a family of space time block codes achieving full diversity with linear receivers in this paper we propose a design scheme for a family of space time block codes stbcs that achieve full diversity when linear receivers such as zero forcing zf or minimum mean square error mmse receivers are used new stbcs obtained based on this design scheme are characterized by their special structure that combines overlays orthogonal stbcs ostbcs and toeplitz codes together which are called group orthogonal toeplitz codes gotcs by choosing different parameters codes with different symbol rates and orthogonality can be obtained it is indicated that the existing stbcs achieving full diversity with linear receivers such as the toeplitz codes and overlapped alamouti codes oacs recently proposed in the literature and the ostbcs are three members of the gotcs with different parameters it is also shown that the time reversal space time block codes tr stbcs and delay diversity codes ddcs for frequency selective channels are equivalent to oacs and toeplitz codes respectively and thus they both can achieve full space frequency diversity with only linear receivers furthermore simulations show that with linear receivers gotcs outperforming the above mentioned three codes can be obtained from the proposed design scheme

numerical studies of the damped korteweg de vries system we present a numerical analysis of the korteweg de vries kdv system in a bounded interval under the effect of a localized damping mechanism for the sake of completeness we include the proofs of existence and uniqueness of the weak solution by means of the faedo galerkin method error estimates of finite element approximations for both semi discrete and fully discrete schemes in the energy norm are provided and numerical experiments are performed

on a class of fuzzy functional differential equations in this paper we establish the local and global existence and uniqueness results for fuzzy functional differential equations for the local existence and uniqueness we use the method of successive approximations and for global existence and uniqueness we use the contraction principle also we apply these results to fuzzy differential equations with distributed delays and fuzzy population models

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

approximating the solution of nonlinear hammerstein fuzzy integral equations abstract in this paper we prove the convergence of the method of successive approximations used to approximate the solution of nonlinear hammerstein fuzzy integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration this numerical stability is proved and finally some numerical experiments confirm the theoretical results and illustrate the accuracy of the method

on space time code design with a conditional pic group decoding space time code designs based on a partial interference cancellation pic group decoding have been recently proposed the pic group decoding complexity depends on the group size and is between the lowest linear receiver complexity and the highest ml decoding complexity the symbol rate for a space time code achieving full diversity with the pic group decoding is also between those for the linear receivers and the ml decoding in this paper we propose a new decoding called conditional pic group decoding that is between the pic group decoding and the ml decoding with the proposed new decoding we obtain a new design criterion for space time codes to achieve full diversity which is also between the one with the pic group decoding and the one with the ml decoding we then present some designs that satisfy the new criterion and in the meantime have higher symbol rates than that for the pic group decoding

linear decoupled and quasi decoupled space time codes space time transmit diversity results in coupling of transmitted symbols across different antennas which increases the complexity of maximum likelihood decoding symbol coupling can be completely or partially avoided if the space time code stc satisfies specific decoupling conditions examples of such codes are orthogonal space time block codes and quasi orthogonal codes in this letter we study decoupling conditions for a linear full diversity stc quasi decoupled codes are proposed as a partially decoupled full diversity stc of any rate for any number of transmit antennas with minimum decoding delay by optimizing the coding gain of quasi decoupled codes it is shown that quasi orthogonal codes have competitive performance with respect to the alamouti code and the more recent threaded algebraic space time tast codes and abba codes a general full diversity decoupling condition is considered and the general solution to this case which also encompasses previously known orthogonal stcs is derived

blind channel identifiability for generic linear space time block codes linear space time block codes stbcs have proven their effectiveness in performance improvement of wireless multiple input multiple output communication systems their successful decoding however requires reliable channel knowledge at the receiver in this paper we present a semiblind channel estimation method for linear stbc without the usual code orthogonality condition we provide a set of identification conditions that are mostly verifiable a priori in terms of code parameters and antenna array configuration we also present a simple channel estimation algorithm finally we provide simulation results that illustrate the performance of the proposed scheme

space time state trellis codes for mimo systems using reconfigurable antennas we present a novel class of space time trellis codes based on super quasi orthogonal space time codes for a reconfigurable antenna system we call them space time state trellis codes ststcs we design for 4 trellis states and both 2 and 4 branch trellis structures for bpsk and qpsk constellations the proposed codes take advantage of the additional degrees of diversity offered by reconfigurable antennas and changing propagation states they achieve full rate full diversity and high coding gain simulation results demonstrate their good performance ststcs achieve the diversity order expected of four transmit antennas while using only two reconfigurable transmit antennas our code out performs the existing super orthogonal space time trellis code which fails to achieve full diversity in a reconfigurable antenna system the proposed 4 trellis state ststc is designed based on the following performance criteria minimum coding gain distance of the minimum return path cgd mrp performance factor pf rank of the partial valid path rpvp on top of traditional minimum coding gain distance of parallel path cgd pp we show through analysis and simulations that minimum cgd pp is not a sufficient criteria and that additional performance gains are provided by considering the cgd mrp

hybrid arq in multiple antenna slow fading channels performance limits and optimal linear dispersion code design this paper focuses on studying the fundamental performance limits and linear dispersion code design for the mimo arq slow fading channel the optimal average rate of well known harq protocols is analyzed the optimal design of space time coding for the mimo arq channel is discussed information theoretic measures are used to optimize the rate assignment and derive the optimum design criterion which is then used to evaluate the optimality of existing space time codes a different design criterion which is obtained from the error probability analysis of space time coded mimo harq is presented examples are studied to reveal the gain of arq feedback in space time coded mimo systems

