communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold

quantization methods for equal gain transmission with finite rate feedback we consider the design and analysis of quantizers for equal gain transmission egt systems with finite rate feedback based communication in flat fading multiple input single output miso systems egt is a beamforming technique that maximizes the miso channel capacity when there is an equal power per antenna constraint at the transmitter and requires the feedback of t 1 phase angles when there are t antennas at the transmitter in this paper we contrast two popular approaches for quantizing the phase angles vector quantization vq and scalar quantization sq on the vq side using the capacity loss with respect to egt with perfect channel information at transmitter as performance metric we develop a criterion for designing the beamforming codebook for quantized egt q egt we also propose an iterative algorithm based on the well known generalized lloyd algorithm for computing the beamforming vector codebook on the analytical side we study the performance of q egt and derive closed form expressions for the performance in terms of capacity loss and outage probability in the case of i i d rayleigh flat fading channels on the sq side assuming uniform scalar quantization and i i d rayleigh flat fading channels we derive the high resolution performance of quantized egt and contrast the performance with that of vq we find that although both vq and sq achieve the same rate of convergence to the capacity with perfect feedback as the number of feedback bits b increases there exists a fixed gap between the two

on the design of mimo block fading channels with feedback link capacity constraint in this paper we propose a combined adaptive power control and beamforming framework for optimizing multiple input multiple output mimo link capacity in the presence of feedback link capacity constraint the feedback channel is used to carry channel state information only it is assumed to be noiseless and causal with a feedback capacity constraint in terms of maximum number of feedback bits per fading block we show that the hybrid design could achieve the optimal mimo link capacity and we derive a computationally efficient algorithm to search for the optimal design under a specific average power constraint finally we shall illustrate that a minimum mean square error spatial processor with a successive interference canceller at the receiver could be used to realize the optimal capacity we found that feedback effectively enhances the forward channel capacity for all signal to noise ratio snr values when the number of transmit antennas n sub t is larger than the number of receive antennas n sub r the snr gain with feedback is contributed by focusing transmission power on active eigenchannel and temporal power waterfilling the former factor contributed at most 10log sub 10 n sub t n sub r db snr gain when n sub t n sub r while the latter factor s snr gain is significant only for low snr values

optimum sequence multisets for synchronous code division multiple access channels it is shown that the sum capacity of the symbol synchronous code division multiple access channel with equal average input energy constraints is maximized precisely by those spreading sequence multisets that meet welch s lower bound on total squared correlation it is further shown that the symmetric capacity of the channel determined by these same sequence multisets is equal to the sum capacity

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

bit allocation law for multiantenna channel feedback quantization single user case this paper studies the design and optimization of a limited feedback single user system with multiple antenna transmitter and single antenna receiver the design problem is cast in form of the minimizing the average transmission power at the base station subject to the user s outage probability constraint the optimization is over the user s channel quantization codebook and the transmission power control function at the base station our approach is based on fixing the outage scenarios in advance and transforming the design problem into a robust system design problem we start by showing that uniformly quantizing the channel magnitude in db scale is asymptotically optimal regardless of the magnitude distribution function we derive the optimal uniform in db channel magnitude codebook and combine it with a spatially uniform channel direction codebook to arrive at a product channel quantization codebook we then optimize such a product structure in the asymptotic regime of b where b is the total number of quantization feedback bits the paper shows that for channels in the real space the asymptotically optimal number of direction quantization bits should be m 1 2 times the number of magnitude quantization bits where m is the number of base station antennas we also show that the performance of the designed system approaches the performance of the perfect channel state information system as 2 2b m 1 for complex channels the number of magnitude and direction quantization bits are related by a factor of m 1 and the system performance scales as 2 b m as b

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

multimode precoding for mimo systems performance bounds and limited feedback codebook design this correspondence investigates the problem of designing the precoding codebook for limited feedback multiple input multiple output mimo systems we first analyze the asymptotic capacity loss of a suboptimal multimode precoding scheme as compared to optimal waterfilling and show that the suboptimal scheme is sufficient when negligible capacity loss is allowed this knowledge is then applied to the design of the limited feedback codebook in the design the generalized lloyd algorithm is employed where the computation of the centroid is formulated as an optimization problem and solved optimally numerical results show that the proposed codebook design outperforms the comparable algorithms reported in the literature

linear dispersion codes for mimo systems based on frame theory multiple input multiple output mimo wireless communication systems provide high capacity due to the plurality of modes available in the channel existing signaling techniques for mimo systems have focused primarily on multiplexing for high data rate or diversity for high link reliability in this paper we present a new linear dispersion code design for mimo rayleigh fading channels the proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability this is important because as we show designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view various techniques are presented for finding codes with good error probability performance monte carlo simulations illustrate performance of some example code designs in terms of ergodic capacity codeword error probability and bit error probability

