sum power iterative water filling for multi antenna gaussian broadcast channels in this correspondence we consider the problem of maximizing sum rate of a multiple antenna gaussian broadcast channel bc it was recently found that dirty paper coding is capacity achieving for this channel in order to achieve capacity the optimal transmission policy i e the optimal transmit covariance structure given the channel conditions and power constraint must be found however obtaining the optimal transmission policy when employing dirty paper coding is a computationally complex nonconvex problem we use duality to transform this problem into a well structured convex multiple access channel mac problem we exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the mac which can easily be mapped to the optimal bc policies

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

linear precoding via conic optimization for fixed mimo receivers in this paper the problem of designing linear precoders for fixed multiple input multiple output mimo receivers is considered two different design criteria are considered in the first the transmitted power is minimized subject to signal to interference plus noise ratio sinr constraints in the second the worst case sinr is maximized subject to a power constraint it is shown that both problems can be solved using standard conic optimization packages in addition conditions are developed for the optimal precoder for both of these problems and two simple fixed point iterations are proposed to find the solutions that satisfy these conditions the relation to the well known uplink downlink duality in the context of joint transmit beamforming and power control is also explored the proposed precoder design is general and as a special case it solves the transmit rank one beamforming problem simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders

a simple adaptive pi controller for linear systems with constant disturbances it is known that an adaptive controller via high gain output feedback can globally stabilize a class of minimum phase systems with relative degree one however exact output regulation is difficult for systems with disturbances in this paper we consider linear single input single output siso systems with unknown constant disturbances we present a simple adaptive output feedback controller with an integral action and show that it can asymptotically stabilize those disturbed systems the proposed pi type adaptive controller can also deal with the output tracking problem of a step reference

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

generalized linear precoder and decoder design for mimo channels using the weighted mmse criterion we address the problem of designing jointly optimum linear precoder and decoder for a mimo channel possibly with delay spread using a weighted minimum mean squared error mmse criterion subject to a transmit power constraint we show that the optimum linear precoder and decoder diagonalize the mimo channel into eigen subchannels for any set of error weights furthermore we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights we show how to obtain 1 the maximum information rate design 2 qos based design we show how to achieve any set of relative snrs across the subchannels and 3 the unweighted mmse and equal error design for fixed rate systems

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

adaptive stabilization with exponential decay abstract adaptive high gain stabilizers for classes of linear time invariant state space systems are presented the classes cover multi input multi output systems where the state dimension is not known only standard assumptions such as minimum phase and known respectively unknown sign are required the main result is that the adaptive control laws of byrnes and willems can be modified to produce a gurantee of exponentially decaying states

minimizing sum mse implies identical downlink and dual uplink power allocations in the multiuser downlink power allocation for linear precoders that minimize the sum of mean squared errors under a sum power constraint is a non convex problem many existing algorithms solve an equivalent convex problem in the virtual uplink and apply a transformation based on uplink downlink duality to find a downlink solution in this letter we analyze the optimality criteria for the power allocation subproblem in the virtual uplink and demonstrate that the optimal solution leads to identical power allocations in the downlink and virtual uplink we thus extend the known duality results and importantly simplify the existing algorithms used for iterative transceiver design

transmission strategies for the mimo mac with mmse receiver average mse optimization and achievable individual mse region in this work we study the multiuser multiple input multiple output mimo multiple access channel mac under the assumption that the base station performs linear multiuser minimum mean square error mmse detection we derive the average normalized mse and the individual mses of users at first we optimize the average normalized mse with respect to the transmit covariance matrices of the users next adaptive power allocation is applied to further minimize the average normalized mse this leads to the general average normalized mse optimization under a sum power constraint we analyze the optimization problems and their connections by their karush kuhn tucker conditions the covariance matrix optimization is solved by iteratively single user average mse optimization in which the interference is treated as noise we develop an iterative algorithm that performs power allocation and covariance matrix optimization in addition to this we study the achievable mse region we show that the mse region is convex for the two user mimo case furthermore we characterize the optimum power allocation among the users with regard to the single user range we show that the user with the maximum singular value of its channel matrix is the first supported user for low snr values the optimal strategy is to have the best user transmitting only in addition we derive the individual mse using single user mmse detectors and study the fulfillment of mse requirements

