COMM-3.1

Effects of Colored Noise on the Performance of Linear Equalizers
Deva K Borah, Rodney A Kennedy (Telecommunications Eng Group, RSISE, Institute of Advanced Studies, The Australian National University, Canberra ACT 0200, Australia), Inbar Fijalkow (ETIS/ENSEA - Univ. de Cergy-Pontoise, 95014 Cergy-Pontoise Cedex, France)

Performance of equalizers depends on the discrete time model of the input signal and noise. The use of higher sampling rate results in colored noise when the bandwidth of the noise-limiting prefilter is not sufficiently large. It is shown that the mean square error (MSE) performance of linear equalizers becomes sensitive to the decision delay when the input noise is colored, and by using the appropriate delay, a significant improvement in the MSE can be achieved. This is in contrast to the behaviour observed in the white noise case well known in the literature. This behaviour is explained in time domain by showing the contributions to the MSE from the columns of the channel convolution matrix and the noise eigenvectors. In the frequency domain, it is shown that the equalizer exploits the noise correlation to improve the MSE.

COMM-3.2

Performance Analysis of a Recursive Fractional Super-Exponential Algorithm
Joao P Gomes, Victor N Barroso (Instituto Superior Tecnico - Instituto de Sistemas e Robotica)

The super-exponential algorithm is a block-based technique for blind channel equalization and system identification. Due to its fast convergence rate, and no a priori parameterization other than the block length, it is a useful tool for linear equalization of moderately distortive channels. This paper presents a recursive implementation of the super-exponential algorithm for fractionally-sampled PAM signals. Although the resulting algorithm is still block-based, recursive propagation of several key variables allows the block length to be significantly reduced without compromising the algorithm's accuracy or speed, thereby enhancing its ability to track channel variations. The convergence rate is only mildly influenced by specific channel responses, and oversampling provides smaller output variance and almost perfect tolerance to sampling errors. Simulation results demonstrate the effectiveness of the proposed technique.

COMM-3.3

Iterative Algorithms for Optimal State Estimation of Jump Markov Linear Systems
Arnaud Doucet, Christophe Andrieu (Signal Processing Group, University of Cambridge, Department of Engineering)

Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. We present three original deterministic and stochastic iterative algorithms for optimal state estimation of JMLS whose computational complexity at each iteration is linear in the data length. The first algorithm yields conditional mean estimates. The second algorithm is an algorithm that yields the marginal maximum a posteriori (MMAP) sequence estimate of the finite state Markov chain. The third algorithm is an algorithm that yields the MMAP sequence estimate of the continuous state of the JMLS. Convergence results for these three algorithms are obtained. Computer simulations are carried out to evaluate their performance.

COMM-3.4

Prediction-Based Adaptive Blind Equalization: A Performance Study
Jukka Mannerkoski, Visa Koivunen (Signal Processing Lab., Tampere Univ. of Technology, FINLAND), Desmond P Taylor (Dept. of Electrical and Electronic Engineering, Univ. of Canterbury, New Zealand)

Blind equalization of a communication channel using a prediction-based Lattice Blind Equalizer (LBE) is considered. Second order cyclostationary statistics and a single-input multiple-output model arising from fractional sampling of the received data are used. The performance of the LBE algorithm is studied in extensive simulations where commonly used example channels are employed. Convergence in the Mean Square Error (MSE) and Symbol Error Rate (SER) as well as the number of symbols required to open the eye are studied at different SNRs. Robustness in the face of channel order mismatch and channels with common subchannel zeros is considered. The simulation results are compared to the results obtained by the fractionally spaced Constant Modulus Algorithm, the Cyclic-RLS algorithm and the subspace method by Moulines et al.

COMM-3.5

Fixed-lag Blind Equalization and Sequence Estimation in Digital Communications Systems using Sequential Importance Sampling
Tim C Clapp, Simon J Godsill (Department of Engineering, Cambridge University)

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent the transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.

COMM-3.6

Leaky Constant Modulus Algorithms: Sensitivity of Local Minima
Sangarapillai Lambotharan, Jonathon Chambers, Anthony Constantinides (Imperial College of Science, Technology and Medicine)

We propose a new family of mixed constant modulus algorithms for the elimination of local minima associated with the fractionally spaced constant modulus algorithm in the presence of channel noise. A special case of this family is the Leaky Constant Modulus Algorithm (L-CMA). We show that L-CMA aims to minimise jointly the intersymbol interference (ISI) and the noise gain introduced by the equalizer. Moreover, we derive a suitable range of leakage factors for which all local minima due to large noise amplification are eliminated.

COMM-3.7

DIRECT SECOND-ORDER BLIND EQUALIZATION OF POLYPHASE CHANNELS BASED ON A DECORRELATION CRITERION
CONSTANTINOS B PAPADIAS (LUCENT TECHNOLOGIES / BELL LABORATORIES), DAVID GESBERT, AROGYASWAMI J PAULRAJ (INFORMATION SYSTEMS LABORATORY, STANFORD UNIVERSITY)

We consider the problem of linear polyphase blind equalization (BE), i.e. we are interested in equalizing the output of a single-input-multiple-output (SIMO) channel, without observing its input. A recent result by Liu and showed that if the sub-channel polynomials are co-prime in the z-domain, then the equalizer output whiteness is necessary and sufficient for the equalization of a white input. Based on this observation, we propose a simple decorrelation criterion for second-order based BE. Due to its second-order nature, this criterion is insensitive to the distance of the input from Gaussianity, hence it achieves BE even for Gaussian or non-Gaussian inputs. Moreover, unlike other second-order techniques, our approach bypasses channel estimation and computes directly the equalizer. By doing so, it avoids the problem of ill-conditioning due to channel order mismatch which is crucial to other techniques. Combined to its good convergence properties, these characteristics make the proposed technique an attractive option for robust polyphase BE, as evidenced by both our analysis and computer simulation results.

COMM-3.8

Weighted Least-Squares Blind Deconvolution
Simone Fiori, Francesco Piazza (University of Ancona)

The aim of this paper is to present a new cost function for blind deconvolution of non-minimum phase systems. The proposed criterion arises as a natural consequence of a fundamental theorem proved by Benveniste, Goursat and Ruget, and appears to be the weighted square of the difference among two spectra, thus its minimization leads to a weighted least-squares blind deconvolution technique. In order to assess the new theory some simulation results both on ideal (noiseless) and noisy channels are presented.

COMM-3.9

Blind Equalizers for Multipath Channels with Best Equalization Delay
Hui Luo (Digital Video Express, LP), Ruey-Wen Liu (Department of Electrical Engineering, University of Notre Dame)

Recent studies show that equalizers with different equalization delays achieve different performances. The best performed equalizer is not necessarily the one with 0-delay, and often not the case when the channel is non-minimum-phase. In this paper, a blind channel equalization algorithm is presented, by which equalizers with all possible equalization delays can be calculated simultaneously from the second order statistics of received signals. A (blind) evaluation index is then presented for the purpose of selecting the best equalizer. Simulation shows that the best delayed equalizer performs much better than that for other equalization delays and those given by constant modulus algorithm and linear prediction algorithm.

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Last Update: February 4, 1999 Ingo Höntsch