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

analytic approximations to kelvin functions with applications to electromagnetics we present analytical approximations for the real kelvin function ber x and the imaginary kelvin function bei x using the two point quasi fractional approximation procedure we have applied these approximations to the calculation of the current distribution within a cylindrical conductor our approximations are simple and accurate an infinite number of roots is also obtained with the approximation and precision increases with the value of the root our results could find useful applications in problems where analytical approximations of the kelvin functions are needed

a physically based preconditioner for quasi planar scattering problems a physically based preconditioner for iterative method of moments solutions of quasi planar penetrable surface scattering is presented the required preconditioner inverse operation is computed in order operations by first representing the right hand side vector to be multiplied by the preconditioner inverse in terms of its planewave spectrum individual planewave amplitudes are then combined with appropriate fresnel reflection coefficients to generate the solution for induced currents and transformed back to the spatial domain the proposed technique is applied in simulations of scattering from rough surfaces and the number of iterations required to obtain a convergent solution is compared to that achieved by a banded matrix preconditioning method the results show that the physically based preconditioner produces rapid convergence for surfaces with moderate heights and slopes

differential feedback of geometrical mean decomposition precoder for time correlated mimo systems for a time correlated channel we consider the differential feedback of the geometrical mean decomposition gmd precoder which is known to be optimal for a number of criteria when the channel varies slowly we can expect the optimal gmd precoders of consecutive channel uses to be close we consider the feedback of the so called differential precoder and show that it lies in a neighborhood of the identity matrix using matrix perturbation theory furthermore the radius of the neighborhood is shown to be proportional to a time correlation parameter such a characterization allows for subsequent efficient quantization of the differential precoder we show how to design codewords for the prescribed radius by perturbing the identity matrix and applying qr decomposition on the perturbed matrix simulations are given to demonstrate that with a small feedback rate the performance of the proposed differential gmd comes close to the case when perfect channel state information is available to the transmitter for slowly time varying channels like those in indoor and microcellular environments

the generalized forward backward method for analyzing the scattering from targets on ocean like rough surfaces in holliday et al 1995 1996 the iterative forward backward fb method has been proposed to solve the magnetic field integral equation mfie for smooth one dimensional 1 d rough surfaces this method has proved to be very efficient converging in a very small number of iterations nevertheless this solution becomes unstable when some obstacle like a ship or a large breaking wave is included in the original problem in this paper we propose a new method the generalized forward backward gfb method to solve such kinds of complex problems the approach is formulated for the electric field integral equation efie which is solved using a hybrid combination of the conventional fb method and the method of moments mom the latter of which is only applied over a small region around the obstacle the gfb method is shown to provide accurate results while maintaining the efficiency and fast convergence of the conventional fb method some numerical results demonstrate the efficiency and accuracy of the new method even for low grazing angle scattering problems

qmr a quasi minimal residual method for non hermitian linear systems the biconjugate gradient bcg method is the natural generalization of the classical conjugate gradient algorithm for hermitian positive definite matrices to general non hermitian linear systems unfortunately the original bcg algorithm is susceptible to possible breakdowns and numerical instabilities in this paper we present a novel bcg like approach the quasi minimal residual qmr method which overcomes the problems of bcg an implementation of qmr based on a look ahead version of the nonsymmetric lanczos algorithm is proposed it is shown how bcg iterates can be recovered stably from the qmr process some further properties of the qmr approach are given and an error bound is presented finally numerical experiments are reported

on the discretization of the integral equation describing scattering by rough conducting surfaces numerical simulations of scattering from one dimensional 1 d randomly rough surfaces with pierson moskowitz p m spectra show that if the kernel or propagator matrix with zeros on its diagonal is used in the discretized magnetic field integral equation mfie the results exhibit an excessive sensitivity to the current sampling interval especially for backscattering at low grazing angles lgas though the numerical results reported in this paper were obtained using the method of ordered multiple interactions momi a similar sampling interval sensitivity has been observed when a standard method of moments mom technique is used to solve the mfie a subsequent analysis shows that the root of the problem lies in the correct discretization of the mfie kernel we found that the inclusion of terms proportional to the surface curvature regarded by some authors as an additional correction in the diagonal of the kernel matrix virtually eliminates this sampling sensitivity effect by reviewing the discretization procedure for mfie we show that these curvature terms indeed must be included in the diagonal in order for the propagator matrix to be represented properly the recommended current sampling interval for scattering calculations with p m surfaces is also given

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

chebyshev series approximations for the bessel function y n z of complex argument we employ the truncated chebyshev series to approximate the bessel function of the second kind y n z for z 8 detailed manipulations and discussions for y 0 z and y 1 z are given results of numerical experiments are presents are presented to demonstrate the computed accuracy by using the chebyshev series approximations advantages and disadvantages of the chebyshev series approximation compared with other polynomial approximation methods e g the tau method approximations are discussed

green s functions in lossy layered media integration along the imaginary axis and asymptotic behavior this paper presents an efficient technique for evaluating green s functions associated to layered media when formulated as sommerfeld integrals in the space domain the key step in the formulation is that sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane it is shown that with this original choice of the integration contour the numerical effort usually involved in the evaluation of sommerfeld integrals can be greatly reduced specially when large source observer distances are involved one asset of this technique is that it can be easily incorporated into integral equation based cad packages for the efficient analysis of complex printed microwave circuit and antennas in addition the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media green s functions for large source observer distances

