Robust measures for decision feedback equalization in CDMA systems

The central theme is the study of error propagation effects in decision feedback equalizers (DFEs). The thesis contains: a stochastic analysis of error propagation in a tuned DFE; an analysis of the effects of error propagation in a blindly adapted DFE; a deterministic analysis of error propagation through input-output stability ideas; and testing procedures for establishing correct tap convergence in blind adaptation. To a lesser extent, the decision directed equalizer (DDE) is also treated. Characterizing error propagation using finite state Markov process (FSMP) techniques is first considered. We classify how the channel and DFE parameters affect the FSMP model and establish tight bounds on the error probability and mean error recovery time of a tuned DFE. These bounds are shown to be too conservative for practical use and highlight the need for imposing stronger hypotheses on the class of channels for which a DFE may be effectively used. In blind DFE adaptation we show the effect of decision errors is to distort the adaptation relative to the use of a training sequence. The mean square error surface in a LMS type setting is shown to be a concatenation of quadratic functions exposing the possibility of false tap convergence to undesirable DFE parameter settings. Averaging analysis and simulation are used to verify this behaviour on some examples. Error propagation in a tuned DFE is also examined in a deterministic setting. A finite error recovery time problem is set up as an input-output stability problem. Passivity theory is invoked to prove that a DFE can be effectively used on a channel satisfying a simple frequency domain condition. These results give performance bounds which relate well with practice. Testing for false tap convergence in blind adaptation concludes our study. Simple statistic output tests are shown to be capable of discerning correct operation of a DDE. Similar tests are conjectured for the DFE, supported by proofs for the low dimensional cases.

Decision feedback equalizer (DFE) is an efficient scheme for suppressing intersymbol interference (ISI) in vestigial sideband (VSB) based digital TV (DTV) receivers. However, it suffers from the phenomenon of error propagation (EP). This paper considers the use of soft decisions in mitigating EP in a DFE. An optimized soft decision algorithm using the hyperbolic tangent function in the decision device is proposed to improve performance over reducing EP. Furthermore, in order to speed up the EP simulation process, a simple but effective modification is made in the feedback tap weight updating process. Computer simulation results show that the proposed soft decision algorithm nearly meets the ideal DFE (i.e., without erroneous decision) performance, which is far better in performance when compared to the erasure algorithm.

By embedding a decision-feedback equalizer (DFE) into the structure of a maximum-likelihood sequence estimator (MLSE), an adaptive combined DFE/MLSE scheme is proposed. In this combined DFE/MLSE, the embedded DFE has three functions: (i) prefiltering the received signals and truncating the equivalent channel response into the desired one, (ii) compensating for channel distortions, and (iii) providing the MLSE detector with predicted values of input signals. Since the embedded MLSE detector operates on the predicted signals the detected symbols at the output of the DFE/MLSE do not suffer any delay and can be directly fed back into the embedded DFE so that the error propagation, which usually takes place in a conventional DFE, can be greatly reduced. Analytical and simulation results indicate that the performance is significantly improved by the DFE/MLSE compared to the conventional DFE while its computation complexity is much less than that of the conventional MLSE receiver. The combined DFE/MLSE can use different adaptive structures (block-updating, sliding window updating or symbol-by-symbol updating) to meet different performance objectives. Moreover, the proposed DFE/MLSE provides a trade-off between performance and complexity with a parameter m representing the MLSE detection depth as well as the number of predicting steps of the embedded DFE. For some particular values of m, this scheme is capable of emulating the conventional DFE, MLSE-VA, adaptive LE-MLSE equalizer, adaptive DDFSE, and adaptive BDFE without detection delay.

This paper considers equalization of the slow fading channel for a serial data transmission application. Linear and decision-feedback adaptive equalization techniques are contrasted. The error propagation effect in decision-feedback equalizers is analyzed by a Markov process model. The error probability magnification is computed for both fixed and fading channels and for both binary and quaternary phase-shift-keying (PSK) transmission. The results show that the error propagation effect is small and in regions of practical error probabilities the decision-feedback equalizer is superior to its linear counterpart. Parameters of a practical decisionfeedback equalizer are estimated and a performance evaluation is performed. The implicit diversity gain is shown to be significant and the intersymbol interference penalty is found to be less than 1 dB. Because the intersymbol interference penalty is small, more complex nonlinear processors such as the Viterbi algorithm cannot be recommended for this application. Time jitter effects for the equalizer are included in a calculation of average error probability.

