a general framework for transmission with transceiver distortion and some applications a general theoretical framework is presented for analyzing information transmission over gaussian channels with memoryless transceiver distortion which encompasses various nonlinear distortion models including transmit side clipping receive side analog to digital conversion and others the framework is based on the so called generalized mutual information gmi and the analysis in particular benefits from the setup of gaussian codebook ensemble and nearest neighbor decoding for which it is established that the gmi takes a general form analogous to the channel capacity of undistorted gaussian channels with a reduced effective signal to noise ratio snr that depends on the nominal snr and the distortion model when applied to specific distortion models an array of results of engineering relevance is obtained for channels with transmit side distortion only it is shown that a conventional approach which treats the distorted signal as the sum of the original signal part and a uncorrelated distortion part achieves the gmi for channels with output quantization closed form expressions are obtained for the effective snr and the gmi and related optimization problems are formulated and solved for quantizer design finally super nyquist sampling is analyzed within the general framework and it is shown that sampling beyond the nyquist rate increases the gmi for all snr values for example with binary symmetric output quantization information rates exceeding one bit per channel use are achievable by sampling the output at four times the nyquist rate

magic identities for the conformal four point integrals the minkowski metric case abstract the original magic identities are due to j m drummond j henn v a smirnov and e sokatchev they assert that all n loop box integrals for four scalar massless particles are equal to each other 3 the authors give a proof of the magic identities for the euclidean metric case only and claim that the result is also true in the minkowski metric however the minkowski case is much more subtle and requires specification of the relative positions of cycles of integration to make these identities correct in this article we prove the magic identities in the minkowski metric case and in particular specify the cycles of integration our proof of magic identities relies on previous results from 7 8 where we give a mathematical interpretation of the n loop box integrals in the context of representations of a lie group u 2 2 and quaternionic analysis the main result of 7 8 is a weaker operator version of the magic identities no prior knowledge of physics or feynman diagrams is assumed from the reader we provide a summary of all relevant results from quaternionic analysis to make the article self contained

on improved bounds on the decoding error probability of block codes over interleaved fading channels with applications to turbo like codes we derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved rician fading channels coherently detected and maximum likelihood ml decoded we assume that the fading coefficients during each symbol are statistically independent due to a perfect channel interleaver and that perfect estimates of these fading coefficients are provided to the receiver the improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity and are found by generalizing some previously introduced upper bounds for the binary input additive white gaussian nose awgn channel the advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low density parity check ldpc codes and it is especially pronounced in a portion of the rate region exceeding the cutoff rate our generalization of the duman and salehi bound duman and salehi 1998 duman 1998 which is based on certain variations of gallager s 1965 bounding technique is demonstrated to be the tightest reported upper bound we therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo like codes referring to the optimal ml decoding for certain ensembles of uniformly interleaved turbo codes the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms

performance of precoded ofdm with channel estimation error pair wise error probability pep is analyzed in the presence of channel estimation error cee for group linear constellation precoded orthogonal frequency division multiplexing glcp ofdm it is observed that the cee does not reduce the diversity order but contributes to a loss of coding gain furthermore the proposed optimal power allocation scheme based on the derived pep has performance that converges to the performance with perfect channel state information when the number of subcarriers to the channel length ratio increases

a massive feynman integral and some reduction relations for appell functions new explicit expressions are derived for the one loop two point feynman integral with arbitrary external momentum and masses m12 and m22 in d dimensions the results are given in terms of appell functions manifestly symmetric with respect to the masses mi2 equating our expressions with previously known results in terms of gauss hypergeometric functions yields reduction relations for the involved appell functions that are apparently new mathematical results

linear universal decoding for compound channels over discrete memoryless channels dmc linear decoders maximizing additive metrics afford several nice properties in particular if suitable encoders are employed the use of decoding algorithms with manageable complexities is permitted for a compound dmc decoders that perform well without the channel s knowledge are required in order to achieve capacity several such decoders have been studied in the literature however there is no such known decoder which is linear hence the problem of finding linear decoders achieving capacity for compound dmc is addressed and it is shown that under minor concessions such decoders exist and can be constructed a geometric method based on the very noisy transformation is developed and used to solve this problem

tracking performance of least squares mimo channel estimation algorithm in this paper the tracking performance analysis of the least squares ls multiple input multiple output mimo channel estimation and tracking algorithm is presented mimo channel estimation is a novel application of the ls algorithm that presents near optimum performance by karami and shiva in 2003 and 2006 in this paper the mean square error mse of tracking of the ls mimo channel estimator algorithm is derived as a closed form function of the doppler shift forgetting factor channel rank and the length of training sequences in the analysis all training symbols are considered as randomly generated equal power vectors on the unit circle or in other words phase shift keying psk signaling by evaluating this function some insights into the tracking behavior of the ls mimo channel estimator are achieved then the calculated tracking error is compared with the tracking error derived from monte carlo simulation for quaternary psk based training signals to verify the validation of the presented analysis finally the optimum forgetting factor is derived to minimize the error function and it is shown that the optimum forgetting factor is highly dependent on the training length doppler shift and eb no also it is concluded that in low eb no values the number of transmitter antennas has negligible effect on the optimal value of the forgetting factor

