adaptive minimum bit error rate equalization for binary signaling we consider the design and adaptation of a linear equalizer with a finite number of coefficients in the context of a classical linear intersymbol interference channel with gaussian noise and a memoryless decision device if the number of equalizer coefficients is sufficient the popular minimum mean squared error mmse linear equalizer closely approximates the optimal linear equalizer that directly minimizes bit error rate ber however when the number of equalizer coefficients is insufficient to approximate the channel inverse the minimum ber equalizer can outperform the mmse equalizer by as much as 16 db in certain cases we propose a simple stochastic adaptive algorithm for realizing the minimum ber equalizer compared to the least mean square algorithm the proposed algorithm can provide a substantial reduction in ber with no increase in complexity

adaptive minimum symbol error rate equalization for quadrature amplitude modulation we propose the adaptive minimum symbol error rate algorithm which is a low complexity technique for adapting the coefficients of a linear equalizer in systems using pulse amplitude or quadrature amplitude modulation the proposed algorithm very nearly minimizes error probability in white gaussian noise and can significantly outperform the minimum mean squared error equalizer by as much as 16 db when the number of equalizer coefficients is small relative to the severity of the intersymbol interference

codes for a long silence we determine the exact exponential asymptotics of the maximum number of n length binary strings any two of which differ in the following strong sense there must be a coordinate in which one of them has a 1 in correspondence with a predetermined position within a long run of zeros in the other string we discuss some generalizations and implications of this result

lie point symmetry and some new soliton like solutions of the konopelchenko dubrovsky equations abstract in this paper the infinite dimensional symmetry groups of the 2 1 dimensional konopelchenko dubrovsky kd equation is found by the classical lie group method the symmetry groups are used to perform symmetry reduction and together with tanh function method we obtain soliton like solutions moreover a characterization of the corresponding lie algebra is given

on the inverse scattering transform of the 2 1 toda equation abstract the method of solution to the 2 1 dimensional toda equation is described in some detail this equation reduces directly to the well know toda lattice in 1 1 dimension and by an appropriate asymptotic reduction to the kadomtsev petviashvili equation in a continuous limit the solution exhibits a number of interesting aspects depending on certain choices of signs of which there are four in the equation for two choices of sign the equation is well posed and linearly stable unstable for the other choices of sign the equation is linearly illposed in these cases we can relate the solution to a boundary value problem and give a formal construction of the solution for one choice of signs in the illposed case an analogue of the sommerfeld radiation condition is developed in order to identify a unique solution in general the method of solution of the toda molecule equation requires an implementation of the dbar technique to cases where the associated eigenfunctions possess both smooth regions of nonholomorphicity and a discontinuity across a curve which in this problem is the unit circle special lump type solutions and solutions depending on suitable arbitrary functions are presented

exact pairwise error probability of space time codes we describe a simple technique for the numerical calculation within any desired degree of accuracy of the pairwise error probability pep of space time codes over fading channels this method applies also to the calculation of e q spl radic spl xi for any nonnegative random variable spl xi whose moment generating function spl phi sub spl xi s e exp s spl xi is known its application to the multiple antenna independent rayleigh fading channel and to the rayleigh block fading channel is discussed and illustrated by two simple examples

computation of the exact bit error rate of coherent m ary psk with gray code bit mapping the problem of calculating the average bit error probability bep of coherent m ary phase shift keying psk over a gaussian channel has been studied previously in the literature a solution to the problem for systems using a binary reflected gray code brgc to map bits to symbols was first presented by p j lee see ibid vol com 34 p 488 91 1986 we show that the results obtained by lee are incorrect for m spl ges 16 we show that the reason for this is an invalid assumption that the bit error rate ber is independent of the transmitted symbols an assumption which has also propagated to textbooks we give a new expression for the ber of m psk systems using the brgc and compare this with lee s results

