This paper is written to provide both a historical review of past work and an overview of recent advances in time-frequency signal analysis and time-varying higher-order spectra. The paper is organized as follows: Section 1 discusses the need for time-frequency signal analysis (TFSA), as opposed to either time or frequency analysis. Section 2 covers the many faceted developments which occurred in TFSA in the 1980s and early 1990s. It covers bilinear or energetic time-frequency distributions (TFDs). Section 3 deals with a generalization of bilinear TFDs to multilinear Polynomial TFDs and their relationship to time-varying higher order spectra (TVHOS). Section 4 provides a coverage of the Wigner-Ville trispectrum, which is a particular TVHOS, used for analyzing signals affected by Gaussian multiplicative noise. Section 5 is devoted to conclusions.

Landing in poor weather is a crucial problem for the air transportation system. To aid the pilots for these conditions several solutions have been suggested and/or implemented including instrument landing systems (ILS) and microwave landing systems (MLS) that put the responsibility of the landing to a large extent in the hands of the airport facilities. These systems even though useful are not available due to their high costs even in a few major metropolitan airports. This shortcoming has generated interest in providing all weather capabilities not on the landing facility but on the vehicle itself. The Synthetic Vision System Technology Demonstration sponsored by the United States Federal Aviation Administration (FAA) and the U.S. Air Force represents an effort to respond to the above needs. In this paper we present a summary of a typical synthetic vision system. This system consists of a scanning 35 GHz radar, a scanning antenna, a signal/image processor and a head up display (HUD). The pilot is presented a final perspective image of the scene sensed by the radar with associated flight guidance symbology. This system is implemented in real time hardware and has been undergoing tower and flight testing under a variety of weather conditions since early 1992.

This paper illustrates a vehicle imaging technique for ground traffic control applications. The imaging is performed by exploiting the vehicle motion with respect to a pair of linear arrays. The method for estimating the vehicular velocity from the data collected by one of the arrays is described, and the theoretical accuracy of the estimate is discussed in detail through the evaluation of the Rao-Cramer bound. In particular it is recognized that the maximum likelihood solution is based on the radon transform of the data. Experimental results obtained with a field operating prototype are finally shown.

In this paper, the coherent signal-subspace method (CSM) is extended for estimation of bearing, elevation and range of multiple, near-field, broad-band sources. Analytical results are also derived to justify the effectiveness of the near-field CSM. It is shown that the coherently averaged sample covariance matrix in the near-field CSM has complex Wishart distribution with number of degrees-of-freedom equaling the time-bandwidth product, provided that (1) the frequency components of the array output are statistically independent and Gaussian distributed, and (2) the errors between all the actual source locations and the preliminary estimate of the source cluster center are upperly bounded by a small constant. Some simulation results are provided to show the effectiveness of the near-field CSM.

A high resolution DOA estimation technique in the presence of noise with unknown covariance matrix has been provided. This method provides high resolution at a reasonable computational burden. In this paper, a performance analysis of the DOA estimates obtained by this technique is provided using perturbation theory. Simulation results are presented to compare with the theoretical results. They show very good agreement.

In this paper, a new Fourier domain reconstruction algorithm is presented which utilizes the information contained in the known region of the spectrum to estimate the frequency samples in the missing-cone area. Unlike conventional two-dimensional extrapolation techniques, this method uses bi-directional extrapolation to maximize the amount of known information in each extrapolation step. By fully utilizing the information of the measured data, the resulting image provides a more accurate estimation of the electron density distribution. The resolution improvement achieved is mainly due to the proper utilization of the available information in the measurements during the image formation process.

A new method for numerically integrating partial differential equations (PDEs) has been under study for the last few years. This method is based on principles of multidimensional (MD) Kirchhoff circuits and multidimensional wave digital filters (MD WDFs), which explains why it has probably not been discovered earlier. It makes wide use of methods and results that have been developed by extensive research in the areas of circuit theory and digital signal processing, but that are rather unknown outside of the small circle of experts on MD WDFs. Instead of talking about MD WDFs we prefer using, within the context of numerical integration, the designation `discrete multidimensionally passive (MD-passive) dynamical systems.'