characterization and computation of optimal distributions for channel coding this paper concerns the structure of capacity achieving input distributions for stochastic channel models and a renewed look at their computational aspects the following conclusions are obtained under general assumptions on the channel statistics i the capacity achieving input distribution is binary for low signal to noise ratio snr the proof is obtained on comparing the optimization equations that determine channel capacity with a linear program over the space of probability measures ii simple discrete approximations can nearly reach capacity even in cases where the optimal distribution is known to be absolutely continuous with respect to lebesgue measure iii a new class of algorithms is introduced based on the cutting plane method to iteratively construct discrete distributions along with upper and lower bounds on channel capacity it is shown that the bounds converge to the true channel capacity and that the distributions converge weakly to a capacity achieving distribution

diversity and channel estimation errors we study the relation between a training based detector and a coherent maximum likelihood detector we prove that under quite general conditions the diversity gains associated with these two receivers are equal finally we discuss the relation between our analysis and a related result in the literature

a geometrical angle on feynman integrals a direct link between a one loop n point feynman diagram and a geometrical representation based on the n dimensional simplex is established by relating the feynman parametric representations to the integrals over contents of n 1 dimensional simplices in non euclidean geometry of constant curvature in particular the four point function in four dimensions is proportional to the volume of a three dimensional spherical or hyperbolic tetrahedron which can be calculated by splitting into birectangular ones it is also shown that the known formula of reduction of the n point function in n 1 dimensions corresponds to splitting the related n dimensional simplex into n rectangular ones

capacity and power allocation for fading mimo channels with channel estimation error in this correspondence we investigate the effect of channel estimation error on the capacity of multiple input multiple output mimo fading channels we study lower and upper bounds of mutual information under channel estimation error and show that the two bounds are tight for gaussian inputs assuming gaussian inputs we also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds under perfect feedback for the ergodic capacity the optimal strategy is a modified waterfilling over the spatial antenna and temporal fading domains this strategy is close to optimum under small feedback delays but when the delay is large equal powers should be allocated across spatial dimensions for the outage capacity the optimal scheme is a spatial waterfilling and temporal truncated channel inversion numerical results show that some capacity gain is obtained by spatial power allocation temporal power adaptation on the other hand gives negligible gain in terms of ergodic capacity but greatly enhances outage performance

energy efficiency in the low snr regime under queueing constraints and channel uncertainty energy efficiency of fixed rate transmissions is studied in the presence of queueing constraints and channel uncertainty it is assumed that neither the transmitter nor the receiver has channel side information prior to transmission the channel coefficients are estimated at the receiver via minimum mean square error mmse estimation with the aid of training symbols it is further assumed that the system operates under statistical queueing constraints in the form of limitations on buffer violation probabilities the optimal fraction of power allocated to training is identified spectral efficiency bit energy tradeoff is analyzed in the low power and wideband regimes by employing the effective capacity formulation in particular it is shown that the bit energy increases without bound in the low power regime as the average power vanishes a similar conclusion is reached in the wideband regime if the number of noninteracting subchannels grow without bound with increasing bandwidth on the other hand it is proven that if the number of resolvable independent paths and hence the number of noninteracting subchannels remain bounded as the available bandwidth increases the bit energy diminishes to its minimum value in the wideband regime for this case expressions for the minimum bit energy and wideband slope are derived overall energy costs of channel uncertainty and queueing constraints are identified and the impact of multipath richness and sparsity is determined

general results for massive n point feynman diagrams with different masses general expressions are obtained for scalar one loop massive feynman diagrams with any number of external lines and with arbitrary momenta of these lines with arbitrary values of masses and powers of denominators of internal lines the space time dimension n also being arbitrary special cases are considered when two or more masses are equal to 0 the results are represented in terms of hypergeometric functions

inverse scattering inverse source theory the inverse scattering inverse source problem associated with the inhomogeneous helmholtz wave equation the special case sturm liouville acoustic wave equation and the time independent schrodinger equation is treated to this end the concepts of a reference wave velocity and an associated free reference space green s function spectrum are introduced a modified kirchhoff surface integral containing only the gradient of the real part of this free reference space green s function spectrum and the fields on a measurement surface is formulated yielding an integral equation for the unknown fields and sources in the interior of the closed piecewise smooth surface on which the remotely sensed fields are known a well posed analytic closed form solution of this integral equation for the unknown fields and their laplacians is obtained with the aid of a modified spatial fourier transform in which the reference velocity is continually varied in such a fashion that the ewald sphere shell sweeps to fill

everything you always wanted to know about training guidelines derived using the affine precoding framework and the crb in this paper affine precoding is used to investigate the tradeoffs that exist while using the transmitter resources on training versus information symbols the channel input is a training vector superimposed on a linearly precoded vector of symbols a block fading frequency selective multi input multi output mimo channel is considered to highlight the tradeoffs between training and data symbols the fisher information matrix fim is derived under two circumstances the random parameter vector to be estimated contains 1 only fading channel coefficients and 2 unknown data symbols as well as the channel coefficients while strategy 1 corresponds to the receiver structure in which the channel is estimated initially and the channel measurement is utilized to retrieve the data symbols strategy 2 corresponds to the structure in which channel and symbol estimations are performed jointly the interesting outcome of the study in this paper is that minimizing the channel cramer rao bound crb for strategies 1 and 2 under a total average transmit power constraint leads to different affine precoder design guidelines

