norm ball shrinks until it captures the perturbing vector minimizing the mse numerical results show that the proposed algorithm outperforms conventional vp precoding and the p sphere encoding but at higher complexity consequently we investigate a couple of simplified techniques employing the mmse criterion which perform almost as well as the proposed precoding technique but are less complex

incremental grassmannian feedback schemes for multi user mimo systems the communication of side information forms a key component of several effective strategies for transmitter adaptation to slowly fading channels when the relevant side information is a subspace the feedback scheme can be viewed as a lossy source compression scheme on the grassmannian manifold memoryless vector quantization on each fading block is a viable compression scheme but it neglects any temporal correlation between the blocks in this paper we propose an incremental approach to grassmannian quantization that takes advantage of temporal correlation the approach leverages existing codebooks for memoryless quantization schemes and employs a quantized form of geodesic interpolation two schemes that implement the principles of the proposed approach are presented in the first scheme the choice of the step size in the incremental update is adapted to a first order gaussmarkov model for the channel which enables the use of higher resolution codebooks in the second scheme a single bit is allocated to the step size which enables adaptation of the step size to the channel realization rather than the channel statistics this provides substantial robustness against mismatches in the model for the temporal correlation a distinguishing feature of the proposed approach is that the direction of the geodesic interpolation is specified implicitly using a point in a conventional codebook as a result the approach has an inherent ability to recover autonomously from errors in the feedback path simulation results demonstrate that these features result in improved performance over some existing schemes in a variety of channel environments

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

a vector perturbation with user selection for multiuser mimo downlink recent works on multiuser mimo study have shown that the linear growth of capacity in single user mimo system can be translated to the multiuser mimo scenario as well in this paper we propose a method pursuing performance gain of vector perturbation in multiuser downlink systems instead of employing the maximum number of mobile users for communication we use small part of them as virtual users for improving reliability of users participating communication by controlling parameters of the virtual users including information and perturbation vector we obtain considerable improvement in the effective snr simulation results on the realistic multiuser miso and mimo downlink systems show that the proposed method brings substantial performance gain over the standard vector perturbation with marginal overhead in computations

iterative precoder design and user scheduling for block diagonalized systems the block diagonalization bd scheme is a low complexity suboptimal precoding technique for multiuser multiple input multiple output mimo downlink channels which completely precancels the multiuser interference accordingly the precoder of each user lies in the null space of other users channel matrices in this paper we propose an iterative algorithm using qr decompositions qrds to compute the precoders specifically to avoid dealing with a large concatenated matrix we apply the qrd to a sequence of matrices of lower dimensions one problem of bd schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints when the number of users is large a set of users must be selected and selection algorithms should be designed to exploit the multiuser diversity gain finding the optimal set of users requires an exhaustive search which has too high computational complexity to be practically useful based on the iterative precoder design this paper proposes a low complexity user selection algorithm using a greedy method in which the precoders of selected users are recursively updated after each selection step the selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices which is related to the eigenvalues by the hadamard and schur inequalities an asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the mimo broadcast channel the numerical results show that the proposed algorithm achieves a good trade off between sum rate performance and computational complexity when users suffer different channel conditions providing fairness among users is of critical importance to address this problem we also propose two fair scheduling fs algorithms one imposing fairness in the approximation of the data rate and another directly imposing fairness in the product of the squared row norms of the effective channel matrices

coordinated beamforming with relaxed zero forcing the sequential orthogonal projection combining method and rate control in this paper coordinated beamforming based on relaxed zero forcing rzf for transmitter receiver pair multiple input single output miso and multiple input multiple output mimo interference channels is considered in the rzf coordinated beamforming conventional zero forcing interference leakage constraints are relaxed so that some predetermined interference leakage to undesired receivers is allowed in order to increase the beam design space for larger rates than those of the zero forcing zf scheme or to make beam design feasible when zf is impossible in the miso case it is shown that the rate maximizing beam vector under the rzf framework for a given set of interference leakage levels can be obtained by sequential orthogonal projection combining sopc based on this exact and approximate closed form solutions are provided in two user and three user cases respectively and an efficient beam design algorithm for rzf coordinated beamforming is provided in general cases furthermore the rate control problem under the rzf framework is considered a centralized approach and a distributed heuristic approach are proposed to control the position of the designed rate tuple in the achievable rate region finally the rzf framework is extended to mimo interference channels by deriving a new lower bound on the rate of each user