a new ml based interference cancellation technique for layered space time codes this paper presents a new and simple decoding algorithm for layered space time block codes such as the two independent alamouti s codes which are also called the double space time transmit diversity dsttd system by using group interference suppression and successive interference cancellation we can treat dsttd as two independent space time block codes stbc we can then decode both of these stbc s through a simple maximum likelihood ml detector with null space based interference cancellation we also compare the proposed interference cancellation ic scheme with the conventional mmse ic scheme the performance of the proposed ic scheme is comparable to that of the mmse ic scheme while the complexity reduction factor of the proposed scheme can be up to 5 compared to the mmse ic scheme

one sided fuzzy numbers and applications to integral equations from epidemiology in this paper we present the algebraic and topological structure of one sided fuzzy numbers and introduce the notion of side preserving fuzzy number valued function we define the dual decomposition of a commutative monoid and prove that the sets of left sided fuzzy numbers and right sided fuzzy numbers realize a dual decomposition of the additive monoid of all fuzzy numbers we prove the usefulness of right sided fuzzy numbers in epidemiology presenting an application of these fuzzy numbers to a mathematical model for the spread of infectious diseases with a rate of contact that varies seasonally

error estimation in the approximation of the solution of nonlinear fuzzy fredholm integral equations using a fixed point technique the sequence of successive approximations and a recent quadrature formula for fuzzy number valued functions it is constructed a numerical method for the solution of nonlinear fuzzy fredholm integral equations moreover the error estimate of the method and a criterion to stop the corresponding algorithm are given

new error estimate in the iterative numerical method for nonlinear fuzzy hammerstein fredholm integral equations in this paper we obtain the error estimation of the iterative method based on quadrature formula to solve nonlinear fuzzy fredholm integral equations of the second kind given in fuzzy sets syst 245 2014 1 17 in terms of uniform and partial modulus of continuity moreover we extend in the context of using the modulus of continuity the notion of numerical stability of the solution with respect to the first iteration

quadratic extension field codes for free space optical intensity communications in this paper we propose a space time code construction with a symbol rate of two for free space optical multiple input multiple output fso mimo communication systems unlike the radio frequency space time coding design that deals with complex symbols holding phase and magnitude information the phase detection in wireless optical communications remains very challenging this restricts optical mimo codes to carry positive magnitude information belonging to a finite range to meet these requirements we propose to design the fso mimo codes considering first the whole real space mathbb r followed by a bipolar to unipolar conversion to fit in the intensity margin we consider the mimo configurations with two or four transmitters lasers we base our shape preserving construction on quadratic extension fields that linearly combine the real symbols to form a full diversity space time code with a symbol rate equal to two for each configuration we show how to optimize the choice of the algebraic field numbers to jointly optimize the non vanishing code determinant and the bipolar to unipolar attenuation factor

galerkin runge kutta discretizations for parabolic equations with time dependent coefficients a new class of fully discrete galerkin runge kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients unlike any classical counterpart this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction in support of this claim error estimates are proved and computational results are presented additionally since the time stepping equations involve coefficient matrices changing at each time step a preconditioned iterative technique is used to solve the linear systems only approximately nevertheless the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients furthermore it is noted that special runge kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method

a new generic maximum likelihood metric expression for space time block codes with applications to decoding the metric expression for a generic linear space time block code stbc is studied using a different approach to vectorization and a new representation of the metric the new representation lends itself to a simple measure of reliability based on the sum of inner products and provides a quantifiable definition for minimum distance of a stbc this provides the framework for a new family of near maximum likelihood ml and ml decoding algorithms it also has applications in the development of optimality test criteria for stbcs as well as in the design of stbcs with low decoding complexity

towards the accuracy of iterative numerical methods for fuzzy hammerstein fredholm integral equations abstract an iterative numerical method based on the three point quadrature formula is applied to solve nonlinear fuzzy hammerstein fredholm integral equations of the second kind and provides more accurate results than the trapezoidal quadrature iterative method also we obtain the error estimation of the iterative method in terms of the uniform and partial modulus of continuity moreover we investigate the concept of numerical stability of the iterative method with respect to the choice of the initial approximation illustrative examples are included to demonstrate the accuracy and efficiency of the iterative method

quasi orthogonal time reversal space time block coding for frequency selective fading channels quasi orthogonal space time block codes qo stbcs are a powerful code family designed for more than two transmit antennas in contrast to their orthogonal counterparts designed for the same number of transmit antennas qo stbcs are able to provide full rate transmission rate while original qo stbcs enjoy only a partial diversity the recently proposed rotated versions of qo stbcs achieve the maximum diversity order which is equal to the number of transmit antennas since qo stbcs have been originally proposed for frequency flat fading channels it is a challenging design problem to apply them over frequency selective channels the dispersive nature of such channels results in intersymbol interference which needs to be carefully handled at the receiver in this paper we investigate time domain equalization for qo stbc exploiting the embedded quasi orthogonal structure to design low complexity receivers we also present diversity gains for the proposed scheme through pairwise error probability pep derivation and analysis which are further confirmed by monte carlo simulations

low complexity maximum likelihood decoder for four transmit antenna quasi orthogonal space time block code this letter proposes a very low complexity maximum likelihood ml detection algorithm based on qr decomposition for the quasi orthogonal space time block code qstbc with four transmit antennas called the lc ml decoder the proposed algorithm enables the qstbc to achieve ml performance with significant reduction in computational load for any high level modulation scheme

