Tap-selectable decision-feedback equalization

This paper presents an adaptive tap assignment technique for improving the performance of a previously reported reduced-complexity decision-feedback equalizer (DFE) for broadband band wireless systems. The spacings of individual feedforward taps of the DFE are made selectable so that, when the channel consists of a sparsely distributed multipath with a large delay spread (e.g. “hilly terrain” (HT) delay profiles), the equalizer span can be increased without increasing the total number of taps. We propose simple tap selection algorithms and show that they provide: (1) performance gains over a contiguous-tap approach in various outdoor delay profiles and (2) improved robustness against fast fading     

Low-complexity adaptive decision-feedback equalization of MIMO channels

A new adaptive MIMO channel equalizer is proposed based on adaptive generalized decision-feedback equalization and ordered-successive interference cancellation. The proposed equalizer comprises equal-length subequalizers, enabling any adaptive filtering algorithm to be employed for coefficient updates. A recently proposed computationally efficient recursive least squares algorithm based on dichotomous coordinate descents is utilized to solve the normal equations associated with the adaptation of the new equalizer. Convergence of the proposed algorithm is examined analytically and simulations show that the proposed equalizer is superior to the previously proposed adaptive MIMO channel equalizers by providing both enhanced bit error rate performance and reduced computational complexity. Furthermore, the proposed algorithm exhibits stable numerical behavior and can deliver a trade-off between performance and complexity.     

Introducing erasures in decision-feedback equalization to reduceerror propagation

A simple modification of the decision feedback equalizer (DFE) slicer is proposed to reduce the effect of error propagation. A comparison of the performance of the modified DFE and conventional DFE is made for specific channels. On these channels, the modified DFE performs only marginally better than the conventional DFE in terms of average error probability, but may offer some advantages in terms of error probability conditioned on specific input sequences and in terms of the distribution of error burst lengths. Some examples are given, concerning binary PAM and multilevel quadrature amplitude modulation (M-QAM) systems     

Mitigating error propagation in decision-feedback equalization for multiuser CDMA

This letter presents a robust decision-feedback equalization design that mitigates the error-propagation problem for multiuser direct-sequence code-division multiple-access systems under multipath fading. Explicit constraints for signal energy preservation are imposed on the filter weight vector to monitor and maintain the quality of the hard decisions in the nonlinear feedback loop. Such a measure protects the desired signal power against the detrimental effect of erroneous past decisions, thus providing the leverage to curb error propagation.     

Interference suppression for space-time coded CDMA via decision-feedback equalization

A single-user receiver structure is proposed for space-time coded code-division multiple-access (CDMA) downlink in a multiuser frequency-selective channel. This structure is a two-dimensional (2-D) decision-feedback equalizer (2D-DFE) whose filters are optimized based on the MMSE criterion to mitigate noise, intersymbol interference (ISI), and multiuser interference (MUI) with a moderate complexity. By modeling the spreading codes of the interfering users as random sequences, system performance was evaluated using the Gaussian approximation. Two models for the desired user's spreading sequence have been considered and compared. Our numerical results show that in both cases the 2D-DFE exhibits significant performance improvement over the standard space-time coded RAKE, especially in interference-limited conditions. It is also observed that the gain obtained by using DFE in a MISO channel is less that in a SISO channel and this problem can be solved by providing diversity at the receiver.     

Optimized decision-feedback equalization for convolutional coding with reduced delay

Error propagation is a significant problem with the decision-feedback equalizer (DFE) at low-to-moderate signal-to-noise ratios. In particular, when a DFE is concatenated with a convolutional code, the burst errors associated with error propagation can severely degrade performance, since the convolutional code is optimized for the additive white Gaussian noise channel. In this paper, we explore the compensation of error propagation in the DFE so as to break up error bursts and improve performance with convolutional codes, without incurring larger overall decoding delay. We propose certain stationary error models and derive a modified DFE (MDFE) based on these models which can compensate for the error propagation. The MDFE differs from the conventional DFE only in its tap values. The incorporation of the bias into the model and the removal of the bias during the design process is discussed. Simulations explore the performance of the MDFE for both uncoded and convolutionally coded systems. With coding, the MDFE can significantly improve on the conventional DFE in terms of bit-error rate, and the MDFE without interleaving can improve on the conventional DFE with interleaving in terms of decision delay.     

