Asymptotic analysis of stabilisation technique for the blindfractionally spaced equaliser

The authors propose a technique to counteract the ill-conditioning of the blind fractionally spaced equaliser. The technique involves whitening the signal at the equaliser input and introducing a leakage term in the cost function minimised by the equaliser. The result is that, when applied to the Godard quartic cost function and to the infinitely long equaliser, such a technique yields optimal equalisation and actually counteracts the ill-conditioning     

Testing for the convergence of a linear decision directed equaliser

Adaptation algorithms for blind equalisation of communication channels suffer from the presence of local equilibria that may cause convergence to incorrect equaliser parameter settings. In this paper we consider an infinite impulse response (IIR) channel which is to be equalised by a linear transversal filter and a slicer connected in tandem, and use the correlation statistics of the sequence at the slicer output to determine if convergence to a desirable equilibrium has occurred. In particular, we show that if the input sequence to an IIR channel is binary, assuming values ±1, and its autocorrelation sequence is known a priori, the slicer output has the same autocorrelation sequence if, and only if, the slicer output is a possibly delayed and/or sign-inverted replica of the channel input. A Neyman-Pearson test is constructed, based on this result, to make a decision as to whether or not the equaliser has converged to an open-eye parameter setting. A method for estimating a lower bound on the equalisation delay that draws upon a classical correlation based impulse response estimation technique is discussed. Finally, simulation examples are presented to verify the theoretical results and to illustrate their application     

Decision feedback demodulation-based adaptive linear equalisers fordifferentially coherent DPSK systems

The authors propose to combine linear feedback equalisation and decision feedback demodulation for the equalisation of differentially coherent PSK signalling. By modifying the equaliser output based on the decision feedback demodulation before feeding back, the proposed equaliser can be made to behave like one with a decision feedback structure. Indeed, computer simulation results demonstrate that this equaliser performs much better than existing equalisers, such as linear equalisers for differentially coherent detection. Furthermore its performance is even comparable to that of a decision feedback equaliser with coherent detection     

Low complexity concurrent constant modulus algorithm and soft decision directed scheme for blind equalisation

The recently introduced concurrent constant modulus algorithm (CMA) and decision-directed (DD) scheme provides a state-of-the-art low-complexity blind equalisation technique for high-order quadrature amplitude modulation (QAM) channels. At a small cost of slightly more than doubling the complexity of the standard CMA blind equaliser, this concurrent CMA and DD blind equaliser achieves a dramatic improvement in equalisation performance over the CMA. In the paper, a new blind equalisation scheme is proposed based on concurrent CMA and a novel soft decision-directed (SDD) adaptation. The proposed concurrent CMA and SDD blind equaliser has simpler computational requirements than the concurrent CMA and DD algorithm. Extensive simulation shows that it has the same steady-state equalisation performance as the concurrent CMA and DD algorithm and a faster convergence speed over the latter scheme     

Subband equaliser for chromatic dispersion of optical fibre

An oversampled subband equaliser is designed for chromatic dispersion of singlemode optical fibre. The signal of each subband is equalised individually and delayed to align with other subbands. From simulation, the overall number of equaliser taps is approximately reduced by the upsampling ratio.     

Improved convergence of fractionally-spaced constant modulusequalisers in presence of noise

The constant modulus algorithm (CMA) applied to a fractionally spaced equaliser, with length and zero constraints on the channel, has been shown to be globally convergent when there is no channel noise. However, in the presence of channel noise, the performance of the CMA can suffer because of the existence of undesired local minima corresponding to different delays. A new technique is introduced, based on the Gram-Schmidt orthogonalisation, to obtain convergence to an optimum delay where the mean square error is minimum     

Global convergence and mixing parameter selection in thecross-correlation constant modulus algorithm for the multi-userenvironment

Surface topography of the mixed cross-correlation and constant modulus algorithm (CC-CMA) is undertaken to provide a suitable range for the mixing parameter to avoid ill-convergence. Previous work indicated that the mixing parameter k should be chosen to be greater than 4/3, but this result was based upon an assumption of perfect equalisation of previous equaliser outputs. The authors relax this perfect equalisation assumption and obtain a tighter bound for the mixing parameter in the case of a two-user system as well as a multi-user system. In a two-user transmission scheme, they suggest that the value of k should be chosen as 4. It is shown that for a multi-user system the cross-correlation of the soft decision of the previous equaliser output may result in ill-convergence and a hybrid equalisation method, which employs a hard decision on the equaliser output in the cross-correlation term of the CC-CMA algorithm after a start-up period is therefore proposed. Simulation studies are included to support the results     