the evaluation of bessel functions via exp arc integrals a standard method for computing values of bessel functions has been to use the well known ascending series for small argument and to use an asymptotic series for large argument with the choice of the series changing at some appropriate argument magnitude depending on the number of digits required in a recent paper d borwein j borwein and r crandall 1 derived a series for an exp arc integral which gave rise to an absolutely convergent series for the j and i bessel functions with integral order such series can be rapidly evaluated via recursion and elementary operations and provide a viable alternative to the conventional ascending asymptotic switching in the present work we extend the method to deal with bessel functions of general non integral order as well as to deal with the y and k bessel functions

bistatic scattering from a three dimensional object over a randomly rough surface using the fdtd algorithm a numerical finite difference time domain approach for electromagnetic scattering from an object over a randomly rough surface in three dimensional 3 d model is developed rough surface is truncated in numerical simulation by using the periodic surface extension and one period of the rough surface with dependence of the correlation length is used for scattering computation generation of the incident wave upon the rough surface is presented a numerical model and algorithm of a single object on or above a rough surface are developed polarized bistatic scattering from the object and rough surface is obtained based on numerical distribution of the near zone fields comparison with conventional two dimensional model is also discussed

wright functions as scale invariant solutions of the diffusion wave equation the time fractional diffusion wave equation is obtained from the classical diffusion or wave equation by replacing the first or second order time derivative by a fractional derivative of order 0 2 using the similarity method and the method of the laplace transform it is shown that the scale invariant solutions of the mixed problem of signalling type for the time fractional diffusion wave equation are given in terms of the wright function in the case 0 1 and in terms of the generalized wright function in the case 1 2 the reduced equation for the scale invariant solutions is given in terms of the caputo type modification of the

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

on the minimum differential feedback for time correlated mimo rayleigh block fading channels in this paper we investigate the differential channel state information csi feedback problem for a general multiple input multiple output mimo system over time correlated rayleigh block fading channels specifically we derive the closed form minimum differential feedback rate in the presence of channel estimation errors and quantization distortion with the feedback channel capacity constraint we further study the ergodic capacity in a periodic feedback system in terms of the minimum differential feedback rate and the feedback interval through theoretical analysis we find that there exists an optimal differential feedback interval to achieve the maximum ergodic capacity analytical results are verified by simulations in a practical periodic differential feedback system employing water filling precoder and lloyd s quantization algorithm

variable rate transmission for mimo time correlated channels with limited feedback in this paper we consider variable rate transmission for time correlated mimo multi input multi output channels with limited feedback the number of bits loaded on each sub channel of the mimo system is dynamically assigned according to the current channel condition and fed back to the transmitter as the channel is time correlated bit loading is a vector signal that is also time correlated we propose to feedback bit loading using predictive coding which is known to be a powerful quanti zation technique when the underlying signal is correlated in time assuming the channel is a first order gauss markov random process we derive the predictor for the bit loading to be coded and analyze the corresponding prediction error variance when the channel is varying slowly by exploiting the prediction error variance we adapt the quantizer of the prediction error to have a smaller quantization error furthermore we show that the pre diction error variance is proportional to a term that depends only on the time correlation coefficient this leads to the conclusion that a codebook that is designed for a particular time correlation coefficient can be easily modified to a codebook for a different correlation coefficient without redesign simulations are presented to demonstrate that the proposed predictive coding can achieve a very good approximation of the desired transmission rate with a very low feedback rate

electromagnetic scattering from a rough layer propagation inside layer expansion method combined to an updated bmia cag approach an efficient method is developed to calculate the bistatic scattering coefficient bsc from a stack of two one dimensional rough interfaces separating homogeneous media the propagation inside layer expansion pile method recently published by dechamps was efficient with a complexity o n2 n being the number of samples per interface to reduce this complexity a fast method valid for a single rough surface the banded matrix iterative approach canonical grid bmia cag is combined to the pile method furthermore the calculation of the coupling interactions between both interfaces are also accelerated using a new method similar to the bmia cag the pile method reaches then a complexity of only o nlogn a study of the convergence of the pile is done and compared to another efficient method the forward backward

reflection from an array of conducting plates using classic edge mode current densities a new reflection coefficient is derived for a frequency selective surface composed of conducting rectangular plates the current density induced on the plates is assumed to follow the classic edge mode behavior observed by meixner using very simple functions to describe the spatial dependence of the current a simple frequency dependent solution is derived this solution is a function of the 0th and 1st order bessel functions of the first kind the new approach provides very accurate results compared to the moment method and to measured data it also provides an analytic solution that demonstrates a cause and effect correspondence between the array geometry and performance

a new polynomial approximation for jν bessel functions abstract new approximate solutions to the order bessel function of the first kind are derived the solution is expressed as a polynomial for bessel function of all fractional order polynomial comparisons are made between the exact solution and the new approximation one utility of this derivation is to allow researchers to analytically evaluate integrals containing bessel functions

