The forgetting factor is the main control parameter of the recursive least-squares (RLS) algorithm, which is set to balance between the estimate accuracy and the tracking capability. Targeting a better performance compromise, different variable forgetting factor RLS (VFF-RLS) algorithms have been previously developed. Usually, they require additional control mechanisms and/or extra parameters, which are difficult to handle in practice. In this letter, we present an elegant yet practical VFF-RLS algorithm, in the framework of system identification. Simulation results obtained in the context of acoustic echo cancellation indicate its reliable performance.

Interference originating from ground-based active sources, such as radar systems, can represent a substantial obstacle to achieving high-quality and dependable Synthetic Aperture Radar (SAR) imagery. This interference can lead to partial image degradation, errors in image interpretation, and deviations in parameter extraction. Notably, the Sentinel-1, operating in C-band, is among the most widely used SAR remote sensing satellites. Given the prevalence of ground-based radar systems operating in the C-band, interference significantly impacts Sentinel-1 data, thereby necessitating effective mitigation strategies. In this article, we propose an innovative approach for mitigating interference in SAR images by employing a combination of a filter bank time-frequency distribution (dual of the classical Short-Time Fourier Transform) computed on the spectrum of the range compressed signal and a linear combination of order statistics (L-statisics). The methodology involves sorting each constant-time line of the time-frequency distribution matrix in ascending order, which places the interference at the right-hand side of the time-frequency plane. Subsequently, the interference-free range profile is determined by coherently summing along the frequency axis of the bins identified as unaffected by interference (the first q% of frequency bins from the sorted distribution). The method is evaluated on a dataset acquired by Sentinel-1A on 26.04.2021 over the city of Doha, Qatar, which is affected by interference from a radar of the Patriot Missile System.

The identification of long-length impulse responses represents a challenge in the context of many applications, like echo cancellation. Recently, the problem has been addressed in the framework of low-rank systems, using a decomposition of the impulse response based on the nearest Kronecker product and low-rank approximations. As a result, the original system identification problem that involves a long-length finite impulse response filter is reshaped as a combination of two (much) shorter filters, which leads to significant advantages. In this context, the benchmark Wiener filter can be formulated in terms of an iterative algorithm, where the estimates of the two component filters are sequently updated. However, matrix inversion operations are required within this algorithm. In this article, we develop a new version of the decomposition-based iterative Wiener filter, which relies on the conjugate gradient (CG) method and avoids matrix inversion. Simulations performed in the framework of echo cancellation indicate the good performance of the proposed solution, which outperforms the conventional Wiener filter (implemented using CG updates) and inherits the advantages of the decomposition-based approach.

This paper presents a multi-channel ground-based bistatic SAR receiver architecture designed to perform single-pass tomography using the Sentinel-1 satellites as transmitters of opportunity. The bistatic receiver presents only 3 imaging channels, which is an extreme case for single-pass tomographic estimation. The three antennas are placed in a non-uniform configuration, such that the two antenna separations are in a 2:1 ratio. For a fixed array length, the non-uniform 3-element array will extend the maximum unambiguous height (relative to the 3-element uniform array), while keeping the elevation resolution cell around the Rayleigh limit. In the proposed processing flow, for each Sentinel-1 overpass on the envisaged orbits, the bistatic SAR image of each channel is focused on a two-dimensional grid, and afterwards the elevation profile of a given area is computed using the Capon estimator. The proposed architecture was evaluated in a measurement campaign performed between June-November 2021 using an electronic target with two transmit antennas placed on a vertical pole situated at 58.5 m from the ground receiver. For an array length of 2.6 m, the overall root mean squared error of the relative height was below 10 cm, while the unambiguous interval and the height resolution cell were around 3.75 m and 1.2 m, respectively. The experimental data from this measurements campaign provide the first quantitative assessment of spaceborne transmitter/stationary receiver single-pass bistatic SAR tomography in a controlled environment. In the long term, these results may contribute to future multi-static spaceborne SAR missions for which a single-pass tomographic capability is envisioned.