error rate evaluation of linear equalization and decision feedback equalization with error propagation we propose applying an approximate fourier series to evaluate efficiently the bit error rate ber performance of finite length linear equalization le and decision feedback equalization dfe by extending the fourier series we enable ber calculations for quadrature phase shift keying qpsk transmission on complex channels with in phase and crosstalk intersymbol interference isi the ber calculation is based on determining the residual isi samples and background gaussian noise variance at the equalizer output for static channels or for realizations of quasi static fading channels a simple bound on the series error magnitude in terms of the fourier series parameters ensures the required accuracy and precision improved state transition probability estimates are derived and verified by simulation for an approximate markov model of the dfe error propagation for the case in which residual isi exists even when the previous decisions stored in the feedback filter fbf are correct we demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs our analysis includes symbol spaced and fractionally spaced minimum mean square error mmse le zero forcing zf le and mmse dfe with and without error propagation on static isi channels and multipath channels with quasi static rayleigh fading a comparison between suboptimum and optimum receiver filtering in conjunction with equalization and an assessment of the accuracy of some widely used equalization ber approximations and bounds

jointly minimum ber transmitter and receiver fir mimo filters for binary signal vectors a theory is developed for jointly minimizing the bit error rate ber between the desired and decoded signals with respect to the coefficients of transmitter and receiver finite impulse response fir multiple input multiple output mimo filters the original signal is assumed to be a vector time series with equally likely memoryless bernoulli vector components the channel model constitutes of a known fir mimo transfer function and gaussian additive noise independent of the original signal the channel input signal is assumed to be power constrained based on the formulas obtained an iterative numerical optimization algorithm is proposed when compared with other design methods available in the literature the proposed method yields better results due to the generality of the model considered and the joint optimization of the transmitter receiver pair

log concavity property of the error probability with application to local bounds for wireless communications a clear understanding of the behavior of error probability ep as a function of signal to noise ratio snr and other system parameters is fundamental for assessing the design of digital wireless communication systems we propose an analytical framework based on the log concavity property of the ep which we prove for a wide family of multidimensional modulation formats in the presence of gaussian disturbances and fading based on this property we construct a class of local bounds for the ep that improve known generic bounds in a given region of the snr and are invertible as well as easily tractable for further analysis this concept is motivated by the fact that communication systems often operate with performance in a certain region of interest roi and thus it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all snrs we present a possible application of these local bounds but their relevance is beyond the example made in this paper

multidimensional nonlinear evolution equations and inverse scattering abstract in this paper we will review some recent work done in the field of integrable nonlinear evolution equations and inverse scattering we will concentrate on the basic underlying areas and refer interested readers to suitable references for complete details specifically background material can be found in various texts on this subject e g 1 by ablowitz and segur more recent references will be given as necessary the outline of the paper is as follows 1 1 introductory remarks 2 2 a discussion of two separate but related issues namely a solving certain nonlinear evolutions equations in infinite space and b inverse scattering these are important problems having many physical applications moreover they are related to each other by what we refer to as the inverse scattering transform ist 3 3 at the end of the paper we will make some remarks on the possibility of solving nonlinear evolution equations in high dimensions i e equations with more than two spatial and one time variable by using the ist method as we now understand it

on optimum power allocation for the v blast a unified analytical framework for optimum power allocation in the unordered v blast algorithm and its comparative performance analysis are presented compact closed form approximations for the optimum power allocation are derived based on average total and block error rates the choice of the criterion has little impact on the power allocation and overall the optimum strategy is to allocate more power to lower step transmitters and less to higher ones high snr approximations for optimized average block and total error rates are given the snr gain of optimization is rigorously defined and studied using analytical tools including lower and upper bounds high and low snr approximations the gain is upper bounded by the number of transmit antennas for any modulation format and type of fading channel while the average optimization is less complex than the instantaneous one its performance is almost as good at high snr a measure of robustness of the optimized algorithm is introduced and evaluated the optimized algorithm is shown to be robust to perturbations in individual and total transmit powers based on the algorithm robustness a pre set power allocation is suggested as a low complexity alternative to the other optimization strategies which exhibits only a minor loss in performance over the practical snr range

bounds on the zero error capacity of the input constrained bit shift channel new lower and upper bounds on a maximal achievable rate fur runlength limited codes capable of correcting any combination of bit shift errors i e a zero error capacity of the bit shift channel are presented the lower bound is a generalization of the bound obtained by shamai and zehavi 1991 it is shown that in certain cases the upper and the lower bounds asymptotically coincide