distributed differential space time coding for wireless relay networks distributed space time coding is a cooperative transmission scheme for wireless relay networks with this scheme antennas of the distributive relays work as transmit antennas of the sender and generate a space time code at the receiver it achieves the maximum diversity although the scheme needs no channel information at relays it does require full channel information both the channels from the transmitter to relays and the channels from relays to the receiver at the receiver in this paper we propose a differential transmission scheme which requires channel information at neither relays nor the receiver for wireless relay networks as distributed space time coding can be seen as the counterpart of space time coding in the network setting this scheme is the counterpart of differential space time coding compared to coherent distributed space time coding the differential scheme is 3db worse in addition we show that alamouti square real orthogonal and sp 2 codes can be used differentially in networks with corresponding numbers of relays we also propose distributed differential space time codes that work for networks with any number of relays using circulant matrices

blind stbc identification for multiple antenna ofdm systems this paper addresses the problem of space time block code stbc identification for multiple antenna ma orthogonal frequency division multiplexing ofdm systems operating over frequency selective channels for the first time in literature previous investigations published on the topic of stbc identification were restricted to single carrier systems operating over frequency flat channels ofdm systems make this topic more challenging to handle since the identifiers work in frequency selective channels with little or no knowledge of the beginning of the ofdm blocks ofdm parameters and frequency selective channel coefficients we show that by taking advantage of the space time redundancy stbc identification can be performed by exploiting the cross correlation of the signals received from different antennas as a discriminating feature using this feature we develop a binary hypothesis test for decision making the proposed method does not require information about the channel coefficients modulation format noise power or timing of the ofdm and stbc blocks moreover it does not need accurate knowledge of either clock timing information or ofdm parameters including the number of sub carriers and cyclic prefix length extensive simulation experiments have verified the effectiveness of the proposed method

the icosian code and the e_8 lattice a new 4 times 4 space time code with nonvanishing determinant this paper introduces a new rate 2 full diversity space time code for four transmit antennas and one receive antenna the 4times4 codeword matrix consists of four 2times2 alamouti blocks with entries from q i radic5 and these blocks can be viewed as quaternions which in turn represent rotations in r 3 the alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron this algebraic structure is different from the golden code but the complex entries are taken from a common underlying field the minimum determinant is bounded below by a constant that is independent of the signal constellation and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the e 8 lattice

block wise qr decomposition for the layered and hybrid alamouti stbc mimo systems algorithms and hardware architectures unlike the channel matrix in the spatial division multiplexing sdm multiple input multiple output mimo communication system the equivalent channel matrix in the layered alamouti space time block coding stbc mimo system comprised 2 by 2 alamouti sub blocks one novel property found by sayed about the qr decomposition qrd of this equivalent channel matrix is that the produced q and r matrices are also matrices with alamouti sub blocks taking advantage of this property we propose a new block wise complex givens rotation bcgr based algorithm and a triangular systolic array tsa to compute the qrd of the equivalent channel matrix in an alamouti block by block manner implementation results reveal that our new tsa can compute qrds of 4 by 4 equivalent channel matrices faster than any architecture that has been developed for the sdm mimo system this property of fast qrd makes our tsa very attractive for the layered alamouti stbc mimo system combined with the orthogonal frequency division multiplexing our new bcgr based approach can also be applied to the hybrid alamouti stbc mimo system which is also a system with equivalent channel matrix consisting of alamouti sub blocks

numerical solution of two dimensional nonlinear hammerstein fuzzy integral equations based on optimal fuzzy quadrature formula in this paper our aim is to provide an efficient iterative method of successive approximations to approximate solution of linear and nonlinear two dimensional hammerstein fuzzy integral equations by defining and developing an optimal quadrature formula for classes of two dimensional fuzzy number valued functions of lipschitz type after the introduction of the optimal formula we prove the convergence of the method of successive approximations used to approximate the solution of two dimensional hammerstein fuzzy integral equations and investigate the numerical stability of the presented method with respect to the choice of the first iteration finally some illustrative numerical experiments confirm the theoretical results and demonstrate the accuracy of the method

multiuser detection of alamouti signals in a mimo multiple access channel where users employ space time block codes stbc interference cancellation can be used to suppress co channel interference and recover the desired signal of each user at the receiver leveraging the special properties of alamouti matrices we first show that spatial multiplexing of alamouti signals retains the space time diversity gain of alamouti signaling using our proposed low complexity alamouti blast mmse a blast algorithm next in contrast to traditional transmit diversity that focuses on stbc construction at the transmitter this paper looks at transmit diversity from the perspective of the receiver in other words the receiver gets to choose the stbciquests which are favourable to the channel assuming a fixed blast receive algorithm in a multiusermac setting we first present a systematic methodology to exploit different decomposition structure in alamouti matrices each with different tradeoff between performance and decoding complexity using possibly different mimo receive algorithms we then demonstrate that the notion of angles the inner product of two quaternionic vectors between multiuser channels determines the performance of mimo receive algorithms as an application of the general theory we transform the decoding problem for several types of quasi orthogonal stbc qostbc into multiuser detection of virtual alamouti users building upon our a blast algorithm we propose new algorithms for decoding single user and multiuser qostbc in particular we show that bit error probability is a function of the quaternionic angle between virtual users for a single user or multiple users this angle varies with the type of qostbc and leads to a new form of adaptive modulation called code diversity where feedback instructs the transmitter how to choose from a plurality of codes