In applications involving system identification problems, some characteristics of the impulse response of the system to be identified are usually exploited to design adaptive algorithms with improved performance. In this context, this paper focuses on the identification of systems that own intrinsic symmetric or antisymmetric properties, which can be further formulated by using a combination of bilinear forms. Based on such an approach, the least-mean-square (LMS) and normalized LMS (NLMS) algorithms with symmetric/antisymmetric properties (termed here LMS-SAS and NLMS-SAS) are proposed. Simulation results are shown confirming the improved convergence speed achieved by the proposed algorithms as compared to the conventional LMS and NLMS counterparts for different operating scenarios.

There are different strategies to improve the overall performance of the recursive least-squares (RLS) adaptive filter. In this letter, we focus on the data-reuse approach, aiming to improve the convergence rate/tracking of the algorithm by reusing the same set of data (i.e., the input and reference signals) several times. First, we present a computationally efficient data-reuse RLS algorithm, which is the result of a low complexity implementation of the data-reuse process. Moreover, we extend the idea to the fast RLS algorithm. Simulations performed in the context of echo cancellation support the performance gain.

The identification of room acoustic impulse responses represents a challenging problem in the framework of many important applications related to the acoustic environment, like echo cancellation, noise reduction, and microphone arrays, among others. In this context, the main issues are related to the long length of such impulse responses and their time-variant nature. These raise significant difficulties in terms of the convergence rate, computational complexity, and accuracy of the solution. Recently, a decomposition-based approach was developed for the identification of low-rank systems, which can also be applied (to some extent) for the identification of acoustic impulse responses. This approach exploits the nearest Kronecker product decomposition of the impulse response and solves a high-dimension system identification problem using a combination of low-dimension solutions (provided by shorter filters), thus gaining in terms of both performance and complexity. Nevertheless, it does not consider the intrinsic nature of the room acoustic impulse responses, which contain specific components (e.g., early reflections and late reverberation) that can be very different in nature. In this paper, we propose an improved decomposition-based method (via the Kronecker product) that takes into account these specific components and processes them separately, in order to better exploit their important low-rank features. Following this approach, an iterative Wiener filter is firstly developed, followed by a recursive least-squares (RLS) algorithm designed in the same framework. Both solutions outperform the conventional benchmarks, i.e., the conventional Wiener filter and the RLS algorithm, respectively. Moreover, they achieve superior performances as compared to the recently developed versions based on the nearest Kronecker product decomposition, also owning lower computational complexities than their previous counterparts. Simulations are performed in the framework of acoustic echo cancellation and the obtained results support the performance features of the proposed algorithms.

Exploring polarimetric diversity of Synthetic Aperture Radar (SAR) data is directly applicable to conventional monostatic cases. For this, the mostly used convention is the Backscatter Alignment. While establishing important advantages for the monostatic case (possibility to have equal values on the cross-polarimetric channels), it has been proven to introduce some difficulties for the bistatic case. This appears in relation to the so-called conjugate similarity operation, when (mathematically) asymmetric scattering matrices occur. In this paper, we propose the detailed algorithm which provides a solution to the conjugate similarity operation, in the case of general scattering matrices. The proposed algorithm is based on the real representation matrix transformation. Further, we investigate the characterization of canonical bistatic scatterers (three elementary targets). Raw bistatic polarimetric signals are obtained by using simulations with a computationally electromagnetic (EM) software, capable of complete EM analysis. The eigenvalue classification illustrates the potential of additional information brought using the proposed Real Representation Scattering Matrix (RRSM). The presence of complex eigenvalues is investigated in relation to the bistatic angle and one nonreciprocity parameter.

Equivalent matrix representations in radar polarimetry have long been studied and used as tools for modeling and understanding the scattering mechanisms. We include here the Kennaugh, Graves, or covariance matrices which are today seen as alternative representations of the same physical quantity, the scattering matrix. In this paper, we briefly explore some of the properties of the algebraic real representation of a complex matrix, a mathematical construction which has been introduced in the literature as an alternative way of performing consimilarity transformations (rather than by the usual Graves power decomposition, with applications limited only to those involving symmetric scattering matrices). Besides the theoretical presentation on the subject, the main goals of the paper are to study some of the advantages and limitations of using the 4 × 4 real matrix form and to compare consimilarity transformation results obtained through the real representation to those given by the power representation.