a rate splitting approach to fading channels with imperfect channel state information as shown by medard the capacity of fading channels with imperfect channel state information can be lower bounded by assuming a gaussian channel input x with power p and by upper bounding the conditional entropy h x y hat h by the entropy of a gaussian random variable with variance equal to the linear minimum mean square error in estimating x from y hat h we demonstrate that using a rate splitting approach this lower bound can be sharpened by expressing the gaussian input x as the sum of two independent gaussian variables x 1 and x 2 and by applying medard s lower bound first to bound the mutual information between x 1 and y while treating x 2 as noise and by applying it a second time to the mutual information between x 2 and y while assuming x 1 to be known we obtain a capacity lower bound that is strictly larger than medard s lower bound we then generalize this approach to an arbitrary number l of layers where x is expressed as the sum of l independent gaussian random variables of respective variances p ell ell 1 dotsc l summing up to p among all such rate splitting bounds we determine the supremum over power allocations p ell and total number of layers l this supremum is achieved for l rightarrow infty and gives rise to an analytically expressible capacity lower bound for gaussian fading this novel bound is shown to converge to the gaussian input mutual information as the signal to noise ratio snr grows provided that the variance of the channel estimation error h hat h tends to zero as the snr tends to infinity

fading channels how perfect need perfect side information be the analysis of flat fading channels is often performed under the assumption that the additive noise is white and gaussian and that the receiver has precise knowledge of the realization of the fading process these assumptions imply the optimality of gaussian codebooks and of scaled nearest neighbor decoding here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process we quantify the degradation in performance that results from such estimation errors and demonstrate the lack of robustness of this scheme for some situations we suggest the rule of thumb that in order to avoid degradation the estimation error should be negligible compared to the reciprocal of the signal to noise ratio snr

on the capacity and energy efficiency of training based transmissions over fading channels in this paper the capacity and energy efficiency of training based communication schemes employed for transmission over a priori unknown rayleigh block fading channels are studied initially the case in which the product of the estimate error and transmitted signal is assumed to be gaussian noise is considered in this case it is shown that bit energy requirements grow without bound as the signal to noise ratio snr goes to zero and the minimum bit energy is achieved at a nonzero snr value below which one should not operate the effect of the block length on both the minimum bit energy and the snr value at which the minimum is achieved is investigated flash training and transmission schemes are analyzed and shown to improve the energy efficiency in the low snr regime in the second part of this paper the capacity and energy efficiency of training based schemes are investigated when the channel input vector in each coherence block is subject to peak power constraints the capacity achieving input structure is characterized and the magnitude distribution of the optimal input is shown to be discrete with a finite number of mass points the capacity bit energy requirements and optimal resource allocation strategies are obtained through numerical analysis the improvements in energy efficiency when on off keying ook with fixed peak power and vanishing duty cycle is employed are studied

optimal training signals for mimo ofdm channel estimation in the presence of frequency offset and phase noise we develop robust mean square error mse optimal training signal designs for multiple input multiple output orthogonal frequency division multiplexing channel estimation with frequency offset and phase noise pn and present analytical and simulation results for the frequency offset and pn effects on channel estimation the proposed designs are more advantageous for moderate to high values of signal to noise ratio snr residual frequency offset and pn level at snr 10 db the normalized mse reductions of our proposed training signals at normalized frequency offset v 0 1 0 5 are about 9 and 19 db respectively for one transmit antenna and 6 and 11 db for two transmit antennas

a survey of the near field far field inverse scattering inverse source integral equation the kirchhoff direct integration of the scalar wave equation is reviewed and some properties of the kirchhoff surface integral are discussed from the perspective of the inverse scattering inverse source problem a modified kirchhoff surface integral is introduced leading to a fredholm integral equation of the first kind for the unknown sources induced by the incident field inside a volume in terms of the scattered fields on the surface enclosing this volume the properties and physical meaning of this integral equation are discussed a generalization of this integral equation for the vector electromagnetic wave equations is presented

opportunistic orthogonal writing on dirty paper a simple scheme that achieves the capacity and the reliability function of the wideband costa dirty paper channel is proposed the scheme can be interpreted as an opportunistic version of pulse position modulation ppm this interpretation suggests a natural generalization of the scheme which we show to achieve the capacity per unit cost of gel fand pinsker channels with a zero cost input letter

inverse scattering problems a study in terms of the zeros of entire functions the study of the zeros of functions of several complex variables recently reported is applied to scalar scattered wavefields first an analysis of the role of the zeros of the scattering amplitude leads to an interpretation of the nonuniqueness of inverse source and scattering problems secondly the analytic character of the scattered wavefunction outside the scattering volume and its zero description as well as its role for information transmission is discussed

deterministic coding capacity of networks in the low power regime the deterministic coding capacity of a network is the capacity of a network when nodes are restricted to transmitting reliable information that is asymptotically deterministic functions of the source messages this is a generalization of network coding to wireless networks the main contribution of this paper is to develop new outer bounds on the deterministic coding capacity in the low power regime mathrm snr to 0 this is accomplished by developing a technique for finding the limits of single letter bounds for mathrm snr to 0 even when these cannot be evaluated for finite snr it is shown that these outer bounds are tight in a number of cases including the butterfly network of ahlswede et al in a wireless setting

generalized hypergeometric functions and the evaluation of scalar one loop integrals in feynman diagrams abstract present and future high precision tests of the standard model and beyond for the fundamental constituents and interactions in nature are demanding complex perturbative calculations involving multi leg and multi loop feynman diagrams currently large effort is devoted to the search for closed expressions of loop integrals written whenever possible in terms of known often hypergeometric type functions in this work the scalar three point function is re evaluated by means of generalized hypergeometric functions of two variables finally use is made of the connection between such appell functions and dilogarithms coming from a previous investigation to recover well known results