low complexity sphere decoding algorithm for quasi orthogonal space time block codes space time codes can be decoded by the sphere decoding sd algorithm to reduce the complexity and retain maximum likelihood ml performance in this letter the ml metric of quasi orthogonal space time block codes is written into two independent euclidean norms thus sd can be applied to each function independently the new scheme reduces the complexity by at least 85 for systems with four or more transmit antennas compared with the conventional sd algorithm

numerical solution of nonlinear fuzzy fredholm integral equations using iterative method in this paper we propose an iterative procedure based on quadrature formula to solve nonlinear fuzzy fredholm integral equations of the second kind moreover the error estimation of the proposed method in terms of uniform and partial modulus of continuity is given finally illustrative examples are included in order to demonstrate the accuracy and the convergence of the proposed method

two designs of space time block codes achieving full diversity with partial interference cancellation group decoding a partial interference cancellation pic group decoding based space time block code stbc design criterion was recently proposed by guo and xia where the decoding complexity and the code rate traeoff is dealt when the full diversity is achieved in this paper two designs of stbc are proposed for any number of transmit antennas that can obtain full diversity when a pic group decoding with a particular grouping scheme is applied at receiver with the pic group decoding and an appropriate grouping scheme for the decoding the proposed stbc are shown to obtain the same diversity gain as the ml decoding but have a low decoding complexity the first proposed stbc is designed with multiple diagonal layers and it can obtain the full diversity for two layer design with the pic group decoding and the rate is up to 2 symbols per channel use with pic sic group decoding the first proposed stbc can obtain full diversity for any number of layers and the rate can be full the second proposed stbc can obtain full diversity and a rate up to 9 4 with the pic group decoding some code design examples are given and simulation results show that the newly proposed stbc can well address the rate performance complexity tradeoff of the mimo systems

galerkin runge kutta discretizations for semilinear parabolic equations a new class of fully discrete galerkin runge kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems unlike any classical counterpart this class offers arbitrarily high order convergence without suffering from what has been called order reduction in support of this claim error estimates are proved and computational results are presented furthermore it is noted that special runge kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

on random fuzzy functional differential equations in this paper we prove the existence and uniqueness result for random fuzzy functional differential equations for the existence and uniqueness we use the method of successive approximations some kind of boundedness of the solution is established

space time trellis code design based on super quasi orthogonal block codes with minimum decoding complexity in this letter we propose a new family of space time trellis codes which are constructed by combining a super set of quasi orthogonal space time block codes with minimum decoding complexity with an outer multiple trellis coded modulation encoder a systematic set partitioning method for quadratic amplitude modulation constellations is given the proposed scheme can be used for systems with four or more than four transmit antennas furthermore its decoding complexity is low because its branch metric calculation can be implemented in a symbolwise way simulation results demonstrate that the proposed scheme has a comparable performance as super quasi orthogonal space time trellis codes proposed by jafarkhani and hassanpour while providing a lower decoding complexity

a posteriori error estimates for discontinuous galerkin methods for the generalized korteweg de vries equation we construct analyze and numerically validate a posteriori error estimates for conservative discontinuous galerkin dg schemes for the generalized korteweg de vries gkdv equation we develop the concept of dispersive reconstruction i e a piecewise polynomial function which satisfies the gkdv equation in the strong sense but with a computable forcing term enabling the use of a priori error estimation techniques to obtain computable upper bounds for the error both semidiscrete and fully discrete approximations are treated

the convergence of the fully discrete solution for the roseneau equation abstract in this paper we analyze the boundedness and convergence of the approximate solution to the roseneau equation for the temporal discretization we apply galerkin crank nicolson finite element method and we prove the convergence of order 2 analytically we also prove the convergence of two initial stage approximations

spatially modulated orthogonal space time block codes with non vanishing determinants this paper proposes a multiple input multiple output mimo transmission scheme for m ary modulations called spatially modulated orthogonal space time block coding sm ostbc based on the concept of spatial constellation sc codewords introduced by le at el in the proposed scheme transmit codeword matrices are generated by multiplying sc matrices with codewords constructed from orthogonal space time block codes o stbc the maximum spectral efficiency of the proposed scheme is equal to n t 2 log 2 m bpcu where n t is the number of transmit antennas and m is the modulation order the sc matrices provide a means of carrying information bits together with the o stbc codewords and allow the sm ostbc scheme to achieve second order transmit diversity by satisfying the non vanishing determinant property a systematic method to design the sc codewords for an even number of transmit antennas greater than 3 is presented a single stream maximum likelihood ml decoder which requires a low computational complexity thanks to the structure of the sm ostbc codewords and to the orthogonality of the o stbcs and a sphere decoder with further reduced signal processing complexity are developed the bit error rate ber performance of the proposed scheme is studied by using both theoretical union bound analysis and computer simulations finally simulation results are presented in order to compare ber performance energy efficiency and decoding complexity of the proposed scheme with those of several existing mimo transmission schemes

toward a preferred 4 x 4 space time block code a performance versus complexity sweet spot with linear filter decoding we develop a new 4 4 hadamard precoded quasi orthogonal space time block code qo stbc that enables highly effective near maximum likelihood near ml reliability based prioritized symbol detection using linear filters approximate block error rate minimization is being used to optimize the code rotation angle detailed computational complexity evaluation of the decoder in terms of real multiplications and additions shows significant complexity reduction for symbol alphabet sizes of interest numerical and simulation studies demonstrate negligible bit error rate degradation compared to the state of the art in bit error rate by ml decoded 4 4 codewords