Familiar information measures such as due to Shannon, Kullback, etc., may be related to one basic information measure called the characteristic information I. The latter is the trace of the Fisher information matrix. The relation is a Poisson equation with I as the driving force. Thus, for small-uncertainty cases, given I all these other information measures can be generated as solutions to a Poisson equation. If one of the parameters of the system is time- like, the Poisson equation becomes a wave equation, and the information may be said to `flow.'

In this paper, we establish an architectural framework for parallel time-recursive computation. We consider a class of linear operators that consists of the discrete time, time invariant, compactly supported, but otherwise arbitrary kernel functions. We specify the properties of the linear operators that can be implemented efficiently in a time-recursive way. Based on these properties, we develop a routine that produces a time-recursive architectural implementation for a given operator. This routine is instructive for the design of a CAD tool that will facilitate the architecture derivation. Using this background, we design an architecture for the Modulated Lapped Transform (commonly called Modified Discrete Cosine Transform), which has linear cost in operator counts.

An on-chip VLSI architecture for computation of Fourier transforms is presented. It performs the arithmetic operations in a digit-level pipeline fashion. For this purpose, the implementation of arithmetic operators is based on on-line (i.e., digit-serial and most significant digit first) arithmetic, and the transforms are performed by a parallel-pipeline version of the Cooley- Tukey fast Fourier transform (FFT) algorithm.

The popular QR decomposition based recursive least-squares (RLS) adaptive filtering algorithm (referred to as QRD-RLS) has a limited speed of operation depending on the processing time of each individual cell. A new scaled tangent rotation based STAR-RLS algorithm has been designed which is suitable for fine-grain pipelining and also has a lower complexity. The inter-cell communication is also reduced by about half. A direct application of look-ahead to STAR-RLS can still lead to some increase in hardware. In this paper look- ahead is applied using delayed update operations such that the complexity is reduced while maintaining a fast convergence. The pipelined STAR-RLS (or PSTAR-RLS) algorithm requires the same number of operations (multiplications or divisions) as the serial STAR-RLS algorithm. Practical issues related to the STAR-RLS algorithm such as numerical stability and dynamic range are also examined.

Fine-grain pipelined adaptive decision-feedback equalizer (ADFE) architectures are developed using the relaxed look-ahead technique. This technique, which is an approximation to the conventional look-ahead computation, maintains functionality of the algorithm rather than the input-output behavior. Thus, it results in substantial hardware savings as compared to either parallel processing or look-ahead techniques. The delay relaxation, delay transfer relaxation, and sum relaxation are introduced for purposes of pipelining. Both the conventional and the predictor form of ADFE have been pipelined. The performance of the pipelined algorithms for the equalization of a magnetic recording channel is studied. It is demonstrated via simulations that, for a byte error rate of 10^-7 or less, speed-ups of up to 8 can be easily achieved with the conventional ADFE. The predictor form of ADFE allows much higher speed-ups (up to 32) for less than 1 dB of SNR degradation.

Recently several authors have investigated the use of parametric families of linear filters for discrete frequency estimation. The proposed methods are similar in that they use iterative filtering procedures for estimating the frequencies of underlying periodic components embedded in noise. In this paper we combine parametric filtering with a contraction mapping principle to recursively estimate the frequencies of discrete spectral components. By incorporating the contraction mapping idea with parametric filtering a fundamental property is determined which when satisfied, guarantees the convergence of the iterative procedure. Several examples are provided which illustrate the method.

A new approach for signal extrapolation based on wavelet representation known as scale-time limited extrapolation and a denoising process is investigated in this research. We first examine a new signal modeling technique using wavelets and the corresponding scale-time limited signal extrapolation algorithm. Then, the sensitivity of the algorithm to noise is discussed, and a denoising algorithm based on the time-localization property of the wavelet transform is proposed. By integrating the denoising process and the iterative scale-time limited extrapolation algorithm, we obtain a very robust signal extrapolation algorithm for noisy data. A simulation result of signal extrapolation from noisy observed data is presented to illustrate the performance of the proposed robust signal extrapolation algorithm.