computation of the sommerfeld integral tails using the matrix pencil method the oscillating infinite domain sommerfeld integrals si are difficult to integrate using a numerical procedure when dealing with structures in a layered media even though several researchers have attempted to do that generally integration along the real axis is used to compute the si however significant computational effort is required to integrate the oscillating and slowly decaying function along the tail extrapolation methods are generally applied to accelerate the rate of convergence of these integrals however there are difficulties with the extrapolation methods such as locations for the breakpoints in this paper we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the si in this paper we fit the tail by a sum of finite usually 10 to 20 complex exponentials using the matrix pencil method mpm the integral of the tail of the si is then simply calculated by summing some complex numbers no numerical integration is needed in this process as the integrals can be done analytically good accuracy is achieved with a small number of evaluations for the integral kernel 60 points for the mpm as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods along the tails of the si simulation results show that to obtain the similar accuracy in the evaluation of the si the mpm is approximately 10 times faster than the traditional extrapolation methods moreover since the mpm is robust to the effects of noise this method is more stable especially for large values of the horizontal distances the method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the green s function for a layered media in the spatial domain

high precision evaluation of the bessel functions via hadamard series we present a method of high precision calculation of the bessel functions using hadamard series such series are absolutely convergent expansions involving the normalised incomplete gamma function p a z email protected a z c a and possess early terms that behave like those in an asymptotic expansion in the case of real variables the function p a z acts as a smoothing factor on the terms of the series we show how these series representing the bessel functions of complex argument can be chosen so as to produce rapidly convergent series that possess terms decaying at the geometric rate q k where 0 q 1 and k is the ordinal number of the series we give numerical examples with q 12 13 and 14 the theory is extended to cover the confluent hypergeometric functions f11 a b z and u a b z thereby dealing with many of the special functions arising in mathematical physics

generalized bessel functions in tunnelling ionization we develop two new approximations for the generalized bessel function that frequently arises in the analytical treatment of strong field processes especially in non perturbative multiphoton ionization theories both these new forms are applicable to the tunnelling environment in atomic ionization and are analytically much simpler than the currently used low frequency asymptotic approximation for the generalized bessel function the second of the new forms is an approximation to the first and it is the second new form that exhibits the well known tunnelling exponential

new expansions of bessel functions of first kind and complex argument we present accurate trigonometric expansions of bessel functions of first kind and integer order for complex arguments of the form j v z sum k alpha k s beta k z where alpha k and beta k are constants and s is a sinusoidal function using the new expansions varying levels of accuracy and range of applicability can be achieved by varying the number of terms in the expansions for example a four term expansion of j 0 z yields an average relative error of for vert z vert leq 2 pi and same accuracy is achieved for an eight term expansion for an extended range vert z vert leq 5 pi further a phase and amplitude corrected large argument asymptotic formula is studied such that the lower limit of its usage is reduced to medium magnitude ranges of arguments the new set of formulas can not only be incorporated into math libraries very easily but also be useful for treatment of radiation and scattering problems involving bessel functions

characteristic basis function method for solving electromagnetic scattering problems over rough terrain profiles a computationally efficient algorithm which combines the characteristic basis function method cbfm the physical optics po approach when applicable with the forward backward method fbm is applied for the investigation of electromagnetic scattering from and propagation over large scale rough terrain problems the algorithm utilizes high level basis functions defined on macro domains blocks called the characteristic basis functions cbfs that are constructed by aggregating low level basis functions i e conventional sub domain basis functions the fbm as well as the po approach when applicable are used to construct the aforementioned cbfs the conventional cbfm is slightly modified to handle large terrain problems and is further embellished by accelerating it as well as reducing its storage requirements via the use of an extrapolation procedure numerical results for the total fields as well as for the path loss are presented and compared with either measured or previously published reference solutions to assess the efficiency and accuracy of the algorithm

the biconjugate gradient method for electromagnetic scattering the biconjugate gradient bcg method for solving linear systems is shown to be more efficient than the conjugate gradient cg method for several examples from electromagnetic scattering a remedy for the occasional stagnation of the algorithm is proposed the potential flaw in the bcg algorithm may be avoided when encountered by restarting the algorithm with a perturbed estimate of the solution

metrics based on finite directed graphs and coding invariants given a finite directed graph with n vertices we define a metric d g on mathbb f q n where mathbb f q is the finite field with q elements the weight of a word is defined as the number of vertices that can be reached by a directed path from a vertex within the support of the vector two canonical forms which do not affect the metric are given to each graph based on these forms we characterize each such metric we further use these forms to prove that two graphs with different canonical forms yield different metrics efficient algorithms to check if a set of metric weights define a metric based on a graph are given we provide tight bounds on the number of metric weights required to reconstruct the metric furthermore we give a complete description of the group of linear isometries of the graph metrics and a characterization of the graphs for which every linear code admits a g canonical decomposition considering those graphs we are able to derive an expression of the packing radius of linear codes in such metric spaces finally given a directed graph which determines a hierarchical poset we present sufficient and necessary conditions to ensure the validity of the macwilliams identity and the macwilliams extension property

on two dimensional bessel functions the general properties of two dimensional generalized bessel functions are discussed various asymptotic approximations are derived and applied to analyse the basic structure of the two dimensional bessel functions as well as their nodal lines

