blind identification of mimo fir systems driven by quasistationary sources using second order statistics a frequency domain approach this paper discusses a frequency domain method for blind identification of multiple input multiple output mimo convolutive channels driven by white quasistationary sources the sources can assume arbitrary probability distributions and in some cases they can even be all gaussian distributed we also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored nonstationary signals we demonstrate that by using the second order statistics of the channel outputs under mild conditions on the nonstationarity of sources and under the condition that channel is column wise coprime the impulse response of the mimo channel can be identified up to an inherent scaling and permutation ambiguity we prove that by using the new algorithm under the stated assumptions a uniform permutation across all frequency bins is guaranteed and the inherent frequency dependent scaling ambiguities can be resolved hence no post processing is required as is the case with previous frequency domain algorithms we further present an efficient two step frequency domain algorithm for identifying the channel numerical simulations are presented to demonstrate the performance of the new algorithm

the poisson multiple access channel the poisson multiple access channel mac models many to one optical communication through an optical fiber or in free space for this model we compute the capacity region for the two user case as a function of the allowed peak power focusing on the maximum throughput we generalize our results to the case where the users are subjected to an additional average power constraint and to the many users case we show that contrary to the gaussian mac in the poisson mac the maximum throughput is bounded in the number of users we quantify the loss that is incurred when time division multiple access tdma is employed and show that while in the two user case and in the absence of dark current the penalty is rather mild the penalty can be quite severe in the many users case in the presence of large dark current we introduce a generalized tdma technique that mitigates this loss to a large extent

a comparison of approximate boundary conditions and infinite element methods for exterior helmholtz problems we compare the accuracy of a variety of approximate boundary conditions abcs and two versions of an infinite element method iem for approximating solutions of exterior helmholtz problems the infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not we find that the accuracy of the abcs decreases with increasing frequency and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the iems we show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field

error probability bounds for nuclear detection a collection of static and mobile radiation sensors is tasked with deciding within a fixed time interval whether a moving target carries radioactive material formally this is a problem of detecting weak time inhomogeneous poisson signals target radiation concealed in another poisson signal naturally occurring background radiation each sensor locally processes its observations to form a likelihood ratio which is transmitted once at the end of the decision interval to a fusion center the latter combines the transmitted information to optimally in the neyman pearson sense decide whether the measurements contain a radiation signal or just noise we provide a set of analytically derived upper bounds for the probabilities of false alarm and missed detection which are used to design threshold tests without the need for computationally intensive monte carlo simulations these analytical bounds couple the physical quantities of interest to facilitate planning the motion of the mobile sensors for minimizing the probability of missed detection the network reconfigures itself in response to the target motion to allow more accurate collective decisions within the given time interval the approach is illustrated in numerical simulations and its effectiveness demonstrated in experiments that emulate the statistics of nuclear emissions using a pulsed laser

relationship between the saddlepoint approximation and the modified chernoff bound optical communication a comparison is made of two methods for the computation of the probability that the sum of a gaussian and a nongaussian random variable exceeds a certain threshold value the two methods the saddlepoint approximation sap and the modified chernoff bound are closely related to one another for the computation of error probabilities in digital optical communications where both methods can be applied the modified chernoff bound is found to lie close above the saddlepoint approximation for all cases of practical interest the ratio of signal dependent to additive noise has been established as the parameter dominating the bound tightness since the sap has been reported to be extremely precise this result indicates that the more versatile upper bound can be used with confidence both for performance evaluation and for optimization of optical communication systems

frequency domain blind mimo system identification based on second and higher order statistics we present a novel frequency domain framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs the system frequency response is obtained based on singular value decomposition svd of a matrix constructed based on the power spectrum and slices of polyspectra of the system output by appropriately selecting the polyspectra slices we can create a set of such matrices each of which could independently yield the solution of they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance the freedom to select the polyspectra slices allows us to bypass the frequency dependent permutation ambiguity that is usually associated with frequency domain svd while at the same time allows us compute and cancel the phase ambiguity an asymptotic consistency analysis of the system magnitude response estimate is performed

