Nonlinear Beamforming Research Articles

A Nonlinear Adaptive Beamforming Algorithm Based on Least Squares Support Vector Regression

To overcome the performance degradation in the presence of steering vector mismatches, strict restrictions on the number of available snapshots, and numerous interferences, a novel beamforming approach based on nonlinear least-square support vector regression machine (LS-SVR) is derived in this paper. In this approach, the conventional linearly constrained minimum variance cost function used by minimum variance distortionless response (MVDR) beamformer is replaced by a squared-loss function to increase robustness in complex scenarios and provide additional control over the sidelobe level. Gaussian kernels are also used to obtain better generalization capacity. This novel approach has two highlights, one is a recursive regression procedure to estimate the weight vectors on real-time, the other is a sparse model with novelty criterion to reduce the final size of the beamformer. The analysis and simulation tests show that the proposed approach offers better noise suppression capability and achieve near optimal signal-to-interference-and-noise ratio (SINR) with a low computational burden, as compared to other recently proposed robust beamforming techniques.

Frequency-difference beamforming with sparse arrays

When an acoustic signal is transmitted to a remote receiving array with sufficient aperture and transducer density, the arrival direction(s) of the ray paths linking the source and the array may be determined by beamforming the transducer recordings. However, when the receiving array is sparse, i.e. there are many signal wavelengths between transducers, the utility of conventional beamforming is degraded because of spatial aliasing. Yet, when the signal has sufficient bandwidth, such aliasing may be mitigated or eliminated through use of an unconventional nonlinear beamforming technique that manufactures a desired frequency difference from the recorded signals. When averaged through the signal's frequency band, the output of frequency-difference beamforming is similar to that of conventional beamforming evaluated at the desired difference frequency. Results and comparisons from simple propagation simulations and FAF06 experimental measurements are shown for broadband signal pulses (11-19 kHz) that propagate 2.2 km underwater to a vertical 16-element receiving array having a 3.75-m-spacing between elements (almost 40 signal-center-frequency wavelengths). Here, conventional delay-and-sum beamforming results in the signal's frequency band are featureless, but received ray-path directions are successfully determined using frequency differences that are well below the broadcast signal's frequency band. [Sponsored by ONR.]

Symmetric Complex-Valued RBF Receiver for Multiple-Antenna-Aided Wireless Systems

A nonlinear beamforming assisted detector is proposed for multiple-antenna-aided wireless systems employing complex-valued quadrature phase shift-keying modulation. By exploiting the inherent symmetry of the optimal Bayesian detection solution, a novel complex-valued symmetric radial basis function (SRBF)-network-based detector is developed, which is capable of approaching the optimal Bayesian performance using channel-impaired training data. In the uplink case, adaptive nonlinear beamforming can be efficiently implemented by estimating the system's channel matrix based on the least squares channel estimate. Adaptive implementation of nonlinear beamforming in the downlink case by contrast is much more challenging, and we adopt a cluster-variation enhanced clustering algorithm to directly identify the SRBF center vectors required for realizing the optimal Bayesian detector. A simulation example is included to demonstrate the achievable performance improvement by the proposed adaptive nonlinear beamforming solution over the theoretical linear minimum bit error rate beamforming benchmark.

Fully complex-valued radial basis function networks: Orthogonal least squares regression and classification

We consider a fully complex-valued radial basis function (RBF) network for regression and classification applications. For regression problems, the locally regularised orthogonal least squares (LROLS) algorithm aided with the D-optimality experimental design, originally derived for constructing parsimonious real-valued RBF models, is extended to the fully complex-valued RBF (CVRBF) network. Like its real-valued counterpart, the proposed algorithm aims to achieve maximised model robustness and sparsity by combining two effective and complementary approaches. The LROLS algorithm alone is capable of producing a very parsimonious model with excellent generalisation performance while the D-optimality design criterion further enhances the model efficiency and robustness. By specifying an appropriate weighting for the D-optimality cost in the combined model selecting criterion, the entire model construction procedure becomes automatic. An example of identifying a complex-valued nonlinear channel is used to illustrate the regression application of the proposed fully CVRBF network. The proposed fully CVRBF network is also applied to four-class classification problems that are typically encountered in communication systems. A complex-valued orthogonal forward selection algorithm based on the multi-class Fisher ratio of class separability measure is derived for constructing sparse CVRBF classifiers that generalise well. The effectiveness of the proposed algorithm is demonstrated using the example of nonlinear beamforming for multiple-antenna aided communication systems that employ complex-valued quadrature phase shift keying modulation scheme.

Support Vector Machines for Antenna Array Processing and Electromagnetics

Support Vector Machines (SVM) were introduced in the early 90's as a novel nonlinear solution for classification and regression tasks. These techniques have been proved to have superior performances in a large variety of real world applications due to their generalization abilities and robustness against noise and interferences. This book introduces a set of novel techniques based on SVM that are applied to antenna array processing and electromagnetics. In particular, it introduces methods for linear and nonlinear beamforming and parameter design for arrays and electromagnetic applications.

A general linear model for MEG beamformer imaging

A new general linear model (GLM) beamformer method is described for processing magnetoencephalography (MEG) data. A standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space. A Hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band (not necessary in the case of sustained (DC) fields), enabling the general linear model to be applied and a volumetric T statistic image to be determined. The new method is illustrated by a two-source simulation (sustained field and 20 Hz) and is shown to provide accurate localization. The method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes, respectively, in the case of a scintillating scotoma. The new method brings the advantages of the general linear model to the analysis of MEG data and should prove useful for the localization of changing patterns of activity across all frequency ranges including DC (sustained fields).