efficient analysis of phased arrays of microstrip patches using a hybrid generalized forward backward method green s function technique with a dft based acceleration algorithm a hybrid method based on the combination of generalized forward backward method gfbm and green s function for the grounded dielectric slab together with the acceleration of the combination via a discrete fourier transform dft based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation scattering from electrically large irregularly contoured two dimensional arrays consisting of finite number of probe fed microstrip patches in this method unknown current coefficients corresponding to a single patch are first solved by a conventional galerkin type hybrid method of moments mom green s function technique that uses the grounded dielectric slab s green s function because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions the patch can have any shape the solution for the array currents is then found through gfbm where it sweeps the current computation element by element the computational complexity of this method which is originally being the total number of unknowns for each iteration is reduced to using a dft based acceleration algorithm making use of the fact that array elements are identical and the array is periodic numerical results in the form of array current distribution are given for various sized arrays of probe fed microstrip patches with elliptical and or circular boundaries and are compared with the conventional mom results to illustrate the efficiency and accuracy of the method

symbolic and numerical computation on bessel functions of complex argument and large magnitude the lanczos t method with perturbations proportional to faber polynomials is employed to approximate the bessel functions of the first kind j v z and the second kind y v z the hankel functions of the first kind h v 1 z and the second kind h v 2 z of integer order v for specific outer regions of the complex plane i e z r for some r the scaled symbolic representation of the faber polynomials and the appropriate automated t method approximation are introduced both symbolic and numerical computation are discussed in addition numerical experiments are employed to test the proposed t method computed accuracy for j 0 z and y 0 z for z 8 are presented the results are compared with those obtained from the truncated chebyshev series approximations and with those of the t method approximations on the inner disk z 8 some concluding remarks and suggestions on future research are given

feedback rate capacity loss tradeoff for limited feedback mimo systems multiple input multiple output mimo communication systems can provide large capacity gains over traditional single input single output siso systems and are expected to be a core technology of next generation wireless systems often these capacity gains are achievable only with some form of adaptive transmission in this paper we study the capacity loss defined as the rate loss in bits s hz of the mimo wireless system when the covariance matrix of the transmitted signal vector is designed using a low rate feedback channel for the mimo channel we find a bound on the ergodic capacity loss when random codebooks generated from the uniform distribution on the complex unit sphere are used to convey the second order statistics of the transmitted signal from the receiver to the transmitter in this case we find a closed form expression for the ergodic capacity loss as a function of the number of bits fed back at each channel realization these results show that the capacity loss decreases at least as o 2 sup b 2mmt 2 where b is the number of feedback bits m sub t is the number of transmit antennas and m min m sub r m sub t where m sub r is the number of receive antennas in the high snr regime we present a new bound on the capacity loss that is tighter than the previously derived bound and show that the capacity loss decreases exponentially as a function of the number of feedback bits

scattering at a rough boundary extensions of the kirchhoff approximation a helmholtz integral formula gives the acoustic field reflected from a rough surface in terms of the values of the acoustic field and of its normal derivative at all points on the surface for surface reflection problems in which one or the other of these surface field values are specified we can make use of this formula to derive a boundary surface integral equation on the unspecified field values further a series solution of this equation can be constructed by iteration the zeroth order term of the series being the result predicted by a kirchhoff approximation the nth order iterate of this series requires an n fold integration over the region of the rough surface an integration that does not in general converge absolutely for unboundedly large surfaces for a pressure release surface we consider the first two iterates in detail and using stationary phase approximations replace the required integration by summations in this way the source of the convergence difficulty is made clear and is demo

monte carlo simulations of large scale problems of random rough surface scattering and applications to grazing incidence with the bmia canonical grid method scattering of a te incident wave from a perfectly conducting one dimensional random rough surface is studied with the banded matrix iterative approach canonical grid bmia cag method the bmia cag is an improvement over the previous bmia the key idea of bmia cag is that outside the near field interaction the rest of the interactions can be translated to a canonical grid by taylor series expansion the use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast fourier transform for nonnear field interaction the method can be used for monte carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface we illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns the method is also applied to study scattering from random rough surfaces at near grazing incidence the numerical examples illustrate the importance of using a large surface length for some backscattering problems

an iterative solution of one dimensional rough surface scattering problems based on a factorization of the helmholtz operator an iterative series solution for two dimensional scattering problems derived from a minimally coupled factorization of the helmholtz equation is presented the helmholtz operator is represented as a product of one way wave operators and a corresponding coupling operator coupling between oppositely propagating fields is shown to be predominantly localized and this permits an accurate and numerically efficient approximation of the coupling operator the resulting iterative series is shown to be rapidly convergent for the problem of scattering from impenetrable rough surfaces

a classification of posets admitting the macwilliams identity in this paper all poset structures that admit the macwilliams identity are classified and the macwilliams identities for poset weight enumerators corresponding to such posets are derived it is proved that being a hierarchical poset is a necessary and sufficient condition for a poset to admit the macwilliams identity an explicit relation is also derived between the p weight distribution of a hierarchical poset code and the p weight distribution of the dual code

variants of bicgstab for matrices with complex spectrum recently van der vorst siam j sci statist comput 13 1992 pp 631 644 proposed for solving nonsymmetric linear systems az b a biconjugate gradient bicg based krylov space method called bicgstab that like the biconjugate gradient squared bicgs method of sonneveld does not require matrix vector multiplications with the transposed matrix a t and that has typically a much smoother convergence behavior than bicg and bicgs its nth residual polynomial is the product of the one of bicg i e the nth lanczos polynomial with a polynomial of the same degree with real zeros therefore nonreal eigenvalues of a are not approximated well by the second polynomial factor here the author presents for real nonsymmetric matrices a method bicgstab2 in which the second factor may have complex conjugate zeros moreover versions suitable for complex matrices are given for both methods