holomorphic discrete series for hyperboloids of hermitian type abstract in the present paper we study the holomorphic discrete series h d s for hyperboloids of hermitian type they are the spacesg hwhereg so0 p 2 h so0 p 1 we find some complex hullsy ofg h they correspond to minimalg invariant cones in the lie algebra ofg consider the hardy spacesh2 y and give explicit expressions for the corresponding cauchy szego kernels earlier these expressions were known forp 2 gelfand gindikin andp 1 molchanov we compute the projectionse of thel2 g h onto the images of the hardy spaces the differenceq e e is most interesting it is an analogue of the hilbert transform we study the relations between the h d s forgand the h d s forg h it turns out that forp 2 there is a finite number of representations of the h d s forg hwhich are not representations of the h d s ofg we give explicit expressions for the kernels of the projections on the subspaces of the hardy spaces where the h d s forgacts

analysis in space time bundles iii higher spin bundles the universal cosmos m is the unique four dimensional globally causal space time manifold to which the dirac and maxwell equations among others maximally and covariantly extend a systematic treatment is presented of general fields over m of arbitrary spin considered are fields induced from all irreducible representation of the isotropy group scale extended poincare group to g the connected causal group of m restricted to any species of such fields the k invariant canonical dirac operator k maximal essentially compact subgroup of g is shown g covariant for a unique conformal weight a normalized k finite basis for such fields is constructed the basis actions thereon of the dirac operator infinitesimal generators of g discrete symmetries second order casimir and the essentially unique third order noncentral quantum number enveloping algebra element invariant under k are derived composition series under g of a class of these field spaces namely the extension to m of the relativistic fields considered by bargman and wigner or arbitrary spin and conformal weight are determined distinguishing by invariance and causality features alone the essentially conventional positive energy mass 0 subspaces and massive invariant sub quotient spaces whose unitarity under g is given a new proof the completely positive subclass cf below of representations is determined a more detailed treatment of spin one bundles vector and two form of arbitrary conformal weight is included the exterior derivative transformations are diagonalized and the conformally invariant massive spin one scalar product is identified with a mathematical version of the conventional electromagnetic field lagrangian

frequency selective channel state feedback in multiuser mimo downlink in this paper we derive a novel method for encoding the mimo channel state information csi for frequency selective channels and limited feedback the technique is based on the decomposition of the directional information of a mimo channel in a two coordinate system formed by the tangent space of a grassmann manifold and the tangent space of a unitary group the first component provides a non redundant description of the subspace spanned by a set of channel eigenvectors while the second component provides a non redundant addendum of information to identify the strongest channel vector directions within that subspace one advantage of this feedback representation is that it allows to exploit the correlation of mimo channels by applying standard source coding techniques to the two coordinate components we also provide simulation results of an lte downlink system which show that the proposed csi feedback description offers dramatic throughput improvement over the existing feedback scheme for mu mimo transmission

a comparison of sample size methods for the logrank statistic several methods are available for sample size calculation for clinical trials when survival curves are to be compared using the logrank statistic we discuss advantages and disadvantages of some of these methods and present simulation results under exponential proportional hazards and non proportional hazard situations

