nd convolutional codes i performance analysis a noncoherent coded system which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection is presented in this two part paper where part i focuses on the performance analysis of the system and part ii deals with the structural properties of the underlying convolutional codes these convolutional codes are referred to as nd convolutional codes it is shown that nd convolutional codes provide a general framework for various noncoherent coding systems including differential systems two models of the carrier phase are examined and the relationships between them is established for the first one the carrier phase remains constant for l channels signals whereas for the second one it unvaries throughout the transmission period the regular structure of nd codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities as well as a simple expression for the generalized cutoff rate the exponential rate of the error probability which is the single parameter governing the error performance at large signal to noise ratios is identified via large deviations techniques this parameter leads to the interesting conclusion that increasing l does not necessarily monotonically improve the error performance of the noncoherent system the same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples these examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes some of which are tabulated in part ii of the paper is required

coherent and differentially coherent detections of orthogonally multiplexed orthogonal phase modulated signals the family of orthogonally multiplexed orthogonal phase modulations omopms is investigated in this paper both coherent and differentially coherent signaling formats are considered and compared with the recently reported orthogonally multiplexed orthogonal amplitude modulated omoam signals when constructed from the same basis set both omopm and omoam signals exhibit the identical power spectral density and thus the similar spectral performance characteristics based on the maximum likelihood principle coherent and differentially coherent detection algorithms are developed tight approximate upper bounds are derived and verified by simulation to evaluate the bit error probability characteristics of the maximum likelihood algorithms it is shown that both coherent and differentially coherent omopm can provide a great choice of power and spectral efficiencies ranging among the efficiencies achieved by the classical modulations based on the orthogonal multiplexing technique

regularity of local minimizers of the interaction energy via obstacle problems the repulsion strength at the origin for repulsive attractive potentials determines the regularity of local minimizers of the interaction energy in this paper we show that if this repulsion is like newtonian or more singular than newtonian but still locally integrable then the local minimizers must be locally bounded densities and even continuous for more singular than newtonian repulsion we prove this and some other regularity results by first showing that the potential function associated to a local minimizer solves an obstacle problem and then by using classical regularity results for such problems

the fractional laplacian operator on bounded domains as a special case of the nonlocal diffusion operator we analyze a nonlocal diffusion operator having as special cases the fractional laplacian and fractional differential operators that arise in several applications in our analysis a nonlocal vector calculus is exploited to define a weak formulation of the nonlocal problem we demonstrate that when sufficient conditions on certain kernel functions hold the solution of the nonlocal equation converges to the solution of the fractional laplacian equation on bounded domains as the nonlocal interactions become infinite we also introduce a continuous galerkin finite element discretization of the nonlocal weak formulation and we derive a priori error estimates through several numerical examples we illustrate the theoretical results and we show that by solving the nonlocal problem it is possible to obtain accurate approximations of the solutions of fractional differential equations circumventing the problem of treating infinite volume constraints

inverse source problems for the helmholtz equation and the windowed fourier transform ii in this work we extend the qualitative reconstruction method for inverse source problems for time harmonic acoustic and electromagnetic waves in free space recently developed in r griesmaier m hanke and t raasch siam j sci comput 34 2012 pp a1544 a1562 to a relevant three dimensional setting the reconstruction algorithm relies on the fact that a windowed fourier transform of the far field pattern of the wave radiated by a compactly supported source approximates an exponential ray transform with a purely imaginary exponent of a mollified version of the source a filtered backprojection scheme for the standard ray transform applied to the absolute values of the windowed fourier transform of the far field pattern is used to recover information on the support of the source we provide the theoretical foundation of the method discuss a numerical implementation of the fully three dimensional algorithm and present a series of numerical examples including an inverse scattering problem to s

quadrature quadrature phase shift keying quadrature quadrature phase shift keying q sup 2 psk is a spectrally efficient modulation scheme which utilizes available signal space dimensions in a more efficient way than two dimensional schemes such as qpsk and msk minimum shift keying it uses two date shaping pulses and two carriers which are pairwise quadrature in phase to create a four dimensional signal space and increases the transmission rate by a factor of two over qpsk and msk however the bit error rate performance depends on the choice of pulse pair with simple sinusoidal and cosinusoidal data pulses the e sub b n sub 0 requirement for p sub b e 10 sup 5 is approximately 1 6 db higher than that of msk without additional constraints q sup 2 psk does not maintain a constant envelope however a simple block coding can provide a constant envelope this coded signal substantially outperforms msk and tfm time frequency multiplexing in bandwidth efficiency like msk q sup 2 psk also has self clocking and self synchronizing ability an optimum class of pulse shapes for use in q sup 2 psk format is presented one suboptimum realization achieves the nyquist rate of 2 b s hz using binary detection