asymptotic capacity of multicarrier transmission with frequency selective fading and limited feedback we study the capacity of multicarrier transmission through a slow frequency selective fading channel with limited feedback which specifies channel state information our results are asymptotic in the number of subchannels we first assume independent and identically distributed i i d subchannel gains and show that for a large class of fading distributions a uniform power distribution over an optimized subset of subchannels or on off power allocation gives the same asymptotic growth in capacity as optimal water filling e g with rayleigh fading furthermore the growth in data rate can be achieved with a feedback rate as if the number of active subchannels is bounded the capacity grows only as with the feedback rate of we then consider correlated subchannels modeled as a markov process and study the savings in feedback assuming a fixed ratio of coherence bandwidth to the total bandwidth the ratio between minimum feedback rates with correlated and i i d subchannels converges to zero with e g as for rayleigh fading subchannels satisfying a first order autoregressive process we also show that adaptive modulation or rate control schemes in which the rate on each subchannel is selected from a quantized set achieves the same asymptotic growth rates in capacity and required feedback finally our results are extended to cellular uplink and downlink channel models

characterization of metrics induced by hierarchical posets in this paper we consider metrics determined by hierarchical posets and give explicit formulas for the main parameters of a linear code the minimum distance and the packing covering and chebyshev radii of a code we also present ten characterizations of hierarchical poset metrics including new characterizations and simple new proofs to the known ones

a note on certain integrals of bessel functions in a book on bessel functions by watson 1980 there appear to be minor errors in one particular integral of bessel functions this integral is given a series expansion which may be useful in certain physical problems the asymptotic nature of this series is very briefly discussed

chebyshev expansions for the bessel function _ in the complex plane polynomial based approximations for jo z and j1 z are presented the first quadrant of the complex plane is divided into six sectors and separate approximations are given for i z i 8 can also be used to evaluate the bessel functions yo z and y z and the hankel functions of the first and second kinds

two analytic frequency dependent current density approximations for te scattering from a conducting strip grating two analytic frequency dependent current density approximations are presented for te mode incidence on a conducting strip grating the current densities are assumed to have both a spatial and a frequency dependence the first is based upon using the classic edge mode approximation the second is derived from applying conformal mapping methods and invoking babinet s theorem the solutions are compared to the moment method solution the resultant reflection coefficients are found to be good approximations at all frequencies for narrow strips and at moderately low frequencies for arbitrary strip widths although the solutions are not as accurate as a moment method solution at all frequencies they are computationally faster and provide analytic expressions that demonstrate the relationship between grating dimensions and performance

polynomial approximations to bessel functions a polynomial approximation to bessel functions that arises from an electromagnetic scattering problem is examined the approximation is extended to bessel functions of any integer order and the relationship to the taylor series is derived numerical calculations show that the polynomial approximation and the taylor series truncated to the same order have similar accuracies

the wright functions as solutions of the time fractional diffusion equation we revisit the cauchy problem for the time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order email protected 0 2 by using the fourier laplace transforms the fundamentals solutions green functions are shown to be high transcendental functions of the wright type that can be interpreted as spatial probability density functions evolving in time with similarity properties we provide a general representation of these functions in terms of mellin barnes integrals useful for numerical computation

the numerical computation of bessel functions of the first and second kind for integer orders and complex arguments a rigorous algorithm for computing integer order bessel functions of the first and second kind with complex arguments is discussed the algorithm makes use of backward recurrence for computing bessel functions of the first kind where applicable and of hankel s asymptotic expansion for large arguments the argument is limited only by the ability of the computer to handle large numbers orders up to a few thousand have been computed to 13 digit accuracy

solution stability of iterative schemes utilizing the discrete fourier transform em scattering the fredholm integral equation of the first kind can be solved numerically using iterative schemes which minimize the integral square error when the kernal is of the convolution type the discrete fourier transform dft can be used when evaluating the operator equation in the iterative schemes however the dft imposes an artificial periodicity thus changing the nature of the problem the effect of this on the solution has been studied and convergence investigated by comparison with a method of moments solution a proposed method of avoiding the periodicity problem has been studied the effect of introducing losses in the medium surrounding the scatterer has been investigated provided losses are low there is little effect on the solution

on iterative approaches for electromagnetic rough surface scattering problems iterative techniques developed for solving general systems of linear equations have been applied to systems resulting from electromagnetic rough surface scattering problems previously used iterative procedures that model the multiple scattering of the electromagnetic energy are shown to be mathematically equivalent to the application of stationary iterative procedures to the system of equations resulting from the standard moment method convergence difficulties that are sometimes observed with these approaches are due to the inherent limitations of the stationary techniques the performances of the stationary approaches are compared with that of several conjugate direction based nonstationary iterative procedures through the application to a series of scattering surfaces that yield rapidly changing conditioning of the moment method interaction matrix the stationary algorithms give the quickest convergence when applied to the systems with the best conditioning but the nonstationary techniques prove much more robust in other more ill conditioned situations