In this paper, an evolutionary spectral estimator based on the application of Adaptive Weighted Norm Extrapolation (AWNE) is formulated and illustrated for analysis of nonstationary signals. The AWNE method produces a stationary extension of the data so that computing its Fourier transform yields a nonparametric, high-resolution spectrum estimate. The evolutionary formulation described here uses a time slice of the time-averaged Spectrogram to select the initial weight function (prior spectrum) used in AWNE for each block of data. This function strongly influences the final shape of the resulting spectrum. The resulting Short-Time AWNE (STAWNE) time-frequency representation yields improved frequency-domain resolution, preserves components which last longer than one time block, and is devoid of cross-terms. Comparison with short-time autoregressive spectral estimation yields improved consistency in the spectral energy levels as time varies. Finally, this sequential spectrum estimator is also illustrated for use in range-Doppler imaging of reflectivity surfaces having prominent scatterers by hybrid two-dimensional spectral estimation in-tandem with the discrete Fourier transform.

In this paper we use a non-stationary approach and analyze ultra-wideband (UWB) radar data using time-frequency and time-scale transformations. The time-frequency transformations considered are the Short-Time Fourier Transform (STFT), the Wigner-Ville Distribution (WD), the Instantaneous Power Spectrum (IPS), and the ZAM transform. Two discrete implementations of the Wavelet Transform (DWT) are also investigated: the decimated A- trous algorithm proposed by Holschneider et al, which uses non-orthogonal wavelets; and the Mallat algorithm, which employs orthogonal wavelets. The transients under study are UWB radar returns from a boat (with and without corner reflector) in the presence of sea clutter, multipath, and radio frequency interferences (RFI). Results show that all time-frequency and time-scale transforms clearly detect the transient radar returns corresponding to the boat with a corner reflector. However, as the radar cross section of the target decreases (boat without a corner reflector), results change drastically as the RFI component dominates the signal. Simulations show that the Instantaneous Power Spectrum may be better adapted for localizing the transient among the time-frequency techniques studied. The decimated A-trous algorithm has the best time resolution of the techniques studied as the return appears better localized in the scalogram.

An autoregressive parameter estimation algorithm combined with a generalized expectation- minimization approach is used to provide a recursive procedure for spectral analysis of real data corrupted by sparkling interferences. The prediction filter is stable and estimated with low bias. These properties also guarantee fast convergence. Results of the real data processing are represented.

Noisy environmental conditions significantly reduce the ability to track multiple-targets in sonar imaging systems. The dynamics of the target as a function of time is viewed as a 2-D image in which tracks are viewed as edges. Wavelet analysis is used in the first part of this paper to perform the edge detection, or multiple target tracking, by finding the modulus maximas of the dyadic wavelet transform of the sonar image at different scales. The second part of the paper addresses the complex problem of decentralized multiple target tracking with local decisions. Using the approach developed in the first part of the paper, the high resolution information is wavelet decomposed into multiresolution form with the lowest resolution matching that of the other sensor. An edge mask is created, compressed and transmitted to the low resolution sensor which uses this mask as a weighing function on its wavelet transform. We show that this technique is highly effective in highlighting the targets' tracks information in the low resolution noisy sensor.

This is a review of bootstrap methods, concentrating on basic ideas and applications. It begins with an exposition of the bootstrap principle and gives several examples of its use. Bootstrap methods for testing statistical hypotheses are then reviewed and an analysis of accuracy of bootstrap tests is provided. We discuss how the bootstrap can be used to estimate variance stabilizing transformations that are crucial for the level of accuracy of bootstrap tests. Finally, we describe an application of multiple bootstrap tests to the problem of finding optimum locations of vibration sensors for knock detection in spark ignition engines.

In making an estimate of the power spectrum of a process from a short sample the stationarity assumption used to formulate the spectrum estimate is often violated, so that reliable assessment of the error of the estimate is difficult. Here we examine the problems of detecting narrow-band non-stationarity in short data samples and the influence of such non-stationarity on the variance of spectrum estimates. We decompose the covariance matrix of the eigencoefficients used in multiple-window spectrum estimation methods into a series of known basis matrices with scalar coefficients. For a given bandwidth and sample size, we describe simultaneous orthogonal expansions for both the power (time) function and for the eigencoefficient covariance matrix. The limiting power basis functions are eigenfunctions of a narrow band sinc² kernel while the corresponding basis matrices are trace-orthogonal so that the observable non-stationary is described by a series of quadratic forms.