derivatives of horn hypergeometric functions with respect to their parameters the derivatives of eight horn hypergeometric functions four appell f1 f2 f3 and f4 and four degenerate confluent 1 2 1 and 1 with respect to their parameters are studied the first derivatives are expressed systematically as triple infinite summations or alternatively as single summations of two variable kampe de feriet functions taking advantage of previously established expressions for the derivative of the confluent or gaussian hypergeometric functions the generalization to the nth derivative of horn s functions with respect to their parameters is rather straightforward in most cases the results are expressed in terms of n 2 infinite summations following a similar procedure mixed derivatives are also treated an illustration of the usefulness of the derivatives of f1 with respect to the first and third parameters is given with the study of autoionization of atoms occurring as part of a post collisional process their evaluation setting the coulomb charge to zero provides the

new proofs for the two barnes lemmas and an additional lemma mellin barnes mb representations have become a widely used tool for the evaluation of feynman loop integrals appearing in perturbative calculations of quantum field theory some of the mb integrals may be solved analytically in closed form with the help of the two barnes lemmas which have been known in mathematics already for one century the original proofs of these lemmas solve the integrals by taking infinite series of residues and summing these up via hypergeometric functions this paper presents new elegant proofs for the barnes lemmas which only rely on the well known basic identity of mb representations avoiding any series summations they are particularly useful for presenting and proving the barnes lemmas to students of quantum field theory without requiring knowledge on hypergeometric functions the paper also introduces and proves an additional lemma for a mb integral dz involving a phase factor exp i z

some exact results for n point massive feynman integrals by using the mellin barnes representation for massive denominators some exact results for classes of one loop n point massive feynman integrals are obtained for arbitrary values of the line indices the powers of denominators and of the space time dimension a representation for corresponding massless integral is also derived

nearest neighbor decoding for additive non gaussian noise channels we study the performance of a transmission scheme employing random gaussian codebooks and nearest neighbor decoding over a power limited additive non gaussian noise channel we show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white gaussian noise channel with signal and noise power equal to those of the original channel the results are presented for single user channels as well as multiple access channels and are extended to fading channels with side information at the receiver

coded sampling bound how much training is needed for iterative semi blind channel estimation coherent detection is commonly facilitated by means of pilot aided channel estimation while this approach offers a high estimation accuracy the spectral and power efficiencies are reduced due to the pilot overhead in the case that redundancy due to channel coding is not used for the purpose of channel estimation the maximum pilot spacing for which a time varying channel can be reconstructed without distortion is given by the nyquist shannon sampling theorem in this paper it is shown that if channel coding is taken into account for channel estimation in an iterative fashion the maximum spacing can be significantly extended which results in an increased spectral efficiency towards this goal a so called coded sampling bound is derived this semi analytical bound is compared with the nyquist shannon sampling theorem the presented results indicate that the maximum pilot spacing can be arbitrarily large given a suitable channel code and code rate

on the achievable rate of stationary rayleigh flat fading channels with gaussian inputs in this work a discrete time stationary rayleigh flat fading channel with unknown channel state information at transmitter and receiver side is studied the law of the channel is presumed to be known to the receiver for independent identically distributed i i d zero mean proper gaussian input distributions the achievable rate is investigated the main contribution of this paper is the derivation of two new upper bounds on the achievable rate with gaussian input symbols one of these bounds is based on the one step channel prediction error variance but is not restricted to peak power constrained input symbols like known bounds moreover it is shown that gaussian inputs yield the same pre log as the peak power constrained capacity the derived bounds are compared with a known lower bound on the capacity given by deng and haimovich and with bounds on the peak power constrained capacity given by sethuraman et al finally the achievable rate with i i d gaussian input symbols is compared to the achievable rate using a coherent detection in combination with a solely pilot based channel estimation

the intersymbol interference channel lower bounds on capacity and channel precoding loss the discrete time additive gaussian intersymbol interference isi channel with i i d not necessarily gaussian input signals is considered several new and old lower bounds on the capacity are derived in a unified manner by assuming different front end receiver filters in particular the sampled whitened matched filter swmf and the minimum mean squared error decision feedback equalizer mmse dfe filter the features of the bounds are demonstrated and compared in several examples with binary and quaternary input signals it is also shown that the effect of an ideal post cursor or tail cancellation in an information preserving context depends primarily on the front end filter while as is well known ideal post cursor cancellation at the output of the swmf decreases the information the opposite trend is seen when an mmse dfe front filter is considered this observation reflects the basic theoretical obstacles in precoding i e ideal post cursor cancellation in the presence of a pre cursor it is used to assess the inherent loss in terms of information rates as compared to the rates achievable with the hypothetical ideal post cursor cancellation associated with any post cursor cancellation technique such as precoding dfe or other variants when operating in synergy with the mmse dfe front end filter the effect of the front end filter on an ideally interleaved precoded coded modulation system is also addressed

new properties of hypergeometric series derivable from feynman integrals i transformation and reduction formulae a study in the statistical mechanics of phase transitions has involved certain seemingly simple feynman integrals which have yielded surprisingly significant mathematical results the integrals enable the derivation of new transformation summation and reduction formulae for some single and multiple variable hypergeometric series the main result reported in this paper is a transformation formula a special case of which is a summation formula for a symmetric combination of two non terminating clausen s hypergeometric series of unit argument

multiple antenna signaling over fading channels with estimated channel state information performance analysis multiple antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation in this paper we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance we consider a training based multiple antenna system that reserves a portion of time to sound the channel training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver no channel state information csi is assumed at the transmitter we present a new framework to analyze training based multiple antenna systems by introducing an equivalent system model that specifies the channel by the estimated and hence known channel coefficients and an uncorrelated data dependent multiplicative noise we derive the maximum likelihood ml detector and highlight its behavior in the limiting cases of perfect csi and no csi and its relation to several mismatched detectors we deduce new exact expressions and chernoff bounds of the pairwise error probability pep used to assess word error and bit error rate bounds for ml and mismatched detection finally we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes and present numerical results

