Adaptive nonlinear equalizer using a mixture of gaussians based on-line density estimator

This paper introduces a new adaptive nonlinear equalizer relying on a radial basis function (RBF) model, which is designed based on the minimum bit error rate (MBER) criterion, in the system setting of the intersymbol interference channel plus a co-channel interference. Our proposed algorithm is referred to as the on-line mixture of Gaussians estimator aided MBER (OMG-MBER) equalizer. Specifically, a mixture of Gaussians based probability density function (PDF) estimator is used to model the PDF of the decision variable, for which a novel on-line PDF update algorithm is derived to track the incoming data. With the aid of this novel on-line mixture of Gaussians based sample-by-sample updated PDF estimator, our adaptive nonlinear equalizer is capable of updating its equalizer’s parameters sample by sample to aim directly at minimizing the RBF nonlinear equalizer’s achievable bit error rate (BER). The proposed OMG-MBER equalizer significantly outperforms the existing on-line nonlinear MBER equalizer, known as the least bit error rate equalizer, in terms of both the convergence speed and the achievable BER, as is confirmed in our simulation study

Reliability comparison of transmit/receive diversity and error control coding in low-power medium access control protocols

Low-power medium access control (MAC) protocols used for communication of energy constraint wireless embedded devices do not cope well with situations where transmission channels are highly erroneous. Existing MAC protocols discard corrupted messages which lead to costly retransmissions. To improve transmission performance, it is possible to include an error correction scheme and transmit/receive diversity. It is possible to add redundant information to transmitted packets in order to recover data from corrupted packets. It is also possible to make use of transmit/receive diversity via multiple antennas to improve error resiliency of transmissions. Both schemes may be used in conjunction to further improve the performance. In this study, the authors show how an error correction scheme and transmit/receive diversity can be integrated in low-power MAC protocols. Furthermore, the authors investigate the achievable performance gains of both methods. This is important as both methods have associated costs (processing requirements; additional antennas and power) and for a given communication situation it must be decided which methods should be employed. The authors’ results show that, in many practical situations, error control coding outperforms transmission diversity; however, if very high reliability is required, it is useful to employ both schemes together.

The importance of accurate wind resource assessment for evaluating the economic viability of small wind turbines

The techno-economic performance of a small wind turbine is very sensitive to the available wind resource. However, due to financial and practical constraints installers rely on low resolution wind speed databases to assess a potential site. This study investigates whether the two site assessment tools currently used in the UK, NOABL or the Energy Saving Trust wind speed estimator, are accurate enough to estimate the techno-economic performance of a small wind turbine. Both the tools tend to overestimate the wind speed, with a mean error of 23% and 18% for the NOABL and Energy Saving Trust tool respectively. A techno-economic assessment of 33 small wind turbines at each site has shown that these errors can have a significant impact on the estimated load factor of an installation. Consequently, site/turbine combinations which are not economically viable can be predicted to be viable. Furthermore, both models tend to underestimate the wind resource at relatively high wind speed sites, this can lead to missed opportunities as economically viable turbine/site combinations are predicted to be non-viable. These results show that a better understanding of the local wind resource is a required to make small wind turbines a viable technology in the UK.

An Ensemble Smoother with Error Estimates

A smoother introduced earlier by van Leeuwen and Evensen is applied to a problem in which real obser vations are used in an area with strongly nonlinear dynamics. The derivation is new , but it resembles an earlier derivation by van Leeuwen and Evensen. Again a Bayesian view is taken in which the prior probability density of the model and the probability density of the obser vations are combined to for m a posterior density . The mean and the covariance of this density give the variance-minimizing model evolution and its errors. The assumption is made that the prior probability density is a Gaussian, leading to a linear update equation. Critical evaluation shows when the assumption is justified. This also sheds light on why Kalman filters, in which the same ap- proximation is made, work for nonlinear models. By reference to the derivation, the impact of model and obser vational biases on the equations is discussed, and it is shown that Bayes’ s for mulation can still be used. A practical advantage of the ensemble smoother is that no adjoint equations have to be integrated and that error estimates are easily obtained. The present application shows that for process studies a smoother will give superior results compared to a filter , not only owing to the smooth transitions at obser vation points, but also because the origin of features can be followed back in time. Also its preference over a strong-constraint method is highlighted. Further more, it is argued that the proposed smoother is more efficient than gradient descent methods or than the representer method when error estimates are taken into account

Sparse density estimator with tunable kernels

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

Reflections on practical approaches to involving children and young people in the data analysis process

This article reflects on key methodological issues emerging from children and young people's involvement in data analysis processes. We outline a pragmatic framework illustrating different approaches to engaging children, using two case studies of children's experiences of participating in data analysis. The article highlights methods of engagement and important issues such as the balance of power between adults and children, training, support, ethical considerations, time and resources. We argue that involving children in data analysis processes can have several benefits, including enabling a greater understanding of children's perspectives and helping to prioritise children's agendas in policy and practice. (C) 2007 The Author(s). Journal compilation (C) 2007 National Children's Bureau.