Kernel-Based Nonlinear Beamforming Construction Using Orthogonal Forward Selection With the Fisher Ratio Class Separability Measure

This letter shows that the wireless communication system capacity is greatly enhanced by employing nonlinear beamforming and that the optimal Bayesian beamformer outperforms the standard linear beamformer significantly in terms of a reduced bit error rate, at a cost of increased complexity. A block-data adaptive implementation of the Bayesian beamformer is realized based on an orthogonal forward selection procedure with the Fisher ratio for class separability measure.

Group imaging of task-related changes in cortical synchronisation using nonparametric permutation testing

Synthetic aperture magnetometry (SAM) is a nonlinear beamformer technique for producing 3D images of cortical activity from magnetoencephalography data. We have previously shown how SAM images can be spatially normalised and averaged to form a group image. In this paper we show how nonparametric permutation methods can be used to make robust statistical inference about group SAM data. Data from a biological motion direction discrimination experiment were analysed using both a nonparametric analysis toolbox (SnPM) and a conventional parametric approach utilising Gaussian field theory. In data from a group of six subjects, we were able to show robust group activation at the P < 0.05 (corrected) level using the nonparametric methods, while no significant clusters were found using the conventional parametric approach. Activation was found using SnPM in several regions of right occipital–temporal cortex, including the superior temporal sulcus, V5/MT, the fusiform gyrus, and the lateral occipital complex.

Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures

Many approaches have been studied for the array processing problem when the additive noise is modeled with a Gaussian distribution, but these schemes typically perform poorly when the noise is non-Gaussian and/or impulsive. This paper is concerned with maximum likelihood array processing in non-Gaussian noise. We present the Cramer-Rao bound on the variance of angle-of-arrival estimates for arbitrary additive, independent, identically distributed (iid), symmetric, non-Gaussian noise. Then, we focus on non-Gaussian noise modeling with a finite Gaussian mixture distribution, which is capable of representing a broad class of non-Gaussian distributions that include heavy tailed, impulsive cases arising in wireless communications and other applications. Based on the Gaussian mixture model, we develop an expectation-maximization (EM) algorithm for estimating the source locations, the signal waveforms, and the noise distribution parameters. The important problems of detecting the number of sources and obtaining initial parameter estimates for the iterative EM algorithm are discussed in detail. The initialization procedure by itself is an effective algorithm for array processing in impulsive noise. Novel features of the EM algorithm and the associated maximum likelihood formulation include a nonlinear beamformer that separates multiple source signals in non-Gaussian noise and a robust covariance matrix estimate that suppresses impulsive noise while also performing a model-based interpolation to restore the low-rank signal subspace. The EM approach yields improvement over initial robust estimates and is valid for a wide SNR range. The results are also robust to PDF model mismatch and work well with infinite variance cases such as the symmetric stable distributions. Simulations confirm the optimality of the EM estimation procedure in a variety of cases, including a multiuser communications scenario. We also compare with existing array processing algorithms for non-Gaussian noise.

Results of take-home trial for a nonlinear beamformer used as a noise reduction strategy for cochlear implants

A nonlinear frequency domain beamforming algorithm was evaluated as a noise reduction technique with eight cochlear implant patients, in a take-home trial. The subjects wore the prototype device coupled to the Nucleus processor for 5–8 weeks. The subjects were tested both before and after the take-home trial with a single noise source at 45 deg ipsilateral to the implant and with sentence type material. The results strongly favored the coupled device for noisy environments and indicated no additional benefits from a period of continued use. The subjective reports indicated that the two-microphone coupled device had a more robust sound quality and is preferred in noisy environments to the stand alone device. Currently the performance measures are being extended to cover sentence scores in a diffuse noise field (four speakers at different locations) and the results for both noise jammer arrangements will be reported.

Nonlinear noise filtering and beamforming using the perceptron and its Volterra approximation

The multilayer perceptron, an artificial neural network, is applied to the problem of interference reduction in single- and multiple-sensor systems. The filter is able to operate approximately as a linear trapped delay line if nonlinear processing cannot further reduce the mean-squared error of the output. Supplanting the activation function of the perceptron by a polynomial leads to the finite-order Volterra filter for which optimum weights can be calculated. Preliminary examples using the perceptron in single-sensor noise filtering show output signal-to-noise ratio (SNR) improvements of up to 2.2 dB compared to the optimum linear filter. Experiments with a nonlinear two-microphone beamformer show a 2.7 dB SNR enhancement for a sinusoidal target and an off-axis white noise jammer. For speech inputs under anechoic conditions, the Volterra beamformer achieved an average intelligibility improvement of 5.7%. >

The Canadian seismic array monitor processing system (cansam)

abstractAn on-line digital beamforming and detection system has been operating at the Canadian short-period array near Yellowknife since early 1974. The installation followed the renewed recognition of the important contribution this array can make to worldwide detection and location of small seismic events. System design is based on earlier Canadian experience. Daily event detection logs are available in Ottawa via dialed telephone line. Nonlinear beamforming is used to lower the false alarm rate at given detection level, and it is shown to perform as predicted. During the 6 winter and spring months, the detection threshold is mb 4.0 to 4.1 at 50 per cent false alarm rate. During summer and fall, organized surface-wave noise originating on Great Slave Lake raises this level to mb 4.6 to 4.7.