on the representation of two dimensional scalar wave fields in the complex plane scalar wave fields satisfying the helmholtz equation in two dimensions are represented by means of a complex variable associated with the two dimensional physical plane this characterizes the wave functions as generalizations of analytic functions which allows the existence of a generalized cauchy integral formula constituting the nucleus of well known theorems of optics such as the theorem of helmholtz and kirchhoff and the ewald oseen extinction theorem it also seems useful in the interpretation of inverse diffraction and scattering problems

maximum likelihood receivers for space time coded mimo systems with gaussian estimation errors maximum likelihood ml receivers for space time coded multiple input multiple output mimo systems with gaussian channel estimation errors are proposed two different cases are considered in the first case the conditional probability density function pdf of the channel estimate is assumed gaussian and known in the second case the joint pdf of the channel estimate and the true channel gain is assumed gaussian and known in addition to ml signal detection for space time coded mimo with ml and minimum mean squared error channel estimation ml signal detection without channel estimation is also studied two suboptimal structures are derived the alamouti space time codes are used to examine the performances of the new receivers simulation results show that the new receivers can reduce the gap between the conventional receiver with channel estimation errors and the receiver with perfect channel knowledge at least by half in some cases

bayesian equalization for ldpc channel decoding we describe the channel equalization problem and its prior estimate of the channel state information csi as a joint bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder our approach takes into consideration not only the uncertainty due to the noise in the channel but also the uncertainty in the csi estimate however this solution cannot be computed in linear time because it depends on all the transmitted symbols hence we also put forward an approximation for each symbol s posterior using the expectation propagation algorithm which is optimal from the kullback leibler divergence viewpoint and yields an equalization with a complexity identical to the bcjr algorithm we also use a graphical model representation of the full posterior in which the proposed approximation can be readily understood the proposed posterior estimates are more accurate than those computed using the ml estimate for the csi in order to illustrate this point we measure the error rate at the output of a low density parity check decoder which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates for example for qpsk modulation and a channel with three taps we can expect gains over 0 5 db with same computational complexity as the ml receiver

simple connections between generalized hypergeometric series and dilogarithms connections between generalized hypergeometric series and dilogarithms are investigated some simple relations of an appell s function and dilogarithms are found

gaussian codes and weighted nearest neighbor decoding in fading multiple antenna channels we investigate the fading multiple antenna channel the decoder is assumed to possess imperfect channel fading information a modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information gmi the achievable rate is obtained we show that under certain conditions the achievable rate is equivalent to that of a fading multiple antenna gaussian channel where fading is known to the receiver and is equal to the channel estimation and where noise is due to both the channel noise and the channel estimation error we show that for our communication scheme the minimum mean square error mmse channel estimator is optimal in the sense that it achieves the highest value of gmi and hence the highest communication rate additionally a training based multiple input multiple output mimo scheme in a block fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal to noise ratio snr

variations on the gallager bounds connections and applications there has been renewed interest in deriving tight bounds on the error performance of specific codes and ensembles based on their distance spectrum we discuss many reported upper bounds on the maximum likelihood ml decoding error probability and demonstrate the underlying connections that exist between them in addressing the gallager bounds and their variations we focus on the duman and salehi see ieee trans commun vol 46 p 717 723 1998 variation which originates from the standard gallager bound a large class of efficient bounds or their chernoff versions is demonstrated to be a special case of the generalized second version of the duman and salehi bounds implications and applications of these observations are pointed out including the fully interleaved fading channel resorting to either matched or mismatched decoding the proposed approach can be generalized to geometrically uniform nonbinary codes finite state channels bit interleaved coded modulation systems and it can be also used for the derivation of upper bounds on the conditional decoding error probability

nearest neighbor decoding in mimo block fading channels with imperfect csir this paper studies communication outages in multiple input multiple output mimo block fading channels with imperfect channel state information at the receiver csir using mismatched decoding error exponents we prove the achievability of the generalized outage probability the probability that the generalized mutual information gmi is less than the data rate and show that this probability is the fundamental limit for independent and identically distributed i i d codebooks then using nearest neighbor decoding we study the generalized outage probability in the high signal to noise ratio snr regime for random codes with gaussian and discrete signal constellations in particular we study the snr exponent which is defined as the high snr slope of the error probability curve on a logarithmic logarithmic scale we show that the maximum achievable snr exponent of the imperfect csir case is given by the snr exponent of the perfect csir case times the minimum of one and the channel estimation error diversity random codes with gaussian constellations achieve the optimal snr exponent with finite block length as long as the block length is larger than a threshold on the other hand random codes with discrete constellations achieve the optimal snr exponent with block length growing with the logarithm of the snr the results hold for many fading distributions including rayleigh rician nakagami nakagami and weibull as well as for optical wireless scintillation distributions such as lognormal rice and gamma gamma

