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A great deal of interest has been paid to enhance the radar range resolution for the last decades. One of the techniques is to construct a waveform combining inter-pulse and intra-pulse modulations. In this paper, stepped frequency (SF) waveform is used to represent the former, whereas phase coding (PC) is considered for the latter. To obtain the high-resolution range profile (HRRP) of a target induced by an SF waveform at the receiver, one of the approaches is the frequency domain (FD) algorithm. It has been successfully applied with SF linear frequency modulation waveforms. However, based on our investigations, processing the SFPC waveform with the FD algorithm does not lead to the performance, in terms of peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR), of the single-carrier phase coding (SCPC) waveform processed with a matched filter (MF). To overcome these drawbacks, we propose to split the spectrum of a phase coded pulse into a predetermined number of portions, and then to successively transmit the time-domain transformed versions of these various portions. The received echoes are then processed with a modified version of the FD algorithm. Our analysis and simulations show that the proposed waveform can be characterized by a PSLR and an ISLR close to those of the SCPC processed with MF in some scenarios.

In signal processing, ARMA processes are widely used to model short-memory processes. In various applications, comparing or classifying ARMA processes is required. In this paper, our purpose is to provide analytical expressions of the divergence rates of the Kullback-Leibler divergence, the Renyi divergence (RD) of order α and their symmetric versions for two Gaussian ARMA processes, by taking advantage of results such as the Yule-Walker equations and notions such as inverse filtering. The divergence rates can be interpreted as the sum of different quantities: power of one ARMA process filtered by the inverse filter associated with the second ARMA process, cepstrum, etc. Finally, illustrations show that the ranges of values taken by the divergence rates of the RD are sensitive to α, especially when the latter is close to 1.

International audience; The detrended fluctuation analysis (DFA) and its higher-order variant make it possible to estimate the Hurst exponent and therefore to quantify the long-range dependence of a random process. These methods are popular and used in a wide range of applications where they have been proven to be discriminative to characterize or classify processes. Nevertheless, in practice, the signal may be short-memory. In addition, depending on the number of samples available, there is no guarantee that these methods provide the true value of the Hurst exponent, leading the user to draw erroneous conclusions on the long-range dependence of the signal under study. In this paper, using a matrix formulation and making no approximation, we first propose to analyze how the DFA and its higher-order variant behave with respect to the number of samples available. Illustrations dealing with short-memory data that can be modeled by a white noise, a moving-average process and a random process whose autocorrelation function exponentially decays are given. Finally, to avoid any wrong conclusions, we propose to derive abacuses linking the value provided by the DFA or its variant with the properties of the signal and the number of samples available.

International audience; To estimate the Hurst exponent of a mono-fractal process, the detrended fluctuation analysis (DFA) is based on the estimation of the trend of the integrated process. The latter is subtracted from the integrated process. The power of the residual is then computed and corresponds to the square of the fluctuation function. Its logarithm is proportional to the Hurst exponent. In the last few years, a few variants of this method have been proposed and differ in the way of estimating the trend. Our contribution in this paper is threefold. First, we introduce a new variant of the DFA, based on a regularized least-square criterion to estimate the trend. Then, the influence of the regularization parameter on the fluctuation function is analyzed in two cases: when the process is wide sense stationary and when it is not. Finally, an application is presented in the field of aeronautics to characterize an attentional impairment: the visual tunneling.

A processing chain from the transmitter to the receiver dealing with a stepped frequency waveform combined with phase coding (PC) has been proposed in a recent paper. It consists in splitting the spectrum of a PC pulse into predetermined portions, and then transmitting the corresponding time-domain signals. At the receiver, a modified version of the frequency domain (FD) algorithm is used to process the received echoes. However, this processing chain could be improved. Indeed, alternative modulations could be considered to offer a degree of freedom to the practitioner. In addition, when the number of portions becomes large, the performance of the proposed FD algorithm degrades, the spectrum of the reconstructed waveform being distorted. Therefore, in this paper, the novelty stands in the following items: 1) at the transmitter, the non-linear frequency modulation (NLFM) can be considered as an alternative to PC $2)$ at the receiver, a novel time-domain waveform reconstruction (TWR) is proposed to process the received echoes in the time domain instead of operating in the frequency domain. Our simulations show that, unlike the modified FD algorithm, for any number of portions, the performance obtained using the TWR algorithm is the same at high signal-to-noise ratio (SNR), whereas at low SNR, the larger the number of portions used, the better the performance.