weakly singular weak form integral equations for cracks in three dimensional anisotropic media singularity reduced integral relations are developed for displacement discontinuities in three dimensional anisotropic linearly elastic media an isolated displacement discontinuity is considered first and a systematic procedure is followed to develop relations for the displacement and stress fields induced by the discontinuity the singularity reduced relation for the stress is particularly important since it is in a form which allows a weakly singular weak form traction integral equation to be readily established the integral relations obtained for a general displacement discontinuity are then specialized to an isolated crack and to dislocations the relations for dislocations are introduced to emphasize their direct connection to corresponding results for cracks and to allow earlier independent findings for these two types of discontinuities to be put into proper context next the singularity reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain and a pair of weakly singular weak form displacement and traction integral equations is established these integral equations can be combined to obtain a final formulation which is in a symmetric form and in this way they serve as the basis for a weakly singular symmetric galerkin boundary element method suitable for analysis of cracks in anisotropic media

fuzzy p measure on the real line abstract the fuzzy measurable space on the real line say is defined by means of fuzzy relation less or equal 5 the main properties of are given these results are used for investigation of fuzzy p measure on the principal emphasis is laid on the connections between a fuzzy p measure and its cumulative distribution function a theorem extending a fuzzy p measure to is shown

on the optimality of beamforming with quantized feedback the ergodic capacity of a fading vector channel with multiple transmit antennas and a single receive antenna is explored perfect channel information is assumed to be available at the receiver while the transmitter has only partial knowledge of the direction of the user s channel vector based on quantized feedback we present necessary and sufficient conditions for the optimality of beamforming in such systems the conditions are applicable to all quantized feedback scenarios regardless of the channel distribution number of transmit antennas number of quantization vectors or transmit power the optimality conditions are closely related to the iteration conditions of the lloyd algorithm revealing an interesting link between the optimality of beamforming and the optimality of the vector quantizers using the conditions we prove the capacity optimality of beamforming for several quantized feedback scenarios such as the antenna selection scheme we also point out examples of quantized feedback scenarios where beamforming is not optimal we find that for the independent identically distributed rayleigh fading channel with more than a single bit of quantized feedback there is no capacity benefit from increasing the number of antennas beyond the number of quantization vectors extensions of the necessary and sufficient optimality condition to the multiple input multiple output case are also provided

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

a gmdh based fuzzy modeling approach for constructing ts model in this paper a new learning algorithm based on group method of data handling gmdh is proposed for the identification of takagi sugeno fuzzy model different from existing methods the new approach called ts gmdh starts from simple elementary ts fuzzy models and then uses the mechanism of gmdh to produce candidate fuzzy models of growing complexity until the ts model of optimal complexity has been created the main characteristic of the new approach is its ability to identify the structure of ts model automatically experiments on box jenkins gas furnace data and uci datasets have shown that the proposed method can achieve satisfactory results and is more robust to noise in comparison with other ts modeling techniques such as anfis

an upper bound on the ser of transmit beamforming in correlated rayleigh fading we study the symbol error rate ser of maximum ratio transmission transmit antenna selection and codebook based beamforming in correlated rayleigh fading channels assuming maximum ratio combining is performed at the receiver we derive a universal upper bound on the average ser of the three schemes and prove that the bound is asymptotically tight in high signal to noise ratio snr regions however numerical results show that at medium snr the tightness of the bound depends on the condition number of the channel correlation matrix

analysis of multiple antenna systems with finite rate channel information feedback over spatially correlated fading channels this paper employs a high resolution quantization framework to study the effects of finite rate quantization of the channel state information csi on the performance of miso systems over correlated fading channels the contributions of this paper are twofold first as an application of the general distortion analysis tight lower bounds on the capacity loss of correlated miso systems due to the finite rate channel quantization are provided closed form expressions for the capacity loss in high signal to noise ratio snr and low snr regimes are also provided and their analysis reveals that the capacity loss of correlated miso channels is related to that of i i d fading channels by a simple multiplicative factor which is given by the ratio of the geometric mean to the arithmetic mean of the eigenvalues of the channel covariance matrix second this paper extends the general asymptotic distortion analysis to the important practical problem of suboptimal quantizers resulting from mismatches in the distortion functions source statistics and quantization criteria as a specific application two types of mismatched miso csi quantizers are investigated quantizers whose codebooks are designed with minimum mean square error mmse criterion but the distortion measure is the ergodic capacity loss i e mismatched design criterion and quantizers with codebook designed with a mismatched channel covariance matrix i e mismatched statistics bounds on the channel capacity loss of the mismatched codebooks are provided and compared to that of the optimal quantizers finally numerical and simulation results are presented and they confirm the tightness of theoretical distortion bounds

analysis of multiple antenna systems with finite rate feedback using high resolution quantization theory this paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple antenna systems with finite rate feedback inspired by the results of classical high resolution quantization theory the problem of finite rate quantized communication system is formulated as a general fixed rate vector quantization problem with side information available at the encoder or the quantizer but unavailable at the decoder the framework of the quantization problem is sufficiently general to include quantization schemes with general non mean squared distortion functions and constrained source vectors asymptotic distortion analysis of the proposed general quantization problem is provided by extending the vector version of the bennett s integral specifically tight lower and upper bounds of the average asymptotic distortion are proposed sufficient conditions for the achievability of the distortion bounds are also provided and related to corresponding classical fixed rate quantization problems the proposed general methodology provides a powerful analytical tool to study a wide range of finite rate feedback systems to illustrate the utility of the framework we consider the analysis of a finite rate feedback multiple input single output miso beamforming system over independent and identically distributed i i d rayleigh flat fading channels numerical and simulation results are presented that further confirm the accuracy of the analytical results

