Blind Hammerstein decision feedback equalizer (BHDFE) as a new blind equalizer

The simplified Gaussian clustering algorithm (SGCA) adopting a reduced constellation is derived, then the dual-variance Gaussian clustering algorithm (DVGCA) is proposed, which makes the soft or hard decisions using the SGCA. Since the DVGCA is extremely reduced-complexity and operates in the soft or hard decisions mode according to the variance for error level of the equalizer output, it is effective for blind equalization of high-order quadrature amplitude modulation (QAM) signals. In addition, the blind decision feedback equalizer (DFE) using the DVGCA is presented, which leads to superior performance to ones without a feedback path over the channel with in-band spectral nulls.

For PC DRAM buses, the number of slots per channel has decreased as data rates have increased. This limits the maximum memory capacity per channel. Signal equalization can be used to increase bit-rates for channels with a large number of slots and offer a cost effective method to solve the memory capacity problem. This paper presents a blind adaptive decision feedback equalizer (DFE) that enables high data-rates with a large number of slots per channel. Measurements at 2.6 Gb/s over a four-drop bus are presented.

A decision-feedback equalizer (DFE) is the basis of a recent development of a quadruple diversity troposcatter modem which can operate up to a data rate of 12.6 Mbit/s in a 99% bandwidth of 15 MHz. In this paper a theoretical approach is developed for the calculation of average bit error rate (ABER), including the effects of intersymbol interference due to multipath and the finiteness of the transversal filters used to realize the DFE. By omitting the intersymbol interference effect, the calculation provides a lower bound which can be used to assess the intersymbol interference penalty for a particular DFE structure. The paper includes calculations of a DFE configuration which has a three tap forward filter with tap spacing equal to one-half a symbol interval. Measured performance results from fading channel simulator tests of a three tap forward filter DFE are presented for data rates from 1.5 to 12.6 Mbit/s and for a wide range of multipath statistical conditions. The results for this DFE configuration show (1) excellent agreement between calculated and measured ABER, (2) a small intersymbol interference penalty when the 2σ multipath spread is less than approximnately one-half the data symbol interval, and (3) successful operation at values of multipath spread up to twice the data symbol interval. In a sequel to this paper, the results of a field test of the DFE modem are presented. These live links test results are consistent with both the calculated and simulator measured data presented here.

We present novel blind decision feedback equalization algorithms for VSB-based DTV receivers by modifying a stop-and-go dual-mode constant modulus algorithm (SAG DMCMA) and applying a selective feedback (SF) scheme to stop-and-go, (SAG) based algorithms. The modification of the SAG DMCMA applies the SAG scheme only to the feedback filter tap update of the DFE, thus reducing the loss of information caused by the SAG policy. The SF scheme, in which we choose the equalizer output or the slicer output for the input of the feedback filter in the DFE according to the SAG flag, diminishes error propagation and thus improves convergence performance. Considering VSB modulation and RF-band effects with the baseband-equivalent VSB channel model in our simulations raises the reliability of our results for practical applications.

In this paper, a fast decision feedback equalizer (DFE) with the multi-level modulus algorithm (MLMA) and the two-stage feedback equalizer (FBE) scheme is developed for high-order QAM cable receivers on broadcasting downstream wired cable networks. The proposed fast blind equalization algorithm uses a single-stage convergence strategy with the joint carrier recovery (CR) loop. Compared with the other blind equalizers at the same signal-to-noise ratio (SNR), the proposed blind equalization has faster convergence, less mean square error (MSE), and lower bit error rate (BER) on a wired cable channel at high-order QAM demodulations.

Addresses problems related to the conceptual design of a fully digital synchronous DFE (decision feedback equalizer) and investigates the effects of the necessary quantization of the input signals and coefficients on DFE performance in static and dynamic operation. The analysis is performed taking into account the following topics: the influence of the dynamic range and quantization levels of the input signal and coefficients: the tracking and acquisition algorithm capabilities; comparison of DFE structures; and the extension of robust algorithms to DFEs. An experimental setup including a digital baseband equalizer is described. Results are reported for two kinds of DFE structures and a 16-AQM (quadrature amplitude modulation) modulation format. Specific problems related to the operation of DFEs in digital radio modems are discussed. It is established that the DFE structure is able to track continuous minimum-phase to nonminimum-phase transitions and vice versa without getting out of lock. This is an important result since the DFE outperforms current linear equalizers. >