International audience; Target classification can be of real interest for sea surveillance in both civil and military contexts. To address this issue, we present two approaches based on the Singer model. The latter has the advantage of covering a wide range of motions depending on the values of its parameters. Given noisy observations, the first method aims at estimating the motion model parameters by taking advantage of the properties of the correlation function of the estimated acceleration. It is based on a genetic algorithm. The second approach is on-line and consists in deriving a joint tracking and classification (JTC) method. Based on various simulations, we study their respective relevance in different operational settings. The proposed JTC corresponds to the best compromise in terms of performance and number of samples required.

International audience; The non-linear frequency modulation (NLFM) waveform is one of the existing waveforms that can be used in high range resolution radar applications. However, a high sampling frequency and consequently an expensive ADC are required. To overcome this drawback while taking advantage of the features of the NLFM waveform, we suggest approximating the wideband NLFM waveform by a piecewise linear waveform and using it in a stepped frequency (SF) framework. Thus, a variable chirp rate SF-LFM waveform is proposed where SF is combined with a train of LFM pulses having different chirp rates, durations, and bandwidths. In this paper, these parameters are derived from a tangent-based NLFM waveform. At the receiver, a generalized version of the time domain (TD) algorithm is proposed to process the received echoes. Our purpose is to obtain the high range resolution profile (HRRP) whose properties are of the same magnitude orders as those obtained using a tangent-based NLFM waveform. These properties are the peak sidelobe ratio, the integrated sidelobe, and the range resolution. Toward this goal, a multi-objective optimization issue is addressed to deduce the parameters of the proposed waveform by using two types of approaches based on evolutionary algorithms. Their relevance is compared. Our analysis and simulations show that the proposed approaches attain the targeted performance goals with a smaller sampling frequency at the receiver.

International audience; The detrended fluctuation analysis (DFA) and its variants such as the detrended moving average (DMA) are widely used to estimate the Hurst exponent. These methods are very popular as they do not require advanced skills in the field of signal processing and statistics while providing accurate results. As a consequence, a great deal of interest has been paid to compare them and to better understand their behaviors from a mathematical point of view. In this paper, our contribution is threefold. Firstly, we propose another variant avoiding the discontinuities between consecutive local trends of the DFA by a priori constraining them to be continuous. Secondly, we show that, in all these approaches, the square of the fluctuation function can be presented in a similar matrix form. When the process is wide-sense stationary (w.s.s.), the latter can be seen as the power of the output of a linear filtering whose frequency response depends on the given method. In the general case, an interpretation of the square of the fluctuation function is also given by expressing it as the convolution between the 2D-Fourier transform of two matrices, one whose elements correspond to the instantaneous correlation function of the signal and the other which depends on the detrending method. To end up, an illustration is provided in the field of avionics for the detection of the visual tunneling, a deleterious cognitive state.

The symmetric Kullback–Leibler divergence known as Jeffrey's divergence (JD) has found applications in signal and image processing, from radar clutter modeling to texture analysis. Recently, several studies were done on the JD between ergodic wide-sense stationary autoregressive (AR) and/or moving average (MA) processes. It was shown that the so-called asymptotic JD increment can be useful to compare ergodic wide-sense stationary ARMA processes. An interpretation of the asymptotic JD increment was also proposed. It consists in calculating the power of the first process filtered by the inverse filter associated with the second process, and conversely. However, in some biomedical applications, econometrics and other areas, long-memory processes have rather to be studied. Therefore, this paper aims at addressing the JD between ergodic wide-sense stationary autoregressive fractionally integrated moving average (ARFIMA) processes. More particularly, we study the influence of the ARFIMA parameters on the value of the asymptotic JD increment. Then, we analyze if the interpretation of the asymptotic JD increment based on inverse filtering is still valid for this type of process. Finally, some simulation results illustrate the theoretical analysis.

