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

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

killing spinors and massless spinor fields it is shown that in a space time that admits a killing spinor any solution of the weyl or of the maxwell equations can be used as a potential for another solution of the corresponding equation furthermore it is shown that the new solution can be generated by a single component of the given one which satisfies a decoupled equation for the kerr metric the connection between the procedure presented here and several results previously known is established

wavelet based stochastic seismic response of a duffing oscillator this paper presents formulation for the non stationary response of a duffing oscillator under a seismic excitation process the excitation process is assumed to be characterized through wavelet coefficients and the non linear system is replaced by a stochastic equivalent linear system with time varying parameters an example ground motion process has been used to show that the proposed approach gives accurate response estimates in case of mildly non linear 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

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

symmetry operators for spin 1 2 relativistic wave equations on curved space time the second order linear covariant differential symmetry operators of the source free spin relativistic wave equation are given in a canonical form we find that the operators are constructed from conformal killing spinors examples displaying the correspondence between such operators and others previously known are given

analysis of wavelets in chaotic states for a one degree of freedom system with viscoelastic restraints a qualitative numerical technique is presented for identifying chaotic states of a non linear one sided constrained one degree of freedom 1 d o f deterministic system under a dynamic non conservative load discrete wavelet analysis in its classic and packet versions was used to search for the boundaries of chaotic and non chaotic solutions the results obtained were verified by an analysis of the lyapunov exponents of the investigated system on the basis of numerical tests one can state that wavelet analysis may be a fast and reliable tool suitable for searching for the boundaries of chaotic and non chaotic solutions

symmetry operators for maxwell s equations on curved space time we derive necessary and sufficient conditions that a second order co variant differential operator be a symmetry operator of maxwell s equations in a general curved space time background it is found that such operators are naturally formulated in terms of conformal killing vectors tensors and spinors operators of this type play a role in the solution of maxwell s equations via separation of variables in the kerr background space time

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

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

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

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

wavelet based analysis of the non stationary response of a slipping foundation a wavelet based stochastic formulation has been presented in this paper for the seismic analysis of a rigid block resting on a friction base the ground motion has been modelled as a non stationary process both in amplitude and frequency by using wavelets the proposed formulation is based on replacing the non linear system by an equivalent linear system with time dependent properties the expressions of the instantaneous damping root mean square r m s velocity response and the power spectral density function psdf of the velocity response have been obtained in terms of the input wavelet coefficients for validation of the formulation simulation based on twenty synthetically generated time histories corresponding to an example ground motion process has been carried out the effectiveness of the base isolation system and the effect of the frequency non stationarity on the non linear response have also been studied in detail it has been clearly shown how the frequency non stationarity in the ground motion changes the non linear response

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

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

non factorizable separable systems and higher order symmetries of the dirac operator it is shown that there exist separable systems for the dirac operator on four dimensional lorentzian spin manifolds that are not factorizable in the sense of miller the symmetry operators associated to these new separable systems are of higher order than the dirac operator they are characterized in the second order case in terms of quadratic first integrals of the geodesic flow satisfying additional invariant conditions

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

probabilistic analysis of wind induced vibration mitigation of structures by fluid viscous dampers abstract the high rise buildings usually suffer from excessively large wind induced vibrations and thus vibration control systems might be necessary fluid viscous dampers fvds with nonlinear power law against velocity are widely employed with the transition of design method from traditional frequency domain approaches to more refined direct time domain approaches the difficulty of time integration of these systems occurs sometimes in the present paper firstly the underlying reason of the difficulty is revealed by identifying that the equations of motion of high rise buildings installed with fvds are sometimes stiff differential equations thus an approach effective for stiff differential systems i e the backward difference formula bdf is then introduced and verified to be effective for the equation of motion of wind induced vibration controlled systems comparative studies are performed among some methods including the newmark method kr alpha method energy based linearization method and the statistical linearization method based on the above results a 20 story steel frame structure is taken as a practical example particularly the randomness of structural parameters and of wind loading input is emphasized the extreme values of the responses are examined showing the effectiveness of the proposed approach and also necessitating the refined probabilistic analysis in the design of wind induced vibration mitigation systems

higher symmetries of the laplacian we identify the symmetry algebra of the laplacian on euclidean space as an explicit quotient of the universal enveloping algebra of the lie algebra of conformal motions we construct analogues of these symmetries on a general conformal manifold

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