differential detection of quadrature frequency phase modulated signals this paper proposes a pilot symbol assisted psa signaling format that enables the differential detection of the differentially phase encoded quadrature frequency phase modulated ndqfpm signal using n orthogonal frequencies the psa ndqfpm signal is transmitted on a frame by frame structure the channel considered is an additive white gaussian noise channel where the channel phase varies so slowly that it is assumed constant over one frame duration each frame consists of j nqfpm pilot symbols and i data blocks each containing l ndqfpm symbols with the first symbol differentially phase encoded with respect to pilot symbols based on the maximum likelihood sequence estimation principle the maximum likelihood differential detection ml dd algorithm is developed to detect the psa ndqfpm signal on a block by block basis tight upper and asymptotic bounds are derived and verified by simulation to evaluate the bit error performance of the ml dd algorithm both bandwidth and power efficiencies of psa ndqfpm with ml dd are compared to nqfpm with coherent detection constant envelope nqfpm with coherent detection constant envelope ndqfpm also known as nfsk 4dpsk with ml dd and conventional 2dqfpm also known as dq sup 2 psk with ml dd it is analytically shown that psa ndqfpm with ml dd has lower power efficiency than nqfpm with coherent detection and nfsk 4dpsk with ml dd but still can provide noticeably higher power efficiency than dq sup 2 psk with ml dd when a medium frame length is used due to the use of pilot symbols psa ndqfpm with a medium frame length has marginally lower bandwidth efficiency than its coherent counterpart nqfpm but still yields significantly higher bandwidth efficiency than constant envelope nqfpm and nfsk 4dpsk

analysis of regularization methods for the solution of ill posed problems involving discontinuous operators we consider a regularization concept for the solution of ill posed operator equations where the operator is composed of a continuous and a discontinuous operator a particular application is level set regularization where we develop a novel concept of minimizers the proposed level set regularization is capable of handling changing topologies a functional analytic framework explaining the splitting of topologies is given the asymptotic limit of the level set regularization method is an evolution process which is implemented numerically and the quality of the proposed algorithm is demonstrated by solving an inverse source problem

channel coding with quadrature quadrature phase shift keying q sup 2 psk signals channel coding due to trellis modulation has been proved to be useful for bandlimited channels however these modulations mostly designed with n use of 2d signals are primarily aimed at coding gain only it is pointed out that utilization of all available signal dimensions which is limited by the time bandwidth product may improve the bandwidth efficiency and simultaneously bring an additional coding gain trellis coding with a spectrally efficient 4d signal set based on q sup 2 psk is addressed without any expansion of the q sup 2 psk signal set a simple hand designed 16 state trellis code provides a coding gain of 6 02 db with the same number of states in g ungergoeck s 1982 8 psk trellis the gain is 4 1 db in low intersymbol interference situations the bandwidth efficiency of this coded q sup 2 psk is twice that of coded 8 psk if both operate at 2 b s hz and p sub b e 10 sup 5 the coded q sup 2 psk provides a saving of about 4 db over the coded 8 psk some fully connected trellises with an expanded signal due to 2 use of q sup 2 psk signals are also presented two such codes ar rate 7 8 achieve a gain of 5 45 db with only eight states

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

optimal convergence for discrete variational inequalities modelling signorini contact in 2d and 3d without additional assumptions on the unknown contact set the basic h 1 finite element error estimate of order h with only h 2 regularity on the solution has not been yet established for the simplest two dimensional signorini problem approximated by a discrete variational inequality or the equivalent mixed method and linear finite elements to obtain an optimal error bound in this basic case and also when considering more general cases e g the three dimensional problem quadratic finite elements additional assumptions on the exact solution in particular on the unknown contact set see z belhachmi and f ben belgacem math comp 72 2003 pp 83 104 s hueber and b wohlmuth siam j numer anal 43 2005 pp 156 173 b wohlmuth a popp m gee and w wall comput mech 49 2012 pp 735 747 had to be used in this paper we consider finite element approximations of the two dimensional and three dimensional signorini problems with linear and quadratic finite elements in the analysis we remove all the additional assumptions and pr

residual based a posteriori error estimate for hypersingular equation on surfaces the hypersingular integral equation of the first kind equivalently describes screen and neumann problems on an open surface piece the paper establishes a computable upper error bound for its galerkin approximation and so motivates adaptive mesh refining algorithms numerical experiments for triangular elements on a screen provide empirical evidence of the superiority of adapted over uniform mesh refining the numerical realisation requires the evaluation of the hypersingular integral operator at a source point this and other details on the algorithm are included