Bistatic radar receivers that use an opportunistic transmitter require a reference channel to capture the original transmitted signal, which is then used as a reference signal for constructing the matched-filter during the range compression step. Because the reference signal is received from line-of-sight, it is orders in magnitude larger than the reflections captured by the receive channel. It is generally difficult to construct the system such that the reference signal is not leaked into the received signal, either via coupling in the circuitry or via reflections off objects in the vicinity of the receiver. Due to its much larger amplitude, the reference signal can easily mask smaller targets with its side-lobes. In this paper we propose a novel deconvolution method for bistatic SAR images as a means of eliminating leakage of the reference signal.

Synthetic Aperture Radar Tomography (TomoSAR) is one primary remote sensing technique for deriving elevation estimations and recovering the 3D spatial information of an observed scene. This article presents a novel method for improved single-pass bistatic SAR tomography estimation, in the case of a spaceborne transmitter-stationary receiver architecture, with only three imaging channels at the receiver. The approach is based on the use of the coarray space to create a virtual set of acquisitions, as received from an array with a larger number of antenna elements. The proposed configuration is evaluated through simulations.

From simple scattering mechanism extraction and throughout more complex applications (e.g., land classification, disaster monitoring), polarimetry has become a key element for remote sensing. For the particular case of bistatic polarimetry, the development of a theoretical basis has not been yet aligned with a comprehensive experimental validation. At the moment, an exhaustive search across the polarimetric scientific literature will reveal that for true bistatic geometries (i.e., significant angular separation between transmitter and receiver), only a small number of qualitative investigations have been made and there is still work to be done. In the current paper, one of the most popular polarimetric decomposition methods (H - α) is applied to dual-pol VV-VH data, in both bistatic (space-surface geometry with ground-based receiver) and monostatic configurations. Images from both geometries are displaying a common, urban scene. Comparing the obtained results, objective observations are presented.

The recursive least-squares (RLS) adaptive filter is an appealing choice in system identification problems, mainly due to its fast convergence rate. However, this algorithm is computationally very complex, which may make it useless for the identification of high length impulse responses, like in echo cancellation. In this paper, we focus on a new approach to improve the efficiency of the RLS algorithm. The basic idea is to exploit the impulse response decomposition based on the nearest Kronecker product and low-rank approximation. Thus, a high-dimension system identification problem is reformulated in terms of low-dimension problems, which are tensorized together. Simulations performed in the context of echo cancellation indicate the good performance of the RLS algorithm based on this approach.

The recursive least-squares (RLS) adaptive filter is an appealing choice in many system identification problems. The main reason behind its popularity is its fast convergence rate. However, this algorithm is computationally very complex, which may make it useless for the identification of long length impulse responses, like in echo cancellation. Computationally efficient versions of the RLS algorithm, like those based on the dichotomous coordinate descent (DCD) iterations or QR decomposition techniques, reduce the complexity, but still have to face the challenges related to long length adaptive filters (e.g., convergence/tracking capabilities). In this paper, we focus on a different approach to improve the efficiency of the RLS algorithm. The basic idea is to exploit the impulse response decomposition based on the nearest Kronecker product and low-rank approximation. In other words, a high-dimension system identification problem is reformulated in terms of low-dimension problems, which are combined together. This approach was recently addressed in terms of the Wiener filter, showing appealing features for the identification of low-rank systems, like real-world echo paths. In this paper, besides the development of the RLS algorithm based on this approach, we also propose a variable regularized version of this algorithm (using the DCD method to reduce the complexity), with improved robustness to double-talk. Simulations are performed in the context of echo cancellation and the results indicate the good performance of these algorithms.

In this paper, we develop the Kalman filter for the identification of bilinear forms. In this framework, the bilinear term is defined with respect to the impulse responses of a spatiotemporal model, which resembles a multiple-input/single-output system. Recently, the identification of such bilinear forms was addressed in terms of the Wiener filter and conventional adaptive algorithms, i.e., least-mean-square and recursive least-squares. In this work, apart from the derivation of the Kalman filter tailored for the identification of bilinear forms, a simplified (i.e., low complexity) version of the algorithm is also presented. Simulation results support the theoretical findings and indicate the good performance of the proposed solutions.