The paper addresses two questions of time-varying higher-order spectra (TVHOS), whose solutions are essential for the further development of these methods and their applicability to a wide range of situations. They are: (1) defining cumulant TVHOS and (2) predicting the behavior of TVHOS of composite signals. It is shown first that the cumulant Wigner-Ville trispectrum (as a particular member of cumulant TVHOS), can preserve the essential properties of cumulant higher-order spectra (e.g., eliminates Gaussian additive noise) and at the same time is able to characterize the time-variations of the signal's spectral (i.e., trispectral) content. Secondly, when dealing with composite FM signals, a special kind of `non-oscillating cross-terms' appear in the moment TVHOS time-frequency subspace. These cross-terms cannot be eliminated by smoothing the WVT, but rather by appropriate slicing of the full time-multi-frequency space.

The detection of small floating targets in an ocean environment is discussed in this paper. Because of the time-varying nature of the growler's radar returns, classical detection schemes do not work well. It is shown that these problems can be overcome if the detection is performed in the joint time-frequency plane. The effectiveness of the detection scheme is demonstrated by looking at two specific aspects of the problem: (1) detection of the target when the radar is scanning a certain sector, and (2) when the radar is dwelling in a certain azimuthal direction for a longer period of time.

In this paper we present a new method for adaptively decomposing a multicomponent signal into its components. This method is based on fitting an autoregressive (AR) model to the short-time spectra of the signal. The AR parameters represent the coefficients of the linear predictive (LP) polynomial. The roots of this polynomial constitute a set of center frequencies and bandwidths that characterize the modes of the signal. The decomposition process is achieved by applying a time-varying filter bank to the original multicomponent signal. The characteristics of this filter bank are derived from a subset of the roots of the LP polynomial. We have developed a constraining algorithm to determine that subset based on the boundedness of the bandwidths, and the temporal continuity of the center frequencies of the components. We have applied the proposed decomposition method for the separation of the formants of speech signals.

We investigate the estimation of both the number of waves and the wave parameters for transient wavefields in a geophysical application. Models of the earth have to be verified by seismogram analysis. We present two nonparametric methods for the estimation of wave parameters where one is based on the first-order stationary spectrum and the other one is based on the second-order cumulant spectrum. We also investigate a parametric method for wave parameter estimation which allows us to determine the number of incident waves. The algorithms are applied to synthetic seismic data.

Antenna arrays collect multidimensional data that contains signals arriving from different sources. Neural Network Architectures can separate the different signals, thus enabling parallel processing structures. These structures can solve a multi-signal estimation problem more efficiently than the corresponding single signal estimator. Various of these parallel architectures are evaluated in the context of array signal processing. Specifically, the scheme developed in this paper (section 2) uses the spatial diversity supplied by the aperture associated with the sensors to separate the signals and to apply them to a bank of parallel adaptive filters. These filters are then designed in accordance with a mean square error minimization criterion (i.e., a criterion based on Second Order Statistics). As Second Order Statistics assume linearity or Gaussianity they are sometimes overly restrictive. It is shown how High Order Statistics can be very useful when more general criteria such as statistical independence between the signals to be separated are imposed.

From first principles, a method is presented to generate the minimal region in the n- dimensional frequency space necessary for a complete nonredundant representation of the support of an N-th order joint cumulant spectral function. This region is commonly referred to as the N-th order principal domain (PD) or the support set of the N-th order cumulant spectral function (which is the Fourier transform of the N-th order joint cumulant function). The procedure is derived from a composition of the symmetry operations inherent to an N-fold product of the Fourier transforms of a random time series. For exposition, we present an example using the second-order cumulant spectral function. Explicit representations of the PDs for cumulant spectra of orders up to and including order five are included.

We consider the problem of detecting an unknown, random, stationary, non-Gaussian signal in Gaussian noise. The most commonly used method for this problem is the so-called energy detector which can not distinguish between Gaussian and non-Gaussian signals. Recently the use of bispectrum and/or trispectrum of the signal has been suggested for improving detection performance for non-Gaussian signals. In this paper we suggest the use of an integrated polyspectrum (bispectrum or trispectrum) to possibly further enhance detection performance and to improve computational efficiency of the detectors based upon polyspectrum. We investigate conditions under which use of the integrated bispectrum is appropriate. The detector structure is derived and its performance is evaluated via simulations and comparisons with several other existing approaches.

