Ideal Decision Feedback Equalizer Research Articles

Optimal MSE solution for a decision feedback equalizer

Due to the inherent feedback in a decision feedback equalizer (DFE) the minimum mean square error (MMSE) or Wiener solution is not known exactly. The main difficulty in such analysis is due to the propagation of the decision errors, which occur because of the feedback. Thus in literature, these errors are neglected while designing and/or analyzing the DFEs. Then a closed form expression is obtained for Wiener solution and we refer this as ideal DFE (IDFE). DFE has also been designed using an iterative and computationally efficient alternative called least mean square (LMS) algorithm. However, again due to the feedback involved, the analysis of an LMS-DFE is not known so far. In this paper we theoretically analyze a DFE taking into account the decision errors. We study its performance at steady state. We then study an LMS-DFE and show the proximity of LMS-DFE attractors to that of the optimal DFE Wiener filter (obtained after considering the decision errors) at high signal to noise ratios (SNR). Further, via simulations we demonstrate that, even at moderate SNRs, an LMS-DFE is close to the MSE optimal DFE. Finally, we compare the LMS DFE attractors with IDFE via simulations. We show that an LMS equalizer outperforms the IDFE. In fact, the performance improvement is very significant even at high SNRs (up to 33%), where an IDFE is believed to be closer to the optimal one. Towards the end, we briefly discuss the tracking properties of the LMS-DFE.

Statistics of Electrical Dispersion Compensator Penalties of 10-Gb/s Multimode Fiber Links With Offset Connectors

In this letter, we investigate the penalty after a 10-Gb/s Ethernet signal is detected and processed. We study the statistics of ideal electrical dispersion-compensation (EDC) performance, measured by the penalty of an ideal decision feedback equalizer (PIE-D), of 300-m multimode fiber links to determine the theoretically best possible EDC performance. We calculate the channel responses using two methods: the individual-mode method and the average-mode method. We find a strong dependence of the PIE-D value on the channel model that is used, especially when there is a connector with a large offset in the link. In system design, one should choose a suitable channel model, taking into account the length of the fiber, the magnitude of offset, and the percentage of coverage

Soft-threshold-based multilayer decision feedback equalizer (STM-DFE) algorithm and VLSI architecture

The decision feedback equalizer (DFE) is an efficient scheme to suppress intersymbol interference (ISI) in various communication and magnetic recording systems. However, most cost-effective DFE implementations suffer from the phenomenon of error propagation, which degrades its bit error rate (BER) performance. This paper proposes a soft-threshold-based multilayer DFE (STM-DFE) technique to reduce the BER. It involves very low hardware overhead costs as compared to the conventional DFE. When applied to a practical Lorentzian channel and channels of different eigenvalue spread, the STM algorithm even outperforms the Ideal DFE (IDFE) system (in the IDFE, symbols are correctly fed back without propagation errors). Simulation results show that the proposed scheme can efficiently reduce the burst error length (BEL) as well as BER. Additionally, the hardware overhead to implement the STM-DFE algorithm is negligible compared with the conventional DFE. By using the concepts of Shanbhag and Parhi and of Yang, Wu, and Lai, we also propose the pipelined STM-DFE (PSTM-DFE) architecture for high-speed communication/storage applications.

Tentative chip decision-feedback equalizer for multicode wideband CDMA

We investigate a chip-level minimum mean-square-error (MMSE) decision-feedback equalizer (DFE) for the downlink receiver of multicode wideband code-division multiple-access systems over frequency-selective channels. First, the MMSE per symbol achievable by an optimal DFE is derived, assuming that all interchip interference (ICI) of the desired user can be eliminated. The MMSE of DFE is always less than or at most equal to that of linear equalizers (LE). When all the active codes belong to the desired user, the ideal DFE is able to eliminate multicode interference (MCI) and approach the performance of the single-code case at high signal-to-noise ratio (SNR) range. Second, we apply the hypothesis-feedback equalizer or tentative-chip (TC)-DFE in the multicode scenario. TC-DFE outperforms the chip-level LE, and the DFE that only feeds back the symbols already decided. The performance gain increases with SNR, but decreases with the number of active codes owned by the other users. When all the active codes are assigned to the desired user, TC-DFE asymptotically eliminates MCI and achieves single-user (or code) performance at high SNR, similarly, to the ideal DFE. The asymptotic performance of the DFE is confirmed through bit error rate simulation over various channels.

