Wiener Weights Research Articles

Convolutional neural network for 2D adaptive beamforming of phased array antennas with robustness to array imperfections

AbstractAchieving robust and fast two-dimensional adaptive beamforming of phased array antennas is a challenging problem due to its high-computational complexity. To address this problem, a deep-learning-based beamforming method is presented in this paper. In particular, the optimum weight vector is computed by modeling the problem as a convolutional neural network (CNN), which is trained with I/O pairs obtained from the optimum Wiener solution. In order to exhibit the robustness of the new technique, it is applied on an 8 × 8 phased array antenna and compared with a shallow (non-deep) neural network namely, radial basis function neural network. The results reveal that the CNN leads to nearly optimal Wiener weights even in the presence of array imperfections.

Neurotoxicity of Pesticides: The Roadmap for the Cubic Mode of Action.

Pesticides are used today on a planetary-wide scale. The rising need for substances with this biological activity due to an increasing consumption of agricultural and animal products and to the development of urban areas makes the chemical industry to constantly investigate new molecules or to improve the physicochemical characteristics, increase the biological activities and improve the toxicity profiles of the already known ones. Molecular databases are increasingly accessible for in vitro and in vivo bioavailability studies. In this context, structure-activity studies, by their in silico - in cerebro methods, are used to precede in vitro and in vivo studies in plants and experimental animals because they can indicate trends by statistical methods or biological activity models expressed as mathematical equations or graphical correlations, so a direction of study can be developed or another can be abandoned, saving financial resources, time and laboratory animals. Following this line of research the present paper reviews the Structure-Activity Relationship (SAR) studies and proposes a correlation between a topological connectivity index and the biological activity or toxicity made as a result of a study performed on 11 molecules of organophosphate compounds, randomly chosen, with a basic structure including a Phosphorus atom double bounded to an Oxygen atom or to a Sulfur one and having three other simple covalent bonds with two alkoxy (-methoxy or -ethoxy) groups and to another functional group different from the alkoxy groups. The molecules were packed on a cubic structure consisting of three adjacent cubes, respecting a principle of topological efficiency, that of occupying a minimal space in that cubic structure, a method that was called the Clef Method. The central topological index selected for correlation was the Wiener index, since it was possible this way to discuss different adjacencies between the nodes in the graphs corresponding to the organophosphate compounds molecules packed on the cubic structure; accordingly, "three dimensional" variants of these connectivity indices could be considered and further used for studying the qualitative-quantitative relationships for the specific molecule-enzyme interaction complexes, including correlation between the Wiener weights (nodal specific contributions to the total Wiener index of the molecular graph) and the biochemical reactivity of some of the atoms. Finally, when passing from SAR to Q(uantitative)-SAR studies, especially by the present advanced method of the cubic molecule (Clef Method) and its good assessment of the (neuro)toxicity of the studied molecules and of their inhibitory effect on the target enzyme - acetylcholinesterase, it can be seen that a predictability of the toxicity and activity of different analogue compounds can be ensured, facilitating the in vivo experiments or improving the usage of pesticides.

Multispectral Satellite Image Denoising via Adaptive Cuckoo Search-Based Wiener Filter

Satellite image denoising is essential for enhancing the visual quality of images and for facilitating further image processing and analysis tasks. Designing of self-tunable 2-D finite-impulse response (FIR) filters attracted researchers to explore its usefulness in various domains. Furthermore, 2-D FIR Wiener filters which estimate the desired signal using its statistical parameters became a standard method employed for signal restoration applications. In this paper, we propose a 2-D FIR Wiener filter driven by the adaptive cuckoo search (ACS) algorithm for denoising multispectral satellite images contaminated with the Gaussian noise of different variance levels. The ACS algorithm is proposed to optimize the Wiener weights for obtaining the best possible estimate of the desired uncorrupted image. Quantitative and qualitative comparisons are conducted with 10 recent denoising algorithms prominently used in the remote-sensing domain to substantiate the performance and computational capability of the proposed ACSWF. The tested data set included satellite images procured from various sources, such as Satpalda Geospatial Services, Satellite Imaging Corporation, and National Aeronautics and Space Administration. The stability analysis and study of convergence characteristics are also performed, which revealed the possibility of extending the ACSWF for real-time applications as well.

Flower Pollination Algorithm for Adaptive Beamforming of Phased Array Antennas

This paper introduces the flower pollination algorithm (FPA) as an optimization technique suitable for adaptive beamforming of phased array antennas. The FPA is a new nature-inspired evolutionary computation algorithm that is based on pollinating behaviour of flowering plants. Unlike the other nature-inspired algorithms, the FPA has fewer tuning parameters to fit into different optimization problems. The FPA is used to compute the complex beamforming weights of the phased array antenna. In order to exhibit the robustness of the new technique, the FPA has been applied to a uniform linear array antenna with different array sizes. The results reveal that the FPA leads to the optimum Wiener weights in each array size with less number of iterations compared with two other evolutionary optimization algorithms namely, particle swarm optimization and cuckoo search.