performance of multiuser detection for optical cdma ii asymptotic analysis for pt i see ibid vol 43 no 11 p 2803 2811 1995 this paper presents characterizations of optimum multiuser detection in intensity modulation direct detection cdma channels based on asymptotic analysis of simple bounds on optimum performance technical difficulties in applying large deviation techniques to the evaluation of asymptotic multiuser efficiencies are rigorously addressed these same difficulties also lead to the derivation of conditions under which the linear multiuser detection achieves known interference hence optimum performance asymptotic analysis of the conventional correlation receiver including derivation of the optimal decision threshold for on off signaling formats is also presented

qr factorization based blind channel identification with second order statistics most eigenstructure based blind channel identification and equalization algorithms with second order statistics need svd or evd of the correlation matrix of the received signal in this paper we address new algorithms based on qr factorization of the received signal directly without calculating the correlation matrix this renders the qr factorization based algorithms more robust against ill conditioned channels i e those channels with almost common zeros among the subchannels first we present a block algorithm that performs the qr factorization of the received data matrix as a whole then a recursive algorithm is developed based on the qr factorization by updating a rank revealing ulv decomposition compared with existing algorithms in the same category our algorithms are computationally more efficient the computation in each recursion of the recursive algorithm is on the order of o m sup 2 if only equalization is required where m is the dimension of the received signal vector our recursive algorithm preserves the fast convergence property of the subspace algorithms thus converging faster than other adaptive algorithms such as the super exponential algorithm with comparable computational complexities moreover our proposed algorithms do not require noise variance estimation numerical simulations demonstrate the good performance of the proposed algorithms

multiaccess quantum channels shared communication channels are subject to multiple access interference transmitter and receiver design techniques that explicitly deal with this interference have been shown to improve substantially the performance of communication systems over radio frequency and other classical channels quantum multiple access communication channels on the other hand have received comparatively little attention in this paper an input output model for multiple access quantum channels relevant to optical communications is proposed the model accounts for multiaccess interference signal attenuation and random noise and can be used in the analysis and design of communication systems using a result from optimization a perturbation method is developed to find the minimum achievable error probability in small interference channels it is shown that the quantum measurement that minimizes the error probability in a no interference channel is robust in the presence of small multiaccess interference the results are illustrated with numerical examples which show that optimal quantum detectors can significantly outperform conventional detectors even for moderate levels of crosstalk

performance analysis of direct detection optical cdma communication systems with avalanche photodiodes direct detection optical code division multiple access cdma communication systems with avalanche photodiode apd photodetectors are investigated a chernoff upper bound modified chernoff upper bound and gaussian approximation on the probability of bit error are presented for general apds and arbitrary

the stability of infinite element schemes for transient wave problems the transformation of conjugated infinite elements from the frequency domain to the time domain is described this procedure yields discrete numerical models for transient acoustics which are local in space and time these can be integrated in time to solve unsteady problems of radiation or scattering in infinite domains provided that the discrete equations themselves are stable with time the conditions under which this is true are investigated in this article a numerical study is presented which shows that the stability of the numerical scheme depends critically upon the form of the inner surface of the infinite element domain solutions for test problems are presented to demonstrate that such criteria also apply when the equations are discretised in time and that stable solutions can be obtained using implicit time integration schemes when simple criteria are correctly applied axisymmetric spherical and spheroidal formulations are considered

subspace based channel shortening for the blind separation of convolutive mixtures a novel subspace based channel shortening procedure is proposed based on the structure of the delayed autocorrelation matrices of the observation process this purely second order approach applies to overdetermined multiple input multiple output mimo channels with independent white sources the channel may be sparse and its length is assumed to be unknown through successive deflations the problem can be transformed into an instantaneous blind source separation bss problem which is simpler to solve using for example independent component analysis ica techniques the algorithm is computationally fast although it requires large input datasets such data can be acquired either through large numbers of sensors or by using increased data sampling rate when not enough data are available the method can still be used for reducing the channel length thus simplifying the problem for subsequent treatment

