interference alignment with asymmetric complex signaling settling the host madsen nosratinia conjecture it has been conjectured by ho madsen and nosratinia that complex gaussian interference channels with constant channel coefficients have only one degree of freedom regardless of the number of users while several examples are known of constant channels that achieve more than 1 degree of freedom these special cases only span a subset of measure zero in other words for almost all channel coefficient values it is not known if more than 1 degree of freedom is achievable in this paper we settle the host madsen nosratinia conjecture in the negative we show that at least 1 2 degrees of freedom are achievable for all values of complex channel coefficients except for a subset of measure zero for the class of linear beamforming and interference alignment schemes considered in this paper it is also shown that 1 2 is the maximum number of degrees of freedom achievable on the complex gaussian 3 user interference channel with constant channel coefficients for almost all values of channel coefficients to establish the achievability of 1 2 degrees of freedom we use the novel idea of asymmetric complex signaling i e the inputs are chosen to be complex but not circularly symmetric it is shown that unlike gaussian point to point multiple access and broadcast channels where circularly symmetric complex gaussian inputs are optimal for interference channels optimal inputs are in general asymmetric with asymmetric complex signaling we also show that the 2 user complex gaussian x channel with constant channel coefficients achieves the outer bound of 4 3 degrees of freedom i e the assumption of time variations frequency selectivity used in prior work to establish the same result is not needed

decomposition of generalized frequency response functions for nonlinear systems using symbolic computation a symbolic manipulation procedure which both computes and automatically decomposes the generalized frequency response functions of nonlinear rational polynomial and integrodifferential equation models into a set of closed form nth order transfer functions is presented the symbolic representation exposes the explicit relationship between the model parameters and the nonlinear transfer functions in the frequency domain and leads to important insights into the characterization of nonlinear systems examples for each model type are included to demonstrate the symbolic transfer function approach

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

nonlinear system identification using gaussian inputs the paper is concerned with the identification of nonlinear systems represented by volterra expansions and driven by stationary zero mean gaussian inputs with arbitrary spectra that are not necessarily white procedures for the computation of the volterra kernels both in the time as well as in the frequency domain are developed based on cross cumulant information the derived kernels are optimal in the mean squared error sense for noncausal systems order recursive procedures based on minimum mean squared error reduction are derived more general input output representations that result when the volterra kernels are expanded in a given orthogonal base are also considered

an investigation into the characteristics of non linear frequency response functions part 1 understanding the higher dimensional frequency spaces the characteristics of generalized frequency response functions gfrfs of non linear systems in higher dimensional space are investigated using a combination of graphical and symbolic decomposition techniques it is shown how a systematic analysis can be achieved for a wide class of non linear systems in the frequency domain using the proposed methods the paper is divided into two parts in part 1 the concepts of input and output frequency subdomains are introduced to give insight into the relationship between one dimensional and multi dimensional frequency spaces the visualization of both magnitude and phase responses of third order generalized frequency response functions is presented for the first time in part 2 symbolic expansion techniques are introduced and new methods are developed to analyse the properties of generalized frequency response functions of non linear systems described by the narmax class of models case studies are included in part 2 to illustrate the application of the new methods

adaptive nonlinear system identification in the short time fourier transform domain in this paper we introduce an adaptive algorithm for nonlinear system identification in the short time fourier transform stft domain the adaptive scheme consists of a parallel combination of a linear component represented by crossband filters between subbands and a quadratic component which is modeled by multiplicative cross terms we adaptively update the model parameters using the least mean square lms algorithm and derive explicit expressions for the transient and steady state mean square error mse in frequency bins for white gaussian inputs we show that estimation of the nonlinear component improves the mse performance only when the power ratio of nonlinear to linear components is relatively high furthermore as the number of crossband filters increases a lower steady state mse may be obtained at the expense of slower convergence experimental results support the theoretical derivations

a digital method of modeling two input quadratic systems with general random inputs a digital method of estimating linear and quadratic transfer functions of a two input multiple output quadratically nonlinear system with general i e non gaussian as well as gaussian random inputs is described the approach is based on a frequency domain second order volterra functional series representation for a two input multiple output system practical applications where it is important to have the capability to model dual input nonlinear systems include ground vibration tests of aircraft where two random exciting forces are applied in order to inject sufficient energy into all modes of the system and experimental studies of transition to turbulence in fluids and plasmas where the two inputs consist of two different velocity components and plasma density and potential fluctuations respectively the approach described is being utilized to investigate such applications

hyperbolic parabolic singular perturbation for nondegenerate kirchhoff equations with critical weak dissipation we consider the hyperbolic parabolic singular perturbation problem for a nondegenerate quasilinear equation of kirchhoff type with weak dissipation this means that the dissipative term is multiplied by a coefficient b t which tends to 0 as t the case where b t 1 t p with p 1 but they remain true in the critical case p 1

