Bernard Mulgrew

A clustering technique for digital communications channel equalization using radial basis function networks

The application of a radial basis function network to digital communications channel equalization is examined. It is shown that the radial basis function network has an identical structure to the optimal Bayesian symbol-decision equalizer solution and, therefore, can be employed to implement the Bayesian equalizer. The training of a radial basis function network to realize the Bayesian equalization solution can be achieved efficiently using a simple and robust supervised clustering algorithm. During data transmission a decision-directed version of the clustering algorithm enables the radial basis function network to track a slowly time-varying environment. Moreover, the clustering scheme provides an automatic compensation for nonlinear channel and equipment distortion. Computer simulations are included to illustrate the analytical results.

Adaptive Bayesian equalizer with decision feedback

A Bayesian solution is derived for digital communication channel equalization with decision feedback. This is an extension of the maximum a posteriori probability symbol-decision equalizer to include decision feedback. A novel scheme utilizing decision feedback that not only improves equalization performance but also reduces computational complexity greatly is proposed. It is shown that the Bayesian equalizer has a structure equivalent to that of the radial basis function network, the latter being a one-hidden-layer artificial neural network widely used in pattern classification and many other areas of signal processing. Two adaptive approaches are developed to realize the Bayesian solution. The maximum-likelihood Viterbi algorithm and the conventional decision feedback equalizer are used as two benchmarks to asses the performance of the Bayesian decision feedback equalizer. >

Iterative frequency estimation by interpolation on Fourier coefficients

The estimation of the frequency of a complex exponential is a problem that is relevant to a large number of fields. In this paper, we propose and analyze two new frequency estimators that interpolate on the Fourier coefficients of the received signal samples. The estimators are shown to achieve identical asymptotic performances. They are asymptotically unbiased and normally distributed with a variance that is only 1.0147 times the asymptotic Crame/spl acute/r-Rao bound (ACRB) uniformly over the frequency estimation range.

Applying radial basis functions

Discusses the application of neural networks to general and radial basis functions and in particular to adaptive equalization and interference rejection problems. Neural-network-based algorithms strike a good balance between performance and complexity in adaptive equalization, and show promise in spread spectrum systems.

Smart antenna arrays for CDMA systems

There are a diverse range of products and services currently on the market, but cellular or personal communications services (PCS) radio networks probably have the highest public profile. These services provide highly mobile, widely accessible two-way voice and data communications links. In general, the most complex and expensive part of the radio path for these systems is the base station. As a result, manufacturers have been designing networks that have high efficiency in terms of the bandwidth occupied and the number of users per base station. Base station antenna arrays are a promising method for providing large capacity increases in cellular mobile radio systems. This article considers channel-modeling issues, receiver structures, and algorithms, and looks at the potential capacity gains that can be achieved. It considers antenna arrays for the mobile-to-base-station or reverse link of a CDMA cellular system. It begins with an introduction to CDMA communications systems and also addresses the general topic of antenna array receivers.

Adaptive minimum-BER linear multiuser detection for DS-CDMA signals in multipath channels

The problem of constructing adaptive minimum bit error rate (MBER) linear multiuser detectors is considered for direct-sequence code division multiple access (DS-CDMA) signals transmitted through multipath channels. Based on the approach of kernel density estimation for approximating the bit error rate (BER) from training data, a least mean squares (LMS) style stochastic gradient adaptive algorithm is developed for training linear multiuser detectors. Computer simulation is used to study the convergence speed and steady-state BER misadjustment of this adaptive MBER linear multiuser detector, and the results show that it outperforms an existing LMS-style adaptive MBER algorithm presented by Yeh et al. (see Proc. Globecom, Sydney, Australia, p.3590-95, 1998).

Complex-valued radial basis function network, part II: application to digital communications channel equalisation

Abstract In the first part of this paper, a complex-valued multi-output radial basis function network was proposed and two learning algorithms were derived. This second part investigates the adaptive realisation of a Bayesian solution for 4-QAM digital communications channel equalisation using the complex single-output radial basis function network. It is shown that the optimal Bayesian equaliser is structurally equivalent to the complex radial basis function network, and this intimate connection is exploited to develop fast training algorithms for implementing a Bayesian equaliser based on the latter. A novel strategy of utilising decision feedback is employed to improve equaliser performance as well as to reduce computational complexity. The conventional decision feedback equaliser and the maximum likelihood sequence estimator are used as two benchmarks to assess the performance of this Bayesian decision feedback equaliser.

Gradient radial basis function networks for nonlinear and nonstationary time series prediction

We present a method of modifying the structure of radial basis function (RBF) network to work with nonstationary series that exhibit homogeneous nonstationary behavior. In the original RBF network, the hidden nodes function is to sense the trajectory of the time series and to respond when there is a strong correlation between the input pattern and the hidden nodes center. This type of response, however, is highly sensitive to changes in the level and trend of the time series. To counter these effects, the hidden nodes function is modified to one which detects and reacts to the gradient of the series. We call this new network the gradient RBF (GRBF) model. Single and multistep predictive performance for the Mackey-Glass chaotic time series were evaluated using the classical RBF and GRBF models. The simulation results for the series without and with a tine-varying mean confirm the superior performance of the GRBF predictor over the RBF predictor.

Active control of nonlinear noise processes in a linear duct

This paper investigates two scenarios in active noise control (ANC) that lead to performance degradation with conventional linear control techniques. The first scenario addresses the noise itself. The low-frequency noise, traveling as plane waves in a duct, is usually assumed to be broadband random or periodic tonal noise. Linear techniques applied to actively control this noise have been shown to be successful. However, in many practical applications, the noise often arises from dynamical systems, which cause the noise to be nonlinear and deterministic or stochastic, colored, and non-Gaussian. Linear techniques cannot fully exploit the coherence in the noise and, therefore, perform suboptimally. The other scenario is that the actuator in an ANC system has been shown to be nonminimum phase. One of the tasks of the controller, in ANC systems, is to model the inverse of the actuator. Obviously, a linear controller is not able to perform that task. To combat the problems, as mentioned above, a nonlinear controller has been implemented in the ANC system. It is shown in this paper that the nonlinear controller consists of two parts: a linear system identification part and a nonlinear prediction part. The standard filtered-x algorithms cannot be used with a nonlinear controller, and therefore, the control scheme was reconfigured. Computer simulations have been carried out and confirm the theoretical derivations for the combined nonlinear and linear controller.

Complex-valued radial basis function network, Part I: network architecture and learning algorithms

Abstract The paper proposes a complex radial basis function network. The network has complex centres and connection weights, but the nonlinearity of its hidden nodes remains a real-valued function. This kind of network is able to generate complicated nonlinear decision surfaces or to approximate an arbitrary nonlinear function in complex multi-dimensional space, and it provides a powerful tool for nonlinear signal processing involving complex signals. The paper is divided into two parts. The first part introduces the network architecture and derives both block-data and recursive learning algorithms for this complex radial basis function network. The complex orthogonal least squares algorithm is a batch learning algorithm capable of constructing an adequate network structure, while a complex version of the hybrid clustering and least squares algorithm offers real-time adaptation capability. The identification of a nonlinear communications channel model is used to illustrate these two learning algorithms. In the second part of the paper, a practical application of this complex radial basis function network is demonstrated using digital communications channel equalisation.