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

explicitly symmetrical treatment of three body phase space we derive expressions for three body phase space that are explicitly symmetrical in the masses of the three particles we study geometrical properties of the variables involved in elliptic integrals and demonstrate that it is convenient to use the jacobian zeta function to express the results in four and six dimensions

superimposed training for ofdm a peak to average power ratio analysis orthogonal frequency division multiplexing ofdm transmission with superimposed training is considered in this paper one major disadvantage of ofdm is the significant amplitude fluctuations i e high peak to average power ratios pars high pars require large backoff of the average operating power of a radio frequency rf power amplifier pa in order to linearly amplify the signal thus reducing the dc to rf power conversion efficiency the par of the ofdm signal is examined with superimposed training and its complementary cumulative distribution function ccdf is derived achievable lower and upper bounds on the ccdf are also determined in addition the par change is linked to the effective signal to noise ratio snr and thus the bit error rate ber performance under the fixed dc power constraint simulation results are presented to illustrate the proposed par and power analysis for ofdm with superimposed training

one loop derivation of the wilson polygon mhv amplitude duality we discuss the origin of the wilson polygon mhv amplitude duality at a perturbative level it is shown that the duality for the mhv amplitudes at the one loop level can be proven upon a particular change of variables in feynman parametrization and with the use of the relation between feynman integrals at different space time dimensions some generalization of the duality which implies the insertion of a particular vertex operator at the wilson triangle is found for the 3 point function we discuss the analytical structure of wilson loop diagrams and present the corresponding landau equations the geometrical interpretation of the loop diagram in terms of the hyperbolic geometry is discussed

mismatched decoding revisited general alphabets channels with memory and the wide band limit the mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given possibly suboptimal decoding rule this quantity has been studied extensively for single letter decoding rules over discrete memoryless channels dmcs here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single letter decoding rules we also study the wide band limit and in particular the mismatch capacity per unit cost and the achievable rates on an additive noise spread spectrum system with single letter decoding and binary signaling

capacity bounds via duality with applications to multiple antenna systems on flat fading channels a technique is proposed for the derivation of upper bounds on channel capacity it is based on a dual expression for channel capacity where the maximization of mutual information over distributions on the channel input alphabet is replaced with a minimization of average relative entropy over distributions on the channel output alphabet we also propose a technique for the analysis of the asymptotic capacity of cost constrained channels the technique is based on the observation that under fairly mild conditions capacity achieving input distributions escape to infinity the above techniques are applied to multiple antenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown or only partially known at the receiver it is demonstrated that for high signal to noise ratio snr the capacity of such channels typically grows only double logarithmically in the snr to better understand this phenomenon and the rates at which it occurs we introduce the fading number as the second order term in the high snr asymptotic expansion of capacity and derive estimates on its value for various systems it is suggested that at rates that are significantly higher than the fading number communication becomes extremely power inefficient thus posing a practical limit on practically achievable rates upper and lower bounds on the fading number are also presented for single input single output siso systems the bounds coincide thus yielding a complete characterization of the fading number for general stationary and ergodic fading processes we also demonstrate that for memoryless multiple input single output miso channels the fading number is achievable using beam forming and we derive an expression for the optimal beam direction this direction depends on the fading law and is in general not the direction that maximizes the snr on the induced siso channel using a new closed form expression for the expectation of the logarithm of a noncentral chi square distributed random variable we provide some closed form expressions for the fading number of some systems with gaussian fading including siso systems with circularly symmetric stationary and ergodic gaussian fading the fading number of the latter is determined by the fading mean fading variance and the mean squared error in predicting the present fading from its past it is not directly related to the doppler spread for the rayleigh ricean and multiple antenna rayleigh fading channels we also present firm nonasymptotic upper and lower bounds on channel capacity these bounds are asymptotically tight in the sense that their difference from capacity approaches zero at high snr and their ratio to capacity approaches one at low snr

two loop feynman integrals for ϕ4 theory with long range correlated disorder two loop massive feynman integrals for 4 field theoretical model with long range correlated disorder are considered massive integrals for the vertex function 4 including two or three massless propagators for generic space dimension and for any value of the correlation parameter are evaluated analytically applying mellin barnes method as well as familiar representation for one loop integrals obtained expressions are presented in the form of hypergeometric functions

two dimensional scattered fields a description in terms of the zeros of entire functions a general description of n dimensional fourier transforms is given in terms of their complex zero surfaces the properties of these surfaces are analyzed and then applied to two dimensional scattered electromagnetic fields in the fraunhofer region it is shown that the properties of two dimensional fields differ inherently from those of one dimensional fields and that they lead to a reduced ambiguity for object reconstruction from intensity data a way of estimating this ambiguity is given

on the volume of hyperbolic polyhedra where v1k is the volume vol 2 sj of the apex sjk sj c s to wjk schl ifli proved this formula for spherical simplices in 1936 h kneser gave a second very skilful proof of l see i l l and 4 sect 5 1 for both the spherical and hyperbolic cases up to a change of sign in the latter case but even for a three dimensional non euclidean simplex the integration of this schl li differential is practically impossible in fact the most basic objects in polyhedral geometry are orthoschemes or orthogonal simplices first introduced by schl fli an n orthoscheme r is an n simplex with vertices po pn such that

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

negative dimensional integration revisited feynman diagrams are the best tool we have to study perturbative quantum field theory for this very reason the development of any new technique that allows us to compute feynman integrals is welcome by the middle of the 1980s halliday and ricotta suggested the possibility of using negative dimensional integrals to tackle the problem the aim of this work is to revisit the technique as such and check on its possibilities for this purpose we take a box diagram integral contributing to the photon photon scattering amplitude in quantum electrodynamics using the negative dimensional integration method our approach enables us to quickly reproduce the known results as well as six other solutions as yet unknown in the literature these six new solutions arise quite naturally in the context of negative dimensional integration method revealing a promising technique to handle feynman integrals