Linear system identification is a key problem in many important applications, among which echo cancelation is a very challenging one. Due to the long length impulse responses (i.e., echo paths) to be identified, there is always room (and needs) to improve the performance of the echo cancelers, especially in terms of complexity, convergence rate, robustness, and accuracy. In this paper, we propose a new way to address the system identification problem (from the echo cancelation perspective), by exploiting an optimal approximation of the impulse response based on the nearest Kronecker product decomposition. Also, we make a first step toward this direction, by developing an iterative Wiener filter based on this approach. As compared to the conventional Wiener filter, the proposed solution is much more attractive since its gain is twofold. First, the matrices to be inverted (or, preferably, linear systems to be solved) are smaller as compared to the conventional approach. Second, as a consequence, the iterative Wiener filter leads to a good estimate of the impulse response, even when a small amount of data is available for the estimation of the statistics. Simulation results support the theoretical findings and indicate the good results of the proposed approach, for the identification of different network and acoustic impulse responses.

In this letter, the identification problem of bilinear forms with the Wiener filter is addressed. The contribution is twofold. First, a different approach is introduced, by defining the bilinear term with respect to the impulse responses of a spatiotemporal model, in the context of multiple-input/single-output systems. Second, two versions of the Wiener filter (namely direct and iterative) are developed in this context. Moreover, the advantage of the iterative Wiener filter is outlined as compared to the direct solution. The results of the simulations, which are performed from a system identification perspective, support the theoretical findings.

This paper proposes a detector of multi-component non-stationary signals based on the matched signal transform (MST). In the MST domain, a non-stationary signal is localized at its frequency modulation rate with the transform's basis modulation function. The MST can be numerically implemented either as a freestanding discrete version of an integral transform, or for faster computation, as a time resampled version of the original signal followed by a fast Fourier transform. We analyze the noise statistics in the MST domain and derive the analytical forms of the probability density function for both implementations, considering the non-stationary signal embedded in white Gaussian noise. We propose a detector based on the squared magnitude of the MST and show how its detection performances depend on the chosen implementation. All the theoretical derivations are validated through Monte Carlo simulations.

This letter proposes a micro-Doppler (m-D) reconstruction method for spaceborne synthetic aperture radar (SAR) images using azimuth time-frequency tracking of the phase history. The algorithm involves an azimuth defocusing of the SAR image in order to gain access to the phase history, followed by a time-frequency tracking algorithm. The tracking in azimuth is based on local polynomial phase modeling using as estimator for the polynomial coefficients the high-order ambiguity function. The approach is presented in the context of vibration estimation for infrastructure monitoring applications, with an emphasis on the estimation of vibration parameters from the reconstructed m-D. The procedure is tested and compared with state-of-the-art methods by various simulation scenarios in keeping with typical high-resolution SAR imaging parameters. Finally, the developed algorithm is applied on real data acquired by the TerraSAR-X satellite over the Puylaurent water dam in France.

This paper proposes a parameters estimation algorithm for signals composed of multiple non-stationary components having the same basis modulation function which is described by an a priori known model and depends on a few unknown parameters. The procedure is based on time warping the signal in turn with every basis function resulted from different model parameters combinations and evaluating the concentration of the warped signal spectrum. The estimated parameters of the model are the ones which provide the best spectral concentration. Onwards, the amplitude, phase and modulation rate for each component are determined from the signal warped with the optimal basis function. The algorithm is tested with simulations and real data consisting of de-chirped radar signals and acoustic signals with harmonic components from underwater mammals.

This paper proposes a vibration-induced micro-Doppler estimation method for oscillating targets in synthetic aperture radar (SAR) images using azimuth time-frequency tracking and a matched signal transform. The approach involves an azimuth defocusing of the SAR image in order to access the phase history. The tracking in azimuth is based on local polynomial phase modeling using as estimator for the polynomial coefficients the high-order ambiguity function. The vibration frequency is obtained from the spectrum of the tracked instantaneous frequency law, while the oscillation amplitude is estimated using a matched signal transform. The procedure is tested by simulations and on real SAR images acquired by the TerraSAR-X satellite over the Puylaurent water-dam in France.