on convexity of error rates in digital communications convexity properties of error rates of a class of decoders including the maximum likelihood min distance one as a special case are studied for arbitrary constellations bit mapping and coding earlier results obtained for the additive white gaussian noise channel are extended to a wide class of noise densities including unimodal and spherically invariant noise under these broad conditions symbol and bit error rates are shown to be convex functions of the signal to noise ratio snr in the high snr regime with an explicitly determined threshold which depends only on the constellation dimensionality and minimum distance thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way it is the decreasing nature of the noise power density around the decision region boundaries that ensures the convexity of symbol error rates in the general case the known high low snr bounds of the convexity concavity regions are tightened and no further improvement is shown to be possible in general the high snr bound fits closely into the channel coding theorem all codes including capacity achieving ones whose decision regions include the hardened noise spheres from the noise sphere hardening argument in the channel coding theorem satisfy this high snr requirement and thus has convex error rates in both snr and noise power we conjecture that all capacity achieving codes have convex error rates convexity properties in signal amplitude and noise power are also investigated some applications of the results are discussed in particular it is shown that fading is convexity preserving and is never good in low dimensions under spherically invariant noise which may also include any linear diversity combining

ber minimized ofdm systems with channel independent precoders we consider the minimization of uncoded bit error rate ber for the orthogonal frequency division multiplexing ofdm system with an orthogonal precoder we analyze the ber performance of precoded ofdm systems with zero forcing and minimum mean squared error mmse receivers in the case of mmse receivers we show that for quadrature phase shift keying qpsk there exists a class of optimal precoders that are channel independent examples of this class include the discrete fourier transform dft matrix and the hadamard matrix when the precoder is the dft matrix the resulting optimal transceiver becomes the single carrier system with cyclic prefix sc cp system we also show that the worst solution corresponds to the conventional ofdm system the conventional ofdm system has the largest ber in the case of zero forcing receivers the design of optimal transceiver depends on the signal to noise ratio snr for higher snr solutions of optimal precoders are the same as those of mmse receivers

a matrix spectral problem in one complex space dimension the inverse spectral method for an n n spectral problem is studied via the delta problem for a one dimensional complex space the complex mkdv equations are explicitly solved as an example

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

normalized adaptive channel equalizer based on minimal symbol error rate existing minimum symbol error rate equalizers were derived based on the symbol error rate objective function due to the complexity of the objective function the derivation is not straightforward in this paper we present a new approach to derive the minimum symbol error rate adaptive equalizers the problem is formulated as minimizing the norm between two subsequent parameter vectors under the constraint of symbol error rate minimization the constrained optimization problem then is solved with the lagrange multiplier method which results in an adaptive algorithm with normalization simulation results show that the proposed algorithm outperforms the existing adaptive minimum symbol error rate equalizer in convergence speed and steady state performance

zero error capacity of binary channels with memory we begin a systematic study of the problem of the zero error capacity of noisy binary channels with memory and solve some of the non trivial cases

a new integrable davey stewartson type equation a new integrable nonlinear partial differential equation pde in 2 1 dimensions is derived starting from the konopelchenko dubrovsky equation we use an asymptotically exact reduction method based on fourier expansion and spatio temporal rescaling and obtain a new integrable davey stewartson type equation in order to demonstrate the integrability of the new equation by the inverse scattering method we apply the reduction technique to the lax pair of the konopelchenko dubrovsky equation and find the corresponding lax pair of the new equation the new equation reduces to the davey stewartson or the nonlinear schrodinger equation by appropriate limits

explicit exact solutions for the 2 1 dimensional konopelchenko dubrovsky equation in this paper we construct new explicit exact solutions for the coupled the 2 1 dimensional konopelchenko dubrovsky equation kd equation by using a improved mapping approach and variable separation method by means of the method new types of variable separation solutions including solitary wave solutions periodic wave solutions and rational function solutions for the kd system are successfully obtained the improved mapping approach and variable separation method can be applied to other higher dimensional coupled nonlinear evolution equations