quadratic system identification using higher order spectra of i i d signals the properties of higher order moment sequences and higher order spectral moments of an i i d independent identically distributed process up to fourth order are discussed these properties are utilized to develop algorithms to identify time invariant nonlinear systems which can be represented by second order volterra series and which are subjected to an i i d input a relatively simple solution for estimating the linear and quadratic transfer functions which requires neither the calculation of the higher order spectral moments of the input for various frequencies nor the calculation of the inverse of matrix is shown to exist even though the second order volterra series is not an orthogonal model for an i i d input unless the input is a white gaussian process

modeling and identification of nonlinear systems in the short time fourier transform domain in this paper we introduce a novel approach for improved nonlinear system identification in the short time fourier transform stft domain we first derive explicit representations of discrete time volterra filters in the stft domain based on these representations approximate nonlinear stft models which consist of parallel combinations of linear and nonlinear components are developed the linear components are represented by cross band filters between subbands while the nonlinear components are modeled by multiplicative cross terms we consider the identification of quadratically nonlinear systems and show that a significant reduction in computational cost as well as substantial improvement in estimation accuracy can be achieved over a time domain volterra model particularly when long memory systems are considered experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach

hyperbolic parabolic singular perturbation for quasilinear equations of kirchhoff type abstract we consider a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtain parameter dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of kirchhoff type and the corresponding quasilinear parabolic equation for this purpose we show time decay estimates for hyperbolic parabolic singular perturbation problem for linear equations with a time dependent coefficient

mixed order response function estimation from multi input non linear systems abstract in this work a novel formalism to estimate the vector linear and leading non linear impulse response functions from the experimental data observed from a multi input system allowing for correlation between the inputs is presented time series statistical moments are estimated from the data and used as the basis of a set of simultaneous equations in the unknown response functions these simultaneous equations are solved using standard matrix methods for the unknown response functions the response functions of a system provide a unique description of the physical process under investigation unlike many of the other time series methods available the ability of the technique to correctly estimate the response functions of a multi input non linear system to a high degree of accuracy is demonstrated using a numerical example where the properties of the system are known and there is strong correlation between the input data this novel technique is then used to estimate from the time series the first linear and second order response functions of the coupled convective and radiative processes that act at the internal surface of the ceiling of a building the estimated first and second order response functions all show discernible structure the area volume under the estimated response functions of each process are respectively the first and second order gains or heat transfer coefficients for that process the response functions of each process estimated were employed to predict the surface heat flux in an out of sample section given the convective and radiative driving forces which was compared with the measured heat flux and showed an excellent agreement

necessary condition on the dissipative term for the asymptotically free property of dissipative kirchhoff equations abstract it is known that the solutions of linear abstract dissipative wave equation with integrable coefficient of the dissipation term are asymptotically free namely the solutions have the same asymptotic behavior as that of the solutions of an abstract free wave equation in this paper we conclude that the integrability is not enough for asymptotic free property of kirchhoff equation by showing the following for the existence of a non trivial asymptotically free solution of abstract kirchhoff equation with initial data in some class an essentially stronger decay condition on the coefficient of dissipation term is necessary

identification of a class of nonlinear systems under stationary non gaussian excitation this paper provides new solutions to the nonlinear system identification problem when the input to the system is a stationary non gaussian process we propose the use of a model called the hammerstein series which leads to significant reductions in both the computational requirements and the mathematical tractability of the nonlinear system identification problem we show that unlike the volterra series one can obtain closed form expressions for the hammerstein series kernels and the quadratic coherence function in the non gaussian case estimation of the kernels and quadratic coherence function is discussed a comparison with a nonlinear system identification approach that uses the volterra series is provided an automotive engineering application illustrates the usefulness of the proposed method

blind equalization and identification of nonlinear and iir systems a least squares approach a deterministic approach to blind nonlinear channel equalization and identification is presented this approach applies to nonlinear channels that can be approximately linearized by either finite memory finite order volterra filters or by a finite number of finite memory nonpolynomial nonlinearities both the nonlinear equalizers and the linearized channels are identified this method also applies to blind identification of linear iir channels general conditions for existence and uniqueness are discussed and numerical examples are given

frequency response functions for nonlinear rational models a recursive algorithm which maps a general class of nonlinear rational model defined as the ratio of two polynomial functions into the frequency domain is derived using the harmonic expansion method the new algorithm provides for the first time a direct analytic map from the time domain rational model parameters to the higher order frequency response functions complex nonlinear time domain behaviours can be analysed and interpreted in the frequency domain and simulated examples are included to illustrate the concepts involved

a digital method of modeling quadratically nonlinear systems with a general random input without assuming particular statistics of the input a practical digital method of estimating linear and quadratic transfer functions of a nonlinear time invariant system that can be described by volterra series of up to second order is presented the method is tested and validated by analyzing input output data of a known quadratically nonlinear system it is used when there is little knowledge about the input statistics or the input is non gaussian it is also noted that the ordinary coherence functions cannot be used in explaining the input output power transfer relationship of a quadratic system excited by a non gaussian input signal with respect to the practical application of the method the relationship between the mean square errors involved in the transfer function estimates and the number of averages taken from the spectral estimation is qualitatively discussed