achieving the welch bound with difference sets consider a codebook containing n unit norm complex vectors in a k dimensional space in a number of applications the codebook that minimizes the maximal cross correlation amplitude i sub max is often desirable relying on tools from combinatorial number theory we construct analytically optimal codebooks meeting in certain cases the welch lower bound when analytical constructions are not available we develop an efficient numerical search method based on a generalized lloyd algorithm which leads to considerable improvement on the achieved i sub max over existing alternatives we also derive a composite lower bound on the minimum achievable i sub max that is effective for any codebook size n

mimo transmit beamforming under uniform elemental power constraint we consider multi input multi output mimo transmit beamforming under the uniform elemental power constraint this is a nonconvex optimization problem and it is usually difficult to find the optimal transmit beamformer first we show that for the multi input single output miso case the optimal solution has a closed form expression then we propose a cyclic algorithm for the mimo case which uses the closed form miso optimal solution iteratively the cyclic algorithm has a low computational complexity and is locally convergent under mild conditions moreover we consider finite rate feedback methods needed for transmit beamforming we propose a simple scalar quantization method as well as a novel vector quantization method for the latter method the codebook is constructed under the uniform elemental power constraint and the method is referred as vq uep we analyze vq uep performance for the miso case specifically we obtain an approximate expression for the average degradation of the receive signal to noise ratio snr caused by vq uep numerical examples are provided to demonstrate the effectiveness of our proposed transmit beamformer designs and the finite rate feedback techniques

multiple beamforming with perfect coding perfect space time block codes pstbcs achieve full diversity full rate nonvanishing constant minimum determinant uniform average transmitted energy per antenna and good shaping however the high decoding complexity is a critical issue for practice when the channel state information csi is available at both the transmitter and the receiver singular value decomposition svd is commonly applied for a multiple input multiple output mimo system to enhance the throughput or the performance in this paper two novel techniques perfect coded multiple beamforming pcmb and bit interleaved coded multiple beamforming with perfect coding bicmb pc are proposed employing both pstbcs and svd with and without channel coding respectively with csi at the transmitter csit the decoding complexity of pcmb is substantially reduced compared to a mimo system employing pstbc providing a new prospect of csit especially because of the special property of the generation matrices pcmb provides much lower decoding complexity than the state of the art svd based uncoded technique in dimensions 2 and 4 similarly the decoding complexity of bicmb pc is much lower than the state of the art svd based coded technique in these two dimensions and the complexity gain is greater than the uncoded case moreover these aforementioned complexity reductions are achieved with only negligible or modest loss in performance

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

optimal transmitter eigen beamforming and space time block coding based on channel mean feedback optimal transmitter designs obeying the water filling principle are well documented they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems we design in this paper an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams the optimality pertains to minimizing an upper bound on the symbol error rate which leads to better performance than maximizing the expected signal to noise ratio snr at the receiver coupled with orthogonal space time block codes two directional eigen beamforming emerges as a more attractive choice than conventional one directional beamforming with uniformly improved performance without rate reduction and without essential increase in complexity with multiple receive antennas and reasonably good feedback quality the two directional eigen beamformer is also capable of achieving the best possible performance in a large range of transmit power to noise ratios without a rate penalty

noncoherent trellis coded quantization a practical limited feedback technique for massive mimo systems accurate channel state information csi is essential for attaining beamforming gains in single user su multiple input multiple output mimo and multiplexing gains in multi user mu mimo wireless communication systems state of the art limited feedback schemes which rely on pre defined codebooks for channel quantization are only appropriate for a small number of transmit antennas and low feedback overhead in order to scale informed transmitter schemes to emerging massive mimo systems with a large number of transmit antennas at the base station one common approach is to employ time division duplexing tdd and to exploit the implicit feedback obtained from channel reciprocity however most existing cellular deployments are based on frequency division duplexing fdd hence it is of great interest to explore backwards compatible massive mimo upgrades of such systems for a fixed feedback rate per antenna the number of codewords for quantizing the channel grows exponentially with the number of antennas hence generating feedback based on look up from a standard vector quantized codebook does not scale in this paper we propose noncoherent trellis coded quantization ntcq whose encoding complexity scales linearly with the number of antennas the approach exploits the duality between source encoding in a grassmannian manifold for finding a vector in the codebook which maximizes beamforming gain and noncoherent sequence detection for maximum likelihood decoding subject to uncertainty in the channel gain furthermore since noncoherent detection can be realized near optimally using a bank of coherent detectors we obtain a low complexity implementation of ntcq encoding using an off the shelf viterbi algorithm applied to standard trellis coded quantization we also develop advanced ntcq schemes which utilize various channel properties such as temporal spatial correlations monte carlo simulation results show the proposed ntcq and its extensions can achieve near optimal performance with moderate complexity and feedback overhead