A joint decision feedback equalizer (DFE) and variable trace-back depth trellis decoding (VTD) scheme (VTD-DFE) is proposed for the ATSC DTV receivers. Compared with previous arts, error propagation can be further decreased by adopting a trellis decoder with a variable trace-back depth (TBD) for the decision device in the DFE. Convergence is also greatly speeded by using a slice error detector, which performs slice prediction according to the corresponding confidence value of the decision symbol provided by TCM decoding. Simulation results show that the proposed VTD-DFE leads to an improvement of convergence performance in terms of both the convergence speed and the stability, especially when SNR is low

Severe intersymbol interference (ISI) is one of the main obstacles for reliable signal reception in ATSC DTV systems. Decision feedback equalizers (DFEs) are commonly used to suppress the ISI. However, DFEs may suffer from error propagation due to incorrect symbol decisions from the symbol slicer. This phenomenon deteriorates the performance even more when the post-cursor ISI is strong. In order to reduce error propagation, we present a novel hybrid equalization scheme for ATSC channels. The proposed scheme consists of an adaptive decision feedback sparsening filter (DFSF), and an iterative maximum a posteriori (MAP) equalizer based on the belief propagation (BP) algorithm. In the first stage, instead of removing all the ISI from post cursors, the DFSF employs a modified feedback filter which leaves the strongest post-cursor ISI taps uncorrected. As a result, a long ISI channel is equalized to a sparse channel having only a small number of nonzero taps. In the second stage, a belief propagation algorithm is applied to mitigate the residual ISI. Since the channel is typically time-varying and suffers from Doppler fading, the DFSF is adapted using the least mean square (LMS) algorithm, such that the amplitude and the locations of the nonzero taps of the equalized sparse channel appear to be fixed. As such, the channel appears to be static during the second stage of equalization which consists of the BP detector. Simulation results demonstrate that the proposed scheme outperforms the traditional DFE in symbol error rate, under both static channels and dynamic ATSC channels.

SC-FDMA (Single-Carrier Frequency Division Multiple Access) is employed in the 3GPP LTE (Long-Term Evolution) standard as the uplink transmission scheme. The SC-FDMA signal has a low PAPR. This makes it well-suited to power efficient transmission at the mobile terminal. Although it is a common assumption to use frequency-domain linear equalization in SC-FDMA, a decision feedback equalizer (DFE) composed of a frequency-domain feedforward filter and a time-domain feedback filter can provide enhanced performance. Even when error propagation is taken into account, results show that a DFE still offers a significant performance gain over the conventional LE for uncoded SC-FDMA. This paper demonstrates that SC-FDMA with DFE is capable of increasing the throughput in a power limited channel by up to 41% compared to LE. Alternatively, for a given peak transmit power, the use of a DFE can achieve a 14% coverage extension in NLOS and 19% in LOS.

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.

Decision feedback equalizers (DFE) employing energy constraints have been successfully used to limit the feedback of wrong decisions that lead to the well known error propagation phenomenon. This paper extends the energy constraint formulation proposed for the scalar DFE, to the class of block memoryless DFE structures that employ zero-padding transmission redundancy. We further show how to make use of fast order recursive relations in order to obtain the filters efficiently. Computer simulations verify the improved BER performance of the proposed scheme over its unconstrained block DFE counterpart.

This paper considers a combined coding and equalization technique applied to the magnetic recording channel. The optimization of the coded-equalization scheme for this channel requires balancing the coding rate with its associated distance gain and equalization loss. A major concern in a coded-equalization scheme using decision feedback equalization (DFE) is error propagation. A new indicator to measure the effect of error propagation when using soft decision decoding is proposed. For medium to high normalized recording densities (S>1.5), it is shown that error propagation significantly degrades the theoretical performance of a detection scheme which combines a partial response DFE and simple trellis codes. In fact, this combined system performs worse than the uncoded one. The addition of delayed decision feedback sequence estimation (DDFSE) to limit the effect of error propagation is then investigated. With a moderate decoding complexity, positive coding gains have been achieved at such densities when choosing the partial response polynomial according to the derived indicator.