minimum bit error rate design for space time equalization based multiuser detection a novel minimum bit error rate mber space time equalization ste based multiuser detector mud is proposed for multiple receive antenna assisted space division multiple access systems it is shown that the mber ste aided mud significantly outperforms the standard minimum mean square error design in terms of the achievable bit error rate ber adaptive implementations of the mber ste are considered and both the block data based and sample by sample adaptive mber algorithms are proposed the latter referred to as the least ber lber algorithm is compared with the most popular adaptive algorithm known as the least mean square lms algorithm it is shown that in case of binary phase shift keying the computational complexity of the lber ste is about half of that required by the classic lms ste simulation results demonstrate that the lber algorithm performs consistently better than the classic lm salgorithm both in terms of its convergence speed and steady state ber performance

stochastic unbiased minimum mean error rate algorithm for decision feedback equalizers capitalizing on a well known minimum mean square error mmse property for decision feedback equalization dfe along with the use of stochastic gradient approach we formulate an adaptive minimum error rate mer algorithm for dfe over m ary pam channels to be named as stochastic unbiased minimum mean error rate summer comparisons are made between our algorithm and existing mer algorithms in the literature also by invoking the central limit theorem we present an analytical proof that an unbiased mmse equalizer will approach an mer equalizer when the equalizer length approaches infinity thereby we obtain a lower bound expression for mer

integrable non isospectral flows associated with the kadomtsev petviashvili equations in 2 1 dimensions the symmetries of the kadomtsev petviashvili kp equations in 2 1 dimensions yield two hierarchies of integrable non linear evolution equations nee one is the familiar family of isospectral flows the kp hierarchy the other is non isospectral and its flows have coefficients which depend linearly on x and y the spectral methods used to solve kp can be used to solve all these nee an underlying infinite dimensional lie algebra is used to determine all the lax pairs for both families and it also determines their symplectic structures constants of the motion are constructed for the non isospectral cases

symmetry reductions of the lax pair for the 2 1 dimensional konopelchenko dubrovsky equation based on the symbolic computational system maple the similarity reduction arising from the classical lie point symmetries of the lax pair for the 2 1 dimensional konopelchenko dubrovsky kd equation is carried out we obtain several interesting reductions by analyzing not only the reduced lax pair but also the kd equation reduced under the same symmetry group we find that the reduced lax pairs do not always lead to the reduced kd equation

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

combined partial bar and riemann hilbert inverse methods for integrable non linear evolution equations in 2 1 dimensions the authors give a natural combination of partial bar and riemann hilbert problem inverse methods for an n th order scalar spectral problem which solves a number of integrable non linear evolution equations in two space and one time 2 1 dimensions the theory embraces the two kadomtsev petviashvili equations 1970 and their lump solutions

the inverse problem for ordinary differential operators on the line on etudie le probleme inverse sur la ligne pour l operateur p d n q n 2 d n 2 q 0 d d idx pour tout ordre n 2 et sans hypothese de propriete d auto adjoint

convexity properties in binary detection problems the author investigates the convexity properties of error probability in the detection of binary valued scalar signals corrupted by additive noise it is shown that the error probability of the maximum likelihood receiver is a convex function of the signal power when the noise has a unimodal distribution based on this property the results of the optimal time sharing strategies of transmitters and jammers and of the optimal use of multiple channels are obtained

minimum bayes risk adaptive linear equalizers this paper introduces bayes risk expected loss as a criterion for linear equalization since the probability of error is equal to the bayes risk br for a particular binary loss function this work is a natural generalization of previous works on minimum probability of error pe equalizers adaptive equalization algorithms are developed that minimize the br like the minimum pe equalizers the br algorithms have low computational complexity which is comparable to that of the lms algorithm the advantage of the br criterion is that the loss function can be specified in a manner that accelerates adaptive equalizer convergence relative to the minimum pe adaptive algorithm as illustrated in simulation examples besides introducing a new criterion this paper provides another independent contribution to the field of pe minimizing equalization while most prior works focus on m ary qam type modulations with rectangular decision regions this paper uses upper bounds on the probabilities of certain events to yield tractable mathematics that apply to two dimensional constellations with arbitrarily shaped decision regions the resulting adaptive algorithm use the full information available in the phase of the error signal whereas previous algorithms use a quantized version of this error phase