the optimality of transmit beamforming a unified view the optimality of transmit beamforming for a multiple antenna system with partial limited feedback is investigated and a single general necessary and sufficient condition for beamforming to achieve ergodic capacity is derived the condition obtained is universal applicable to all partial limited feedback scenarios in all ergodic fading channel distributions regardless of the number of transmit receive antennas or transmit power using the universal condition we explore the optimality of beamforming for the quantized mean feedback scheme which unifies previous results for the separate cases of mean feedback and quantized feedback numerical results are provided to complement the analysis

ensemble properties of rvq based limited feedback beamforming codebooks the ensemble properties of random vector quantization rvq codebooks for limited feedback beamforming in multiinput multioutput mimo systems are studied with the metrics of interest being the received ssr snr loss and mutual information loss both relative to a perfect channel state information csi benchmark the simplest case of unskewed codebooks is first studied in the correlated mimo setting and these loss metrics are computed as a function of the number of bits of feedback b transmit antenna dimension nt and spatial correlation in particular it is established that 1 the loss metrics are a product of two components a quantization component and a channel dependent component 2 the quantization component which is also common to analysis of channels with i i d fading decays as b increases at the rate 2 b nt 1 3 the channel dependent component reflects the condition number of the channel further the precise connection between the received ssr snr loss and the squared singular values of the channel is shown to be a schur convex majorization relationship finally the ensemble properties of skewed codebooks that are generated by skewing rvq codebooks with an appropriately designed fixed skewing matrix are studied based on an estimate of the loss expression for skewed codebooks it is established that the structure of a good skewing matrix is critically dependent on the condition numbers of the effective channel product of the true channel and the skewing matrix and the skewing matrix

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

solution of multivariable fuzzy equations abstract a method for the solution of multivariable fuzzy equations and inequalities is proposed the proposed method is an extension of sanchez technique for a single fuzzy equation a numerical example is given

limited feedback for temporally correlated mimo channels with other cell interference limited feedback improves link reliability with a small amount of feedback from the receiver to the transmitter in cellular systems the performance of limited feedback will be degraded in the presence of other cell interference when the base stations have limited or no coordination this paper establishes the degradation in sum rate of users in a cellular system due to uncoordinated other cell interference and feedback delay a goodput metric is defined as the rate when the bits are successfully received at the mobile station and used to derive an upper bound on the performance of limited feedback systems with delay this paper shows that the goodput gained from having delayed limited feedback decreases doubly exponentially as the delay increases the analysis is extended to precoded spatial multiplexing systems where it is shown that the same upper bound can be used to evaluate the decay in the achievable sum rate to reduce the effects of interference zero forcing interference nulling is applied at the receiver where it is shown that the effect of the interference on the achievable sum rate can be suppressed by nulling out the interferer numerical results show that the decay rate of the goodput decreases when the codebook quantization size increases and when the doppler shift in the channel decreases

kerdock codes for limited feedback precoded mimo systems codebook based limited feedback is a practical way to obtain partial channel state information at the transmitter in a precoded multiple input multiple output wireless system in this correspondence we propose a systematic codebook design the proposed kerdock codebook consists of multiple mutually unbiased unitary basis matrices with quaternary alphabet and the identity matrix we propose to derive the beamforming and precoding codebooks from this base codebook eliminating the requirement to store multiple codebooks furthermore we show that quaternary alphabet facilitates efficient codebook storage and codeword search we derive the chordal distance for two and four antenna codebooks showing that the proposed codebooks compare favorably with prior designs monte carlo simulations compare achievable rates and error rates for different codebooks sizes

symmetric weak form integral equation method for three dimensional fracture analysis a symmetric galerkin boundary element method is developed for the analysis of linearly elastic isotropic three dimensional solids containing fractures the formulation is based upon a weak form displacement integral equation and a weak form traction integral equation recently developed by li and mear 1997 these integral equations are only weakly singular and their validity requires only that the boundary displacement data be continuous hence allowing standard co elements to be employed as part of the numerical implementation a special crack tip element is developed which has a novel feature in that there exist degrees of freedom associated with the nodes at the crack front as a result a higher degree of approximation is achieved for the relevant displacement data on the crack and further the stress intensity factors are obtained directly in terms of the crack front nodal data various examples are treated for cracks in unbounded domains and for cracks in finite domains including both embedded and surface breaking cracks and it is demonstrated that highly accurate results can be achieved using relatively coarse meshes

multicarrier beamforming with limited feedback a rate distortion approach this paper studies the optimal use of limited rate feedback of channel state information csi in the case of a wideband multicarrier channel with multiple transmit antennas and a single receive antenna with full knowledge of the csi the receiver should compute the optimal beamforming vectors jointly quantize them and feed them back to the transmitter the achievable forward data rate depends on the rate of the feedback link the optimal tradeoff between the forward and feedback rates is characterized using rate distortion theory in the limit of infinite number of subcarriers with fixed amount of feedback per subcarrier the distortion metric is the difference between the forward rate achieved with limited feedback and the capacity with perfect csi at the transmitter the rate distortion function gives the forward rate as a function of the feedback rate numerical results show that to achieve a target forward rate the required feedback rate can be substantially reduced by joint quantization of the beamformers across subcarriers a simple quantizer amenable to practical implementation is shown to approach the rate distortion bound with near linear computational complexity