International audience; Jeffrey’s divergence (JD), which is the symmetric version of the Kullback-Leibler divergence, has been used in a wide range ofapplications, from change detection to clutter homogeneity analysis in radar processing. It has been calculated between the jointprobability density functions of successive values of autoregressive (AR) processes. In this case, the JD is a linear function ofthe variate number to be considered. Knowing the derivative of the JD with respect to the number of variates is hence enough tocompare noise-free AR processes. However, the processes can be disturbed by additive uncorrelated white noises. In this paper,we suggest comparing two noisy 1st-order AR processes. For this purpose, the JD is expressed from the JD between noise-freeAR processes and the bias the noises induce. After a transient period, the derivative of this bias with respect to the variate numberbecomes constant as well as the derivative of the JD. The resulting asymptotic JD increment is then used to compare noisy ARprocesses. Some examples illustrate this theoretical analysis.

In signal and image processing, Jeffrey's divergence (JD) is used in many applications for classification, change detection, etc. The previous studies done on the JD between ergodic wide-sense stationary (WSS) autoregressive (AR) and/or moving average (MA) processes state that the asymptotic JD increment, which is the difference between two JDs based on k and ( k − 1 ) -dimensional random vectors when k becomes high, tends to a constant value, except JDs which involve a 1st-order MA process whose power spectral density (PSD) is null for one frequency. In this paper, our contribution is threefold. We first propose an interpretation of the asymptotic JD increment for ergodic WSS ARMA processes: it consists in calculating the power of the first process filtered by the inverse filter associated with the second process and conversely. This explains the atypical cases identified in previous works and generalizes them to any ergodic WSS ARMA process of any order whose PSD is null for one or more frequencies. Then, we suggest comparing other random processes such as noisy sums of complex exponentials (NSCE) by using the JD. In this case, the asymptotic JD increment and the convergence speed towards the asymptotic JD are useful to compare the processes. Finally, NSCE and pth-order AR processes are compared. The parameters of the processes, especially the powers of the processes, have a strong influence on the asymptotic JD increment.

This paper proposes a new method for identifying ARMA models in the presence of additive white noise. The method operates with two main steps. First, the noisy ARMA model is approximated by the sum of an high-order AR model with an additive white noise. The parameters of the high-order AR model as well as the driving noise and the additive noise variances are estimated by using an errors-in-variables approach. Second, the coefficients of the ARMA model are extracted from those of the AR model previously identified by means of existing techniques. In particular, three different methods are considered and compared for solving the second step. The effectiveness of the described identification procedure has been tested by Monte Carlo simulations and compared with a prediction error method.

Even if they can be outperformed by other methods, the detrended fluctuation analysis (DFA) and the detrended moving average (DMA) are widely used to estimate the Hurst exponent because they are based on basic notions of signal processing. For the last years, a great deal of interest has been paid to compare them and to better understand their behaviors from a mathematical point of view. In this paper, our contribution is the following: we first propose to express the square of the so-called fluctuation function as a 2D Fourier transform (2D-FT) of the product of two matrices. The first one is defined from the instantaneous correlations of the signal while the second, called the weighting matrix, is representative of each method. Therefore, the 2D-FT of the weighting matrix is analyzed in each case. In this study, differences between the DFA and the DMA are pointed out when the approaches are applied on non-stationary processes.