We introduce a new tool called state dependent embedding for developing nonlinear adaptive filters. We use the embedding to develop a new quadratic lattice whitener with only scalar coefficients. The whitener is shown to be a linear lattice with a modified update equation. We demonstrate that scalar state dependent coefficients can be directly updated in this application, thus providing a very efficient nonlinear lattice structure. We describe lattice joint process estimator structures. For Gaussian inputs, we note that only some kernels of the series expansion describing the nonlinearity contribute to input eigenvalue spread. We suggest a reduced complexity escalator structure that exploits this finding. Finally we provide a simplification to the layered structure presented.

This paper demonstrates that order-recursive least squares (ORLS) algorithms based on orthogonal transformations and hyperbolic transformations can be systematically constructed in two steps. The first step is to determine the structure of the ORLS algorithm according to the property of the data vector in the LS estimation and the requirements to the output. The second step is to determine the proper implementation of building blocks of the ORLS structure using orthogonal or hyperbolic transformations. The canonical ORLS structure and some possible orthogonal/hyperbolic implementations of their building blocks are presented. It is also shown that some of the orthogonal transformations are only applicable to certain types of ORLS structures and not to others.

Recently, the QR decomposition (QRD) method has been extensively used in the recursive least squares (RLS) adaptive filtering problems. And the least squares lattice (LSL) algorithm has been rederived based on the QRD method. On the other hand, in order to increase the throughput in the general RLS, a triangular systolic array for block processing based on the QRD method with Householder transformations has been derived. In this paper, we derive an adaptive FIR lattice filter structure for block processing based on QRD with Householder transformations.

The sequence of Givens rotations used to update the upper triangular matrix R in a recursive QR decomposition may also be used to update the inverse transpose matrix R^-H. Alternative forms of square-root-free Givens rotation for updating the inverse transpose matrix are derived by representing and storing it in a different factorized form from that used before. The modified Givens rotations do not involve explicit division by the exponential forget factor and lead to an update algorithm equivalent to the one derived by Sakai using Recursive Modified Gram Schmidt orthogonalization.

An algorithm has been developed to control the antenna array beam pattern for multiple beam antenna (MBA) or phased array systems. The algorithm is motivated by military satellite communications applications where the uplink received antenna is desired to provide beamforming capability for selective earth coverage and jamming protection. The problem can be formulated as to determine the control weight to meet the user gain and jammer null requirements in their known directions subject to the norm constraint of the weight defined by the power conservation law. The algorithm makes use of an orthogonal decomposition of the weight vector into the constraint weight vector and the zero-output weight vector. If the constraint weight vector satisfies the norm bound constraint, the zero-output vector can further be optimized to minimize the deviation of the resulting weight from the quiescent weight. If the constraint weight vector does not satisfy the norm bound constraint, a recursive procedure has been developed which provides flexibility in the determination of the constraint vectors, the constraint order and the constraint phase optimization. This algorithm provides a practical means to achieve the constraints subject to the norm bound condition.

This paper presents a novel, fully parallel algorithm for robust linearly constrained minimum variance beamforming. The robustness results from the use of an adjustable constraint to compensate for the unavoidable small mismatch between the nominal and the actual steering vector of the signal-of-interest. The need for parallelism follows from the large computational demands of beamforming algorithms and by the high data rates which are typically present in communications applications. The algorithm exhibits good numerical properties as it is based on orthogonal transformations only. A systolic architecture is presented on which the throughput is independent of the size of the beamformer.

In a previous work, a time domain algorithm was proposed to adaptively estimate a rational and orthonormal spanning of a rational subspace. However, its convergence was not proved and it seems that asymptotic misbehavior may occur. A new algorithm is proposed, for which satisfactory convergence properties hold. It provides robustness with regard to the signal model and shows an especially good asymptotical performance for small SNR.

The nonlinear nature of the family of fast RLSL algorithms has hindered the study of the numerical properties from a general framework. As more and more applications for these types of fast filters have been realized, the numeric properties have become an essential part of algorithm and hardware development. Most work in the past has been algorithm specific, drawing from a stochastic or a numerical analysis viewpoint. We discuss the numeric behavior of errors propagating between successive filter stages in time and discuss satisfactory conditions which guarantee a stable solution.