A comparison of passband and baseband transmission schemes for HDSL

Using an ideal decision feedback equalizer (DFE), the SNR of quadrature amplitude modulation (QAM) and baseband pulse amplitude modulation (PAM) in the presence of self near-end crosstalk is computed for a large sample of loops within a carrier serving area (CSA). When baud-space feedforward filters are used, PAM has 1-2 dB more SNR than QAM, where the type of PAM is the 2B1Q line code. However, when using fractionally spaced feedforward equalizers (FSEs), the SNRs of 2B1Q and QAM are almost equal for loops at the extreme range of a CSA. Four- and 16-state trellis-coded modulation is applied to PAM and QAM. Coded and uncoded PAM and QAM are simulated with parallel decision feedback estimation. Viterbi receivers and coding gains are computed. QAM has up to 1 dB higher coding gains that PAM. However, the higher coding gains of QAM do not compensate for the lower SNR of uncoded QAM, and coded QAM has worse performance than coded PAM in the presence of self near-end crosstalk. The error rates of PAM and QAM with impulse noise are computed using a collection of measured impulse noise events. Results indicate that QAM has a lower error rate than PAM in the presence of impulse noise.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Combined coding and precoding for PAM and QAM HDSL systems

A system is described for high-speed digital subscriber line (HDSL) applications. It uses trellis coding combined with Tomlinson (1971) precoding. Theoretical performance results are provided for uncoded pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) assuming an ideal decision feedback equalizer (DFE) that includes an optimum feedforward filter. The similarities and differences in behavior are explained. It is shown that combined coding and Tomlinson precoding can achieve the equalization performance of the DFE and full coding gain of the trellis code. Simulation results are given to show that about 3.4 dB additional margin is obtained by using a four-dimensional eight-state trellis code. The receiver complexity is increased by it is quite manageable. >

Reduced-state sequence estimation for coded modulation of intersymbol interference channels

The authors investigated the detection of trellis codes designed for channels that are intersymbol interference free when they operate in the presence of intersymbol interference. A well-structured reduced-state sequence estimation (RSSE) algorithm is described which can achieve the performance of maximum-likelihood sequence estimation (MLSE) with drastically reduced complexity. Well-defined reduced-state trellises are first constructed by merging the states of the ML supertrellis using set partitioning principles. Then the Viterbi algorithm is used to search these trellises. A special case of RSSE, called parallel decision-feedback decoding, uses the encoder trellis, yet on channels with large attenuation distortion it can provide a significantly better performance than linear equalization. The performance of RSSE is examined analytically and through simulation, and then compared to that of MLSE and ideal decision-feedback equalization. It is noted that the performance advantage of RSSE can be obtained without significantly increasing the decoding delay or complicating an adaptive implementation. >

Channels leading to rapid error recovery for decision feedback equalizers

The authors define the DFE (decision feedback equalizer) system of interest and their finite-error-recovery-time problem. They present their basic result, which establishes that whenever the channel satisfies a simple frequency-domain constraint, the error recovery time of an ideal DFE is always finite. They also include four applications of this theorem, including analysis of a real channel. Convergence rates and explicit bounds, given an exponential overbound on the channel impulse response, are presented. Results of greater practical interest, where the authors relax most of the major idealized assumptions, are also given. The authors present the result for M-ary data and relate the error recovery time bound back to the binary case. A formula for the error probability, given a high signal-to-noise-ratio channel, is provided. >