Bayesian Decision Feedback Equalizer Research Articles

A New Equalization Algorithms for Distortion Signal Extraction in Mobile Wireless System

In the high-speed mobile wideband communication system, motions of receivers, transmitters or wireless environments generate Doppler frequency. The Doppler effect and instantaneous fading frequency induces serious waveform distortion in the received signal. To solve these problems, the paper presents an improved equalization model, the new model combines the Bayesian detector and decision feedback equalizer (DFE) to form a new effective BDFE structure, which is superior to traditional equalization structure in the mobile environment. Further, a new algorithm is given to achieve faster convergence and smaller steady-state error, the new algorithm take Marr function as a basis function, and two parameters shape the profile of function, with the simulation tool, the optimization values are obtained for the new model and algorithm. The experimental results show that the new algorithm can improve the output SNR up to 6 dB gain with the new BDFE model.

BER analysis of Bayesian equalization using orthogonal hyperplanes

Bayesian symbol-by-symbol detection using a finite sequence observation space has been the subject of renewed research interest. The Bayesian transverse equalizer (BTE) and Bayesian decision feedback equalizer (BDFE) are two common Bayesian detectors. It is often difficult to evaluate the bit-error rate (BER) performance of these Bayesian detectors since the BER cannot be analytically evaluated and the high complexity of these detectors makes simulation techniques computationally prohibitive, especially at low BERs. We propose a framework to evaluate the BER for the BTE and a lower bound on the BER for the BDFE. This framework is based on finding an approximation of the conditional error probability for each of the noiseless channel states in the observation space. The optimal Bayesian decision boundary is approximated by a set of hyperplanes, and each hyperplane is rotated some minimal angle to make them mutually orthogonal/parallel. The conditional probability of error can be readily evaluated on the topology of orthogonal/parallel rotated hyperplanes. Our BER evaluation is accurate and does not require simulations. A reduced complexity approach to evaluate the BER is also developed.

Bayesian Decision Feedback Equalizer with Receiver Diversity Combining

A combining method for receiver diversity, followed by a Bayesian decision feedback equalizer, is proposed. This eigenvector based combining maximizes the desired part energy of combined channel, on which the equalizer performance mainly depends. The validity of the proposed method is demonstrated by simulations.

Importance sampling simulation for evaluating lower-bound symbol error rate of the Bayesian DFE with multilevel signaling schemes

For the class of equalizers that employs a symbol-decision finite-memory structure with decision feedback, the optimal solution is known to be the Bayesian decision feedback equalizer (DFE). The complexity of the Bayesian DFE, however, increases exponentially with the length of the channel impulse response (CIR) and the size of the symbol constellation. Conventional Monte Carlo simulation for evaluating the symbol error rate (SER) of the Bayesian DFE becomes impossible for high channel signal-to-noise ratio (SNR) conditions. It has been noted that the optimal Bayesian decision boundary separating any two neighboring signal classes is asymptotically piecewise linear and consists of several hyperplanes when the SNR tends to infinity. This asymptotic property can be exploited for efficient simulation of the Bayesian DFE. An importance sampling (IS) simulation technique is presented based on this asymptotic property for evaluating the lower bound SER of the Bayesian DFE with a multilevel pulse amplitude modulation (M-PAM) scheme under the assumption of correct decisions being fed back. A design procedure is developed, which chooses appropriate bias vectors for the simulation density to ensure asymptotic efficiency (AE) of the IS simulation.

Importance sampling simulation for evaluating the lower-bound BER of the Bayesian DFE

An importance sampling (IS) simulation technique, originally derived by Iltis (1995) for Bayesian equalizers, is extended to evaluate the lower-bound bit error rate of the Bayesian decision feedback equalizer (under the assumption of correct decisions being fed back). Using a geometric translation approach, it is shown that the two subsets of opposite-class channel states are always linearly separable. A design procedure is presented, which chooses appropriate bias vectors for the simulation density to ensure asymptotic efficiency of the IS simulation.

Adaptive Bayesian decision feedback equaliser for alpha-stable noise environments

In some communication systems the channel noise is known to be non-Gaussian due, largely, to impulsive phenomena. The performance of signal processing algorithms designed under the Gaussian assumption may degrade seriously in such environments. In this paper we investigate the problem of adaptive channel equalisation in an impulsive noise environment. The impulsive interfering noise is modelled as an α-stable process. We first derive the optimum Bayesian decision feedback equaliser and present a novel analytical framework for the evaluation of systems in infinite variance environments. A family of generalised adaptive channel identification algorithms for this infinite variance noise environment is also presented. The combination of a Bayesian equaliser and a channel estimator operating as an adaptive channel equaliser is experimentally studied and its performance is compared with that of a traditional system designed under the Gaussian assumption. The experimental data suggest that the proposed combination of equaliser and channel estimator outperforms the traditionally designed adaptive equaliser in terms of error probability. We finally provide some useful approximations concerning the practical implementation of an α-stable adaptive equaliser.