The detrended fluctuation analysis (DFA) is widely used to estimate the Hurst exponent. Although it can be outperformed by wavelet based approaches, it remains popular because it does not require a strong expertise in signal processing. Recently, some studies were dedicated to its theoretical analysis and its limits. More particularly, some authors focused on the so-called fluctuation function by searching a relation with an estimation of the normalized covariance function under some assumptions. This paper is complementary to these works. We first show that the square of the fluctuation function can be expressed in a similar matrix form for the DFA and the variant we propose, called Continuous-DFA (CDFA), where the global trend is constrained to be continuous. Then, using the above representation for wide-sense-stationary processes, the statistical mean of the square of the fluctuation function can be expressed from the correlation function of the signal and consequently from its power spectral density, without any approximation. The differences between both methods can be highlighted. It also confirms that they can be seen as ad hocwavelet based techniques.

The purpose of this paper is to share our positive experience about the collaboration launched a few years ago between UTP (Panama) and Bordeaux INP (France) in the field of signal processing. This collaboration involves research and education activities. This has led to numerous internships of French students in Panama, mobilities of researchers, common research papers, and the 1st double diploma signed between France and a country of Central America. Thus, this paper presents the various aspects of the collaboration.

In this paper, we first propose to analyze the properties of the Kullback-Leibler divergence between wide-sense stationary random processes that can be modeled by ARMA or ARFIMA processes. This study makes it possible to introduce a new feature useful to compare two random processes and called "the asymptotic KL increment". The latter depends on various parameters such as the inverse filters associated to the random processes. An interpretation of "the asymptotic KL increment" is also given. Then, we propose to use it in order to compare the inter-beat intervals, which characterize the cardiac rhythm, when the subjects are either in a calm and soothing situation or under stress.

When using Bayesian estimation techniques, the algorithm is strongly sensitive to the system evolution model and more particularly to the setting of the state-noise covariance matrix. Recently, Bayesian non-parametric models and in particular Dirichlet processes (DPs) have been proposed as a scalable solution to this issue. They assume that the system can switch between an infinite number of state-space representations corresponding to different values of the state-noise covariance matrix. In this framework, jointly estimating the state vector and the covariance matrix is a non-linear non-Gaussian problem. The inference is thus classically carried out using particle filtering techniques. In this case, the choice of the proposal distribution for the particles is of paramount importance regarding the estimation accuracy. A first contribution of this paper is to derive an approximation of the optimal proposal distribution of the particle filter when a DP prior is placed on the distribution of the state-noise covariance matrix. Then, an alternative DP-based formulation of the inference problem is proposed to reduce its dimensionality. It takes advantage that the possible functional forms of the state-noise covariance matrices are known up to a reduced number of time-switching hyperparameters in many applications. An approximation of the optimal proposal distribution is also derived. Finally, the relevance of both proposed approaches is analyzed in the framework of target tracking and a comparative study with existing methods is carried out. HighlightsWe address the joint estimations of the state vector and the state-noise covariance matrix.We use Bayesian non-parametric methods implemented by particle filtering.Two approaches are presented.In both cases, the optimal proposal distribution is derived.Both proposed algorithms are applied to target tracking.

Micro-Doppler induced by mechanical vibrating or rotating structures in a radar target is possibly useful for its detection, classification and recognition. In a previous work, pseudo-Zernike moments (PZMs) were used as micro-Doppler features for classification. Despite of their promising classification rates, the choice of PZMs is debatable because other types of moments exist. In this paper, our purpose is to compare various kinds of micro-Doppler features such as Zernike moments, PZMs, orthogonal Mellin-Fourier moments, Legendre moments and Krawtchouk moments in order to evaluate which moments are the most relevant in terms of reconstruction ability, computational cost and micro-Doppler classification rate. Advantages and drawbacks of each family of moments are also given. Through the simulations we carried out, when the signal is disturbed by an additive white noise and the signal-to-noise ratio is low, the use of Krawtchouk moments as micro-Doppler features turns out to be the best compromise.