channel adaptive quantization for limited feedback mimo beamforming systems multiple input multiple output mimo wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques in the absence of full channel knowledge at the transmitter the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low rate feedback channel in the literature quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution commonly the uncorrelated rayleigh distribution when the channel is not uncorrelated rayleigh however these quantization strategies result in a degradation of the receive signal to noise ratio snr in this paper switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution the codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel the convergence properties of the codebook selection algorithm are studied assuming a block stationary model for the channel in the case of a nonstationary channel it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in snr simulation results show that in the case of correlated channels the snr performance of the link can be significantly improved by adaptation compared with nonadaptive quantization strategies designed for uncorrelated rayleigh fading channels

analytical expressions for spatial domain green s functions in layered media accurate and efficient formulas for computing spatial domain green s functions are presented in this paper to apply the formulas we only require a set of sample points of the spectral domain green s function sdgf on an integration path avoiding its singularities and an infinite domain tail path since the sampling is carried out for the integrand excluding the bessel function the number of sample points required is much smaller than the numerical integration method this aspect of the proposed method proves to be very advantageous for evaluating closed form green s functions at large source observer distances it is shown that the proposed formulas provide accurate results for both the near and far field regions as well as a wide range of material parameters such as lossless lossy left handed materials as well as multilayered substrates

the method of ordered multiple interactions for closed bodies boundary integral methods for calculating bistatic scatter start with a specified sample grid over the surface that defines the scatterer whereas standard method of moments mom implementations can be applied independent of the mesh structure the method of ordered multiple interactions momi effectively defines a surface trajectory over the sample grid this paper introduces source directed slice sampling whereby a variant of the momi method applied to three dimensional 3d objects becomes a strict forward backward recursion applications of momi to 1d rough surfaces first demonstrated the rapid convergence that can be obtained when the surface sampling follows the projected direction of the incident radiation with a 3d object source directed sampling can be implemented with no projection although the surface must be resampled for each new source direction the first iteration of the momi recursion makes a partial backward correction with strict forward backward sampling the initial forward sweep which we call the forward approximation often provides a good approximation to the source currents the results are demonstrated for the scalar problem but the extension to the vector problem is straightforward

the multiple sweep method of moments msmm analysis of electrically large bodies this paper presents the multiple sweep method of moments msmm analysis of the radiation and scattering from electrically large smooth perfectly conducting bodies the msmm is an o n sup 2 recursive method for solving the large matrix equations which arise in the method of moments mm analysis of electrically large bodies in the msmm the body is split into p sections and the currents on these sections are found in a recursive fashion the first msmm recursion or sweep includes the dominant scattering mechanisms and each subsequent recursion or sweep includes higher order mechanisms thus as the electrical size of the body increases fewer and fewer sweeps are required to accurately compute the current on the body

tapered wave with dominant polarization state for all angles of incidence typical applications of the method of moments mom to rough surface three dimensional 3 d electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave it is shown how such a wave can be constructed as a superposition of plane waves avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence the proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a least squared error property of the wave issues in the application to 3 d scattering from an object over a rough surface are discussed approximate 3 d scalar and vector tapered waves which can be evaluated without resorting to any numerical integrations are derived and important limitations to the accuracy and applicability of these approximations are pointed out

a fast finite difference method for propagation predictions over irregular inhomogeneous terrain propagation of electromagnetic waves over irregular inhomogeneous terrain is solved by a finite difference scheme the method is fast and requires considerably less memory than the integral equation methods the method requires a storage space of order o n and an execution time of order o n sup 2 fields generated by a te sub 2 line source are represented in an integral form in terms of the field over a flat constant impedance plane the incident field and the field scattered by the terrain irregularities and inhomogeneities accurate expressions are provided for the incident field and the green s function whose evaluation is otherwise accomplished by the rather time consuming sommerfeld s integrals measured equation of invariance is used to terminate the computational domain the sparse matrix generated by the method is inverted by the ricatti transform numerical results are presented for the ground wave as well as for the sky wave comparison is made for known geometries to establish the validity and limitations of the method

a new numerical method for rough surface scattering calculations a new approach to solving the magnetic field integral equation mfie for the current induced on a infinite perfectly conducting rough surface is presented by splitting the propagator matrix into contributions from the left and from the right of the point of observation a second kind integral equation can be formed with a new born term and a new kernel following discretization of this new integral equation the unknown currents can be determined more rapidly and with significantly less storage requirements than conventional lu decomposition where the time saving factor is roughly n 3 where n is the number of current samples on the surface and the usual storage requirements associated with matrix inversion are eliminated while the new born term is usually adequate for scattered field calculations the new discretized integral equation can be iterated to amy desired accuracy with no apparent convergence problems results are presented for one dimensional rough surfaces with rms heights exceeding one wavelength and rms slopes exceeding 40 which illustrate the robustness of the new born term

volterra approximation for low grazing angle shadowing on smooth ocean like surfaces a new mathematical and numerical technique has been developed for calculating the electromagnetic current on smooth one dimensional perfectly conducting surfaces for low grazing angles the surfaces can have large vertical displacements compared with the incident wavelength resulting in considerable shadowing the new technique which is based on approximating the usual fredholm integral equation for the surface current by a volterra equation is highly accurate with the boundary conditions typically satisfied with errors of less than 1 for x band 3 cm wavelength at a 5 degree grazing angle