adaptive fe be coupling for strongly nonlinear transmission problems with coulomb friction we analyze an adaptive finite element boundary element procedure for scalar elastoplastic interface problems involving friction where a nonlinear uniformly monotone operator such as the p laplacian is coupled to the linear laplace equation on the exterior domain the problem is reduced to a boundary domain variational inequality a discretized saddle point formulation of which is then solved using the uzawa algorithm and adaptive mesh refinements based on a gradient recovery scheme the galerkin approximations are shown to converge to the unique solution of the variational problem in a suitable product of l p and l 2 sobolev spaces

an inverse source problem for maxwell s equations in magnetoencephalography consider an inverse source problem for maxwell s equations which arises in determining locations of epileptic foci in the living human brain the human brain is modeled as a heterogeneous medium where the electric permittivity magnetic permeability and conductivity may all be functions a current dipole is used to model the epilepsy the inverse source problem in this context is to determine the current dipole from boundary measurements of the fields in this paper a new computational method is introduced for solving the inverse problem the method is based on a low frequency asymptotic analysis of maxwell s equations our method is constructive and has good convergence properties a crucial step of the method is to construct special test functions uniqueness and stability results for the inverse problem are also established the method and results are expected to find applications particularly in magnetoencephalography

differential detection in quadrature quadrature phase shift keying q sup 2 psk systems a generalized quadrature quadrature phase shift keying q sup 2 psk signaling format is considered for differential encoding and differential detection performance in the presence of additive white gaussian noise awgn is analyzed symbol error rate is found to be approximately twice the symbol error rate in a quaternary dpsk system operating at the same e sub b n sub 0 however the bandwidth efficiency of differential q sup 2 psk is substantially higher than that of quaternary dpsk in differential detection it is quite reasonable to suspect that errors tend to occur in pairs it is shown that when the error is due to awgn the ratio of double error rate to single error rate can be very high and the ratio may approach zero at high signal to noise ratio in an attempt to improve the error rate performance differential detection through maximum likelihood decoding based on multiple or n symbol observations is considered

equilibration techniques for solving contact problems with coulomb friction abstract in this paper we consider residual and equilibrated error indicators for contact problems with coulomb friction the contact problem is handled within the abstract framework of saddle point problems more precisely the non penetration constraint and the friction law is realized as a variationally consistent weak formulation in terms of a localized dual lagrange multiplier space thus from the displacement we can easily compute in a local post process the lagrange multiplier which acts as a neumann condition on the possible contact zone having computed the discrete lagrange multiplier we can apply standard error estimators by replacing the unknown neumann data by its approximation as it is shown in 1 this results in an error estimator for a one sided contact problem without friction here we consider more general situations and discuss two additional contact terms which measure the non conformity of the discrete lagrange multiplier numerical results in two and three dimensions illustrate the flexibility of the approach and show the influence of the material parameters on the adaptive refinement process

space time adaptive finite elements for nonlocal parabolic variational inequalities abstract this article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction both in the domain and on the boundary for a large class of parabolic variational inequalities associated to the fractional laplacian we obtain a priori and a posteriori error estimates and study the resulting space time adaptive mesh refinement procedures particular emphasis is placed on mixed formulations which include the contact forces as a lagrange multiplier corresponding results are presented for elliptic problems our numerical experiments for 2 dimensional model problems confirm the theoretical results they indicate the efficiency of the a posteriori error estimates and illustrate the convergence properties of space time adaptive as well as uniform and graded discretizations

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

hp adaptive ipdg tdg fem for parabolic obstacle problems for a parabolic obstacle problem two equivalent hp fem discretization methods based on interior penalty discontinuous galerkin in space and discontinuous galerkin in time are presented the first approach is based on a variational inequality vi formulation and the second approach on a mixed method in which the non penetration condition is resolved by a lagrange multiplier the discrete lagrange multiplier is a linear combination of biorthogonal basis functions allowing to write the discrete vi constraints as a set of complementarity problems employing a penalized fischer burmeister non linear complementarity function the discrete mixed problem can be solved by a locally q quadratic converging semi smooth newton ssn method the hierarchical a posteriori error estimator for the vi formulation which under the saturation assumption is both efficient and reliable allows hp adaptivity the numerical experiments show improved convergence compared to uniform and h adaptive meshes furthermore an a priori error estimate is given for the vi formulation