In some multi-object tracking scenarios such as convoys or road constrained motions, it can be advantageous to track groups of targets sharing common motion characteristics, even if they are not necessarily close to each other. The objective is twofold: reducing the computational cost while increasing the accuracies of the individual trajectory estimates. In a previous communication, we introduced a generic model based on hierarchical random finite sets (RFSs) to represent these types of multigroup multi-target scenarios. A first RFS is used to represent the multi-group state: the number of groups, their common motion characteristics and their target compositions are assumed to be random variables. Then, for each group, a second layer of RFSs represents the multi-target state assuming that the number of targets inside a group and their trajectories are also random variables. The main contribution of this paper is to derive a filter dedicated to the state estimation of hierarchical RFSs from sequential sensor measurements. The proposed solution is based on the labeled multi-Bernoulli filter to estimate the group characteristics, which interacts with a bank of probability hypothesis density filters to address the multi-target layer.

Jeffrey’s divergence (JD) is used in many applications, from change detection to classification. Several studies were done on the JD between ergodic wide-sense stationary autoregressive and moving average (ARMA) processes. It was shown that the derivate of the JD between the probability density functions of k consecutive samples of two ARMA processes tends to the so-called asymptotic JD increment. This latter is enough to compare the processes and amounts to calculating the power of the first process filtered by the inverse filter associated with the second process and conversely. In this paper, our purpose is to study if this result can be extended to ARFIMA processes. As a first step, a special case, namely the JD between wide-sense stationary fractionally integrated white noises, is addressed. The influences of the process parameters on the asymptotic JD increment are analyzed. Our investigations validate the inverse filtering interpretation of the JD.

Like other divergences, Jeffrey's divergence (JD) is used for change detection, for model comparison, etc. Recently, a great deal of interest has been paid to this symmetric version of the Kullback-Leibler (KL) divergence. This led to analytical expressions of the JD between autoregressive (AR) processes, moving-average (MA) processes, either noise-free or disturbed by additive white noises, as well as ARMA processes. In this paper, we propose to study the JD between processes that are defined as sums of complex-valued sinusoidal processes disturbed by additive white noises. We show that the JD tends to a stationary behavior when the number of variates becomes large. The derivative of the JD becomes a constant that depends on the parameters defining the processes. The convergence speed towards this stationary regime depends on the differences between the normalized angular frequencies. The smaller the difference, the slower the convergence. This result can be obtained by interpreting some steps to compute the JD as orthogonal projections. Some examples illustrate the theoretical analysis.

Various works have been carried out about the Jeffrey's divergence (JD) which is the symmetric version of the Kullback-Leibler (KL) divergence. An expression of the JD for Gaussian processes can be deduced from the definition of the KL divergence and the expression of the Gaussian-multivariate distributions of k-dimensional random vectors. It depends on the k × k Toeplitz covariance matrices of the stationary processes. However, the resulting computational cost may be high as these matrices must be inverted and it is all the higher as k increases. To circumvent this problem, a recursive expression can be obtained for real 1st-order autoregressive (AR) processes. When they are disturbed by additive uncorrelated white noises, we showed that when k becomes large, the derivative of the JD with respect to k tends to be constant. This constant is sufficient to compare the noisy AR processes. In this paper, we propose to extend our work to AR moving-average (MA) processes with one AR term and one MA term. Some examples illustrate the theoretical analysis.

Comparing processes or models is of interest in various applications. Among the existing approaches, one of the most popular methods is to use the Kullback-Leibler (KL) divergence which is related to Shannon’s entropy. Similarly, the Renyi divergence of order α can be deduced from the Renyi entropy. When α tends to 1, it leads to the KL divergence. In this paper, our purpose is to derive the expression of the Renyi divergence between the probability density functions of k consecutive samples of two real first-order moving average (MA) processes by using the eigen-decompositions of their Toeplitz correlation matrices. The resulting expression is compared with the expressions of the Rao distance and the Jeffrey’s divergence (JD) based on the eigenvalues. The way these quantities evolve when k increases is then presented. When dealing with unit-zero MA processes, the derivate is infinite for the JD and finite for the others. The influence of α is also studied.