predictive coding of bit loading for time correlated mimo channels with a decision feedback receiver in this paper we consider variable rate transmission over a slowly varying multiple input multiple output mimo channel with a decision feedback receiver the transmission rate is adapted to the channel by dynamically assigning bits to the subchannels of the mimo system predictive quantization is used for the feedback of bit loading to take advantage of the time correlation inherited from the temporally correlated channel due to the use of decision feedback at the receiver the bit loading is related to the cholesky decomposition of the channel gram matrix assuming the channel is modeled by a slowly varying gauss markov process we show that the nested submatrices generated during the process of cholesky decomposition can be updated as time evolves based on the update we derive the optimal predictor of the next bit loading for predictive quantization furthermore we derive the statistics of the prediction error which are then exploited to design the quantizer to achieve a smaller quantization error simulations are given to demonstrate that the proposed predictive quantization gives a good approximation of the desired transmission rate with a low feedback rate

weights which respect support and nn decoding in this work we explore a family of metrics over a finite field mathbb f q which respect the support of vectors we show how these metrics can be obtained from the edge labeled hamming cube and based on this representation we give a description of the group of linear isometries for q 2 next we introduce the concept of conditional sum of metrics and determine what are the conditions that out of two metrics respecting the support give rise to a new such metric finally we introduce the labeled poset block metrics a new family of metrics which respects support of vectors filling a gap existing in the known universe of such metrics for this family we give a full description of the group of linear isometries and determine sufficient conditions to ensure the existence of a macwilliams identity

new frequency dependent edge mode current density approximations for tm scattering from a conducting strip grating two new frequency dependent strip grating current densities are derived for tm mode incidence on a conducting strip grating the current densities are assumed to be the product of a spatial function and a frequency function one spatial function is the traditional frequency independent edge mode current density the other is found by the use of conformal mapping the frequency function is derived by use of the radiation integral and the periodic green s function the new resultant current densities are both exact for small strip widths the conformally mapped solution is also valid for wide strips and is exact in the limit as the strip width equals the grating period although the solutions are not as accurate as the moment method at all frequencies they produce computationally faster solutions and offer further insight into strip grating behavior

forward backward method with spectral acceleration for scattering from layered rough surfaces a fast method of moments is presented to calculate electromagnetic wave scattering from layered one dimensional rough surfaces the formulation is provided for m stratified homogeneous regions separated by m 1 rough surfaces and solved using point matching and pulse basis functions compared to the single surface case the solution of scattering from m 1 surfaces requires significantly more memory and computational time to facilitate the solution the forward backward method with spectral acceleration is applied as an example a dielectric layer on a perfect electric conductor surface is studied the numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation the accuracy efficiency and convergence of the method are then studied for various rough surfaces and layer permittivities

new approximations to j sub 0 and j sub 1 bessel functions new approximate solutions to the 0th and 1st order bessel functions of the first kind are derived the formulations are based upon using a new integral with no previously known solution the new integral in the limiting case is identical to the 0th order bessel function integral it is solved in closed form and the solution is expressed as a simple even order polynomial with integer coefficients the polynomial coefficients are all of integer value the 1st order bessel function approximation can then be found through a simple derivative comparisons are made between the exact solution classic solutions and the new approximation the new approximation proves to be much more accurate than the classic small argument approximation it is also sufficiently accurate to bridge the gap between the classic large and small argument approximations and has potential applications in allowing one to analytically evaluate integrals containing bessel functions

two point quasifractional approximant in physics truncation error the quasifractional approximation method is developed in a systematic manner this method uses simultaneously the power series and at a second point the asymptotic expansion the usual form of the approximants is two or more rational fractions in terms of a suitable variable combined with auxiliary nonfractional functions coincidence in the singularities in the region of interest is pursued equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant an upper bound is obtained for the truncation error for a certain class of functions which contains most of the functions for which this method has been applied so far it is shown that quasifractional approximants can be derived as a mixed german and latin polynomial problem in the context of hermite pade approximation theory

application of multiregion model to em scattering from a dielectric rough surface with or without a target above it an efficient multiregion model is extended by the single integral equation sie method for the first time to calculate electromagnetic em scattering from a dielectric rough surface with or without a perfectly electric conducting target above it in the multiregion model the rough surface is divided into multiple regions depending on their positions along the rough surface and the energy distribution of the incident wave two intermediate regions are chosen as the dominant regions in which the method of moment is adopted if a target is located above the surface the target is also included in the dominant region hence the new model can markedly reduce the number of unknowns compared with full sie analysis mutual couplings between different regions are approximately considered based on magnetic and electric field integral equations from which closed form approximations for currents in other regions are derived

limited feedback beamforming over temporally correlated channels feedback of quantized channel state information csi called limited feedback enables transmit beamforming in multiple input multiple output mimo wireless systems with a small amount of overhead due to its efficiency beamforming with limited feedback has been adopted in several wireless communication standards prior work on limited feedback commonly adopts the block fading channel model where temporal correlation in wireless channels is neglected in this paper we consider temporally correlated channels and design single user transmit beamforming with limited feedback analytical results concerning csi feedback are derived by modeling quantized csi as a first order finite state markov chain these results include the information rate of the csi quantizer output the bit rate a csi feedback channel is required to support and the effect of feedback delay on throughput in particular based on the theory of markov chain convergence rate feedback delay is proved to reduce the throughput gain due to csi feedback at least exponentially furthermore an algorithm is proposed for csi feedback compression in time combining the results in this work leads to a new method for designing limited feedback beamforming as demonstrated by a design example