on line blind multichannel equalization based on mutually referenced filters this paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time varying communication channels in the context of channel diversity we introduce the concept of mutually referenced equalizers mres in which several filters are considered the outputs of which act as training signals for each other a corresponding constrained multidimensional mean square error mse cost function is derived the minimization of which is shown to be a necessary and sufficient condition for equalization the links with a standard linear prediction problem are demonstrated the proposed technique exhibits properties of important practical concern 1 the proposed algorithm is globally convergent 2 simple closed form solutions exist for the mres but the mres also lend themselves readily to adaptive implementation in particular the recursive least squares rls algorithm can be used to offer optimal convergence rate 3 the mre method provides a solution for all equalization delays which results in robustness properties with respect to snr and ill defined channel lengths

performance of cumulant based inverse filters for blind deconvolution chi and wu 1963 proposed a class of inverse filter criteria j sub r m using rth order and rth order cumulants where r is even and m r spl ges 2 for blind deconvolution equalization of a nonminimum phase linear time invariant lti system with only non gaussian measurements the inverse filter criteria j sub r m for r 2 are frequently used such as wiggins 1978 criterion donoho s 1981 criteria and tugnait s 1993 inverse filter criteria for which the identifiability of the lti system is based on infinite signal to noise ratio snr we analyze the performance of the inverse filter criteria j sub 2 m r 2 when the snr is finite the analysis shows that the inverse filter associated with j sub 2 m is related to the minimum mean square error mmse equalizer in a nonlinear manner with some common properties such as perfect phase but not perfect amplitude equalization furthermore the former approaches the latter either for higher snr cumulant order m or for wider system bandwidth moreover as the mmse equalizer does the inverse filter associated with j sub 2 m also performs noise reduction besides equalization some simulation results as well as some calculation results are provided to support the proposed analytic results

the design and performance analysis for several new classes of codes for optical synchronous cdma and for arbitrary medium time hopping synchronous cdma communication systems new families of spread spectrum codes are constructed that are applicable to optical synchronous code division multiple access cdma communications as well as to arbitrary medium time hopping synchronous cdma communications proposed constructions are based on the mappings from integer sequences into binary sequences the authors use the concept of number theoretic quadratic congruences and a subset of reed solomon codes similar to the one utilized in the welch costas frequency hop fh patterns the properties of the codes are as good as or better than the properties of existing codes for synchronous cdma communications both the number of code sequences within a single code family and the number of code families with good properties are significantly increased when compared to the known code designs possible applications are presented to evaluate the performance of the proposed codes a new class of hit arrays called cyclical hit arrays is recalled which give insight into the previously unknown properties of the few classes of number theoretic fh patterns cyclical hit arrays and the proposed mappings are used to determine the exact probability distribution functions of random variables that represent interference between users of a time hopping or optical cdma system expressions for the bit error probability in multi user cdma systems are derived as a function of the number of simultaneous cdma system users the length of signature sequences and the threshold of a matched filter detector the performance results are compared with the results for some previously known codes

solution of 3d laplace and helmholtz equations in exterior domains using hp infinite elements abstract this work is devoted to a convergence study for infinite element discretizations for laplace and helmholtz equations in exterior domains the proposed approximation applies to separable geometries only combining an hp fe discretization on the boundary of the domain with a spectral like representation resulting from the separation of variables in the radial direction the presentation includes a convergence proof for the laplace equation and a stability analysis for the variational formulation of the helmholtz equation in weighted sobolev spaces the theoretical investigations are verified and illustrated with numerical examples for the exterior spherical domain

an iterative method using conditional second order statistics applied to the blind source separation problem this paper is concerned with the problem of blind separation of an instantaneous mixture of sources bss which has been addressed in many ways when power spectral densities of the sources are different methods using second order statistics are sufficient to solve this problem otherwise these methods fail and others higher order statistics etc must be used in this paper we propose an iterative method to process the case of sources with the same power spectral density this method is based on an evaluation of conditional first and second order statistics only restrictions on characteristics of sources are given to reach a solution and proofs of convergence of the algorithm are provided for particular cases of probability density functions robustness of this algorithm with respect to the number of sources is shown through computer simulations a particular case of sources that have a probability density function with unbounded domain of definition is described here the algorithm does not lead directly to a separation state but to an a priori known mixture state finally prospects of links with contrast functions are mentioned with a possible generalization of them based on results obtained with particular sources