In this article, we share our positive experience about the creation of a Telecom showcase in our engineering school, which is an exhibition of old technology to help students learn about previous habits and think about some of the consequences of rapid innovation. This project was done in collaboration with industrial partners such as Thales and Orange. It includes the following steps: collecting objects, organizing and rendering the objects accessible to students, disseminating the history of the telecommunications industry by using a website and quizzes and helping students see how the telecommunications industry and engineers have contributed to social and cultural evolution. This exhibit is particularly useful for the Minute Telecom, inspired from the Minute Physics, where the students are invited to create a video on theoretical concepts such as Shannon's theorem, mobile communication systems or the impact of innovation on user habits.

This paper deals with the analysis of the Jeffrey's divergence (JD) between an autoregressive process (AR) and a sum of complex exponentials (SCE), whose magnitudes are Gaussian random values, which is then disturbed by an additive white noise. As interpreting the value of the JD may not be necessarily an easy task, we propose to give an expression of the JD and to analyze the influence of each process parameter on it. More particularly, we show that the ratios between the variance of the additive white noise and the variance of the AR-process driving process on the one hand, and the sum of the ratios between the SCE process power and the AR-process PSD at the normalized angular frequencies on the other hand, has a strong impact on the JD. The 2-norm of the AR-parameter has also an influence. Illustrations confirm the theoretical part.

In this paper, single-target tracking using radar measurements is addressed. Recently, algorithms based on Bernoulli random finite sets have proved efficient in a cluttered environment. However, in Bayesian approaches, the choice of the motion model impacts the trajectory estimation accuracy. To select an appropriate set of motion models, a joint tracking and classification (JTC) algorithm can be used. The principle is to consider different target classes depending on their maneuvrability, each of them being associated to a set of motion models. In this context, additional information such as a target length extent measurement can improve both classification and trajectory estimation. Therefore, we propose a multiple-model Bernoulli filter to perform JTC. To jointly estimate the trajectory and the target length which is constant, a Rao-Blackwellized approach is considered. Another contribution is that a bank of probabilistic data association filters is run instead of Kalman filters to account for false detections.

Time series models play a key-role in many applications from biomedical signal analysis to applied econometric. The purpose of this paper is to compare 1 st -order moving-average (MA) models by using dissimilarity measures such as the Jeffrey's divergence (JD), which is the symmetric version of the Kullback-Leibler divergence (KL). The MA models can be real or complex. They can also be disturbed by additive white noises or not. Analytical expressions are first proposed and analyzed. Then, the JD is used to compare more than two 1 st -order MA models in order to extract MA model subsets. In the latter case, we suggest analyzing the higher-order singular values of a tensor defined from the JDs between models over time to deduce the number of subsets and their cardinals. Simulation results illustrate the theoretical analysis. HighlightsAnalytical Jeffrey's Divergence expressions are provided for 1st-order MA models.Real or complex, noise-free or noisy 1st-order MA model cases are studied.Time evolution of the Jeffrey's Divergence depends on the 1st-order MA parameters.Comparative study with other dissimilarity measures (Rao distance, etc.) is done.Two methods are proposed to compare more than two 1st-order MA models.

This paper deals with model comparison based on the Jeffrey's divergence (JD). More particularly, after providing the JD between the joint distributions of k consecutive values of a white noise and the ones of a real moving-average or autoregressive model, the JD between real 1st-order MA and real 1st-order AR models is studied. Except when the 1st MA parameter is equal to 1, we show that, after a transient period, the JD between both models is incremented by a constant value that depends on the model parameters while k is incremented by 1. The JD is hence characterized by this increment and it is not necessary to consider a lot of samples.