Code-aided adaptive equaliser for mobile communication systems

A new structure for a code-aided adaptive equaliser is proposed for mobile communication systems. The structure aims to improve the tracking capability of a receiver that combines equalisation and coding. Simulation results show that the code-aided adaptive equaliser performs particularly well over mobile channels that fade at a moderate rate. Compared to a conventional equaliser, an order of magnitude reduction in bit error rate is achieved     

Fuzzy adaptive decision feedback equaliser

As a new approach to the equalisation of nonlinear channels, a fuzzy adaptive decision feedback equaliser based on a fuzzy adaptive filter is proposed. With perfect knowledge of the channel, the proposed method not only improves equalisation performance but also reduces the computational complexity compared with the conventional fuzzy adaptive filter     

Turbo equalisation in non-Gaussian impulsive noise

Turbo equalisation is a state-of-the-art receiving scheme for coded data transmission over channels introducing intersymbol interference (ISI). The author investigates turbo equalisation performance in the presence of ISI and impulsive noise. The design imperfections contributing to the non-robustness of the standard turbo equaliser to outliers are identified, and a novel turbo equaliser, at almost no additional increase in complexity, is proposed for joint mitigation of ISI and impulsive noise. The proposed turbo equaliser incorporates a Talwar penalty function into the maximum a posteriori (MAP) component equaliser to serve two purposes. First, it improves the estimation of the transition probabilities for all transitions through the trellis and for subsequent determination of the a posteriori log-likelihood ratio. Secondly, it absorbs the outliers and prevents them from spreading into the MAP constituent decoder. Simulation results based on Proakis's channel models show that the proposed turbo equaliser achieves a dramatic improvement over the standard turbo equaliser in impulsive noise. At a bit error rate (BER) of 10/sup -2/, the performance gain is as large as 3.5 to 5 dB, and as large as 7 to 8 dB at a BER of 10/sup -3/.     

Adaptive equalisation for DECT systems operating in low time-dispersive channels

DECT (digital European cordless telecommunication) is the current standard for cordless indoor communication in Europe. In this work the authors present a scheme to increase the coverage area of DECT links in multipath propagation by the application of channel equalisation. The equaliser is a decision feedback equaliser using a recursive least squares algorithm for adaptation. As a training sequence for the equaliser, the standardised packet synchronising word of the DECT TDMA slots is used.<>     

Robustness evaluation of a minimal RBF neural network fornonlinear-data-storage-channel equalisation

The authors present a performance-robustness evaluation of the recently developed minimal resource allocation network (MRAN) for equalisation in highly nonlinear magnetic recording channels in disc storage systems. Unlike communication systems, equalisation of signals in these channels is a difficult problem, as they are corrupted by data-dependent noise and highly nonlinear distortions. Nair and Moon (1997) have proposed a maximum signal to distortion ratio (MSDR) equaliser for data storage channels, which uses a specially designed neural network, where all the parameters of the neural network are determined theoretically, based on the exact knowledge of the channel model parameters. In the present paper, the performance of the MSDR equaliser is compared with that of the MRAN equaliser using a magnetic recording channel model, under Conditions that include variations in partial erasure, jitter, width and noise power, as well as model mismatch. Results from the study indicate that the less complex MRAN equaliser gives consistently better performance robustness than the MSDR equaliser in terms of signal to distortion ratios (SDRs)     

Dispersion slope equaliser using bend-induced positive dispersionslope in coiled pure-silica fibre

The dispersion slope of a dispersion-shifted fibre has been successfully equalised by using a bend-induced positive dispersion slope in a singlemode fibre. We realised the bent fibre dispersion slope equaliser by using a 1.3 μm zero-dispersion pure silica core fibre (PSM). This equaliser provides a dispersion slope of -12.54 ps/nm² /km in the 1.5 μm region     