a fast recursive algorithm for g stbc this paper proposes a fast recursive algorithm for group wise space time block code g stbc which takes full advantage of the alamouti structure in the equivalent channel matrix to reduce the computational complexity with respect to the existing efficient algorithms for g stbc the proposed algorithm achieves better performance and usually requires less computational complexity

on the relation of ostbc and code rate one qstbc average rate ber and coding gain recently the statistical properties of the equivalent channel representation of a multiple input multiple output mimo system employing code rate one quasi orthogonal space time block codes qstbc which are constructed by using orthogonal space time block codes ostbc as building elements was characterized based on these characterizations we analyze the average rate or mean mutual information the bit error rate performance and the coding gain achieved with qstbc for any number of receive and nt 2n n ges 2 transmit antennas first we study constellation rotation using a systematic approach in order to maximize the coding gain and to achieve full diversity qstbc moreover we present an upper bound on the coding gain we derive a lower and upper bound on the ber performance for qstbc furthermore we analyze the average rate achievable with qstbc in case of an uninformed transmitter and also the case in which the transmitter knows the mean channel matrix whereas the receiver has perfect csi along with the analysis we compare all the results of these performance measures with the results achieved with ostbc revealing important connections between ostbc and qstbc for example the coding gain of a qstbc is upper bounded by the coding gain of the underlying ostbc also the ber of a qstbc for nt transmit and nr receive antennas is tightly lower bounded by the ber of a full diversity providing intersymbol interference free system in addition to that we show that gains in terms of average rate by using a qstbc and thus with higher nt instead of the underlying ostbc are only attainable if the available channel state information at the transmitter csit is utilized finally we illustrate our theoretical results using numerical simulations

on some high order accurate fully discrete galerkin methods for the korteweg de vries equation we construct and analyze fully discrete galerkin finite element methods of high order of accuracy for the numerical solution of the periodic initial value problem for the korteweg de vries equation the methods are based on a standard space discretization using smooth periodic splines on a uniform mesh for the time stepping we use two schemes of third resp fourth order of accuracy which are modifications of well known diagonally implicit runge kutta methods and require the solution of two resp three nonlinear systems of equations at each time step these systems are solved approximately by newton s method provided the initial iterates are chosen in a specific accurate way we show that only one newton iteration per system is needed to preserve the stability and order of accuracy of the scheme under certain mild restrictions on the space mesh length and the time step we prove l2 error estimates of optimal rate of convergence for both schemes

application of simpson quadrature rule and iterative method for solving nonlinear fuzzy delay integral equations abstract in this study firstly we present an iterative method by using simpson quadrature formula for solving nonlinear fuzzy delay integral equations in addition the convergence analysis of the proposed method is investigated also we prove numerical stability analysis of the method by means of choosing the perturbation in the first iteration finally numerical examples to illustrate applicability of this method are presented

orthogonal space time block codes with sphere packing orthogonal designs have received considerable attention in the development of efficient modulation and coding methods for future multi antenna wireless communication systems due to their special properties in this paper we propose a class of space time block codes constructed by combining orthogonal designs with sphere packing for an arbitrary number of transmit antennas the structure of the orthogonal designs is exploited to guarantee full diversity and sphere packing is used to improve the coding advantage space time block code construction from block orthogonal designs is also considered the full diversity property is ensured by rotating the sphere packing underlying the code and the optimal rotation angle is determined for a class of sphere packing code design examples are provided for two and four transmit antennas and various transmission rates the simulation results show that by jointly designing the symbols in the orthogonal designs the performance of the block codes can be significantly increased

iterative method for numerical solution of two dimensional nonlinear fuzzy integral equations in this paper we prove the convergence of the method of successive approximations used to approximate the solution of two dimensional nonlinear fuzzy fredholm integral equations of the second kind also we present an iterative procedure based on quadrature formula to solve such equations the error estimation of the proposed method is given in terms of uniform and partial modulus of continuity finally some numerical experiments confirm the theoretical results and illustrate the accuracy of the method

application of quasi orthogonal space time block codes in beamforming it is well known that when channel information is available at the transmitter transmit beamforming scheme can be employed to enhance the performance of a multiple antenna system recently jongren et al and zhou giannakis proposed a new performance criterion based on partial channel side information at the transmitter with this criterion an optimal beamforming matrix was constructed for the orthogonal space time block codes however the same method has not been applied to the recently proposed quasi orthogonal space time block codes qstbcs due to the nonorthogonal nature of the quasi orthogonal designs in this paper the issue of combining beamforming with qstbcs is addressed based on our asymptotic analysis we extend the beamforming scheme from jongren et al and construct the beamforming matrices for the quasi orthogonal designs the proposed beamforming scheme accomplishes high transmission rate as well as high order spatial diversity the new qstbc beamformer can be presented as a novel four directional or eight directional eigen beamformer that works for systems with four or more transmit antennas simulations for systems with multiple transmit antennas demonstrate significant performance improvement over several other widely used beamforming methods at various snrs and for channels with different quality of feedback

comments on a new ml based interference cancellation technique for layered space time codes in this comment we justify that the computational complexity proposed in the paper a new ml based interference cancellation technique for layered space time codes ieee trans on communications vol 57 no 4 pp 930 936 2009 is o n3 rather than the claimed o n2 where n is the number of receive antennas

convergence of galerkin approximations for the korteweg de vries equation standard galerkin approximations using smooth splines on a uniform mesh to 1 periodic solutions of the korteweg de vries equation are analyzed optimal rate of convergence estimates are obtained for both semidiscrete and second order in time fully discrete schemes at each time level the resulting system of nonlinear equations can be solved by newton s method it is shown that if a proper extrapolation is used as a starting value then only one step of the newton iteration is required