Robust Radial Velocity Estimation of Moving Targets Based on Adaptive Data Reconstruction and Subspace Projection Algorithm

In practice, inevitable image coregistration error and channel phase mismatch will significantly degrade the estimation performance of the target radial velocity in the ground moving target indication processing with multichannel synthetic aperture radar (SAR) systems. To overcome this problem, a new radial velocity estimation method using the subspace projection (SP) algorithm with adaptive data reconstruction is proposed in this letter. Based on the joint-pixel signal model, the Wiener weight vector is used to reconstruct the multichannel data vector of the pixel containing the moving target. Then, the SP algorithm is adopted to deal with the radial velocity estimation with the reconstructed single “snapshot” data. The validity and robustness are verified by both simulations and real SAR data experiments.

Non-Wiener Mean Weight Behavior of LMS Transversal Equalizers With Sinusoidal Interference

The least mean-square (LMS) algorithm is generally expected to operate near the corresponding Wiener filter solution. An important exception occurs when the algorithm is used to adapt a transversal equalizer in the presence of additive narrowband interference. For this application, the steady-state LMS equalizer behavior does not correspond to that of the fixed Wiener equalizer: the mean of its weights is different from the Wiener weights, and its mean-square error performance may be significantly better than the Wiener performance. Assuming a large interference-to-signal ratio (ISR), we present the solution for the mean of the LMS weight vector in steady state, based on the Butterweck expansion of the weight update equation. The analytical results are valid for all (mean-square stable) step-sizes. Simulation results are included to support the analytical results and show that the analytical results predict the simulation results accurately, over a wide range of ISR.

Clipped Input RLS Applied to Vehicle Tracking

A new variation to the RLS algorithm is presented. In the clipped RLS algorithm (CRLS), proposed in updating the filter weights and computation of the inverse correlation matrix, the input signal is quantized into three levels. The convergence of the CRLS algorithm to the optimum Wiener weights is proved. The computational complexity and signal estimation error is lower than that of the RLS algorithm. The CRLS algorithm is used in the estimation of a noisy chirp signal and in vehicles tracking. Simulation results in chirp signal detection shows that this algorithm yields considerable error reduction and less computation time in comparison to the conventional RLS algorithm. In the presence of strong noise, also using the proposed algorithm in tracking of 59 vehicles shows an average of 3.06% reduction in prediction error variance relative to conventional RLS algorithm.

Analysis of the Multistage CM Array/Signal Canceler for Digital Communication Signals

The multistage constant modulus (CM) array is a blind adaptive beamformer that can separate cochannel digital communication signals. It consists of several identical stages connected in a cascade structure. Each stage is composed of a multichannel linear equalizer (MCLE) and a multichannel signal canceler (MCSC). The MCLE generates a linear estimate of one cochannel signal impinging on the antenna array. This captured source is removed from the input by the MCSC, which is a parallel connection of adaptive FIR filters, one for each antenna element. In this paper, we describe the architecture of the multistage CM array/signal canceler, and derive the Wiener weights for the MCLE and the MCSC. A discrete-time channel model with fractional sampling at the antenna array is employed. It is demonstrated that the power of the source captured by the first stage is reduced to the noise floor at the input of the next stage, whereas the other sources pass through essentially unchanged. Computer simulations are presented to illustrate the capture behavior of the multistage system.

Letter: Optimal echo path modelling using chaotic modulated speech

AbstractA novel modulating scheme is presented that allows optimal echo path modelling using, real time least mean square (LMS) system identification techniques. The systems of interest are usually based on a class of digital adaptive filters (DAFs). The modelling convergence rate derived from the optimal Wiener weights defines the performance criterion. A novel chaotic based modulation regime utilising the logistic mapping is exploited to whiten the speech power spectral density (PSD) whilst preserving the signal bandwidth requirements. The whitened signal optimises the convergence rate and allows adaptation times to be calculated without a‐priori knowledge of the speech signal's second order statistics. Software simulations are reported for an ensemble of conversational speech realisations and it is shown that the described modulation scheme significantly improves the convergence rate and guarantees optimal modelling independent of the input speech signal statistics. Furthermore, the noise whitened input signal circumvents control supervisory problems usually associated with uncoded speech inputs.