indirect finite element evaluation of two dimensional finite part integral using fourier transformation a broad class of engineering problems in fracture mechanics thermal fluid transport and electromagnetic theory involve the evaluation of two dimensional finite part integrals of the form a method for evaluation of such integrals is developed by deriving an equivalent integral using fourier transformation this equivalent integral does not involve a kernel with singular behaviour consequently standard numerical integration methodologies with conventional analytical evaluation techniques can be used in the finite element computations the accuracy and convergence of the developed numerical procedure are successfully demonstrated by numerical examples for planar fracture geometries

a galerkin symmetric and direct bie method for kirchhoff elastic plates formulation and implementation a variational boundary element formulation is proposed for the solution of the elastic kirchhoff plate bending problem the stationarity conditions of an augmented potential energy functional are first discussed after addressing the topic of the choice of the test functions a regularization process based on integrations by parts is developed which allows to express the formulation in terms of double integrals the inner being at most weakly singular and the outer regular standard integration procedures may then be applied for their numerical evaluation in the presence of both straight and curved boundaries the normal slope and the vertical displacement must be c0 and c1 continuous respectively numerical examples show through comparisons with analytical solutions that a high accuracy is achieved

capacity analysis of mimo systems using limited feedback transmit precoding schemes this paper employs a high resolution quantization framework to study the effects of finite rate feedback of the channel state information csi on the performance of multiple input multiple output mimo systems over independently and identically distributed i i d rayleigh flat fading channels the contributions of this paper are twofold first we extend the general distortion analysis of vector quantizers to deal with complex source variables necessary and sufficient conditions that guarantee a concise high resolution distortion analysis in the complex domain is presented second as an application of the proposed complex distortion analysis tight lower bounds on the capacity loss due to the finite rate channel quantization are provided for mimo systems employing a fixed number of equal power spatial beams based on the obtained closed form analytical results it is shown that the system capacity loss decreases exponentially as the ratio of the quantization rate to the total degrees of freedom of the channel state information to be quantized moreover mimo csi quantizers using mismatched codebooks that are only optimized for high signal to noise ratio snr and low snr regimes are also investigated to quantify the penalties incurred by the use of mismatched codebooks in addition the analysis is extended to deal with mimo systems using multi mode spatial multiplexing transmission schemes with finite rate csi feedback finally numerical and simulation results are presented which confirm the tightness of the derived theoretical distortion bounds

sgbem fem coupling for analysis of cracks in 3d anisotropic media a weakly singular symmetric galerkin boundary element method sgbem is coupled with the standard finite element method fem in order to establish an accurate and efficient numerical technique for analysis of fractures in three dimensional anisotropic linearly elastic media in the strategy the weakly singular sgbem developed by rungamornrat and mear textitint j solids struct 2008 45 1283 1301 comput methods appl mech engrg 2008 197 4319 4332 is utilized to model a small scale region containing the crack while the possibly large and complex compliment region is treated by the fem the coupled technique exploits the positive features of both methods the sgbem proves to be a convenient and highly accurate method for obtaining mixed mode stress intensity factors along the crack front whereas the fem is very efficient for modeling large scale problems in the absence of cracks an important aspect of the formulation and implementation of the technique is that continuity of displacement and traction across the interface between the sgbem and fem regions is enforced in a weak sense this allows the two regions one modeled by the sgbem and the other by the fem to be discretized independently without the need for the resulting meshes to conform on the interface separating the regions and this flexibility in the discretization process leads to a significant reduction in the modeling effort to demonstrate the utility and accuracy of the technique several boundary value problems involving both embedded and surface breaking cracks are treated and it is shown that the coupled technique yields highly accurate stress intensity factors that exhibit only a slight dependence upon mesh refinement copyright 2010 john wiley sons ltd

a galerkin symmetric boundary element method in elasticity formulation and implementation a symmetric boundary element method based on a weighted residual galerkin approach for elastoplastic analysis is revisited and its computer implementation for two dimensional homogeneous problems is described

subtractive clustering based modeling of job sequencing with parametric search in this paper an extended subtractive clustering based fuzzy system identification method and the sugeno type reasoning mechanism are used for modeling job sequencing problems this approach can be used to build a fuzzy model of the sequencing system from an existing sequence output data and possible job attributes input data the single machine weighted flowtime problem is used as an example to demonstrate the proposed methodology the effects of data scarcity on the modeling performance is studied by using three data sets with varying degrees of available data furthermore a parametric search on various clustering parameters is performed to identify the best model as a result of parametric search ranges of clustering parameters that provide best models are also identified