a controllable canonical form implementation of time domain impedance boundary conditions for broadband aeroacoustic computation a new method which can be effectively and efficiently applied in the simulations of broadband noise problems is proposed for time domain impedance boundary condition implementations by using the so called controllable canonical form that is well known in linear system usually the impedance boundary condition can be defined in frequency domain as a rational polynomial function with poles in the negative half of the complex plane to guarantee stability otherwise causality might be violated in the corresponding time domain implementation to address this issue various methodologies have been proposed previously that usually lead to complicated polynomials whose numerical implementations are often indirect and intricate the proposed method with a controllable canonical form on the other hand directly transforms the frequency domain transfer function a quotient of rational polynomials to an equivalent state space model which consists of a series of first order ordinary differential equations that can be numerically implemented in a straightforward way the proposed method is demonstrated by using two benchmark problems a two dimensional gaussian pulse propagating in a uniform flow with a lined wall and the test cases from the nasa langley grazing incidence tube experiments good agreements demonstrate the potential of the proposed computational method

a semiclassical analysis of optical code division multiple access a model noncoherent optical asynchronous cdma system is described the error rate for a single user matched filter receiver that is valid for arbitrary photomultipliers and signature sequence sets adheres to the semiclassical model of light and does not depend on approximations for large user groups strong received optical fields or chip synchronism is analyzed the exact minimum probability of error and optimal threshold are compared to those obtained with user synchronism and multiple access interference mai distribution approximations for the special case of unity gain photodetectors and prime sequences it is shown that the approximation of chip synchronism yields a weak upper bound on the exact error rate it is demonstrated that the approximations of perfect optical to electrical conversion and gaussian distributed mai yield a poor approximation to the minimum error rate and an underestimate of the optimal threshold arbitrarily tight bounds are developed on the error rate for unequal energies per bit in the case when the signal energies coincide these bounding expressions are considerably easier to compute than the exact error rate

multiuser detections for optical cdma networks based on expectation maximization algorithm in this paper we introduce new unblind and blind multiuser detectors for an optical code division multiple access system the detectors have two soft and hard stages in the soft stage a soft estimation of the interference is obtained by solving an unconstrained maximum likelihood problem via the iterative expectation maximization em algorithm then the hard stage detects the user information bit by solving a one dimensional boolean constrained problem conditioned on knowing the interference our results reveal that the proposed detectors have very low complexity and are robust against changes in parameters moreover the numerical results illustrate that despite of their simplicities our detectors substantially outperform other well known suboptimum detectors such as multistage and decorrelating detectors

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

multiple access channels with point process observations optimum demodulation the derivation and analysis of optimum multiuser detectors for additive rate and additive light poisson multiple access channels are studied the observed point process models the output of an ideal photodetector illuminated by several synchronous or asynchronous users who modulate coherent light of the same frequency dynamic programming based decision rules for the asynchronous multiple access channel exhibit the same computational complexity as their synchronous counterparts and are shown to be optimum under the criteria of minimum error probability and maximum likelihood sequence detection upper and lower bounds on the minimum uncoded bit error rate achievable with arbitrary signal constellations are obtained in terms of the error probability of binary hypothesis testing problems a particular case of these results namely the single user finite length intersymbol interference problem solves the error rate analysis of optimum direct detection systems for dispersive optical fibers

performance of multiuser detection for optical cdma i error probabilities characterization of optimum multiuser performance in intensity modulation direct detection optical cdma channels is addressed analysis is based on some simple bounds on optimum performance provided by receivers with side information or by a linear decorrelating receiver numerical comparisons of the performance bounds are obtained via application of saddlepoint approximations to the multiuser photocount statistics general analytical relations comparing these approximations to similar asymptotic approximations based on the chernoff bound are also derived the numerical results illustrate the fundamental importance of two of the performance bounds in addition the numerical error probability results verify the relevance of the asymptotically based performance analysis for optical cdma in part ii