A nonlinear analytical model for the quantized LMS algorithm-the arbitrary step size case

This paper extends conditional moment techniques previously developed for the study of nonlinear versions of the LMS algorithm to the study of the effects of quantizers in the finite precision case. Deterministic nonlinear recursions are derived for the mean and second moment matrix of the weight vector about the Wiener weight for white Gaussian data models and small algorithm step sizes /spl mu/. These recursions are solved numerically and shown to be in very close agreement with the Monte Carlo simulations during all phases of the adaptation process. A design example is presented that demonstrates how the theory can be used to select the number of quantizer bits and the adaptation step size /spl mu/ to yield a desired transient behavior and cancellation performance.

A nonlinear analytical model for the quantized LMS algorithm-the power-of-two step size case

Presents a study of the quantization effects in the finite precision LMS algorithm with power-of-two step sizes. Deterministic nonlinear recursions are presented for the mean and second-moment matrix of the weight vector about the Wiener weight for white Gaussian data models and small algorithm step size /spl mu/. The numerical solutions of these recursions are shown to agree very closely with the Monte Carlo simulations during all phases of the adaptation process. Design examples demonstrate the selection of the number of quantizer bits and the adaptation step size /spl mu/ to yield a desired transient behavior and cancellation performance. The results obtained indicate that previous models are too conservative in predicting the converged MSE for a given number of bits.

On the optimum gain parameter in LMS adaptation

In this correspondence, the optimum selection of the adaptation parameter μ in LMS adaptive estimation is discussed for a white data covarianee matrix. It is shown via analysis and numerical evaluation, that the optimum selection of μ is a complicated function of the number of filter taps, the initial weight setting, the Wiener weights, and the number of learning samples, μ is not chosen, in general, to yield the most rapid transient response. For most cases of interest, a smaller value of μ will be selected for slower adaptation and smaller misadjustment error at the end of the learning phase.

Analysis of the normalized LMS algorithm with Gaussian inputs

The LMS adaptive filter algorithm requires a priori knowledge of the input power level to select the algorithm gain parameter μ for stability and convergence. Since the input power level is usually one of the statistical unknowns, it is normally estimated from the data prior to beginning the adaptation process. It is then assumed that the estimate is perfect in any subsequent analysis of the LMS algorithm behavior. In this paper, the effects of the power level estimate are incorporated in a data dependent μ that appears explicitly within the algorithm. The transient mean and second-moment behavior of the modified LMS (NLMS) algorithm are evaluated, taking into account the explicit statistical dependence of μ upon the input data. The mean behavior of the algorithm is shown to converge to the Wiener weight. A constant coefficient matrix difference equation is derived for the weight fluctuations about the Wiener weight. The equation is solved for a white data covariance matrix and for the adaptive line enhancer with a single-frequency input in steady state for small μ. Expressions for the misadjustment error are also presented. It is shown for the white data covariance matrix case that the averaging of about ten data samples causes negligible degradation as compared to the LMS algorithm. In the ALE application, the steady-state weight fluctuations are shown to be mode dependent, being largest at the frequency of the input.

Time correlation statistics of the LMS adaptive algorithm weights

The transient and steady-state weight correlation statistics of both the real and complex LMS adaptive filters are obtained when the inputs are independent samples from real and circularly Gaussian processes, respectively. A matrix relationship is derived between the covariance matrix of the weight vector at two different times and the covariance matrix of the weights at one time. These expressions show that the weight fluctuations have the same time constants as the mean behavior of the LMS algorithm itself (i.e., the weights are correlated over the same number of iterations that it takes for the algorithm to converge to the Wiener weights for stationary inputs).

On the joint characteristic function of the complex scalar LMS adaptive weight

In this paper, the joint characteristic function of the single weight complex scalar LMS adaptive algorithm is studied. An integral equation is derived for the joint characteristic function of the real and imaginary parts of the weight. This integral equation is used to obtain the weight moments and is approximately solved for a sufficiently small adaptation parameter μ. It is shown that, for small μ and in steady state, the real and imaginary parts of the weights are statistically independent Gaussian random variables with means equal to the Wiener weight. These results are applied to a detection problem using the weight magnitude square as the detection statistic. Assuming the weight is also Gaussian during the transient phase of adaptation, the detection performance is optimized over μ for a fixed number of data samples and a known observation interval. The optimum selection of μ approaches zero so that the adaptation process reduces to a cross-correlation operation. When the observation interval is not known a priori, a μ bounded away from zero is required. This detector is shown to be 3 dB degraded from the optimum narrow-band envelope detector using the same number of data samples.

Weight modulation effects in the adaptive line enhancer

The steady-state behavior of the adaptive line enhancer is modeled by the sum of two filters, the Wiener weight filter and a weight misadjustment filter. The effects of randomly time-varying coefficients in the weight misadjustment filter are modeled so as to display line broadening of single frequency ALE inputs.