hybrid polynomial filters for gaussian and non gaussian noise environments traditional polynomial filtering theory based on linear combinations of polynomial terms is able to approximate important classes of nonlinear systems the linear combination of polynomial terms however yields poor performance in environments characterized by gaussian and heavy tailed distributions weighted median and weighted myriad filters in contrast are well known for their outlier suppression and detail preservation properties it is shown here that the weighted median and weighted myriad methodologies are naturally extended to the polynomial sample case yielding hybrid filter structures that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers for both gaussian and heavy tailed distributions environments moreover the introduced hybrid polynomial filter classes are well motivated by analysis of cross and square term statistics of gaussian and heavy tailed distributions a presented asymptotic tail mass analysis shows that polynomial terms both under gaussian and heavy tailed noise statistics have heavier tails than the observed samples indicating that robust combination methods should be utilized to avoid undue influence of outliers further analysis shows weighted median processing of polynomial terms for the gaussian noise case and weighted median and weighted myriad processing of cross and square terms respectively for the heavy tailed noise case are justified from a maximum likelihood perspective filters parameter optimization procedures are also presented finally the effectiveness of hybrid filters is demonstrated through simulations that include temporal spectrum and bispectrum analysis

mildly degenerate kirchhoff equations with weak dissipation global existence and time decay abstract we consider the hyperbolic parabolic singular perturbation problem for a degenerate quasilinear kirchhoff equation with weak dissipation this means that the coefficient of the dissipative term tends to zero when t we prove that the hyperbolic problem has a unique global solution for suitable values of the parameters we also prove that the solution decays to zero as t with the same rate of the solution of the limit problem of parabolic type

system utility maximization with interference processing for cognitive radio networks in spectrum underlay cognitive radio networks secondary users sus are allowed to reuse the spectrum allocated to a primary system the interference between sus actually carries information and can potentially be exploited to improve the network performance through information theoretic interference processing in this paper we design an optimal joint power and rate control algorithm that maximizes the secondary system utility subject to the interference temperature constraints of primary users based on the capacity approaching interference processing scheme called as the han kobayashi scheme the optimal solution is difficult to achieve because the optimization problem is in general non convex to make the optimization problem tractable this paper first transforms the problem into a monotonic optimization problem through exploiting its hidden monotonicity we then devise an effective algorithm to obtain the global optimal solution to the joint power and rate control problem in the han kobayashi scheme the key idea behind the proposed algorithm is to construct a sequence of shrinking polyblocks that approximate the upper boundary of the feasible region with increasing precision numerical results further show that the achieved utility of our scheme significantly outperforms the utility of conventional schemes which treat the interference between sus as the noise

application of higher order spectral analysis to cubically nonlinear system identification in this study digital higher order spectral analysis and frequency domain volterra system models are utilized to yield a practical methodology for the identification of weakly nonlinear time invariant systems up to third order the primary focus is on consideration of random excitation of nonlinear systems and thus the approach makes extensive use of higher order spectral analysis to determine the frequency domain volterra kernels which correspond to linear quadratic and cubic transfer functions although the volterra model is nonlinear in terms of its input it is linear in terms of its unknown transfer functions thus a least squares approach is used to determine the optimal in a least squares sense set of linear quadratic and cubic transfer functions of particular practical note is the fact that the approach of this paper is valid for non gaussian as well as gaussian random excitation it may also be utilized for multitone inputs the complexity of the problem addressed in this paper arises from two principal causes 1 the necessity to work in a 3d frequency space to describe cubically nonlinear systems and 2 the necessity to characterize the non gaussian random excitation by computing higher order spectral moments up to sixth order a detailed description of the approach used to determine the nonlinear transfer functions including considerations necessary for digital implementation is presented

an attractor for the singularly perturbed kirchhoff equation with supercritical nonlinearity abstract we consider a quasilinear wave equation of kirchhoff type u t t 1 u 2 u u t f u g x where 0 is a small parameter without any growth restrictions on the nonlinearity f u we prove the existence of a finite dimensional global attractor on an appropriate bounded phase space the key step is the estimate of the difference between the solutions of a quasilinear dissipative hyperbolic equation of kirchhoff type and the corresponding quasilinear parabolic equation