flexible codebook design for limited feedback systems via sequential smooth optimization on the grassmannian manifold grassmannian quantization codebooks play a central role in a number of limited feedback schemes for single and multi user multiple input multiple output mimo communication systems in practice it is often desirable that these codebooks possess additional properties that facilitate their implementation beyond the provision of good quantization performance although some good codebooks exist their design tends to be a rather intricate task the goal of this paper is to suggest a flexible approach to the design of grassmannian codebooks based on sequential smooth optimization on the grassmannian manifold and the use of smooth penalty functions to obtain additional desirable properties as one example the proposed approach is used to design rank 2 codebooks that have a nested structure and elements from a phase shift keying psk alphabet in some numerical comparisons codebooks designed using the proposed methods have larger minimum distances than some existing codebooks and provide tangible performance gains when applied to a simple mimo downlink scenario with zero forcing beamforming per user unitary beamforming and rate control pu 2rc and block diagonalization signalling furthermore the proposed approach yields codebooks that attain desirable additional properties without incurring a substantial degradation in performance

transmit designs for the mimo broadcast channel with statistical csi we investigate the multiple input multiple output broadcast channel with statistical channel state information available at the transmitter the so called linear assignment operation is employed and necessary conditions are derived for the optimal transmit design under general fading conditions based on this we introduce an iterative algorithm to maximize the linear assignment weighted sum rate by applying a gradient descent method to reduce complexity we derive an upper bound of the linear assignment achievable rate of each receiver from which a simplified closed form expression for a near optimal linear assignment matrix is derived this reveals an interesting construction analogous to that of dirty paper coding in light of this a low complexity transmission scheme is provided numerical examples illustrate the significant performance of the proposed low complexity scheme

sequential monitoring of survival data with the wilcoxon statistic when a spending function is used in sequential data monitoring of a clinical trial it is important to know the information fraction at the times of interim analysis in a maximum duration designed study the information fraction is unknown when data are monitored and it has to be estimated the modified wilcoxon statistic developed by peto and peto and modified by prentice is often used to compare two survival curves in a clinical trial we give guidelines for estimating the information fraction in a maximum duration trial when this statistic is employed when there is a relatively low event rate or the survival time is approximately exponential the information fraction for the peto peto prentice wilcoxon statistic is very close to that of the popular logrank statistic in other cases it would be helpful to estimate the information fraction as a function of elapsed calendar time we discuss both group sequential and continuous monitoring

a limited feedback joint precoding for amplify and forward relaying this paper deals with the practical precoding design for a dual hop downlink with multiple input multiple output mimo amplify and forward relaying first assuming that full channel state information csi of the two hop channels is available a suboptimal dual hop joint precoding scheme i e precoding at both the base station and relay station is investigated based on its structure a scheme of limited feedback joint precoding using joint codebooks is then proposed which uses a distributed codeword selection to concurrently choose two joint precoders such that the feedback delay is considerably decreased finally the joint codebook design for the limited feedback joint precoding system is analyzed and results reveal that independent codebook designs at the base station and relay station using the conventional grassmannian subspace packing method is able to guarantee that the overall performance of the dual hop joint precoding scheme improves with the size of each of the two codebooks simulation results show that the proposed dual hop joint precoding system using distributed codeword selection scheme exhibits a rate or ber performance close to the one using the optimal centralized codeword selection scheme while having lower computational complexity and shorter feedback delay

compactly embedded cartan algebras and invariant cones in lie algebras on considere une theorie generale des cones invariants et la signification d une classification potentielle de toutes les paires l w d une algebre de lie l et d un cone invariant w on montre le role fondamental joue par les sous algebres de cartan

on sophus lie s fundamental theorem sophus lie s third theorem asserts that for every finite dimensional lie algebra there is a local lie group with the given algebra as tangent algebra at the identity in particular each subalgebra of the lie algebra of a local lie group determines a local subgroup whose lie algebra is the given one recent interest in subsemigroups and local subsemigroups of lie groups motivate the investigation to which extent local semigroups in lie groups are determined by infinitesimal generators it is known that the set l s of tangent vectors at the identity of a local semigroup s with identity in a local lie group g is an additively closed convex subset of the lie algebra l g which is topologically closed and contains 0 its largest vector subspace h is a subalgebra and all automorphisms of l g of the form eadx with x h leave l s invariant as a whole with adx y x y we call an additively and topologically closed convex subset w containing 0 in a lie algebra l a lie wedge if it satisfies eadxw w for all x w t w in this paper we show that lie wedges are precisely the infinitesimal generators of local semigroups in lie groups more precisely we show that in a banach lie algebra l for every lie wedge w whose edge w w has a closed vector space complement in l there is an open ball b around 0 in l such that the cambell hausdorff series x y x y 12 x y converges absolutely for x y b and there is a subset s b with i 0 s ii s s b s and l s w