design and analysis of transmit beamforming based on limited rate feedback this paper deals with design and performance analysis of transmit beamformers for multiple input multiple output mimo systems based on bandwidth limited information that is fed back from the receiver to the transmitter by casting the design of transmit beamforming based on limited rate feedback as an equivalent sphere vector quantization svq problem multiantenna beamformed transmissions through independent and identically distributed i i d rayleigh fading channels are first considered the rate distortion function of the vector source is upper bounded and the operational rate distortion performance achieved by the generalized lloyd s algorithm is lower bounded although different in nature the two bounds yield asymptotically equivalent performance analysis results the average signal to noise ratio snr performance is also quantified finally beamformer codebook designs are studied for correlated rayleigh fading channels and a low complexity codebook design that achieves near optimal performance is derived

capacity of a multiple antenna fading channel with a quantized precoding matrix given a multiple input multiple output mimo channel feedback from the receiver can be used to specify a transmit precoding matrix which selectively activates the strongest channel modes here we analyze the performance of random vector quantization rvq in which the precoding matrix is selected from a random codebook containing independent isotropically distributed entries we assume that channel elements are independent and identically distributed i i d and known to the receiver which relays the optimal rate maximizing precoder codebook index to the transmitter using b bits we first derive the large system capacity of beamforming rank one precoding matrix as a function of b where large system refers to the limit as b and the number of transmit and receive antennas all go to infinity with fixed ratios rvq for beamforming is asymptotically optimal i e no other quantization scheme can achieve a larger asymptotic rate we subsequently consider a precoding matrix with arbitrary rank and approximate the asymptotic rvq performance with optimal and linear receivers matched filter and minimum mean squared error mmse numerical examples show that these approximations accurately predict the performance of finite size systems of interest given a target spectral efficiency numerical examples show that the amount of feedback required by the linear mmse receiver is only slightly more than that required by the optimal receiver whereas the matched filter can require significantly more feedback

bit interleaved coded multiple beamforming with imperfect csit this paper addresses the performance of bit interleaved coded multiple beamforming bicmb 1 2 with imperfect knowledge of beamforming vectors most studies for limited rate channel state information at the transmitter csit assume that the precoding matrix has an invariance property under an arbitrary unitary transform in bicmb this property does not hold on the other hand the optimum precoder and detector for bicmb are invariant under a diagonal unitary transform in order to design a limited rate csit system for bicmb we propose a new distortion measure optimum under this invariance based on this new distortion measure we introduce a new set of centroids and employ the generalized lloyd algorithm for codebook design we provide simulation results demonstrating the performance improvement achieved with the proposed distortion measure and the codebook design for various receivers with linear detectors we show that although these receivers have the same performance for perfect csit their performance varies under imperfect csit

novel transmit beamforming schemes for time selective fading multiantenna systems transmit beamforming has been widely adopted for wireless systems with multiple transmit antennas for a block fading channel the grassmannian beamformer has been shown to provide very good performance for finite rate feedback however the original grassmannian beamformer does not take the time domain correlation of the channel fading into consideration in this paper based on a first order autoregressive ar1 dynamic fading model we develop two new classes of beamforming algorithms that exploit the interframe correlations in the channel fading we first introduce an algorithm based on a standard predictive vector quantization pvq approach and the resulting pvq beamformer accomplishes superior power delivery at the receiver however the error performance of the pvq beamformer is not satisfactory at high signal to noise ratios and it also has a high implementation complexity to resolve these issues we then develop a novel successive beamforming sbf algorithm the new sbf scheme uses the knowledge of the previous fading blocks to aid the beamforming codebook design of the current fading block the beamforming codebook is constructed based on the successive partition of the surface of a spherical cap the new sbf scheme accomplishes nearly the same performance as that of the pvq beamformer and it has a much simpler implementation through numerical simulations we demonstrate that the proposed beamformers outperform the other previously proposed beamformers at various fading scenarios

finite element solution of a boundary integral equation for mode i embedded three dimensional fractures the singular integral equation governing the opening of a mode i embedded three dimensional fracture in an infinite solid was solved by applying the finite element method the strategy is to formulate the equation into weak form and to transfer the differentiation from the singular term 1 r in the equation to the test function a numerical algorithm was thus developed the numerical solutions for circular and elliptical fractures under the action of polynomial pressure distributions were compared with the analytical solutions by green and sneddon 12 irwin 13 shah and kobayashi14 and nishioka and atluri 16 the results have demonstrated that the numerical method reported is accurate and efficient

grassmannian beamforming for multiple input multiple output wireless systems transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple input multiple output mimo wireless systems unfortunately optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector both are hard to realize in this article a quantized maximum signal to noise ratio snr beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter by using the distribution of the optimal beamforming vector in independent and identically distributed rayleigh fading matrix channels the codebook design problem is solved and related to the problem of grassmannian line packing the proposed design criterion is flexible enough to allow for side constraints on the codebook vectors bounds on the codebook size are derived to guarantee full diversity order results on the density of grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or snr loss monte carlo simulations are presented that compare the probability of error for different quantization strategies