quaternionic analysis representation theory and physics we develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group we first review the cauchy fueter and poisson formulas and explain their representation theoretic meaning the requirement of unitarity of representations leads us to the extensions of these formulas in the minkowski space which can be viewed as another real form of quaternions representation theory also suggests a quaternionic version of the cauchy formula for the second order pole remarkably the derivative appearing in the complex case is replaced by the maxwell equations in the quaternionic counterpart we also uncover the connection between quaternionic analysis and various structures in quantum mechanics and quantum field theory such as the spectrum of the hydrogen atom polarization of vacuum one loop feynman integrals we also make some further conjectures the main goal of this and our subsequent paper is to revive quaternionic analysis and to show profound relations between quaternionic analysis representation theory and four dimensional physics

at low snr asymmetric quantizers are better we study the capacity of the discrete time gaussian channel when its output is quantized with a 1 bit quantizer we focus on the low signal to noise ratio snr regime where communication at very low spectral efficiencies takes place in this regime a symmetric threshold quantizer is known to reduce channel capacity by a factor of 2 i e to cause an asymptotic power loss of approximately 2 db here it is shown that this power loss can be avoided by using asymmetric threshold quantizers and asymmetric signaling constellations to avoid this power loss flash signaling input distributions are essential consequently 1 bit output quantization of the gaussian channel reduces spectral efficiency threshold quantizers are not only asymptotically optimal at every fixed snr a threshold quantizer maximizes capacity among all 1 bit output quantizers the picture changes on the rayleigh fading channel in the noncoherent case a 1 bit output quantizer causes an unavoidable low snr asymptotic power loss in the coherent case however this power loss is avoidable provided that we allow the quantizer to depend on the fading level

design and analysis of successive decoding with finite levels for the markov channel this paper proposes a practical successive decoding scheme with finite levels for the finite state markov channels fsmcs where there is no a priori state information at the transmitter or the receiver the design employs either a random interleaver or a deterministic interleaver with an irregular pattern and an optional iterative estimation and decoding procedure within each level the interleaver design criteria may be the achievable rate or the extrinsic information transfer exit chart depending on the receiver type for random interleavers the optimization problem is solved efficiently using a pilot utility function while for deterministic interleavers a good construction is given using empirical rules simulation results demonstrate that the new successive decoding scheme combined with irregular low density parity check ldpc codes can approach the identically and uniformly distributed i u d input capacity on the markov fading channel using only a few levels

one loop n point equivalence among negative dimensional mellin barnes and feynman parametrization approaches to feynman integrals we show that at one loop order negative dimensional mellin barnes mb and feynman parametrization fp approaches to feynman loop integral calculations are equivalent starting with a generating functional for two and then for n point scalar integrals we show how to reobtain mb results using negative dimensional and fp techniques the n point result is valid for different masses arbitrary exponents of propagators and dimension

multidimensional phase space and sunset diagrams we derive expressions for the phase space of a particle of momentum p decaying into n particles that are valid for any number of dimensions these are the imaginary parts of so called sunset diagrams which we also obtain the results are given as a series of hypergeometric functions which terminate for odd dimensions and are also well suited for deriving the threshold behavior

ndim achievements massive arbitrary tensor rank and n loop insertions in feynman integrals one of the main difficulties in studying quantum field theory in the perturbative regime is the calculation of d dimensional feynman integrals in general one introduces the so called feynman parameters and associated with them the cumbersome parametric integrals solving these integrals beyond the one loop level can be a difficult task the negative dimensional integration method ndim is a technique whereby such a problem is dramatically reduced we present the calculation of two loop integrals in three different cases scalar ones with three different masses massless with arbitrary tensor rank with and n insertions of a two loop diagram

the conformal four point integrals magic identities and representations of u 2 2 abstract in 3 5 we found mathematical interpretations of the one loop conformal four point feynman integral as well as the vacuum polarization feynman integral in the context of representations of a lie group u 2 2 and quaternionic analysis then we raised a natural question of finding mathematical interpretation of other feynman diagrams in the same setting in this article we describe this interpretation for all conformal four point integrals using this interpretation we give a representation theoretic proof of an operator version of the magic identities for the conformal four point integrals described by the box diagrams the original magic identities are due to j m drummond j henn v a smirnov and e sokatchev they assert that all n loop box integrals for four scalar massless particles are equal to each other 2 the authors give a proof of the magic identities for the euclidean metric case only and claim that the result is also true for the minkowski metric case however the minkowski case is much more subtle in this article we prove an operator version of the magic identities in the minkowski metric case and in particular specify the relative positions of cycles of integration that make these identities correct no prior knowledge of physics or feynman diagrams is assumed from the reader we provide a summary of all relevant results from quaternionic analysis to make the article self contained

an information theoretic foundation of synchronized detection the constrained capacity of a coherent coded modulation cm digital communication system with data aided channel estimation and a discrete equiprobable symbol alphabet is derived under the assumption that the system operates on a flat fading channel and uses an interleaver to combat the bursty nature of the channel it is shown that linear minimum mean square error channel estimation directly follows from the derivation and links average mutual information to the channel dynamics based on the assumption that known training symbols are transmitted the achievable rate of the system is optimized with respect to the amount of training information needed furthermore the results are compared to the additive white gaussian noise channel and the case when ideal channel state information is available at the receiver

optimal placement of training for frequency selective block fading channels the problem of placing training symbols optimally for orthogonal frequency division multiplexing ofdm and single carrier systems is considered the channel is assumed to be quasi static with a finite impulse response of length l 1 samples under the assumptions that neither the transmitter nor the receiver knows the channel and that the receiver forms a minimum mean square error mmse channel estimate based on training symbols only training is optimized by maximizing a tight lower bound on the ergodic training based independent and identically distributed i i d capacity for ofdm systems it is shown that the lower bound is maximized by placing the known symbols periodically in frequency for single carrier systems under the assumption that the training symbols are placed in clusters of length spl alpha spl ges 2l 1 it is shown that the lower bound is maximized by a family of placement schemes called qpp spl alpha where qpp stands for quasi periodic placement these placement schemes are formed by grouping the known symbols into as many clusters as possible and then placing these clusters periodically in the packet for both ofdm and single carrier systems the optimum energy tradeoff between training and data is also obtained