capacity approaching space time codes for systems employing four transmitter antennas the design of space time codes that are capable of approaching the capacity of multiple input single output miso antenna systems is a challenging problem yet one of high practical importance while a remarkably simple scheme of alamouti 1998 is capable of attaining the channel capacity in the case of two transmitter and one receiver antennas 2 1 no such schemes are known for the case of more than two transmitter antennas we propose a family of space time codes that are especially designed for the case of four transmitter antennas and that are shown to allow the attainment of a significant fraction of the open loop shannon capacity of the 4 1 channel

semiorthogonal space time block codes in this paper a new class of full diversity rate one space time block codes stbcs called semiorthogonal algebraic space time block codes sast codes is proposed sast codes are delay optimal when the number of transmit antennas is even the sast codeword matrix has a generalized alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols sast codes with maximal coding gain are constructed by using rate one linear threaded algebraic space time ltast codes compared with ltsat codes sast codes not only reduce the complexity of maximum likelihood detection but also provide remarkable performance gain they also outperform other stbc with rate one or less sast codes also perform well with suboptimal detectors such as the vertical bell laboratories layered space time v blast nulling and cancellation receiver finally sast codes attain nearly 100 of the shannon capacity of open loop multiple input single output miso channels

group decodable space time block codes with code rate 1 high rate space time block codes stbc with code rate 1 in multi input multi output mimo systems are able to provide both spatial multiplexing gain and diversity gain but have high maximum likelihood ml decoding complexity since group decodable quasi orthogonal code structure can reduce the decoding complexity we present in this paper systematic methods to construct group decodable high rate stbc with full symbol wise diversity gain for arbitrary transmit antenna number and code length we show that the proposed group decodable stbc can achieve high code rate that increases almost linearly with the transmit antenna number and the slope of this near linear dependence increases with the code length comparisons with existing low rate and high rate codes such as orthogonal stbc and algebraic stbc are conducted to show the decoding complexity reduction and good code performance achieved by the proposed codes

on channel orthogonalization using space time block coding with partial feedback orthogonal space time block codes ostbcs yield full diversity gain even while requiring only a linear receiver such full rate rate one orthogonal designs are available for complex symbol constellations only for n 2 transmit antennas in this paper we propose a new family of full rate space time block codes stbcs using a single parameter feedback for communication over rayleigh fading channels for n 3 4 transmit antennas and m receive antennas the proposed rate one codes achieve full diversity and the performance is similar to maximum receiver ratio combining the decoding complexity of these codes are only linear even while performing maximum likelihood decoding the partial channel information is a real phase parameter that is a function of all the channel gains and has a simple closed form expression for n 3 4 this feedback information enables us to derive channel orthogonal designs starting from quasi orthogonal stbcs the feedback complexity is significantly lower than conventional closed loop transmit beamforming we compare the proposed codes with the open loop ostbcs and also with the closed loop equal gain transmission egt scheme which uses equal power loading on all antennas simulated error rate performances indicate that the proposed channel orthogonalized stbcs significantly outperform the open loop orthogonal designs for the same spectral efficiency moreover even with significantly lower feedback and computational complexity the proposed scheme outperforms the egt technique for m n

benchmarking the propagator method for nonlinear systems a burgers korteweg devries equation abstract a new method for solving a generalized burgers korteweg devries bkdv equation is presented this new method consists of two symbiotic aspects analytical and numerical respectively the analytical aspect consists of obtaining the propagators which are the nonlinear analogues of green s functions for the bkdv equation and subsequently using these propagators to obtain the bkdv solution as a fixed point integral equation the numerical aspect consists of developing a highly efficient and accurate method for solving this integral equation benchmarking comparisons using the korteweg devries and burgers equations indicate that our new method is efficient accurate and robust

numerical solutions of the nonlinear fuzzy hammerstein volterra delay integral equations in this paper an iterative numerical method that solves nonlinear fuzzy hammerstein volterra integral equations with constant delay is developed by using the error estimates a practical stopping criterion of the algorithm is obtained the convergence and the numerical stability of the method is proved and its accuracy is illustrated on three numerical examples the study of this integral equation is important because it has as a particular case the fuzzy variant of a mathematical model from epidemiology

widely linear alamouti receiver for the reception of real valued constellations corrupted by interferences the alamouti saic maic concept orthogonal space time block codes stbc and the alamouti scheme in particular are of particular interest in multiple input multiple output mimo systems since they achieve full spatial diversity over fading channels and are decoded from linear processing at the receiver nevertheless due to the expensive spectral resource increasing network capacity requires the development of interference cancellation ic techniques allowing several users to share the same spectral resources without impacting the transmission quality in this context several ic schemes have been developed during this last decade where each user is equipped with multiple antennas and employs stbc at transmission however these ic techniques require multiple antennas at reception which remains a challenge at the handset level due to cost and size limitations for this reason low complexity single antenna interference cancellation saic techniques currently operational in gsm handsets have been developed recently for single antenna users using real valued modulations or complex filtering of real valued modulations by using a widely linear wl filtering at reception extension to multiple antennas at reception is called multiple antenna interference cancellation maic technique the purpose of this paper is to extend the saic maic technology to users using both real valued constellations such as amplitude shift keying ask constellations and the alamouti scheme at transmission a wl minimum mean square error mmse receiver completely new for ic purposes in the context of radio communications systems using the alamouti scheme is proposed and analyzed this receiver which corresponds to the maximum likelihood ml receiver for synchronous intranetwork interferences is able to separate up to 2 n alamouti users from n antennas at reception hence saic capability for n 1