mber space time decision feedback equalization assisted multiuser detection for multiple antenna aided sdma systems this paper proposes a space time decision feedback equalization st dfe assisted multiuser detection mud scheme for multiple receiver antenna aided space division multiple access systems a minimum bit error rate mber design is invoked for the mud which is shown to be capable of improving the achievable bit error rate performance and enhancing the attainable system capacity over that of the standard minimum mean square error mmse design an adaptive implementation of the mber st dfe assisted mud is proposed using a stochastic gradient based least bit error rate algorithm which is demonstrated to consistently outperform the classical least mean square lms algorithm while achieving a lower computational complexity than the lms algorithm for the binary signalling scheme our simulation results demonstrate that the mber st dfe assisted mud is more robust to channel estimation errors as well as to potential error propagation imposed by decision feedback errors compared to the mmse st dfe assisted mud

adaptive minimum symbol error rate decision feedback equalization for multilevel pulse amplitude modulation the design of decision feedback equalizers dfes is typically based on the minimum mean square error mmse principle as this leads to effective adaptive implementation in the form of the least mean square algorithm it is well known however that in certain situations the mmse solution can be distinctly inferior to the optimal minimum symbol error rate mser solution we consider the mser design for multilevel pulse amplitude modulation block data adaptive implementation of the theoretical mser dfe solution is developed based on the parzen window estimate of a probability density function furthermore a sample by sample adaptive mser algorithm called the least symbol error rate lser is derived for adaptive equalization applications the proposed lser algorithm has a complexity that increases linearly with the equalizer length computer simulation is employed to evaluate the proposed alternative mser design for equalization application with multilevel signaling schemes

a class of integrable davey stewartson type systems a new integrable davey stewartson type class of systems of partial differential equations in 2 1 dimensions is derived from a previously known integrable equation by means of an asymptotically exact nonlinear reduction method based on fourier expansion and spatio temporal rescaling the integrability by the inverse scattering method is explicitly demonstrated because the reduction technique is applied to the lax pair of the starting equation and the corresponding lax pair of the class of systems of equations is found the particular characteristics of the reduction method imply that the new systems are likely to be of applicative relevance

analysis of decision feedback detection for mimo rayleigh fading channels and the optimization of power and rate allocations for an uncoded k transmit n receive antenna coherent narrow band communication system employing a decorrelating decision feedback detector d dfd the exact average over channel realizations joint error probability jep as well as the average per symbol error probabilities seps are derived without making any simplifying assumptions on error propagation it is proved that the diversity orders of the jep and the sep of every symbol is limited by error propagation to n k 1 based on our exact error probability analysis however we suggest an optimization of jep over nonnegative quadrature amplitude modulation qam constellation sizes rates and average powers across transmitters which yield significant improvements over the usual equal power and equal rate assignment in fact the jep of such an optimized design has the much improved diversity order of n which is also the diversity order obtained through the optimum maximum likelihood ml detector moreover it is seen that these simple optimized designs can achieve a significant fraction of the spl epsi outage capacity even without outer codes it is also known but only through simulations that when the symbols are detected in certain channel realization dependent orders it is possible to improve substantially over fixed order detection in the case of the equal rate and equal power assignment we provide an analysis for a recently proposed channel dependent ordering rule and show that it does not provide an improvement of the diversity order of the jep beyond n k 1 another ordering rule that was proposed earlier to maximize the worst case post detection signal to noise ratio snr under the perfect feedback assumption is shown to be optimal under a more compelling criterion that does not involve that simplifying assumption while efficiently computable this ordering rule is seen to perform almost as well as the optimal channel dependent ordering rule that minimizes the conditional jep and hence the jep nevertheless a multiple input multiple output mimo system with an optimized rate and power allocation and a fixed order of detection is not only less complex but also has a significantly lower jep than that of the equal power equal rate system where transmitters are detected in a channel dependent order optimal or otherwise