Blind equalization using parallel Bayesian decision feedback equalizer

The purpose of this paper is to propose a new method for blind equalization using parallel Bayesian decision feedback equalizer (DFE). Blind equalization based on decision-directed algorithm, including the previous proposed Chen’s blind Bayesian DFE, cannot give the correct convergence without the suitable initialization corresponding to the small inter-symbol interference. How to find the suitable initialization becomes the key for the correct convergence. Here, the “start” vector with several states is used to obtain several channel estimates which are the initial channel estimates in proposed method. In these initial channel estimates, the best one which has converged toward the correct result in some degree must exist. The decision-directed algorithm for parallel blind Bayesian DFE is purchased from these initial channel estimates respectively. Evaluating the Bayesian likelihood which is defined as the accumulation of the natural logarithm of the Bayesian decision variable, the correct channel estimates corresponding to the maximum Bayesian likelihood can be found. Compared with Chen’s blind Bayesian DFE, the proposed method presents better convergence performance with less computational complexity. Furthermore, the proposed algorithm works satisfactorily even for channel with severe ISI and in-band spectral null, while Chen’s blind Bayesian DFE fails.

Asymptotic Bayesian decision feedback equalizer using a set of hyperplanes

We present a signal space partitioning technique for realizing the optimal Bayesian decision feedback equalizer (DFE). It is known that when the signal-to-noise ratio (SNR) tends to infinity, the decision boundary of the Bayesian DFE is asymptotically piecewise linear and consists of several hyperplanes. The proposed technique determines these hyperplanes explicitly and uses them to partition the observation signal space. The resulting equalizer is made up of a set of parallel linear discriminant functions and a Boolean mapper. Unlike the existing signal space partitioning technique of Kim and Moon (1998), which involves complex combinatorial search and optimization in design, our design procedure is simple and straightforward, and guarantees to achieve the asymptotic Bayesian DFE.

Fuzzy implementation of a Bayesian equaliser in the presence of intersymbol and co-channel interference

The authors investigate the problem of channel equalisation in the presence of co-channel interference (CCI), intersymbol interference and additive white gaussian noise. The optimal Bayesian decision feedback equaliser decision function for this problem is derived and an elegant fuzzy implementation of the optimal solution is proposed. This fuzzy implemented equaliser is able to provide performance close to the optimal equaliser with a substantial reduction in computational complexity. The equaliser consists of a fuzzy equaliser with an input processing block for co-channel compensation. This preprocessor can be used under severe-to-moderate CCI and can be removed under low CCI conditions. Simulation studies demonstrate the performance of the fuzzy equaliser developed.

Space translation properties and the minimum-BER linear-combiner DFE

Decision feedback in a decision feedback equaliser (DFE) performs a space translation that maps the DFE onto a transversal equaliser in the translated observation space. Properties of DFEs can therefore be analysed more easily by exploiting this geometric translation property. This approach is used to analyse the conventional DFE that employs a linear combination of the channel observations and the past decisions (the linear-combiner DFE). It is demonstrated that the usual minimum mean square error (MMSE) solution does not achieve the full performance potential of the linear-combiner DFE structure. A bit error rate (BER) expression for the linear-combiner DFE with binary signalling is obtained, and a method is proposed to optimally set the coefficients of the linear-combiner DFE. The performance of this minimum-BER (MBER) linear-combiner DFE is much closer to that of the optimal Bayesian DFE, compared with the MMSE linear-combiner DFE.

Bayesian decision feedback equaliser for overcoming co-channel interference

The authors derive a Bayesian decision feedback equaliser which incorporates co-channel interference compensation. By exploiting the structure of co-channel interfering signals, the proposed Bayesian decision feedback equaliser is able to distinguish an interfering signal from white noise and utilises this information to improve performance. Adaptive implementation of this Bayesian decision feedback equaliser includes identifying the channel model using the least mean square algorithm and estimating the co-channel states by means of an unsupervised clustering scheme. Simulation involving a binary signal constellation is used to compare both the theoretical and adaptive performance of this Bayesian decision feedback equaliser with those of the maximum likelihood sequence estimator. The results obtained indicate that, in the presence of severe co-channel interference, the Bayesian decision feedback equaliser employing the proposed simple scheme to compensate co-channel interference can outperform the maximum likelihood sequence estimator that only treats co-channel interference as an additional coloured noise.

Adaptive Bayesian decision feedback equalizer for dispersive mobile radio channels

The paper investigates adaptive equalization of time-dispersive mobile radio fading channels and develops a robust high performance Bayesian decision feedback equalizer (DFE). The characteristics and implementation aspects of this Bayesian DFE are analyzed, and its performance is compared with those of the conventional symbol or fractional spaced DFE and the maximum likelihood sequence estimator (MLSE). In terms of computational complexity, the adaptive Bayesian DFE is slightly more complex than the conventional DFE but is much simpler than the adaptive MLSE. In terms of error rate in symbol detection, the adaptive Bayesian DFE outperforms the conventional DFE dramatically. Moreover, for severely fading multipath channels, the adaptive MLSE exhibits significant degradation from the theoretical optimal performance and becomes inferior to the adaptive Bayesian DFE.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Complex-valued radial basis function network, Part II: Application to digital communications channel equalisation

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.

Fast blind equalisation based on a bayesian decision feedback equaliser

A blind Bayesian decision feedback equaliser is derived for joint channel and data estimation. The nature of this algorithm leads to an efficient parallel implementation. Convergence can be achieved in less than 50 symbols when a binary symbol constellation is used. >

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. >