recursive algorithm for evaluating vertex type feynman integrals an algorithm for evaluating vertex type loop integrals is considered it is based on applying the integration by parts technique as an example a class of massless integrals corresponding to triangle diagrams is considered the presented method can also be applied to loop diagrams with a larger number of external lines as well as to integrals with massive denominators

optimal design and placement of pilot symbols for channel estimation the problem of designing and placing pilot symbols for the estimation of frequency selective random channels is considered the channel is assumed to be a block fading model with finite impulse response fir for both single input single output siso and multiple input multiple output mimo channels under the assumption of independent and identical distributed channel taps the cramer rao bound crb on the mean square error mse of semi blind channel estimators is derived and minimized with respect to pilot symbols and their placement it is shown that the optimal strategy is to place pilot symbols satisfying certain orthogonality condition in such a way that data and pilot symbols with higher power are in the middle of the packet the results also indicate that the optimal pilot placements are independent of channel probability distribution for constant modulus symbols we show that the quasi periodic placement and its generalization in the multiuser case turn out to be optimal we further consider estimating channels with correlated taps and show that the previous placement strategy is also optimal among orthogonal pilot sequences

full rank and rank deficient precoding schemes for single carrier block transmissions in block mode transmission inserting a cyclic prefix cp between two consecutive blocks provides an efficient way of removing interblock interference and simplifies equalization of frequency selective channels at the receiver here we address optimal training design for channel estimation in such systems our investigations focus on affine precoding schemes in designing the precoder least squares channel estimation is constrained to be decoupled from symbol detection which results in orthogonal precoding schemes if the precoding matrix is full rank the data rate or bandwidth has to be traded off to accommodate training we propose a full rank orthogonal single carrier frosc precoding with a low peak to average power ratio then in order to improve bandwidth efficiency we propose a rank deficient orthogonal single carrier drosc precoding scheme symbol recovery is still possible thanks to the finite alphabet property of the data symbols

on the effect of receiver estimation error upon channel mutual information our goal in this paper is to study the effect of the receiver structure upon the achievable data rates we consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output mimo wireless channel to encompass a number of transmission schemes we study this problem utilizing affine precoding which is a unified model of linearly precoded data symbols with superimposed training we focus on bayesian receivers that estimate both the unknown fading coefficients and the data symbols the receiver may adopt either of the following strategies to retrieve the data symbols strategy i the receiver obtains joint bayesian channel and symbol estimates strategy ii the receiver obtains a bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols for both strategies we provide lower bounds on the mutual information between the data symbols and their corresponding estimates and we relate these bounds to the symbol cramer rao bound crb matrices in contrast to strategy ii for strategy i the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error for strategy ii we show that asymptotically as the size of the transmission block grows there is no loss of information after the maximum a posteriori map estimate of gaussian symbols we also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint

an asymptotic expression for the information and capacity of a multidimensional channel with weak input signals an asymptotic expression is derived for the shannon mutual information between the input and output signals for a relatively large class of continuous alphabet memoryless channels in the case of weak input signals when the input space is multidimensional the authors extend a result of ibragimov and khas minskii 1972 from the one dimensional to the n dimensional case the asymptotic expression obtained relates the shannon 1948 mutual information function and the fisher information matrix this expression is used to derive an asymptotic expression for the capacity of continuous alphabet memoryless channels with vector valued weak input signals this asymptotic capacity involves the largest eigenvalue of the fisher information matrix evaluated at the zero input signal

information theoretic proofs of entropy power inequalities while most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information up to now shannon s entropy power inequality epi is an exception existing information theoretic proofs of the epi hinge on representations of differential entropy using either fisher information or minimum mean square error mmse which are derived from de bruijn s identity in this paper we first present an unified view of these proofs showing that they share two essential ingredients 1 a data processing argument applied to a covariance preserving linear transformation 2 an integration over a path of a continuous gaussian perturbation using these ingredients we develop a new and brief proof of the epi through a mutual information inequality which replaces stam and blachman s fisher information inequality fii and an inequality for mmse by guo shamai and verdu used in earlier proofs the result has the advantage of being very simple in that it relies only on the basic properties of mutual information these ideas are then generalized to various extended versions of the epi zamir and feder s generalized epi for linear transformations of the random variables takano and johnson s epi for dependent variables liu and viswanath s covariance constrained epi and costa s concavity inequality for the entropy power

on the sensitivity of a suboptimal precoding scheme for frequency selective block based channels with respect to channel inaccuracies water filling is the precoding scheme that achieves capacity in gaussian parallel or block based channels a suboptimal precoding scheme which has been observed to perform quite close to water filling in some cases of great interest is when all active eigenvectors of the input data covariance matrix receive the same power both techniques require perfect channel knowledge at the transmitter in this work we consider the sensitivity of the suboptimal scheme when a channel estimate is used at the transmitter as if it were the true channel using tools from matrix perturbation theory we derive closed form expressions and bounds relating the channel estimation error covariance matrix with the mean mutual information decrease we thus uncover the factors that determine the behavior of the suboptimal precoding scheme under channel uncertainties simulations are in agreement with our theoretical results