Infrastructure monitoring applications can require the tracking of slowly moving points of a certain structure. Given a certain point from a structure to be monitored, in the context of available spaceborne synthetic aperture radar (SAR) products, where the image is already focused in a slant range-azimuth grid, it is not obvious if this point is the scattering center, if it is in layover or if it is visible from the respective orbit. This paper proposes a scattering centers detection and tracking procedure based on refocusing a set of SAR images on a provided high-resolution grid of the structure. The refocusing procedure is designed for high-resolution spotlight and sliding spotlight SAR images and consists of an azimuth defocusing followed by a modified back-projection algorithm on the given set of points. The scattering centers of the refocused image are detected in the 4-D tomography framework by testing if the main response is at zero elevation in the local elevation-velocity spectral distribution obtained using the Capon estimator. The mean displacement velocity is estimated from the peak response on the zero elevation axis, whereas the displacements time series for detected single scatterers is obtained as phase difference of complex amplitudes. The algorithm is tested by simulations with an emphasis on its behavior for a low number of satellite passes and applied on real data acquired with the TerraSAR-X satellite over the Puylaurent dam. The relative displacements between scattering regions show very good agreement with in situ measurements.

In echo cancellation, the main goal is to recover the near-end signal from the error signal of the adaptive filter, which identifies the echo path. In this context, the Kalman filter represents a very appealing choice, since its basic criterion follows the minimization of the system misalignment (instead of the usual error-based cost function). In this paper, we propose a Kalman filter with individual control factors, in terms of using a different level of uncertainty for each coefficient of the filter. As compared to the basic Kalman filter (which imposes the same uncertainty for all the coefficients of the impulse response), the proposed algorithm achieves better performance, especially in terms of the steady-state misalignment.

Infrastructure monitoring applications can require the tracking of slowly moving points of a certain structure. Given a certain point from a structure to be monitored, in the context of available SAR products where the image is already focused in a slant range - azimuth grid, it is not obvious if this point is the scattering center, if it is in layover or if it is visible from the respective orbit. This paper proposes a scattering center monitoring procedure based on refocusing a set of SAR images on a provided high-resolution DEM of the structure. The scattering centers of the refocused image are detected in the 4-D tomography framework by testing if the main response is at zero elevation in the local elevation-velocity spectral distribution obtained using the Capon estimator. The algorithm is validated on real data acquired with the TerraSAR-X satellite over the Puylaurent water dam in France during March-June 2012. The relative displacements between scattering regions show very good agreement with the in situ measurements.

The frequency-modulated continuous-wave (FMCW) radar is an alternative to the pulse radar when the distance to the target is short. Typical FMCW radar implementations have a homodyne architecture transceiver which limits the performances for short-range applications: The beat frequency can be relatively small and placed in the frequency range affected by the specific homodyne issues (dc offset, self-mixing, and 1/f noise). In addition, one classical problem of an FMCW radar is that the voltage-controlled oscillator adds a certain degree of nonlinearity which can cause a dramatic resolution degradation for wideband sweeps. This paper proposes a short-range X-band FMCW radar platform which solves these two problems by using a heterodyne transceiver and a wideband nonlinearity correction algorithm based on high-order ambiguity functions and time resampling. The platform's displacement measurement capability was tested on range profiles and synthetic aperture radar images acquired for various targets. The displacements were computed from the interferometric phase, and the measurement errors were situated below 0.1 mm for metal bar targets placed at a few meters from the radar.

In this paper, we study the time-domain Kalman filter in the context of echo cancellation. We explain the fundamental differences between the Kalman filter and the recursive least-squares (RLS) algorithm. Also, we show that the normalized least-mean-square (NLMS) algorithm has a clear relationship with the Kalman filter. Furthermore, a simplified Kalman filter is derived and by a judicious choice of its parameters, this algorithm behaves like a variable step-size adaptive filter. Simulation results indicate the good performance of the optimal and simplified Kalman filtering algorithms.

A frequency modulated continuous wave (FMCW) X-band radar platform for millimetric displacements measurement of short-range targets is presented in this paper. The platform's transceiver is based on a heterodyne architecture because the beat frequency is relatively small for short-range targets and it can be placed in the frequency range influenced by the specific homodyne architecture problems: DC offset, self-mixing and 1/f noise. The platform's displacement measurement capability was tested on range profiles and SAR images acquired for various targets. The displacements were computed from the interferometric phase. The measurement errors were situated below 0.1 mm for metal bar targets placed at a few meters from the radar.