theory and applications of fuzzy volterra integral equations formulations of fuzzy integral equations in terms of the aumann integral do not reflect the behavior of corresponding crisp models consequently they are ill adapted to describe physical phenomena even when vagueness and uncertainty are present a similar situation for fuzzy odes has been obviated by interpretation in terms of families of differential inclusions the paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations the investigation is restricted to volterra type equations with mildly restrictive conditions but the methods are capable of extensive generalization to other types and more general assumptions the results are illustrated by integral equations relating to control models with fuzzy uncertainties

single symbol ml decoding for orthogonal and quasi orthogonal stbc in clipped mimo ofdm systems using a clipping noise model with gaussian approximation an efficient way to reduce the peak to average power ratio papr in ofdm systems is clipping after the clipping in an mimo ofdm system the additive noise may not be white in this paper we develop fast single symbol ml decoding algorithms for orthogonal space time block codes ostbc and linearly transformed quasi orthogonal space time block codes qostbc in clipped mimo ofdm systems by using a clipping noise model with gaussian approximation by using the statistics of the clipping distortions our newly developed fast ml decoding algorithms improve the performance for clipped mimo ofdm systems with ostbc and qostbc while the decoding complexities are not increased simulation results are presented to illustrate the improvement

generalized distributive law for ml decoding of space time block codes the problem of designing good space time block codes stbcs with low maximum likelihood ml decoding complexity has gathered much attention in the literature all the known low ml decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast decodable conditionally multigroup decodable structure of a code we refer to this well known technique of decoding stbcs as conditional ml cml decoding in this paper we introduce a new framework to construct ml decoders for stbcs based on the generalized distributive law gdl and the factor graph based sum product algorithm we say that an stbc is fast gdl decodable if the order of gdl decoding complexity of the code with respect to the constellation size m is strictly less than m where is the number of independent symbols in the stbc we give sufficient conditions for an stbc to admit fast gdl decoding and show that both multigroup and conditionally multigroup decodable codes are fast gdl decodable for any stbc whether fast gdl decodable or not we show that the gdl decoding complexity is strictly less than the cml decoding complexity for instance for any stbc obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable the gdl decoder provides about 12 times reduction in complexity compared to the cml decoder similarly for the golden code which is conditionally multigroup decodable the gdl decoder is only half as complex as the cml decoder

ill posedness for fuzzy fredholm integral equations of the first kind and regularization methods abstract in this study the concept of ill posedness for fuzzy fredholm integral equations of the first kind was first proposed an efficient regularization method based on classic tikhonov regularization scheme to determine the approximate solution of the fuzzy fredholm integral equations of the first kind is presented to support our investigation some examples are illustrated

worst case robust mimo transmission with imperfect channel knowledge in this paper we consider robust transmit strategies against the imperfectness of the channel state information at the transmitter csit for multi input multi output mimo communication systems following a worst case deterministic model the actual channel is assumed to be inside an ellipsoid centered at a nominal channel the objective is to maximize the worst case received signal to noise ratio snr or to minimize the worst case chernoff bound of the error probability thus leading to a maximin problem moreover we also consider the qos problem as a complement of the maximin design which minimizes the transmit power consumption and meanwhile keeps the received snr above a given threshold for any channel realization in the ellipsoid it is shown that for a general class of power constraints both the maximin and qos problems can be equivalently transformed into convex problems or even further into semidefinite programs sdps thus efficiently solvable by the numerical methods the most interesting result is that the optimal transmit directions i e the eigenvectors of the transmit covariance are just the right singular vectors of the nominal channel under some mild conditions this result leads to a channel diagonalizing structure as in the cases of perfect csit and statistical csit with mean or covariance feedback and reduces the complicated matrix valued problem to a scalar power allocation problem then we provide the closed form solution to the resulting power allocation problem

low ml decoding complexity stbcs via codes over the klein group in this paper we give a new framework for constructing low ml decoding complexity space time block codes stbcs using codes over the klein group k almost all known low ml decoding complexity stbcs can be obtained via this approach new full diversity stbcs with low ml decoding complexity and cubic shaping property are constructed via codes over k for number of transmit antennas n 2m m 1 and rates r 1 complex symbols per channel use when r n the new stbcs are information lossless as well the new class of stbcs have the least known ml decoding complexity among all the codes available in the literature for a large set of n r pairs

on full diversity space time block codes with partial interference cancellation group decoding in this paper we propose a partial interference cancellation pic group decoding strategy scheme for linear dispersive space time block codes stbc and a design criterion for the codes to achieve full diversity when the pic group decoding is used at the receiver a pic group decoding decodes the symbols embedded in an stbc by dividing them into several groups and decoding each group separately after a linear pic operation is implemented it can be viewed as an intermediate decoding between the maximum likelihood ml receiver that decodes all the embedded symbols together i e all the embedded symbols are in a single group and the zero forcing zf receiver that decodes all the embedded symbols separately and independently i e each group has and only has one embedded symbol after the zf operation is implemented the pic group decoding provides a framework to adjust the complexity performance tradeoff by choosing the sizes of the information symbol groups our proposed design criterion group independence for the pic group decoding to achieve full diversity is an intermediate condition between the loosest ml full rank criterion of codewords and the strongest zf linear independence condition of the column vectors in the equivalent channel matrix we also propose asymptotic optimal ao group decoding algorithm which is an intermediate decoding between the mmse decoding algorithm and the ml decoding algorithm the design criterion for the pic group decoding can be applied to the ao group decoding algorithm because of its asymptotic optimality it is well known that the symbol rate for a full rank linear stbc can be full i e nt for nt transmit antennas it has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver the intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the pic group decoding this therefore provides a complexity performance rate tradeoff some design examples are given