The autoregressive models (AR) and moving-average models (MA) are regularly used in signal processing. Previous works have been done on dissimilarity measures between AR models by using a Riemannian distance, the Jeffrey's divergence (JD) and the spectral distances such as the Itakura-Saito divergence. In this paper, we compare the Rao distance and the JD for MA models and more particularly in the case of 1st-order MA models for which an analytical expression of the inverse of the covariance matrix is available. More particularly, we analyze the advantages of the Rao distance use. Secondly, the simulation part compares both dissimilarity measures depending on the MA parameters but also on the number of data available.

For a high-resolution radar, an extended target is characterized by a few main scatterers spread over several range gates not necessarily consecutive. The joint detections and localizations of these scatterers are of particular interest in order to estimate the range profile and identify the target. In this paper, we study a detector based on the Generalized Likelihood Ratio Test considering the unknown locations of the scatterers. Given the number of scatterers and using order statistics results, we derive approximations of the probability of false alarm and the probability of detection and localization which can be a relevant measure of performance in this context. Finally, a comparative study is carried out with other existing detectors.

When using Bayesian estimation techniques for target tracking, the algorithm accuracy is induced by the choice of the system evolution model. Information on the type of target and its maneuver capability can then be helpful to choose relevant motion models. Joint tracking and classification (JTC) methods based on target features have thus been introduced. Among them, we recently proposed to take into account the target extent measurements for single-target tracking. In this paper, we extend this work to multi-target tracking (MTT) by using probability hypothesis density (PHD) filters. More precisely, assuming that each target class is characterized by its own kinematic-model set, a multiple-model (MM) PHD filter is used for each class. State estimates from each class are then combined by using class probabilities. Finally, the proposed approach, namely a multiclass MM-GMPHD, is applied to maritime-target tracking and simulation results show the relevance of the proposed approach regarding the tracking of various types of targets.

International audience; In the field of cognitive radio (CR), radio frequency (RF) transceivers must be efficient to save the terminal battery autonomy. Therefore, when designing the CR power amplifier (CR-PA), an obvious objective is to optimize efficiency over a large bandwidth. As a consequence, the CR-PA operates in its non-linear region and then frequency-dependent distortions are generated. This issue is all the more critical as one deals with high peak-to-average power ratio (PAPR) like those of OFDM signals. In this paper, we develop a digital post-distortion and detection technique in order to compensate the non-linearities generated by the CR-PA. It is based on a dynamic Volterra model to take into account the non-linear behavior of the CR-PA. The key feature of the proposed technique is the joint estimations of the model parameters and the CR-PA input samples. For this reason, an extended Kalman filter (EKF) is considered. However, as the model parameters can vary over time, several EKFs are combined by means of an interacting multiple model (IMM) algorithm. Simulation results confirm the relevance of the proposed postdistortion and detection technique.

International audience; This paper deals with digital post-distortion for radio frequency (RF) power amplifiers (PAs) used in cognitive radio (CR) systems. This technique is based on a new approach modelling the PA behavior. The latter characterizes not only the PA non-linearities and memory effects but also its highly-varying behavior with carrier frequency in CR context. Given this modelling, a Kalman algorithm based post-distortion and detection is used to compensate the CR-PA non-linear effect and restore the input signal. This method is suitable for uplink communications in CR context because it saves the consumed power at the transmitter. Finally, this on-line technique does not require known test signals to estimate the PA model parameters.

In this paper, we propose to address the moving average (MA) parameters estimation issue based only on noisy observations and without any knowledge on the variance of the additive stationary white Gaussian measurement noise. For this purpose, the MA process is approximated by a high-order AR process and its parameters are estimated by using an errors-in-variables (EIV) approach, which also makes it possible to derive the variances of both the driving process and the additive white noise. The method is based on the Frisch scheme. One of the main difficulties in this case is to evaluate the minimal AR-process order that must be considered to have a 'good' approximation of the MA process. To this end, we propose a way based on K-means method. Simulation results of the proposed method are presented and compared to existing MA-parameter estimation approaches.