This paper investigates the performance of compromise Viterbi algorithm (VA) and standard equalization techniques by computation and simulation over band-limited channels using fourlevel vestigial sideband (VSB) modulation. Linear channel characteristics from the published telephone channel survey were used as examples of band-limited data transmission channels. One of the principal conclusions drawn from the study is that at data rates of 9600 bits/s and less, the linear characteristics of these channels do not limit performance even with linear equalization. It was found that at this data rate, receivers based on linear equalization are very sensitive to timing and carrier phase over some channels. Thus at 9600 bits/s the decision feedback equalizer was found to be a better choice because it is relatively insensitive to carrier phase and timing considerations. Moreover, at 9600 bits/s no problem with error propagation was encountered with the decision feedback equalizer. As the data rate was increased beyond 9600 bits/s the decision feedback tap gains became large enough to cause severe error propagation. The compromise VA receiver structure was effective at higher data rates and was almost unaffected by channel bandwidth up to 12 000 bits/s.

The author proposed soft decision feedback equalisation for orthogonal frequency division multiplexing (OFDM) transmission over doubly selective channels which is used for turbo equalisation. The doubly selective channel is approximated using the basis expansion model (BEM). The decision feedback equaliser (DFE) is obtained and updated for every sub-carrier which results in a per-tone DFE. On the basis of the Gaussian approximation, expressions for the a priori, the a posteriori and the extrinsic information have been derived for quadrature phase shift keying (QPSK) modulation. For turbo equalisation, where iterative joint channel equalisation and channel decoding is executed, in the first iteration, estimates are based on the feed-forward filter which are fed to the channel decoder. These estimates are not reliable and may incur error propagation and poor turbo equalisation performance. For more reliable estimates in the first iteration, the DFE is initialised as a linear minimum mean square error (LMMSE) equaliser. The per-tone LMMSE soft-output equaliser is also derived, and expressions for the a priori, a posteriori and extrinsic information are obtained viewing the LMMSE equaliser as a special case of the DFE. The extrinsic information in both cases was derived based on the Gaussian approximation. Numerical results for bit-error rate performance assuming the BEM channel model and Jakes' channel model are shown to confirm our findings.

This paper presents a unifying technique for robust feedback filter design in the decision feedback equaliser (DFE). The robustness is needed for combatting error propagation effects which is the major limitation when using DFEs. Numerous constraint strategies for the design of robust DFEs are available in the literature, however, they have been presented in their own ad-hoc context. Consequently there is a desire to give a unified approach to robust feedback filter design. The approach in the current presentation is to first develop a mean square error (MSE) measure which is a function of the feedforward and feedback filters. This measure is then combined with a feedback filter constraint using four existing norm constraint approaches (the L/sub 1/, L/sub 2/, L/sub /spl infin// and the two tap norm). The use of second order cone programming allows these existing norm constraint strategies to be unified and solved in a computationally efficient manner. The evaluation is performed with respect to the impact on error propagation, through the mean and the variance of the burst error length.

In this paper an efficient implementation of decision feed back equalizer (DFE) is carried out using novel memory less distributed arithmetic (NMLDA) filter. In wireless transmission systems, DFEs are used to mitigate the inter-symbol interference (ISI). The ISI is occurred due to multi-path propagation of the transmitted signal. High data rate systems demand higher order filters in DFE architectures which increase complexity in hardware design. In our proposed NMLDA design, we have used multiplexers and enhanced compressor adders in place of memory unit and conventional adders. The proposed design occupies lower area and gives higher throughput, when compared to MAC based filter and all other memory based DA filter architectures. By using proposed NMLDA based DFE, the ISI errors in transmission signal, will be minimized and the performance of the transmission system will be enhanced. We have synthesized the NMLDA of 32-tap, 16-tap, 8-tap and 4-tap filters and implemented them on FPGA device. The proposed design has nearly 70% less number of logical elements than OBC DA and 50% less than MDA and offers better throughput than the existing designs when implemented on Altera Cyclone III EP3C55F484C6.

It is shown that depending on the channel and the operating signal to noise ratio, the onset of error propagation in a decision feedback equaliser (DFE) is a detectable event. With the exploitation of this event using error correcting schemes the run length distribution of the feedback errors can be altered so as to improve the average bit error rate (BER). A novel fractionally spaced DFE using feedback error detection is presented which offers BER improvement over the conventional fractionally spaced DFE with only a small increase in complexity. A number of error correcting schemes are explored, the simplest of which has the lowest BER.