capacity bounds for the gaussian interference channel the capacity region of the two user gaussian interference channel ic is studied three classes of channels are considered weak one sided and mixed gaussian ics for the weak gaussian ic a new outer bound on the capacity region is obtained that outperforms previously known outer bounds the sum capacity for a certain range of channel parameters is derived for this range it is proved that using gaussian codebooks and treating interference as noise are optimal it is shown that when gaussian codebooks are used the full han kobayashi achievable rate region can be obtained by using the naive han kobayashi achievable scheme over three frequency bands equivalently three subspaces for the one sided gaussian ic an alternative proof for the sato s outer bound is presented we derive the full han kobayashi achievable rate region when gaussian codebooks are utilized for the mixed gaussian ic a new outer bound is obtained that outperforms previously known outer bounds for this case the sum capacity for the entire range of channel parameters is derived it is proved that the full han kobayashi achievable rate region using gaussian codebooks is equivalent to that of the one sided gaussian ic for a particular range of channel parameters

on the corner points of the capacity region of a two user gaussian interference channel this paper considers the corner points of the capacity region of a two user gaussian interference channel gic in a two user gic the rate pairs where one user transmits its data at the single user capacity without interference and the other at the largest rate for which reliable communication is still possible are called corner points this paper relies on existing outer bounds on the capacity region of a two user gic that are used to derive informative bounds on the corner points of the capacity region the new bounds refer to a weak two user gic i e when both crosslink gains in standard form are positive and below 1 and a refinement of these bounds is obtained for the case where the transmission rate of one user is within varepsilon 0 of the single user capacity the bounds on the corner points are asymptotically tight as the transmitted powers tend to infinity and they are also useful for the case of moderate snr and inr upper and lower bounds on the gap denoted by delta between the sum rate and the maximal achievable total rate at the two corner points are derived this is followed by an asymptotic analysis analogous to the study of the generalized degrees of freedom where the snr and inr scalings are coupled such that log text inr log text snr alpha geq 0 leading to an asymptotic characterization of this gap which is exact for the whole range of alpha the upper and lower bounds on delta are asymptotically tight in the sense that they achieve the exact asymptotic characterization improved bounds on delta are derived for finite snr and inr and their improved tightness is exemplified numerically

on measuring the system coherency of quadratically nonlinear systems results on modeling quadratic systems described by volterra series up to order two are presented specifically expressions for the linear and quadratic transfer functions and the system coherency are derived it is shown that all the three quantities can be independently computed in the discrete frequency domain in terms of various spectral moments

hyperbolic parabolic singular perturbation for mildly degenerate kirchhoff equations time decay estimates we consider degenerate kirchhoff equations with a small parameter e in front of the second order time derivative it is well known that these equations admit global solutions when e is small enough and that these solutions decay as t with the same rate of solutions of the limit problem of parabolic type in this paper we prove decay error estimates for the difference between a solution of the hyperbolic problem and the solution of the corresponding parabolic problem these estimates show in the same time that the difference tends to zero both as e 0 and as t concerning the decay rates it turns out that the difference decays faster than the two terms separately as t proofs involve a nonlinear step where we separate fourier components with respect to the lowest frequency followed by a linear step where we exploit weighted versions of classical energies

volterra series representation of time frequency distributions this paper addresses a volterra series representation of bilinear or quadratic time frequency distributions that belong to cohen s class whereby the analogy of the bilinear class with a second order double volterra series is utilized in addition a different viewpoint for the bilinear kernel and a complementary interpretation concerning the quadratic time frequency distributions are provided

fast and robust adaptation of dft domain volterra filters in diagonal coordinates using iterated coefficient updates this paper presents a novel data reusing technique for implementing adaptive discrete fourier transform dft domain volterra filters in diagonal coordinates having arbitrary nonlinear order in general a major drawback of such nonlinear filters is the large number of parameters thus a weak excitation of higher order kernels results in a slow convergence for system identification tasks in order to exploit the available innovation of the signals more effectively each data frame is processed for a specified number of iterations in an overlap save scheme thereby enhancing the convergence performance due to inherent recursions of the repeated filtering and updating steps this concept also lends itself to a fast algorithm requiring only a moderate increase in algorithmic complexity over a baseline implementation a detailed comparison of the required number of multiplications is given for several different algorithm versions despite the relatively simple concept the outlined iteration algorithm exhibits significant gains in both adaptation speed and steady state convergence this is demonstrated by various experiments for both stationary noise and speech input considering an application of nonlinear acoustic echo cancellation finally investigations on the tracking behavior for time variant nonlinearities and robustness against misdetection of double talk situations confirm the promising benefits and good trade off of the proposed iterated coefficient updates volterra filters approach

feedback capacity of the gaussian interference channel to within 2 bits we characterize the capacity region to within 2 bits s hz and the symmetric capacity to within 1 bit s hz for the two user gaussian interference channel ic with feedback we develop achievable schemes and derive a new outer bound to arrive at this conclusion one consequence of the result is that feedback provides multiplicative gain at high signal to noise ratio the gain becomes arbitrarily large for certain channel parameters this finding is in contrast to point to point and multiple access channels where feedback provides no gain and only bounded additive gain respectively the result makes use of a linear deterministic model to provide insights into the gaussian channel this deterministic model is a special case of the el gamal costa deterministic model and as a side generalization we establish the exact feedback capacity region of this general class of deterministic ics