blind mimo channel identification from second order statistics using rank deficient channel convolution matrix for multiuser systems several direct blind identification algorithms require that the linear multiple input multiple output mimo system have a full rank convolution matrix this condition requires that the system transfer function be irreducible and column reduced we show that this restrictive identification condition can be relaxed for some direct blind identification methods to accommodate more practical scenarios algorithms such as the outer product decomposition algorithm only require minor length adjustment to its processing window without the column reduced condition this result allows direct blind identification methods to be applicable to mimo without requiring a full rank channel convolution matrix

mapped wave envelope elements for acoustical radiation and scattering wave envelope elements provide an alternative to boundary element methods for the solution of exterior wave problems applications to date have been to axisymmetric geometries and have involved the use of large but finite wave envelope meshes compatibly matched to denser near field meshes of conventional elements in the present paper the wave envelope idea is extended by the inclusion of an element mapping taken directly from infinite element methodology and by modifications to the residual formulation taken in conjunction these two measures permit the outer boundary of the wave envelope region to be moved to infinity while preserving the boundedness of the acoustic mass and stiffness integrals the present formulation is developed initially with reference to a simple one dimensional model and is then applied in two and three dimensions comparisons between computed results and those obtained from analytic solutions where applicable and from boundary element codes demonstrate the effectiveness of the method

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

multichannel adaptive blind deconvolution using the complex cepstrum of higher order cross spectra an adaptive cross spectral blind deconvolution method cross tea for the case in which data are available from several sensors is described unlike ordinary cross spectra higher order cross spectra are separable and this fact is used to identify and deconvolve each system cross tea was tested on four channel qam quadrature amplitude modulation signals and the results are compared to those for tea an autospectral method

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

dispersion and pollution of the fem solution for the helmholtz equation in one two and three dimensions for high wave numbers the helmholtz equation suffers the so called pollution effect this effect is directly related to the dispersion a method to measure the dispersion on any numerical method related to the classical galerkin fem is presented this method does not require to compute the numerical solution of the problem and is extremely fast numerical results on the classical galerkin fem p method is compared to modified methods presented in the literature a study of the influence of the topology triangles is also carried out the efficiency of the different methods is compared the numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well the most effective modified method is the qsfem 1 2 but it is also very complicated in the general setting the residual free bubble 3 4 is effective in one dimension but not in higher dimensions the least square method 1 5 approach lowers the dispersion but relatively little the results for triangular meshes show that the best topology is the criss cross pattern copyright 1999 john wiley sons ltd

monotonicity of likelihood ratio of map correlation detection for ocdma communication in this paper the monotonicity of the likelihood ratio used in the optimal correlation detection is established for optical code division multiple access ocdma the monotonicity property not only guarantees the optimality of the detection it also enables us to calculate the bit error rate bounds for ocdma in the presence of uncertain a priori probabilities

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

analysis of avalanche diode receivers by saddlepoint integration the error probability in a binary fiber optical communication system whose receiver utilizes an avalanche diode detector is calculated by applying the method of numerical saddlepoint integration to laplace inversion integrals for the probabilities of errors of the first and second kinds it is shown how to choose the contours of integration for efficient numerical quadrature the effects of shot noise intersymbol interference and additive gaussian noise are taken into account and the decision level on the receiver output is set to minimize the average probability of error examples show how the method can be used in receiver design to select system parameters such as the output pulsewidth and the sampling time in order to minimize the probability of error

acoustic propagation on irrotational mean flows using transient finite and infinite elements a formulation is presented for the computation of transient wave fields propagating on unbounded irrotational mean flows the numerical scheme is based on an inner mesh of conventional finite elements which is matched to high order multipole infinite elements in the far field the scheme is validated against simple transient test solutions and shown to be effective for large three dimensional problems provided that iterative solvers are used to advance the solution at each time step