Modulation and Equalisation Considerations for High Performance Radio LANs

The European Telecommunications Standards Institute (ETSI) has recently defined a European standard for a high performance radio LAN (known as HIPERLAN). To operate as wired LAN replacements, these systems will operate at 5.2 GHz and support instantaneous bit rates of just under 24 Mb/s. To counteract the time dispersive nature of the indoor radio channel, the use of adaptive equalisation is suggested. In this paper a number of possible modulation and equalisation techniques are presented and, in particular, the Bit Error Rate (BER) performance of quasi-coherent GMSK combined with Decision Feedback Equalisation is explored through computer simulation. The trade off between symbol spaced and fractionally spaced equalisation is considered together with the importance of feedfoward and feedback synchronisation to the channel's power delay profile. The paper also includes a comparison of the RLS and LMS based training algorithms and compares the modem developed under the ESPRIT III LAURA project with that specified in HIPERLAN.The application of dual antenna diversity is investigated and its impact on the number of received error free data packets obtained as a function of signal leval and rms delay spread. The use of such diversity is shown to greatly improve the BER performance of a HIPERLAN modem. The problem of frequency offset is considered and modifications are proposed to the HIPERLAN frame structure to improve the receiver's tolerance to such errors. Important practical issues such as frame and symbol synchronisation, frequency offset correction and hardware implementation are discussed from both the LAURA and HIPERLAN viewpoint.     

Phase equalisation of analogue magnetic recorders by transversal filtering

The `time-reversed-impulse-response? method of phase equalisation is explained theoretically. Experimental results are presented, showing the impulse response of an analogue magnetic recorder before and after phase equalisation. The transversal-filter equaliser (32-tap analogue delay line of 320 ?s length) is adjusted in the time domain so that actual phase-response measurements are not necessary.     

Simple non-coherent equaliser for the DECT system

A non-coherent equaliser structure suitable for DECT-type systems is introduced which performs equalisation at the output of a differential detector. It employs a two-state Viterbi algorithm using a simple channel estimation process. Performance assessments are presented which suggest that the new receiver can yield significant improvements with respect to standard non-coherent receivers in dispersive channels. At the same time, unlike coherent equaliser structures, it remains largely unaffected by both modulation index drifts and frequency offsets     

Hilbert-transformer side-chain phase equaliser for analogue magnetic recording

A substantial amount of phase distortion occurring in analogue magnetic recording can be eliminated by using a simple equalisation scheme which removes the Hilbert-transformed portion of the signal that is added in a normal record/reproduce process. In the phase equaliser, the performance of an ideal Hilbert transformer can be approximated by using a quadrature-phase-shift circuit. The methods of phase equalisation is explained theoretically and oscilloscope photographs of experimental results are presented.     

Iterative decision feedback equalisation with no feedback filter

An iterative modified decision feedback equaliser (I-MDFE) with no feedback filter over broadband channels is proposed. Generally, in the structure of an I-DFE, a soft residual postcursor intersymbol interference (ISI) is removed by a feedback filter (FBF). However, the ISI in the I-MDFE is precancelled prior to the equalisation, which results in no requirement of the FBF. It is demonstrated in the simulation evaluation that the I-MDFE can offer excellent performance under the broadband channel, with shorter filter taps than those of an iterative linear equaliser (I-LE) and the I-DFE     

Application of jacobi algorithm for ISI channels

Here, the Jacobi iterative algorithm is applied to combat intersymbol interference (ISI) caused by frequency-selective channels. The performance bound of the equaliser is analysed in order to gain an insight into its asymptotic behaviour. Because of the error propagation problem, the potential of this algorithm is not reached in an uncoded system. However, its extension to a coded system with the application of the turboprocessing principle results in a new turbo equalisation algorithm, which demonstrates comparable performance with reduced complexity compared with some existing filter-based turbo equalisation schemes; and superior performance compared with some frequency domain solutions, such as orthogonal frequency division multiplexing and single-carrier frequency domain equalisation.     

Performance comparison of SWCE and Kalman-based HSDPA receivers

Equalisers can provide significant improvement in the performance of CDMA-based systems such as UMTS. Naturally, the level of improvement introduced depends on the employed equalisation technique. Reported are the results of an investigation into the performance of a Kalman-based channel-estimator/equaliser for use in high speed downlink packet access (HSDPA) receivers. Also, the performances of the Kalman and the sliding window chip rate equaliser (SWCE) algorithms are compared.