asymptotic information lossless designs and the diversity multiplexing tradeoff it is known that neither the alamouti nor the v blast scheme achieves the zheng tse diversity multiplexing tradeoff dmt of the multiple input multiple output mimo channel with respect to the dmt curve the alamouti scheme achieves the point corresponding to maximum diversity gain only whereas v blast meets only the point corresponding to maximum multiplexing gain it is also known that d blast achieves the optimal dmt for n transmit and n receive antennas but only under the assumption that the leading and trailing zeros are ignored when these zeros are taken into account d blast achieves the point corresponding to zero multiplexing gain but not the point corresponding to zero diversity gain the first scheme to achieve the dmt is the coding scheme of yao and wornell for the case of two transmit and two receive antennas in this paper we introduce the notion of an asymptotic information lossless aill design and obtain a necessary and sufficient condition under which a design is aill analogous to the result that full rank designs achieve the point corresponding to the zero multiplexing gain of the optimal dmt curve we show aill to be a necessary and sufficient condition for a design to achieve the point on the dmt curve corresponding to zero diversity gain we also derive a lower bound on the tradeoff achieved by designs from field extensions and show that the tradeoff is very close to the optimal tradeoff in the case of a single receive antenna a lower bound to the tradeoff achieved by designs from division algebras is presented which indicates that these designs achieve both extreme points corresponding to zero diversity and zero multiplexing gain of the optimal dmt curve finally we present simulations results for n transmit and n receive antennas for n 2 3 4 which suggest that designs from division algebras are likely to have the property of being dmt achieving

space time trellis codes based on channel phase feedback space time coding stc has been proposed recently for multiple antenna wireless communication systems most of the proposed stc schemes use the assumption that either no channel state information or the channel mean covariance information is available at the transmitter in this paper we propose a new stc scheme for a closed loop transmission system where quantized channel phase information is available at the transmitter a new performance criterion is derived for the quasi static fading channel this design criterion is then used to construct a new class of space time trellis codes sttcs the proposed code construction is based on the concatenation of a standard multiple trellis coded modulation outer code with an inner code the inner code is selected from a series of inner codes using the channel phase feedback the series of inner codes are constructed based on the systematic set partitioning of several classes of space time signal designs simulation results show significant performance improvement over the other sttcs in the literature in addition the proposed coding scheme enjoys low peak to average power ratio simple decoding and power efficient low cost implementation

high rate multisymbol decodable stbcs from clifford algebras it is well known that space time block codes stbcs obtained from orthogonal designs ods are single symbol decodable ssd and from quasi orthogonal designs qods are double symbol decodable dsd however there are ssd codes that are not obtainable from ods and dsd codes that are not obtainable from qods in this paper a method of constructing g symbol decodable g sd stbcs using representations of clifford algebras are presented which when specialized to g 1 2 gives ssd and dsd codes respectively for the number of transmit antennas 2a the rate in complex symbols per channel use of the g sd codes presented in this paper is a 1 g 2a g the maximum rate of the dsd stbcs from qods reported in the literature is a 2a 1 which is smaller than the rate a 1 2a 2 of the dsd codes of this paper for 2a transmit antennas in particular the reported dsd codes for 8 and 16 transmit antennas offer rates 1 and 3 4 respectively whereas the known stbcs from qods offer only 3 4 and 1 2 respectively the construction of this paper is applicable for any number of transmit antennas the diversity sum and diversity product of the new dsd codes are studied it is shown that the diversity sum is larger than that of all known qods and hence the new codes perform better than the comparable qods at low signal to noise ratios snrs for identical spectral efficiency simulation results for dsd codes at various spectral efficiencies are provided

fully discrete galerkin methods for the korteweg de vries equation abstract fully discrete schemes for the numerical simulation of solutions of the periodic initial value problem for the korteweg de vries equation are introduced implemented and tested of special interest are stable schemes featuring rates of convergence of order higher than two in both the spatial and temporal variable a careful analysis of the relative and absolute efficiency of these schemes is carried out and one of the schemes is applied to demonstrate that solutions of certain generalized korteweg de vries equations apparently may develop singularities in finite time

design of fully diverse multiple antenna codes based on sp 2 fully diverse constellations i e sets of unitary matrices whose pairwise differences are nonsingular are useful in multiple antenna communications especially in multiple antenna differential modulation since they have good pairwise error properties recently group theoretic ideas especially fixed point free fpf groups have been used to design fully diverse constellations of unitary matrices here we construct four transmit antenna constellations appropriate for differential modulation based on the symplectic group sp 2 they can be regarded as extensions of alamouti s celebrated two transmit antenna orthogonal design which can be constructed from the group sp 1 we further show that the structure of sp 2 codes lends itself to efficient maximum likelihood ml decoding via the sphere decoding algorithm finally the performance of sp 2 codes is compared with that of other existing codes including alamouti s orthogonal design a 4 spl times 4 complex orthogonal design cayley differential unitary space time codes and group based codes

on optimal order error estimates for the nonlinear schro dinger equation implicit runge kutta methods in time are used in conjunction with the galerkin method in space to generate stable and accurate approximations to solutions of the nonlinear cubic schrodinger equation the temporal component of the discretization error is shown to decrease at the classical rates in some important special cases