The Kalman filter is a very interesting signal processing tool, which is widely used in many practical applications. In this paper, we study the Kalman filter in the context of echo cancellation. The contribution of this work is threefold. First, we derive a different form of the Kalman filter by considering, at each iteration, a block of time samples instead of one time sample as it is the case in the conventional approach. Second, we show how this general Kalman filter (GKF) is connected with some of the most popular adaptive filters for echo cancellation, i.e., the normalized least-mean-square (NLMS) algorithm, the affine projection algorithm (APA) and its proportionate version (PAPA). Third, a simplified Kalman filter is developed in order to reduce the computational load of the GKF; this algorithm behaves like a variable step-size adaptive filter. Simulation results indicate the good performance of the proposed algorithms, which can be attractive choices for echo cancellation.

The stereophonic acoustic echo is due to the coupling between two loudspeakers and two microphones. In the classical approach, this configuration is modelled by a two-input/two-output system with real random variables. In this paper, we propose to redesign this scheme as a single-input/single-output system with complex random variables. In this framework, we illustrate the behavior of some basic adaptive algorithms and present a distortion method which is more suitable for this model.

Proportionate-type affine projection algorithms (PAPAs) are very attractive choices for echo cancellation. These algorithms combine the good features (convergence and tracking) of the affine projection algorithm (APA) and the proportionate idea, which exploits the sparseness character of the echo path in order to further increase their convergence rate. In this paper, we develop a variable step-size (VSS) version of a recently proposed PAPA. The new algorithm achieves a good compromise between fast convergence rate and low misadjustment, but also has a low computational complexity as compared to its classical counterparts.

Most of the echo cancellers are equipped with a double-talk detector (DTD) in order to control the behavior of the adaptive filter during double-talk situations. In this paper, we propose a class of DTDs based on the Holder inequality. These DTDs are simple to implement, have low computational complexity, and perform well even for low echo-to-noise ratios. As a particular case, it is shown that the well-known Geigel algorithm can be obtained from this approach.

Regularization plays a fundamental role in adaptive filtering. An adaptive filter that is not properly regularized will perform very poorly. In spite of this, regularization in our opinion is underestimated and rarely discussed in the literature of adaptive filtering. There are, very likely, many different ways to regularize an adaptive filter. In this paper, we propose one possible way to do it based on a condition that intuitively makes sense. From this condition, we show how to regularize four important algorithms: the normalized least-mean-square (NLMS), the signed-regressor NLMS (SR-NLMS), the improved proportionate NLMS (IPNLMS), and the SR-IPNLMS.

The proportionate normalized least-mean-square (PNLMS) algorithm was developed in the context of network echo cancellation. It has been proven to be efficient when the echo path is sparse, which is not always the case in real-world echo cancellation. The improved PNLMS (IPNLMS) algorithm is less sensitive to the sparseness character of the echo path. This algorithm uses the l1norm to exploit sparseness of the impulse response that needs to be identified. In this paper, we propose an IPNLMS algorithm based on the l0norm, which represents a better measure of sparseness than the l1norm. Simulation results prove that the proposed algorithm outperforms the original IPNLMS algorithm.

In this letter, we show that the normalized least-mean-square (NLMS) algorithm and the affine projection algorithm (APA) can be decomposed as the sum of two orthogonal vectors. One of these vectors is derived from an ℓ2-norm optimization problem while the other one is simply a good initialization vector. By replacing this optimization with the basis pursuit, which is based on the ℓ1-norm optimization, we derive the proportionate NLMS (PNLMS) algorithm and the proportionate APA (PAPA). Many other adaptive filters can be derived following this approach, including new ones.

Proportionate-type normalized least-mean-square algorithms were developed in the context of echo cancellation. In order to further increase the convergence rate and tracking, the “proportionate” idea was applied to the affine projection algorithm (APA) in a straightforward manner. The objective of this letter is twofold. First, a general framework for the derivation of proportionate-type APAs is proposed. Second, based on this approach, a new proportionate-type APA is developed, taking into account the “history” of the proportionate factors. The benefit is also twofold. Simulation results indicate that the proposed algorithm outperforms the classical one (achieving faster tracking and lower misadjustment). Besides, it also has a lower computational complexity due to a recursive implementation of the “proportionate history.”