a weakly singular sgbem for analysis of cracks in 3d anisotropic media abstract a weakly singular symmetric galerkin boundary element method sgbem is developed for analysis of fractures in three dimensional anisotropic linearly elastic media the method constitutes a generalization of that by li et al s li m e mear l xiao symmetric weak form integral equation method for three dimensional fracture analysis comput methods appl mech engrg 151 1998 435 459 for isotropic media and is based upon a pair of weak form displacement and traction integral equations recently established by rungamornrat and mear j rungamornrat m e mear weakly singular weak form integral equations for cracks in three dimensional anisotropic media int j solids struct 45 2008 1283 1301 the formulation involves only weakly singular kernels and as a consequence standard c 0 elements can be employed in the numerical discretization the kernels possess a relatively simple form for general anisotropy which involves an equatorial line integral like that associated with the displacement fundamental solution despite their simple form it is still necessary to evaluate these kernels efficiently in the numerical implementation to do so certain symmetry properties associated with the specific material type under consideration are exploited and a simple yet accurate interpolation strategy is introduced another important aspect of the numerical treatment is the use of a special crack tip element which allows highly accurate mixed mode stress intensity factor data to be extracted as a function of position along the crack front this crack tip element was originally introduced by li et al s li m e mear l xiao symmetric weak form integral equation method for three dimensional fracture analysis comput methods appl mech engrg 151 1998 435 459 in their treatment of isotropic media and here it is extended to allow evaluation of the stress intensity factors for generally anisotropic media the element involves extra degrees of freedom associated with the nodes along the crack front with these quantities being directly related to the stress intensity factors and it is capable of representing the asymptotic behavior in the vicinity of the crack front to a sufficiently high order that relatively large crack tip elements can be utilized various examples are treated for cracks in an unbounded domain and for both embedded and surface breaking cracks in a finite domain and it is demonstrated that very accurate results can be obtained even with relatively coarse meshes

performance analysis of quantized beamforming mimo systems multiple input multiple output mimo wireless systems can achieve significant diversity and array gain by using single stream transmit beamforming and receive combining a mimo beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single user scenario the performance of this system in uncorrelated rayleigh flat fading channels is studied from the point of view of signal to noise ratio snr and outage probability in this paper lower bounds are derived on the expected snr loss and the outage probability of systems that have a single receive antenna or two transmit antennas for arbitrary transmit and receive antennas approximations for the snr loss and outage are derived in particular the snr loss in a quantized mimo beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas the analytical expressions are proved to be tight with asymptotically large feedback rate simulations show that the bounds and approximations are tight even at low feedback rates thereby providing a benchmark for feedback system design

power allocation for secondary outage minimization in spectrum sharing networks with limited feedback we address an optimal transmit power allocation problem that minimizes the outage probability of a secondary user su who is allowed to coexist with a primary user pu in a narrowband spectrum sharing cognitive radio network under a long term average transmit power constraint at the secondary transmitter su tx and an average interference power constraint at the primary receiver pu rx with quantized channel state information csi including both the channels from su tx to su rx denoted as g1 and the channel from su tx to pu rx denoted as g0 at the su tx the optimal quantization regions in the vector channel space is shown to have a stepwise structure with this structure the above outage minimization problem can be explicitly formulated and solved by employing the karush kuhn tucker kkt necessary optimality conditions to obtain a locally optimal quantized power codebook a low complexity near optimal quantized power allocation algorithm is derived for the case of large number of feedback bits more interestingly we show that as the number of partition regions approaches infinity the length of interval between any two adjacent quantization thresholds on the g0 axis is asymptotically equal when the average interference power constraint is active similarly we show that when the average interference power constraint is inactive the ratio between any two adjacent quantization thresholds on the g1 axis becomes asymptotically identical using these results an explicit expression for the asymptotic su outage probability at high rate quantization as the number of feedback bits goes to infinity is also provided and is shown to approximate the optimal outage behavior extremely well for large number of bits of feedback via numerical simulations analysis on the extension to multiple secondary users case cognitive multiple access network is also discussed numerical results illustrate that with only a few bits of feedback the derived algorithms provide secondary outage performance very close to that with full csi at the su tx

quantized principal component selection precoding for spatial multiplexing with limited feedback in this paper for spatial multiplexing with limited feedback a quantized principal component selection qpcs precoding scheme is proposed that achieves comparable capacity to the closed loop multiple input multiple output mimo and furthermore adapts to various fading channel conditions without any additional feedback bits and transmit channel state information csi we propose a systematic design method for a codebook consisting of a finite number of unitary matrices based on a maximizing minimum distance criterion in the one dimensional angular domain and show that the method outperforms the grassmannian subspace packing method in various fading channel conditions the proposed qpcs precoding scheme allows for adjustment of the precoding matrix based on limited feedback information on the principal vectors approximating a mimo channel in the angular domain according to various channel conditions furthermore for practical implementation of the qpcs precoding scheme we propose a structured precoder optimization procedure and show that the proposed procedure induces a negligible capacity loss compared with the exhaustive precoder optimization even with considerably reduced complexity