An upper bound on the error probability in decision-feedback equalization

An upper bound on the error probability of a decision-feedback equalizer which takes into account the effect of error propagation is derived. The bound, which assumes independent data symbols and noise samples, is readily evaluated numerically for arbitrary tap gains and is valid for multilevel and nonequally likely data. One specific result for equally likely binary symbols is that if the worst case intersymbol interference when the firstJfeedback taps are Set to zero is less than the original signal voltage, then the error probability is multiplied by at most a factor of2^Jrelative to the error probability in the absence of decision errors at highS/Nratios. Numerical results are given for the special case of exponentially decreasing tap gains. These results demonstrate that the decision-feedback equalizer has a lower error probability than the linear zero-forcing equalizer when there is both a highS/Nratio and a fast roll-off of the feedback tap gains.     

Wide-band digital subscriber access with multidimensional blockmodulation and decision-feedback equalization

The author investigates the potential transmission performance of pair-wire subscriber lines at the higher rate of 800 kb/s, with particular reference to digital subscriber line transmission for ISDN (integrated services digital network) basic access. Block modulation schemes of 1-4 dimensions, at a rate of 2 bits per dimension, are considered. Time-division multiplexing is used to combine the multiple dimensions for transmission over a single-waveform channel, namely, the subscriber line. The channel noise is assumed to be additive and dominated by near-end crosstalk. MMSE (minimum mean-squared error) decision-feedback equalization is used to deal with the noise and the intersymbol interference. Using the theory developed, the potential performance of some simple lines is calculated. The coding gain of a multidimensional modulation scheme is found to be fully preserved after transmission if the equalizer is infinite in length. However, the gain realized can be much lower, or none at all, if the equalizer is only moderate in length. This latter phenomenon is due to the fact that the noise at the decision point is coloured, due to the inability of the equalizer to whiten it sufficiently     

Single-carrier frequency-domain equalization with decision-feedback processing for time-reversal space-time block-coded systems

In this letter, we propose to introduce frequency-domain equalization with decision-feedback processing (FD-DFE) for time-reversal space-time block-coded (TR-STBC) systems with multiple transmit antennas to effectively achieve both spatial diversity and multipath diversity over frequency-selective channels. This letter will also present a theoretical performance analysis result that relates the minimum mean-squared error (MMSE) to a new tight upper bound for the probability of error. It is shown that the new bound is not only valid for the TR-STBC systems, but also valid for single-input single-output, single-input multiple-output, and multiple-input multiple-output systems with MMSE equalization.     

Interior point least squares estimation: transient convergenceanalysis and application to MMSE decision-feedback equalization

In many communication systems, training sequences are used to help the receiver identify and/or equalize the channel. The amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization. In this paper, we propose the use of a new adaptive filtering method called interior point least squares (IPLS) for adaptive equalization. First, we show that IPLS converges exponentially fast in the transient phase. Then, we use the IPLS algorithm to update the weight vector for a minimum-mean-square-error decision-feedback equalizer (MMSE-DFE) in a CDMA downlink scenario. Numerical simulations show that when training sequences are short IPLS consistently outperforms RLS in terms of system bit-error-rate and packet error rate. As the training sequence gets longer IPLS matches the performance of the RLS algorithm     

On adaptive decision-feedback equalization of intersymbolinterference channels in coded modulation systems