Most of the adaptive algorithms used for acoustic echo cancellation (AEC) are designed assuming an exact modeling scenario (i.e., the acoustic echo path and the adaptive filter have the same length) and a single-talk context (i.e., the near-end speech is absent). In real-world AEC applications, the adaptive filter works most likely in an under-modeling situation, i.e., its length is smaller than the length of the acoustic impulse response, so that the under-modeling noise is present. Also, the double-talk case is almost inherent, so that a double-talk detector (DTD) is usually involved. Both aspects influence and limit the algorithm’s performance. Taking into account these two practical issues, a double-talk robust variable step size normalized least-meansquare (VSS-NLMS) algorithm is proposed in this paper. This algorithm is nonparametric in the sense that it does not require any information about the acoustic environment, so that it is robust and easy to control in practice.

Space-time block coding represents a practical and pragmatic method to mitigate the fading effects and to increase the channel capacity, by using spatial diversity. The space-time coding techniques are still preferred in communication systems because of the very simple transmit coding rule and of the relative reduced complexity of the maximum likelihood (ML) receivers with respect to other coding methods (e.g. space-time trellis codes) or other MIMO (Multiple Input Multiple Output) algorithms (e.g., spatial multiplexing). One of the drawbacks when using space-time block codes is the increase in complexity at the ML receiver when increasing the number of transmit antennas and the number of constellation points. This paper deals with this issue and introduces a decoding algorithm applicable only for orthogonal space-time block codes. We show that this decoding algorithm reduces the search space dimension of a regular ML receiver, leading to significant complexity reduction for QAM (Quadrature Amplitude Modulation) constellations.

A wide variety of system identification problems can be efficiently addressed based on the Kronecker product decomposition of the impulse response, together with low-rank approximations. Such an approach solves the original system identification problem using a combination of two shorter filters. In this paper, targeting a higher dimensionality reduction, we develop a solution based on a third-order tensor decomposition. In addition, the problem of approximating the rank of a tensor is avoided thanks to the control of a matrix rank. Then, an iterative Wiener filter is developed, which outperforms both the conventional benchmark and the previously developed counterpart that exploits the second-order decomposition.

The performance of the recursive least-squares (RLS) algorithm is governed by the forgetting factor. This parameter leads to a compromise between (1) the tracking capabilities and (2) the misadjustment and stability. In this letter, a variable forgetting factor RLS (VFF-RLS) algorithm is proposed for system identification. In general, the output of the unknown system is corrupted by a noise-like signal. This signal should be recovered in the error signal of the adaptive filter after this one converges to the true solution. This condition is used to control the value of the forgetting factor. The simulation results indicate the good performance and the robustness of the proposed algorithm.

In acoustic echo cancellation (AEC) applications, where the acoustic echo paths are extremely long, the adaptive filter works most likely in an under-modeling situation. Most of the adaptive algorithms for AEC were derived assuming an exact modeling scenario, so that they do not take into account the under-modeling noise. In this letter, a variable step-size normalized least-mean-square (VSS-NLMS) algorithm suitable for the under-modeling case is proposed. This algorithm does not require any a priori information about the acoustic environment; as a result, it is very robust and easy to control in practice. The simulation results indicate the good performance of the proposed algorithm.

The adaptive algorithms used for acoustic echo cancellation (AEC) have to provide (1) high convergence rates and good tracking capabilities, since the acoustic environments imply very long and time-variant echo paths, and (2) low misadjustment and robustness against background noise variations and double-talk. In this context, the affine projection algorithm (APA) and different versions of it are very attractive choices for AEC. However, an APA with a constant step-size parameter has to compromise between the performance criteria (1) and (2). Therefore, a variable step-size APA (VSS-APA) represents a more reliable solution. In this paper, we propose a VSS-APA derived in the context of AEC. Most of the APAs aim to cancelp(i.e., projection order) previous a posteriori errors at every step of the algorithm. The proposed VSS-APA aims to recover the near-end signal within the error signal of the adaptive filter. Consequently, it is robust against near-end signal variations (including double-talk). This algorithm does not require anyaprioriinformation about the acoustic environment, so that it is easy to control in practice. The simulation results indicate the good performance of the proposed algorithm as compared to other members of the APA family.