The fast recursive least squares (RLS) algorithms have wide applications in signal processing and control. They are computationally efficient. Thus their stability is of major concern. In this paper, we investigate the error propagation and stability of some typical fast RLS algorithms. Through a random example, we show that a typical conventional fast RLS algorithm is weakly unstable in computing both the residuals and the gain vectors and a QR based algorithm is expected to be weakly stable in computing the residuals but weakly unstable in computing the gain vectors. We propose an error correction scheme for computing the gain vectors.

Methods for updating and downdating singular value decompositions (SVDs) and partially reduced bidiagonal forms (partial SVDs) are introduced. The methods are based upon chasing procedures for updating the SVD and downdating procedures for orthogonal decompositions. The main feature of these methods is the ability to separate the singular values into `large' and `small' sets and then obtain an updated bidiagonal form with corresponding `large' and `small' columns. This makes for a more accurate update or dosndate.

Despite its important signal processing applications, the generalized singular value decomposition (GSVD) is under-utilized due to the high updating cost. In this paper, we consider the noise subspace problem and introduce a new approximate GSVD that is easily amenable to updating.

This paper describes the VLSI implementation of a CORDIC based processor element for use in a fault-reconfigurable systolic array to compute the singular value decomposition (SVD) of a matrix. The chip implements a time redundant fault tolerance scheme, which allows processors adjacent to a faulty processor to act as computation backup during the systolic idle time. Also, processors around a fault collaborate to reroute data around the faulty processor. This form of time redundancy is attractive when tolerance to a few faults needs to be achieved with little hardware overhead.

The Texas Instruments' TMS320C40 digital signal processor contains communication hardware which enables processors to be connected together to form multiprocessing systems. Analysis of the devices communication channels suggests that it would be beneficial to use additional communication hardware to maximize system performance. The use of mesh routing chips in conjunction with the processors has been investigated. The two devices are interfaced using two TMS320C40 communication channels. Lower message latencies can be achieved by using TMS320C40 communication channels to perform nearest neighbor communications while using the routing chips to perform all other message routing. However, the use of additional TMS320C40 channels can degrade the rate at which packets are injected and consumed from the network, resulting in under utilization of the network bandwidth.

Many applications of the eigenvalue decomposition of dense matrices are well known. This work was prompted by research in the numerical simulation of disordered electronic systems, in which one of the most common approaches is to diagonalize random Hamiltonian matrices in order to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. In this paper, we describe an effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems. Results of numerical tests and timings are also presented.

A general neural network co-processor has been investigated and designed to adaptively adjust the quantization thresholds of a data quantizer, and thus a data quantizer with minimum quantization loss can be obtained. For a given probability density function and number of quantization levels, the neural network is designed to learn the near optimal quantization uniform step-size which minimizes the loss caused by the quantizer. With this neural network co-processor approach, consistent and substantial performance improvements have been verified on either an AWGN or a Rayleigh fading communication channel with convolutional encoder and maximum likelihood decoder. This general neural network co-processor approach can be applied to any digital signal processing system which has quantization loss, such as digital communication, image data compression, or adaptive signal processing.

Implementing Jacobi algorithms in parallel VLSI processor arrays is a non-trivial task, in particular when the algorithms are parametrized with respect to size and the architectures are parametrized with respect to space-time trade-offs. The paper is concerned with an approach to implement several time-adaptive Jacobi-type algorithms on a parallel processor array, using only Cordic arithmetic and asynchronous communications, such that any degree of parallelism, ranging from single-processor up to full-size array implementation, is supported by a `universal' processing unit. This result is attributed to a gracious interplay between algorithmic and architectural engineering.

An adaptive beamforming (ABF) algorithm is described which can be used for active sonar, particularly a sonar which uses wideband source waveforms such as frequency-modulated (FM) pings, and a bistatic receiver composed of an array of acoustic sensors. The method for obtaining the sensor covariance matrix is critical to this algorithm, and one that works is described and justified. Results using real data with echoes from an undersea target are presented.

This paper addresses the problem of mobile radio propagation channel modeling and underlines the need for further research in this domain. The paper first describes three characteristics of the mobile radio propagation channel which are the propagation-path loss, the time-varying aspect, and the multipath characteristics. It then describes the properties and limitations of the present methods used for channel modeling. The main limitation concerns the non-stationary aspect of the mobile radio propagation channel. Two signal processing approaches are proposed to remedy the problem. Finally, the paper addresses the definition of validation criteria in order to evaluate and quantify the accuracy of each proposed model.