kernel design for reduced interference distributions the authors present a class of time frequency signal representations tfrs called the reduced interference distribution rid an overview of commonly used tfrs is given and desirable distribution properties are introduced particular attention is paid to the interpretation of cohen s class of time frequency distributions of tfrs in the ambiguity temporal correlation spectral correlation and time frequency domains based on the desirable kernel requirements the rid is discussed and further defined a systematic procedure to create rid kernels or equivalently compute rids is proposed some aspects and properties of the rid are discussed the authors estimate design considerations for rids and compare various selections of the primitive window some experimental results demonstrating the performance of the rid are presented

the parametric characteristic of frequency response functions for nonlinear systems the characteristic of the frequency response functions of nonlinear systems can be revealed and analyzed by analyzing of the parametric characteristics of these functions to achieve these objectives a new operator is defined and several fundamental and important results about the parametric characteristics of the frequency response functions of nonlinear systems are developed these theoretical results provide a significant and novel insight into the frequency domain characteristics of nonlinear systems and circumvent a large amount of complicated integral and symbolic calculations which have previously been required to perform nonlinear system frequency domain analysis several new results for the analysis and synthesis of nonlinear systems are also developed examples are included to illustrate potential applications of the new results

identification of cubic systems using higher order moments of i i d signals a simple method for estimating the volterra kernels of cubic systems with a zero mean i i d input is presented this method significantly reduces the computational complexity of volterra kernel estimation compared to the non i i d and non gaussian input case

optimal decay error estimates for the hyperbolic parabolic singular perturbation of a degenerate nonlinear equation abstract we consider a degenerate hyperbolic equation of kirchhoff type with a small parameter e in front of the second order time derivative in a recent paper under a suitable assumption on initial data we proved decay error estimates for the difference between solutions of the hyperbolic problem and the corresponding solutions of the limit parabolic problem these estimates show in the same time that the difference tends to zero both as e 0 and as t in particular in that case the difference decays faster than the two terms separately in this paper we consider the complementary assumption on initial data and we show that now the optimal decay error estimates involve a decay rate which is slower than the decay rate of the two terms in both cases the improvement or deterioration of decay rates depends on the smallest frequency represented in the fourier components of initial data

on the optimality of treating interference as noise it is shown that in the k user interference channel if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user all values in decibel scale then the simple scheme of using point to point gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise tin at every receiver in short tin scheme achieves all points in the capacity region to within a constant gap the generalized degrees of freedom gdof region under this condition is a polyhedron which is shown to be fully achieved by the same scheme without the need for time sharing the results are proved by first deriving a polyhedral relaxation of the gdof region achieved by tin and then providing a dual characterization of this polyhedral region via the use of potential functions and finally proving the optimality of this region in the desired regime

characterization of the pareto boundary for the two user symmetric gaussian interferencechannel we characterize the pareto boundary of the achiev able rate region of the two user symmetric gaussian interference channel when transmitters control their transmission power and receivers have successive interference cancelation capability by identifying the shape of achievable rate region according to the strength of interference channels we find combinations of decod ing and power allocation strategies achieving the pareto boundary we also characterize the pareto boundary of the achievable rate region when time sharing is additionally considered index terms interference channel achievable rate region pareto boundary successive interference cancelation

analysis of the effects of time delay in nonlinear systems using generalised frequency response functions abstract a recursive algorithm for computing the generalised frequency response functions gfrfs of nonlinear time delay systems described by nonlinear differential difference equation models is derived using the operator e n and used to analyse the effects of time delay in nonlinear systems the algorithm shows an explicit relationship between the model parameters and the gfrfs such a relationship provides important insight into the behaviour of nonlinear systems the effect of delay on several properties of nonlinear systems such as harmonic generation gain compression expansion and desensitisation is studied by considering the example of a duffing oscillator with retarded damping results of the studies convincingly demonstrate that the system delay has a significant effect on several important properties of nonlinear systems

frequency domain analysis for non linear volterra systems with a general non linear output function for non linear volterra systems which include a non linear state equation and a general non linear output function the system frequency response functions and some related frequency response characteristics are developed and discussed in this study these new results establish the frequency response functions for this general form of non linear systems by extending some existing theory and provide an analytical insight into the relationship between model parameters and frequency response functions and the relationship between model parameters and the magnitude bound of frequency response functions several examples are given to illustrate the new results

optimal volterra kernel estimation algorithms for a nonlinear communication system for psk and qam inputs a fifth order volterra kernel estimation algorithm which is optimal in the least mean square error sense for a bandpass nonlinear system is derived the algorithm is based on some characteristics of i i d circularly symmetric zero mean complex valued gaussian random variables the proposed algorithm can be used to identify a nonlinear system under uniformly i i d rectangular m qam input and under uniformly i i d m psk input m spl ges 4 with modest modification the same approach has been used to derive an optimal volterra kernel estimation algorithm up to the third order however in some cases a third order model is not of high enough order to capture the nonlinear system characteristics a simulation example is given to show the necessity of deriving a fifth order volterra kernel estimation algorithm and to test for the correctness of the algorithm