analytic expressions and bounds for special functions and applications in communication theory this paper is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory these functions are the well known nuttall q function incomplete toronto function rice ie function and incomplete lipschitz hankel integrals capitalizing on the offered results useful identities are additionally derived between the above functions and humbert phi 1 function as well as for specific cases of the kampede feriet function these functions can be considered as useful mathematical tools that can be employed in applications relating to the analytic performance evaluation of modern wireless communication systems such as cognitive radio cooperative and free space optical communications as well as radar diversity and multiantenna systems as an example new closed form expressions are derived for the outage probability over nonlinear generalized fading channels namely alpha eta mu alpha lambda mu and alpha kappa mu as well as for specific cases of the eta mu and lambda mu fading channels furthermore simple expressions are presented for the channel capacity for the truncated channel inversion with fixed rate and corresponding optimum cutoff signal to noise ratio for single antenna and multiantenna communication systems over rician fading channels the accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results

two level tabulated interaction method for electromagnetic scattering from lossy irregular terrain profiles incorporating back scattering an efficient method is proposed for computing electromagnetic wave propagation over lossy terrain profiles using a coupled surface integral equation formulation the proposed method uses a set of basis functions which can produce a linear system with much fewer unknowns than that created using pulse basis functions in addition the matrix entries can be computed very rapidly using precomputed tabulated values the method improves upon the original tabulated interaction method tim by extending it to lossy profiles allowing for back scatter and by introducing increased accuracy for near field interactions the complexity and numerical analysis demonstrates that the proposed method has an extremely low computational complexity and storage requirement moreover the accuracy of the proposed method is demonstrated by comparing the pathloss against numerically precise solutions and measured data

on a novel iterative method to compute polynomial approximations to bessel functions of the first kind and its connection to the solution of fractional diffusion diffusion wave problems we present an iterative method to obtain approximations to bessel functions of the first kind jp x p 1 via the repeated application of an integral operator to an initial seed function f0 x the class of seed functions f0 x leading to sets of increasingly accurate approximations fn x is considerably large and includes any polynomial when the operator is applied once to a polynomial of degree s it yields a polynomial of degree s 2 and so the iteration of this operator generates sets of increasingly better polynomial approximations of increasing degree we focus on the set of polynomial approximations generated from the seed function f0 x 1 this set of polynomials is useful not only for the computation of jp x but also from a physical point of view as it describes the long time decay modes of certain fractional diffusion and diffusion wave problems

a transformation media based approach for efficient monte carlo analysis of scattering from rough surfaces with objects this paper presents a computational model that utilizes transformation based metamaterials to enhance the performance of numerical modeling methods for achieving the statistical characterization of two dimensional electromagnetic scattering from objects on or above one dimensional rough sea surfaces monte carlo simulation of the rough surface scattering problem by means of differential equation based finite methods such as finite element or finite difference methods usually places a heavy burden on computational resources because at each realization of the monte carlo technique a mesh must be generated anew for each surface realization the main purpose of the proposed approach in this paper is to create a single mesh without repeating mesh generation at each step by introducing a transformation medium above the rough surface in the computational domain of the finite methods material parameters of the medium are obtained by the coordinate transformation technique which is based on the form invariance property of maxwell s equations at each realization only the material parameters are modified with respect to the geometry of surface without changing the mesh in this manner a great reduction in cpu time is achieved the proposed technique is analyzed and validated via various finite element simulations

divergent series and memory of the initial condition in the long time solution of some anomalous diffusion problems we consider various anomalous d dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry the motion of particles is described by a fractional diffusion equation their mean square displacement is given by r 2 t 0 1 resulting in normal diffusive motion if 1 and subdiffusive motion otherwise for the subdiffusive case in sufficiently high dimensions divergent series appear when the concentration or survival probabilities are evaluated via the method of separation of variables while the solution for normal diffusion problems is at most divergent as t 0 the emergence of such series in the long time domain is a specific feature of subdiffusion problems we present a method to regularize such series and in some cases validate the procedure by using alternative techniques laplace transform method and numerical simulations in the normal diffusion case we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single the main decay mode in the long time regime in remarkable contrast long time memory of the initial condition is present in the subdiffusive case as the spatial part 1 r describing the long time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem the weight being dependent on the initial condition interestingly 1 r turns out to be independent of the anomalous diffusion exponent

preconditioned iterative solution of scattering from rough surfaces extensions to the functionally identical forward backward fb and method of ordered multiple interactions iterative techniques have been introduced that improve the convergence characteristics with specific scattering geometries these extensions are shown to be mathematically equivalent to applying preconditioners to the discretized integral equation that is iteratively solved the same preconditioners can be used with any iterative solution technique numerical examples show that the generalized minimal residual gmres and bi conjugate gradient stable bicgstab algorithms give similarly rapid convergence when applied to a preconditioned discretized integral equation

spectral acceleration of the generalized forward backward method the generalized forward backward gfb method was introduced as an iterative method of moments solution to compute the electromagnetic scattering from targets on ocean like rough surfaces in this paper an existing spectral acceleration algorithm is adapted to the gfb the spectral acceleration is presented for both polarizations and for perfect electrically conducting pec and non pec surfaces the accelerated scheme reduces the computational scaling cost of the gfb from o n sup 2 to o n per iteration as the length of the sea surface increases linearly with the number of unknowns n the numerical results demonstrate that the spectral acceleration introduces negligible error while greatly improving the efficiency of the gfb method