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

space division multiple access with a sum feedback rate constraint on a multiantenna broadcast channel simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput which grows double logarithmically with the number of users the sum rate for channel state information csi feedback however increases linearly with the number of users reducing the effective uplink capacity to address this problem a novel space division multiple access sdma design is proposed where the sum feedback rate is upper bounded by a constant this design consists of algorithms for csi quantization threshold based csi feedback and joint beamforming and scheduling the key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small csi quantization errors such that the sum feedback rate constraint is satisfied despite this constraint the proposed sdma design is shown to achieve a sum capacity growth rate close to the optimal one moreover the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates numerical results show that the proposed sdma design is capable of attaining higher sum capacities than existing ones even though the sum feedback rate is bounded

exploiting long term channel correlation in limited feedback sdma through channel phase codebook improving channel information quality at the base station bs is crucial for the optimization of frequency division duplexed fdd multi antenna multiuser downlink systems with limited feedback to this end this paper proposes to estimate a particular representation of channel state information csi at the bs through channel norm feedback and a newly developed channel phase codebook where the long term channel correlation is efficiently exploited to improve performance in particular the channel representation is decomposed into a gain related part and a phase related part with each of them estimated separately more specifically the gain related part is estimated from the channel norm and channel correlation matrix while the phase related part is determined using a channel phase codebook constructed with the generalized lloyd algorithm using the estimated channel representation joint optimization of multiuser precoding and opportunistic scheduling is performed to obtain an sdma transmit scheme computer simulation results confirm the advantage of the proposed scheme over state of the art limited feedback sdma schemes under correlated channel environment

precoding for the multiantenna downlink multiuser snr gap and optimal user ordering this paper develops a practical design method for implementing tomlinson harashima precoding thp in a downlink channel with multiple antennas at the transmitter and a single antenna at each receiver a two step design process is proposed for minimizing the total transmit power while satisfying every user s minimum data rate and maximum bit error rate ber requirements first the ber and rate requirements are converted to virtual rate requirements which account for the gap to capacity introduced by practical quadrature amplitude modulation qam and thp the second step is to determine the transmit covariance matrices which specify the entire thp system that will provide these virtual rates at the minimum total transmit power as one of the main features in the proposed scheme an algorithm for finding the optimal user encoding or presubtraction order in polynomial time is proposed in addition we also propose an algorithm that finds a near optimal order but which is much less complex the proposed method outperforms existing zero forcing based thp systems in term of power efficiency

low complexity non iterative coordinated beamforming in 2 user broadcast channels we propose a new non iterative coordinated beamforming scheme to obtain full multiplexing gain in 2 user mimo systems in order to find the beamforming and combining matrices we solve a generalized eigenvector problem and describe how to find generalized eigenvectors according to the gaussian broadcast channels selected simulation results show that the proposed method yields the same sum rate performance as the iterative coordinated beamforming method while maintaining lower complexity by non iterative computation of the beamforming and combining matrices we also show that the proposed method can easily exploit selective gain by choosing the best combination of generalized eigenvectors