the bispectrum and bicoherence for quadratically nonlinear systems subject to non gaussian inputs in the analysis of data from nonlinear systems both the bispectrum and the bicoherence have emerged as useful tools both are frequently used to detect the influence of a nonlinear system on the joint probability distribution of the system input previous work has provided an analytical expression for the bispectrum of a quadratically nonlinear system output if the input is stationary jointly gaussian distributed this work significantly generalizes the previous analysis by providing an analytical expression for the bispectrum of the response of quadratically nonlinear systems subject to stationary jointly non gaussian inputs possessing arbitrary auto correlation function the expression is then used to determine the optimal input probability density function for detecting a quadratic nonlinearity in a second order system it is also shown how the expression can be used to design an optimal nonlinear filter for detecting deviations from normality in the probability density of a signal

a mixed domain method for identification of quadratically nonlinear systems a new mixed domain method for identifying volterra transfer functions of a nonlinear system which can be represented by a second order truncated volterra series is presented in this paper this method is built on a discrete mixed domain volterra model derived from analyzing both discrete time and frequency domain volterra models of quadratically nonlinear systems it is shown that the conventional discrete frequency domain volterra model can be derived from the discrete mixed domain volterra model by making certain approximations in this sense the frequency domain model can be considered to be a cough version of the mixed domain model and thus cannot outperform the mixed domain model in terms of modeling capability in addition the new method is shown to be able to properly identify the volterra transfer functions even when the output of the quadratically nonlinear system is aliased based on this insight a new anti aliasing frequency domain method which is immune from the output aliasing problem is developed the superiority of these new methods over the conventional method is demonstrated by using them to analyze known quadratically nonlinear systems

estimation of generalized frequency response functions for quadratically and cubically nonlinear systems a new method of estimating the volterra kernels in the frequency domain is introduced based on a non parametric algorithm unlike the traditional non parametric methods using the frequency domain formulations based on discrete fourier transform dft data this new approach uses the time domain measurements directly to estimate the frequency domain response functions

long time existence and singular perturbation results for quasilinear hyperbolic equations with small parameter and dissipation term iii on considere des solutions lisses du probleme aux valeurs initiales hyperbolique quasilineaire eu tt u t ij 1 n a ij i j u 0 u 0 u 0 u t 0 u 1 ou e 0 0 u u x t r x r n on etudie l existence de solutions globales correspondant a des donnees arbitrairement grandes initiales u 0 et u 1 et a leur convergence quand e 0 vers la solution du probleme parabolique correspondant

bandpass sampling criteria for nonlinear systems sampling criteria for nonlinear systems with a band pass input are developed in this paper it is well known that nonlinear systems may produce an output signal with a larger bandwidth than that of their input signal according to the nyquist sampling theorem the sampling rate needs to be at least twice the maximum frequency of the output signal otherwise the sampled output would be aliased however if the input is a bandpass signal the spectrum of the output signal often occupies multiple frequency bands in this case it is possible by using the bandpass sampling concept to sample the output signal at a rate much lower than the nyquist sampling frequency in this paper all conditions in which bandpass sampling can be achieved are derived for nonlinear systems up to the third order furthermore for nonlinear systems higher than the third order some conditions in which bandpass sampling can be guaranteed are derived the result can be used to choose an appropriate sampling frequency for nonlinear systems of an arbitrary order

polyspectrum modeling using linear or quadratic filters the polyspectrum modeling problem using linear or quadratic filters is investigated in the linear case it is shown that if the output pth order cumulant function of a filter driven by a white noise is of finite extent then the filter necessarily has a finite extent impulse response it is proved that every factorable polyspectrum with a non gaussian white noise can also be modeled with a quadratic filter driven by a gaussian white noise it is shown that if the quadratic filter has a finite extent impulse response then the output pth order cumulant function is of finite extent and if the output pth order cumulant function of a quadratic filter is of finite extent then the impulse response may or may not be of finite extent it is shown that there exist finite and infinite extent pth order cumulant functions that are not factorable but can be modeled with quadratic filters

a bound for the magnitude characteristics of nonlinear output frequency response functions part 1 analysis and computation a bound for the magnitude frequency domain characteristics associated with the outputs of a wide class of nonlinear systems is derived as a relatively simple function of the generalized frequency response functions and properties of the system inputs it is shown how the practical computation of the new bound can be easily performed for nonlinear systems with finite but arbitrary order nonlinearities and worked examples are included the paper is divided into two parts in part 1 an expression for the output magnitude bound is derived properties of the result are discussed and general procedures for the practical computation of the bound are developed in part 2 the practical computations associated with applying the bound to the polynomial nonlinear autoregressive model with exogenous input are discussed