time discretization of parabolic problems by the hp version of the discontinuous galerkin finite element method the discontinuous galerkin finite element method dgfem for the time discretization of parabolic problems is analyzed in the context of the hp version of the galerkin method error bounds which are explicit in the time steps as well as in the approximation orders are derived and it is shown that the hp dgfem gives spectral convergence in problems with smooth time dependence in conjunction with geometric time partitions it is proved that the hp dgfem results in exponential rates of convergence for piecewise analytic solutions exhibiting singularities induced by incompatible initial data or piecewise analytic forcing terms for the h version dgfem algebraically graded time partitions are determined that give the optimal algebraic convergence rates a fully discrete hp scheme is discussed exemplarily for the heat equation the use of certain mesh design principles for the spatial discretizations yields exponential rates of convergence in time and space numerical examples confirm the theoretical results

the scattering support we discuss inverse problems for the helmholtz equation at fixed energy specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle we introduce the convex scattering support of a far field a set which will be a subset of the convex hull of the support of any source which can produce it we give several theorems which explain how to compute the convex scattering support and how to relate it to the actual support of a source medium or obstacle 2003 wiley periodicals inc

inverse source problems for maxwell s equations and the windowed fourier transform the inverse source problem for time harmonic maxwell s equations in three dimensional free space is considered given far field observations of a wave radiated by a compactly supported volume current density at a single frequency we generalize a qualitative reconstruction algorithm recently developed in r griesmaier m hanke and t raasch siam j sci comput 34 2012 a1544 a1562 to this three dimensional vector valued setting the method is based on the fact that a windowed fourier transform of the far field data approximates an exponential transverse ray transform with a purely imaginary exponent of a smoothed version of the unknown source applying a filtered backprojection for the standard transverse ray transform to a suitably generalized squared absolute value of the windowed fourier transform of the far field data we recover information on the support of the volume current density we analyze this algorithm discuss its numerical implementation and supplement our theoretical findings

inverse source problems for the helmholtz equation and the windowed fourier transform we consider the inverse source problem for time harmonic acoustic or electromagnetic wave propagation in the two dimensional free space given the radiated far field pattern of the solution to the helmholtz equation for a certain source term we find that the windowed fourier transform of this far field is related to an exponential radon transform with purely imaginary exponent of a smoothed approximation of the source based on this observation we set up a filtered backprojection algorithm to recover information on the unknown source term from a single far field measurement we analyze this algorithm and provide extensive numerical results that illustrate our theoretical findings as one outcome the method is shown to work better the larger the wave number possible extensions of the reconstruction method to limited aperture data and to inverse obstacle scattering problems are briefly sketched

inverse source problem in nonhomogeneous background media the scalar wave inverse source problem isp of determining an unknown radiating source from knowledge of the field it generates outside its region of localization is investigated for the case in which the source is embedded in a nonhomogeneous medium with known index of refraction profile n mathbf r it is shown that the solution to the isp having minimum energy the so called minimum energy source can be obtained via a simple method of constrained optimization this method is applied to the special case when the nonhomogeneous background is spherically symmetric n mathbf r n r and it yields the minimum energy source in terms of a series of spherical harmonics and radial wave functions that are solutions to a sturm liouville problem the special case of a source embedded in a spherical region of constant index is treated in detail and results from computer simulations are presented for this case

uncertainty principles for three dimensional inverse source problems novel uncertainty principles for far fields of time harmonic acoustic or electromagnetic waves radiated by collections of well separated localized sources in two dimensional free space have recently been established in r griesmaier and j sylvester siam j appl math 77 2017 pp 154 180 these uncertainty principles have been utilized to develop stability estimates and reconstruction algorithms for the recovery of the far field radiated by each of the individual sources and the simultaneous restoration of missing data segments in this paper we present generalizations of these uncertainty principles for a relevant three dimensional setting we consider extensions of the reconstruction schemes for far field splitting and data completion including their stability analysis and we discuss the sharpness of our results in the three dimensional case we briefly comment on the numerical implementation of the reconstruction algorithms and include a numerical example

error rate bounds for differential psk differential phase shift keying dpsk and coherent phase shift keying cpsk are two of the techniques widely used in digital communications over channels such as satellite terrestrial radio and voiceband telephone because of the linear nature of the demodulation process in cpsk the error performance of cpsk with various sources of impairments has been exhaustively treated but even with additive gaussian noise only asymptotic approximations are available to determine the detection performance of m ary dpsk m 2 in this note the error performance of nonbinary dpsk in additive gaussian noise channels has been bounded in terms of tabulated functions and various approximations are then derived