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

a sequentially drilled joint congruence sedjoco transformation with applications in blind source separation and multiuser mimo systems we consider a particular form of the classical approximate joint diagonalization ajd problem which we call a sequentially drilled joint congruence sedjoco transformation the problem consists of a set of symmetric real valued or hermitian symmetric complex valued target matrices the number of matrices in the set equals their dimension and the joint diagonality criterion requires that in each transformed diagonalized target matrix all off diagonal elements on one specific row and column corresponding to the matrix index in the set be exactly zeros yet does not care about the other diagonal or off diagonal elements the motivation for this form arises in at least two different contexts maximum likelihood blind or semiblind source separation and coordinated beamforming for multiple input multiple output mimo broadcast channels we prove that sedjoco always has a solution when the target matrices are positive definite we also propose two possible iterative solution algorithms based on defining and optimizing two different criteria functions using newton s method for the first function and successive jacobi like transformations for the second the algorithms convergence behavior and the attainable performance in the two contexts above are demonstrated in simulation experiments

isotropic fading vector broadcast channels the scalar upper bound and loss in degrees of freedom we propose a scalar upper bound on the capacity region of the isotropic fading vector broadcast channel in terms of the capacity region of a scalar fading broadcast channel the scalar upper bound is applicable to the broad class of isotropic fading broadcast channels regardless of the distribution of the users channel magnitudes the distribution of the additive noise experienced by each user or the amount of channel knowledge available at the receiver using this upper bound we prove the optimality of the alamouti scheme in a broadcast setting extend the recent results on the capacity of nondegraded fading scalar broadcast channels to nondegraded fading vector broadcast channels and determine the capacity region of a fading vector gaussian broadcast channel with channel magnitude feedback we also provide an example of a rayleigh fading broadcast channel with no channel state information available to the receiver csir where the bound on the capacity region obtained by a naive application of the scalar upper bound is provably loose because it fails to account for the additional loss in degrees of freedom due to lack of channel knowledge at the receiver a tighter upper bound is obtained by separately accounting for the loss in degrees of freedom due to lack of csir before applying the scalar upper bound

regularized channel diagonalization for multiuser mimo downlink using a modified mmse criterion we propose a regularized channel diagonalization method for a joint transmit receive linear optimization in the downlink of a multiuser multiple input multiple output mimo communication system this method is based on the use of a modified minimum mean square error mmse criterion which employs a weighted information symbol vector for the target and signal scaling the weights for the target are the equivalent channel gain resulting from a zero forcing zf based mimo channel diagonalization a joint iterative algorithm for minimizing the mean square error mse under a total transmit power constraint is derived and its convergence is proved the signal to interference plus noise ratio sinr is analyzed and the sum rates evaluated in a computer simulation the results demonstrate that the proposed method outperforms the existing zf and mmse based methods

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

implementation of group sequential logrank tests in a maximum duration trial summary to control the type i error probability in a group sequential procedure using the logrank test it is important to know the information times fractions at the times of interim analyses conducted for purposes of data monitoring for the logrank test the information time at an interim analysis is the fraction of the total number of events to be accrued in the entire trial in a maximum information trial design the trial is concluded when a prespecified total number of events has been accrued for such a design therefore the information time at each interim analysis is known however many trials are designed to accrue data over a fixed duration of follow up on a specified number of patients this is termed a maximum duration trial design under such a design the total number of events to be accrued is unknown at the time of an interim analysis for a maximum duration trial design therefore these information times need to be estimated a common practice is to assume that a fixed fraction of information will be accrued between any two consecutive interim analyses and then employ a pocock or o brien fleming boundary in this article we describe an estimate of the information time based on the fraction of total patient exposure which tends to be slightly negatively biased i e conservative if survival is exponentially distributed we then present a numerical exploration of the robustness of this estimate when nonexponential survival applies we also show that the lan demets 1983 biometrika 70 659 663 procedure for constructing group sequential boundaries with the desired level of type i error control can be computed using the estimated information fraction even though it may be biased finally we discuss the implications of employing a biased estimate of study information for a group sequential procedure