successive interference mitigation in multiuser mimo channels motivated by the work of dahrouj and yu in applying the han kobayashi transmission strategy for mitigating the intercell interference in a multi cell multi user multiple input single output interference network miso in this paper considers splitting messages into private and common parts in a multi cell multi user mimo in specifically the covariances of the private messages and common messages are designed to optimize either the sum rate or the minimal rate the common messages and private messages are decoded in sequence using successive decoding this paper shows how these difficult optimization problems can be adequately solved by means of d c d ifference of c oncave functions optimization over a simple convex set numerical and simulation results also reveal the great advantage of our proposed solutions for various types of ins in particular the proposed solutions are shown to outperform the algorithm developed by dahrouj and yu for the simpler case of the miso in

blind identification of volterra hammerstein systems this paper is concerned with the blind identification of volterra hammerstein systems two identification scenarios are covered the first scenario assumes that although the input is not available the statistics of the input are a priori known this case appears in communication applications where the input statistics of the transmitter are known to the receiver the second scenario assumes that the input statistics are unknown in the case of known input statistics the input is stationary higher order white noise with arbitrary probability density function under the scenario of unknown input statistics the input is restricted to gaussian white process new cumulant based identification methods are described for the above scenarios the problem is converted into a linear multivariable form and the output cumulants are calculated using kronecker products first initial conditions are determined by a linear system of equations these correspond to the boundary values of the volterra kernels the remaining kernel coefficients can be determined under both identification schemes from a possibly overdetermined system of linear equations

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

undermodeling error quantification for quadratically nonlinear system identification in the short time fourier transform domain in this paper we introduce an estimation error analysis for quadratically nonlinear system identification in the short time fourier transform stft domain the identification scheme consists of a parallel connection of a linear component represented by crossband filters between subbands and a quadratic component which is modeled by multiplicative cross terms we mainly concentrate on two types of undermodeling errors the first is caused by employing a purely linear model in the estimation process i e nonlinear undermodeling and the second is a consequence of restricting the number of estimated crossband filters in the linear component we derive analytical relations between the noise level nonlinearity strength and the obtainable mean square error mse in subbands we show that for low signal to noise ratio snr conditions a lower mse is achieved by allowing for nonlinear undermodeling and utilizing a purely linear model however as the snr increases the performance can be generally improved by incorporating a nonlinear component into the model we further show that as the snr increases a larger number of crossband filters should be estimated to attain a lower mse whether a linear or nonlinear model is employed experimental results support the theoretical derivations

regularity and unitarity of bilinear time frequency signal representations two structural properties of bilinear time frequency representations btfrs of signals are introduced and studied the definition of these properties is based on a linear operator description of btfrs the first property termed regularity has important implications with respect to the recovery of signals from the btfr outcome the derivation of other bilinear signal representations from a btfr the btfrs reaction to linear signal transformations and the construction of bases of induced btfr domain spaces the second property called unitarity is equivalent to validity of moyal s formula 1949 unitarity is thus necessary and sufficient for a closed form solution of optimal signal synthesis and for a btfr formulation or optimal detection estimation methods unitarity also allows the systematic construction of btfr product relations like the wigner distribution s interference formula and the ambiguity function s self transformation property unitarity permits the construction of induced orthogonal projection operators and guarantees the orthonormality of induced basis functions

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

blind identification of bilinear systems this paper is concerned with the blind identification of a class of bilinear systems excited by non gaussian higher order white noise the matrix of coefficients of mixed input output terms of the bilinear system model is assumed to be triangular in this work under the additional assumption that the system output is corrupted by gaussian measurement noise we derive an exact parameter estimation procedure based on the output cumulants of orders up to four results of the simulation experiments presented in the paper demonstrate the validity and usefulness of our approach

matrix based higher order spectral analysis for three wave coupling processes composite linear and quadratic systems produce three wave coupling when stimulated by random phase input sinusoids due to the nonlinearity of the system the output frequencies are arithmetically related to the input using third order cumulant statistics and their associated bispectrum techniques are devised based on phase insensitive matrix structures for detection and frequency estimation of coupling frequencies the separation of the third order cumulant series into symmetric and skew symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation after symmetrization biphases can be easily extracted as coefficients of the cumulant sequence using a generalized eigenvector representation one can relate symmetric and skew symmetric bases by a subspace rotation algorithm biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew symmetric matrices the dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum the radon transform procedure is related to bispectral processing through an isotropic radial slice volterra filter the compact third order kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series

identification of quadratic volterra systems driven by non gaussian processes a nonlinear and time invariant system representable by a volterra series up to second order is considered closed form expressions for the generalized transfer functions of first and second order are derived for non gaussian stationary input processes whose trispectrum vanishes it is shown that the parameters obtained are optimum in the mean square sense once the system is identified a closed form expression for the quadratic coherence is derived this expression simplifies to well known results when the system is linear or its input is gaussian the quadratic coherence is validated using simulated data as input to a known second order volterra filter with known statistic