development of a systematic methodology of fuzzy logic modeling this paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling it has a unified parameterized reasoning formulation an improved fuzzy clustering algorithm and an efficient strategy of selecting significant system inputs and their membership functions the reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation as a result we are no longer restricted to standard extremes in any step of reasoning the fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input output data the fuzzy rules are generated through fuzzy c means fcm clustering major bottlenecks are addressed and analytical solutions are suggested we also address the classification process to extend the derived fuzzy partition to the entire output space in order to select suitable input variables among a finite number of candidates unlike traditional approaches we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required furthermore a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions in order to evaluate the proposed methodology two examples a nonlinear function and a gas furnace dynamic procedure are investigated in detail the significant improvement of the model is concluded compared to other fuzzy modeling approaches

beamforming codebooks for two transmit antenna systems based on optimum grassmannian packings precoding codebook design for limited feedback mimo systems is known to reduce to a discretization problem on a grassmann manifold the case of two antenna beamforming is special in that it is equivalent to quantizing the real sphere the isometry between the grassmannian g2 1 and the real sphere s2 shows that discretization problems in the grassmannian g2 1 are directly solved by corresponding spherical codes notably the grassmannian line packing problem in 2 namely maximizing the minimum distance is equivalent to the tammes problem on the real sphere so that optimum spherical packings give optimum grassmannian packings moreover a simple isomorphism between g2 1 and s2 enables to analytically derive simple codebooks in closed form having low implementation complexity using the simple geometry of some of these codebooks we derive closed form expressions of the probability density function of the relative snr loss due to limited feedback we also investigate codebooks based on other spherical arrangements such as solutions maximizing the harmonic mean of the mutual distances among the codewords which is known as the thomson problem we find that in some special cases grassmannian codebooks based on these other spherical arrangements outperform codebooks from grassmannian packing

quantized multimode precoding in spatially correlated multiantenna channels multimode precoding where the number of independent data streams is adapted optimally can be used to maximize the achievable throughput in multiantenna communication systems motivated by standardization efforts embraced by the industry the focus of this work is on systematic precoder design with realistic assumptions on the spatial correlation channel state information csi at the transmitter and the receiver and implementation complexity for the spatial correlation of the channel matrix we assume a general channel model based on physical principles that has been verified by many recent measurement campaigns we also assume a coherent linear minimum mean square error mmse receiver and knowledge of the spatial statistics at the transmitter along with the presence of an ideal low rate feedback link from the receiver to the transmitter the reverse link is used for codebook index feedback and the goal of this work is to construct precoder codebooks adaptable in response to the statistical information such that the achievable throughput is significantly enhanced over that of a fixed nonadaptive independent and identically distributed i i d codebook design we illustrate how a codebook of semiunitary precoder matrices localized around some fixed center on the grassmann manifold can be skewed in response to the spatial correlation via low complexity maps that can rotate and scale submanifolds on the grassmann manifold the skewed codebook in combination with a low complexity statistical power allocation scheme is then shown to bridge the gap in performance between a perfect csi benchmark and an i i d codebook design

limited feedback design for interference alignment on mimo interference networks with heterogeneous path loss and spatial correlations interference alignment is degree of freedom optimal on k user mimo interference channels and many previous works have studied the transceiver designs however these works predominantly focus on networks with perfect channel state information at the transmitters and symmetrical interference topology in this paper we consider a limited feedback system with heterogeneous path loss and spatial correlations and investigate how the dynamics of the interference topology can be exploited to improve the feedback efficiency we propose a novel spatial codebook design and perform dynamic quantization via bit allocations to adapt to the asymmetry of the interference topology we bound the system throughput under the proposed dynamic scheme in terms of the transmit snr feedback bits and the interference topology parameters it is shown that when the number of feedback bits scales with snr as c s cdot log hbox snr cal o 1 the sum degrees of freedom of the network are preserved moreover the value of scaling coefficient c s can be significantly reduced in networks with asymmetric interference topology

on beamforming with finite rate feedback in multiple antenna systems we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations assuming that the transmitter uses the quantized information for beamforming we derive a universal lower bound on the outage probability for any finite set of beamformers the universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel using the bound it is shown that finite information systems approach the perfect information case as t 1 2 sup b t 1 where b is the number of feedback bits and t is the number of transmit antennas the geometrical bounding technique used in the proof of the lower bound also leads to a design criterion for good beamformers whose outage performance approaches the lower bound the design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook and is equivalent to the problem of designing unitary space time codes under certain conditions finally we show that good beamformers are good packings of two dimensional subspaces in a 2t dimensional real grassmannian manifold with chordal distance as the metric

comparison of clustering algorithms in the identification of takagi sugeno models a hydrological case study in this paper different clustering algorithms are used to identify takagi sugeno models in a data driven manner all but one of these clustering algorithms are based on the minimization of an objective function the other one is the subtractive clustering algorithm to guide the objective function based clustering algorithms an algorithm called clusterfinder is developed in order to determine the optimal number of clusters as a compromise between model complexity and model accuracy the hydrological case study considered concerns the modelling of unsaturated groundwater flow the takagi sugeno models are identified on the basis of an artificially generated training data set for a specific soil type and can be incorporated into a fuzzy rule based groundwater model