sinr constrained beamforming for a mimo multi user downlink system algorithms and convergence analysis consider a multiple input multiple output mimo downlink multi user channel a well studied problem in such a system is the design of linear beamformers for power minimization with the quality of service qos constraints the most representative algorithms for solving this class of problems are the so called minimum mean square error mmse second order cone programming socp algorithm visotksy and madhow optimum beamforming using transmit antenna arrays proc ieee veh technol conf may 1999 vol 1 pp 851 856 wong zheng and ng convergence analysis of downlink mimo antenna system using second order cone programming proc 62nd ieee veh technol conf sep 2005 pp 492 496 and the uplink downlink duality udd algorithm codreanu tolli juntti and latva aho joint design of tx rx beamformers in mimo downlink channel ieee trans signal process vol 55 no 9 pp 4639 4655 sep 2007 the former is based on alternating optimization of the transmit and receive beamformers while the latter is based on the well known uplink dowlink duality theory despite their wide applicability the convergence to karush kuhn tucker kkt solutions of both algorithms is still open in the literature in this paper we rigorously establish the convergence of these algorithms for qos constrained power minimization qcpm problem with both single stream and multiple streams per user cases key to our analysis is the development and analysis of a new mmse dual algorithm which connects the mmse socp and the udd algorithm our numerical experiments show that 1 all these algorithms can almost always reach points with the same objective value irrespective of initialization and 2 the mmse socp mmse dual algorithm works well while the udd algorithm may fail with an infeasible initialization

sequential analysis of the proportional hazards model abstract for the proportional hazards model of survival analysis an appropriate large sample theory is developed for cases of staggered entry and sequential analysis the principal techniques involve an approximation of the score process by a suitable martingale and a random rescaling of time based on the observed fisher information as a result we show that the maximum partial likelihood estimator behaves asymptotically like brownian motion author

sample size reestimation for clinical trials with censored survival data a flexible design with updating of sample size in clinical trials is proposed for censored survival data patients enter trials serially and are subject to random loss to follow up the statistical inference is based on a weighted average of the linear rank statistics where the weight function at each look depends on prior observed data a stopping rule is devised to allow early termination and acceptance of the null hypothesis when the experimental treatment offers no advantage or is inferior to the control the null hypothesis that two survival distributions are equal may be rejected only at the last step when the weight function is used up the overall type i error rate is preserved independent increments for the sequential linear rank statistic is key to deriving asymptotic properties of the test statistic some extensive simulations have been carried out to compare the operating characteristics of the method under different scenarios and for a comparison with the usual log rank test with fixed sam

weighted sum rate maximization for mimo broadcast channels using dirty paper coding and zero forcing methods we consider precoder design for maximizing the weighted sum rate wsr of successive zero forcing dirty paper coding szf dpc for this problem the existing precoder designs often assume a sum power constraint spc and rely on the singular value decomposition svd the svd based designs are known to be optimal but require high complexity we first propose a low complexity optimal precoder design for szf dpc under spc using the qr decomposition then we propose an efficient numerical algorithm to find the optimal precoders subject to per antenna power constraints papcs to this end the precoder design for papcs is formulated as an optimization problem with a rank constraint on the covariance matrices a well known approach to solve this problem is to relax the rank constraints and solve the relaxed problem interestingly for szf dpc we are able to prove that the rank relaxation is tight consequently the optimal precoder design for papcs is computed by solving the relaxed problem for which we propose a customized interior point method that exhibits a superlinear convergence rate two suboptimal precoder designs are also presented and compared to the optimal ones we also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme

active antenna selection in multiuser mimo communications the paper develops a dynamic antenna scheduling strategy for downlink mimo communications where a subset of the receive antennas at certain users is selectively disabled the proposed method improves the signal to leakage plus noise slnr ratio performance of the system and it relaxes the condition on the number of transmit receive antennas in comparison to traditional zero forcing and time scheduling strategies the largest value that the slnr can achieve is shown to be equal to the maximum eigenvalue of a certain random matrix combination and the probability distribution of this eigenvalue is characterized in terms of a whittaker function the result shows that increasing the number of antennas at some users can degrade the slnr performance at other users this fact is used to propose an antenna scheduling scheme that leads to improvement in terms of sinr outage probabilities