second order volterra system identification second order volterra system identification is discussed crosscumulant information is converted into a fredholm integral equation special emphasis is focused on inputs obtained at the output of a linear filter driven by higher order white noise

determination of the analytical parametric relationship for output spectrum of volterra systems based on its parametric characteristics the output frequency response function ofrf of volterra systems can be described as a polynomial function of model parameters however the analytical determination of the ofrf is very computationally intensive especially for higher order ofrf to circumvent this problem a numerical method can be adopted provided that a series of simulation or experimental data for this polynomial function are given in this study it is theoretically shown that the analytical parametric relationship of ofrf up to any order can be determined accurately by using a simple least square method and every specific component of the output spectrum can also be determined explicitly based on the ofrf s parametric characteristics practical techniques to obtain a unique and accurate solution for the least square method are discussed this study provides a fundamental result for the determination of the analytical parametric relationship for this kind of system polynomial functions by using numerical methods

output frequency characteristics of nonlinear systems some interesting properties of output frequencies of volterra type nonlinear systems are particularly investigated these results provide a very novel and useful insight into the super harmonic and inter modulation phenomena in output frequency response of nonlinear systems with consideration of the effects incurred by different nonlinear components in the system the new properties theoretically demonstrate several fundamental output frequency characteristics and unveil clearly the mechanism of the interaction or coupling effects between different harmonic behaviors in system output frequency response incurred by different nonlinear components these results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities they can provide an important guidance to modeling identification control and signal processing by using the volterra series theory in practice

frequency domain truncation of volterra series for weakly non linear systems subject to harmonic excitation new results for model order reduction for weakly non linear systems in the frequency domain are derived based on a parametric modelling approach

a digital technique to estimate second order distortion using higher order coherence spectra a digital spectral method for evaluating second order distortion of a nonlinear system which can be represented by volterra kernels up to second order and which is subjected to a random noise input is discussed the importance of departures from the commonly assumed gaussian excitation is investigated the hinich test is shown to be an appropriate test for orthogonality in the system identification tests for gaussianity of two important sources which are commonly used for gaussian inputs in nonlinear system identification are presented 1 commercial software routines for simulation experiments and 2 noise generators for practical experiments the deleterious effects of assuming a gaussian input when it is not are demonstrated the random input method for evaluating the second order distortion of a nonlinear system is compared with the sine wave input method using both simulation and experimental data the approach is applied to a loudspeaker in the low frequency band

i i r volterra filtering with application to bilinear systems a new nonlinear filtering technique by means of infinite impulse response iir volterra functionals is developed it yields the projection onto the closed class of finite volterra series with separable kernels of arbitrary degree k such an optimal estimator is finitely realizable as a bilinear system with parameters that are computable off line moreover if the original system model is itself bilinear this computation is finitely recursive through higher moments of degree 2 k two simple illustrating examples are developed i estimation of the covariance of the internal white noise driving a linear system and ii filtering of a non gaussian linear system driven by a poisson process the robustness with respect to the observation noise distribution is finally examined

on the maximum achievable sum rate with successive decoding in interference channels in this paper we investigate the maximum achievable sum rate of the two user gaussian interference channel with gaussian superposition coding and successive decoding we first examine an approximate deterministic formulation of the problem and introduce the complementarity conditions that capture the use of gaussian coding and successive decoding in the deterministic channel problem we find the constrained sum capacity and its achievable schemes with the minimum number of messages first in symmetric channels and then in general asymmetric channels we show that the constrained sum capacity oscillates as a function of the cross link gain parameters between the information theoretic sum capacity and the sum capacity with interference treated as noise furthermore we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sum capacity the maximum achievable sum rate drops to that with interference treated as noise we provide two algorithms to translate the optimal schemes in the deterministic channel model to the gaussian channel model we also derive two upper bounds on the maximum achievable sum rate of the gaussian han kobayashi schemes which automatically upper bound the maximum achievable sum rate using successive decoding of gaussian codewords numerical evaluations show that similar to the deterministic channel results the maximum achievable sum rate with successive decoding in the gaussian channels oscillates between that with han kobayashi schemes and that with single message schemes

linear multichannel blind equalizers of nonlinear fir volterra channels truncated volterra expansions model nonlinear systems encountered with satellite communications magnetic recording channels and physiological processes a general approach for blind deconvolution of single input multiple output volterra finite impulse response fir systems is presented it is shown that such nonlinear systems can be blindly equalized using only linear fir filters the approach requires that the volterra kernels satisfy a certain coprimeness condition and that the input possesses a minimal persistence of excitation order no other special conditions are imposed on the kernel transfer functions or on the input signal which may be deterministic or random with unknown statistics the proposed algorithms are corroborated with simulation examples