Recently, Eyuboglu (1988) has shown that adaptive noise-predictive decision-feedback equalization (DFE) can be combined with coded modulation to achieve high-speed data transmission by periodic interleaving. In this paper, we present a new method of adaptive DFE with periodic interleaving for coded modulation systems. The method is an improved version of that proposed by Eyuboglu, where the deinterleaving operation is performed on a vector-by-vector basis, instead of a sample-by-sample basis. Unlike the original system in which the linear equalizer's coefficients can be adjusted only with hard decisions from the threshold detector, the improved structure updates the coefficients of both the linear equalizer and the noise predictor based on soft decisions from the most likely path in the soft decoder. The improved system achieves better error-rate performance than the original with a little increase in hardware complexity. As compared to another improved design reported by Zhou et al. (1990), the new structure also gains advantages in error-rate performance, hardware complexity, and throughput delay     

Linear and decision-feedback per tone equalization for DMT-based transmission over IIR channels

The per-tone equalizer (PTEQ) has been presented as an attractive alternative for the classical time-domain equalizer (TEQ) in discrete multitone (DMT) based systems, such as ADSL systems. The PTEQ is based on a linear minimum mean-square-error (L-MMSE) equalizer design for each separate tone. In this paper, we reconsider DMT modulation and equalization in the ADSL context under the realistic assumption of an infinite impulse response (IIR) model for the wireline channel. First, optimum linear zero-forcing (L-ZF) block equalizers for arbitrary IIR model orders and cyclic prefix (CP) lengths are developed. It is shown that these L-ZF block equalizers can be decoupled per tone, hence they lead to an L-ZF PTEQ. Then, based on the L-ZF PTEQ, low-complexity L-MMSE PTEQ extensions are developed: the linear PTEQ extension exploits frequency-domain transmit redundancy from pilot and unused tones; alternatively, a closely related decision-feedback PTEQ extension can be applied. The PTEQ extensions then add flexibility to a DMT-based system design: the CP overhead can be reduced by exploiting frequency-domain transmit redundancy instead, so that a similar bitrate as with the original PTEQ is achieved at a lower memory and computational cost or, alternatively, a higher bitrate is achieved without a considerable cost increase. Both PTEQ extensions are also shown to improve the receiver's robustness to narrow-band interference.     

Low-complexity iterative equalization for EDGE with bidirectional processing

We present a new and simple iterative equalization scheme for the enhanced data rates for global evolution (EDGE) wireless system. This scheme can significantly reduce the number of trellis states in a maximum a posteriori probability (MAP) equalizer via delayed decision-feedback (DDF) approach. Relying on the mechanism of decision feedback in the DDF trellis, bidirectional processing can be applied to exploit the time diversity of the received signal bursts for a more reliable equalizer output. With mild increase in computational complexity over the more traditional single-directional (Si) DDF turbo equalizer, the bidirectional turbo equalizer can achieve a significant performance gain.     

Minimum mean-squared error decision-feedback equalization fordigital subscriber line transmission with possibly correlated line codes

The author presents a theory on MMSE (minimum mean-squared error) decision-feedback equalization which augments previously published results by allowing both a correlated symbol sequence and a fractionally spaced DFE (decision-feedback equalizer) forward filter. This theory facilitates calculating the potential DSL (digital subscriber line) transmission performance in cases of correlated line codes, especially for situations where one or both of the DFE filters are infinite in length. The situation of an infinite-length DFE is of interest because it provides information on the limit of MMSE equalization and can thus serve as a benchmark against which the performance of a finite-length DFE may be compared. The author also presents a few numerical examples of the performance of MMSE decision-feedback equalization in DSL transmission at ISDN (integrated services digital network) basic access rates with several well-known line codes     

Performance evaluation of experimental 50-Mb/s diffuse infraredwireless link using on-off keying with decision-feedback equalization