stability and robustness properties of universal adaptive controllers for first order linear systems quite recently examples of non linear adaptive controllers have been found that adaptively stabilize any scalar first order linear system in this paper we describe two general classes of such universal adaptive stabilizers that include the previously proposed controllers as special cases different types of perturbations of these controllers are studied and we report on extensive simulation experiments our results demonstrate considerable qualitative differences in the dynamical behaviour of various adaptive universal stabilizers while the previously proposed controllers all exhibit the bursting phenomena we give an explicit example of a stabilizing controller that does not show bursting behaviour

a transfer principle from wiener to poisson space and applications the aim of this work is to construct the stochastic calculus of variations on poisson space and some of its applications via the stochastic analysis on wiener space we define a new gradient operator on wiener space whose adjoint extends the poisson stochastic integral this yields a new decomposition of the ornstein uhlenbeck operator and a substructure of the standard dirichlet structure on wiener space with applications to stochastic analysis on poisson space and infinite dimensional analysis for the exponential density

on exact solutions of differential equations arising in universal adaptive stabilization in this paper we analyse non linear willems byrnes adaptive stabilization of first order linear systems x t ax t bu t x 0 r the willems byrnes control law is u h k x k x2 k 0 r and for each x 0 x0 k 0 k0 r x t 0 k t k x0 as t there are three cases according to whether h is smooth piecewise smooth or piecewise constant for each x0 r k x0 defines a limit pole a bh k x0 r we find that in all cases x0 r a bh k x0 0 is open and dense in the piecewise smooth constant case we solve explicitly the closed loop dynamical equation for x t and k t we find that a bh k x0 0 corresponds to solutions which decay only algebraically

on the mse duality of the broadcast channel and the multiple access channel we present a mean square error mse duality between the broadcast channel and the multiple access channel for multiantenna users communicating with a single base station we introduce three levels of the duality which allow for a problem specific customization with different computational complexities and resolutions the first level preserves the sum mse during the conversion from the uplink to the downlink and vice versa whereas the second level not only keeps the sum mse constant but also ensures the preservation of the individual users mses the third level involves the finest resolution and preserves the individual streams mses and the individual streams signal to interference and noise ratio sinr simultaneously in contrast with hitherto existing mse dualities the proposed sort of duality features a lower complexity since no mse computation detouring is necessary during the conversion to the dual domain and is capable of handling all combinations of active and passive transmitters and receivers moreover we show how two of these three dualities can be exploited to solve the unweighted total sum mse minimization problem and the weighted sum mse minimization in the broadcast channel in an efficient way by revealing the hidden convexity in the first case and drastically reducing the computational complexity in the latter case

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

robust control design for nonlinear uncertain systems with an unknown time varying control direction a continuous robust control design approach is proposed for first order nonlinear systems whose dynamics contain both nonlinear uncertainty and an unknown time varying control direction the so called control direction is the multiplier of the control term in the dynamic equation and it effectively represents the direction of motion under any given control a nonlinear robust control is designed to online and continuously identify sign changes of the unknown control direction and to guarantee stability of uniform ultimate boundedness the proposed robust control design requires only three conditions the nominal system is stable the control direction is smooth and the uncertainty in the system is bounded by a known function the necessity of these conditions is established in this paper continuity of the proposed robust control is achieved by using a so called shifting law that changes smoothly the sign of robust control and tracks the change of the unknown control direction analysis and design is shown by using lyapunov s direct method

high gain robust adaptive controllers for multivariable systems abstract this paper extends the switching free high gain stabilizing adaptive control rules of byrnes and willems to a wide class of adaptive schemes capable of tolerating nonlinear state feedback perturbations

robust tracking control of uncertain nonlinear systems with unknown control directions a global robust tracking control design procedure is proposed for a class of uncertain nonlinear systems the key point is that the signs of multiplicative uncertainties the so called control directions are not assumed to be known a priori the class of systems can be of arbitrary dynamic order and the unmatched additive uncertainties need not satisfy the global lipschitz condition it is proved that under the proposed control all closed loop states are bounded and the tracking error converges to any prescribed small neighborhood of the origin the results of this paper enlarge the class of uncertain nonlinear systems for which global robust tracking control can be designed

improving the robustness of nussbaum type regulators by the use of σ modification local results abstract the bursting phenomenon in a nussbaum type regulator is discussed its cause is associated with some properties of the equilibrium manifold a modification factor is introduced and the resulting equilibrium set is completely characterized using linearization techniques local robustness against bounded disturbances is proved by malkin s theorem and verified by simulation

remarks on the adaptive control of linear plants with unknown high frequency gain abstract adaptive control of first order linear systems of the form x ax bu with the sign of b unknown is considered it is shown that stabilizing adaptive controllers exist that have globally bounded gain and prespecified terminal dynamics