We report an experimental nondirected optical link for short-range, indoor data transmission at 50 Mb/s. The system uses on-off keying (OOK) and achieves low bit-error rates (BERs) in the presence of intersymbol interference, background light noise, and shadowing, with a range of 2.9 m in a skylit room. The transmitter produces an eye-safe Lambertian pattern at 806 nm with an average power of 474 mW. The receiver utilizes a hemispherical concentrator with a hemispherical bandpass optical filter, a 1-cm² silicon p-i-n photodiode, and a high-impedance hybrid preamplifier to achieve a high signal-to-noise ratio (SNR). A high-pass filter is used to mitigate fluorescent light noise, with quantized feedback removing the resulting baseline wander. A decision-feedback equalizer provides resistance to intersymbol interference due to multipath. The system and its components are characterized, and compared to theory. We observe that decision-feedback equalization yields a reduction of multipath power penalties that is in good agreement with theory     

MMSE decision-feedback equalizers: finite-length results

This paper extends a number of results on the infinite-length minimum-mean-square-error decision Feedback equalizer (MMSE-DFE) reported by Cioffi, Dudevoir, Eyuboglu and Forney (see IEEE Trans. Commun., 1995) to the finite-length case. Cholesky factorization and displacement structure theory are demonstrated to be two powerful analytical tools for analyzing the finite-length MMSE-DFE. Our objective throughout the paper is to establish finite-length analogs of the well-known infinite-length MMSE-DFE results. Similarities and differences between the two cases are examined and delineated. Finally, convergence of our derived finite-length results to their well-established infinite-length counterparts is shown     

10-Gb/s upgrade of bidirectional CWDM systems using electronic equalization and FEC

We discuss options for upgrading coarse wavelength-division multiplexed (CWDM) optical access links over standard single-mode fiber (SSMF) by increasing per-channel data rates from 2.5 to 10 Gb/s. We identify electronic equalization and forward error correction (FEC) as the enabling technologies to overcome the dispersion limit of SSMF. In addition, we show how FEC enhances the tolerance to in-band crosstalk, and paves the way toward fully bidirectional CWDM transmission. Due to the lack of CWDM sources rated for 10-Gb/s operation, we demonstrate full-spectrum (1310 to 1610 nm) 10-Gb/s CWDM transmission over standard-dispersion fiber using uncooled, directly modulated lasers specified for 2.5 Gb/s. All 16 CWDM channels could be transmitted over more than 40 km, yielding a capacity-times-distance product of 6.4 Tb/s/km. The longest transmission distance (80 km) was achieved at 1610 nm, equivalent to 1600 ps/nm of chromatic dispersion.     

Delayed decision-feedback sequence estimation

The authors delayed-decision-feedback sequence estimation (DDFSE) for uncoded PAM signals is considered. Estimates on the performance of the algorithm are given, and simulation results are provided for several examples. A more general form of DDFSE applicable to coded modulation systems is also presented. As an example, detection of trellis-coded QPSK (quadrature phase-shift keyed) signals over intersymbol interference channels is discussed     

Noncoherent decision-feedback multiuser detection

The problem of noncoherent multiuser detection for multipulse modulation over the Gaussian multiuser channel is studied. It is assumed that neither the energies nor the carrier phases of the signals of any of the users are available at the receiver. Previously, a post-decorrelative generalized likelihood ratio test (GLRT) based detector was proposed as a solution to this problem. In this paper, we introduce the concept of noncoherent decision feedback (DF) that forms the basis for an improved solution to the same problem. The users are detected sequentially in some fixed order, and the decision for a particular user takes advantage of the reduction of uncertainty associated with the signal space resulting from decisions already made for previous users. In contrast to coherent DF, therefore, the feedforward and feedback transformations in the noncoherent case are themselves functions of the matched filter outputs. An efficient implementation of the noncoherent DF detector for M-ary modulation and ρ-dimensional signal space requires O(M_ρ) computational complexity per user. Upper and lower bounds on its symbol error probability are obtained. It is shown that significant improvements over the post-decorrelative GLRT-based detector are often possible. Sufficient conditions are obtained which guarantee, without ignoring error-propagation effects, that the high signal-to-noise performance of the DF strategy can be as good as its genie-aided version in which perfect past users' decisions are used     

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