There is no doubt about the growing interest for the underwater acoustic communications. Among all existing applications, the objective of the Groupe d'Etudes Sous-Marines de l'Atlantique (GESMA) is to develop a sufficiently robust high data rate acoustic link, named TRIDENT. For that purpose, different kinds of information (texts, images...) could be periodically transmitted through the acoustic channel. A realtime receiver, based on the spatio-temporal blind adaptive decision feedback equalizer, developed and patented by ENST Bretagne [J. Labet et al., 1995], was designed to cope with all perturbations induced by such harsh channels. Some sea trials have been carried out in June 2002. The first results are clearly convincing since most of the 48 sequences of 5 minutes are successfully detected by the DSP-based real-time receiver. This acoustic system allows transmission at data rates ranging from 8 to 25 kbps in horizontal configuration.

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

Block data transmission is an efficient scheme to mitigate the inter-symbol interference (ISI) caused by dispersive channels. Recent research work attempt to obtain optimal designs of precoders given various linear and non-linear receivers. In this paper we focus on the systems with optimal precoder designs based on the minimization of bit error rate (BER) which is the more meaningful criterion in data communications. The linear receivers employed in these systems include zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Recently, block decision feedback equalization (DFE) has also been suggested to be used in the design of such block data transmission systems. We also revisit the jointly optimum designs of the precoder coupled with the DFE receivers. First we derive the block-data error rate for all of these different systems with their corresponding optimal precoders. Then we rank their performance accordingly. Simulation results are also obtained to verify our analysis. Later, we evaluate the computational complexity on the various systems and draw some conclusions on their relative merits. Finally, we derive the lower and upper bounds of bit error rate (BER) considering error propagation for systems employing nonlinear equalizers.

In this work, we innovatively equalize optical intensity-modulated and directly detected (IMDD) four-level pulse amplitude modulation (PAM-4) signals using a complex-valued decision feedback equalizer (CDFE). Through mapping adjacent symbols of PAM-4 signals onto the complex domain, the influence of strongest inter-symbol interference (ISI) can be alleviated during the decision process in a decision feedback equalizer (DFE), effectively combating burst-error propagation when signals are noisy. Moreover, signal-adaptive manipulations of DFE parameters in both the time and the amplitude domain are performed by using an ultra-stable timing recovery and level-adaptive decision. Performance evaluations are made on vertical cavity surface emitting laser (VCSEL) modulated and multimode fiber (MMF) transmitted 100-Gbit/s optical PAM-4 signals. Based on experimental results of the short-reach optical communication, the proposed DFE outperforms the traditional DFE with a 0.5-dB system power budget gain at the 7% overhead (OH) forward error correction (FEC) bit error rate (BER) threshold.

Optical wireless communication (OWC) systems use the atmosphere as a propagation medium. However, a common problem is that from time to time moderate cloud and fog emerge between the receiver and the transmitter. These adverse weather conditions impose temporal broadening and power loss on the optical signal, which reduces the digital signal-to-noise ratio (DSNR), produces significant intersymbol interference (ISI), and degrades the communication system's bit error rate (BER) and throughput. We propose and investigate the use of a combined adaptive bandwidth mechanism and decision feedback equalizer (DFE) to mitigate these atmospheric multipath effects. Based on theoretical analysis and simulations of DSNR penalties, BER, and optimum system bandwidths, we show that a DFE improves the outdoor OWC system immunity to ISI in foggy weather while maintaining high throughput and desired low BER.

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.

As the data rate has been increased over 10 Gb/s with copper interconnect, the intersymbol interference (ISI) caused from the channel loss should be compensated. While a decision feedback equalizer (DFE), which is widely used in the receiver can compensate the ISI, its ability to enhance the signal-to-noise ratio (SNR) is limited especially for high frequency data patterns (alternating data patterns). Even a DFE with a large number of taps, which has powerful compensation capacity for ISI, can improve only limited amount of SNR. To improve SNR, this brief presents a 1/4th baud-rate continuous-time linear equalizer (CTLE) and a two-tap DFE. The 1/4th baud-rate CTLE recovers data to be adequate for the DFE, and remaining ISI is removed by the DFE. To boost the high frequency gain of the DFE, exclusive or merged adders are introduced, so the proposed equalizer is more tolerant against channel noise. It compensates 21.7-dB channel loss and operates with 11.5-Gb/s data rate as it consumes 25.35 mW from 1.3 V supply in a 110-nm CMOS technology.

Decision Feedback Equalizer (DFE) offers a good compromise between complexity and performance for channels with strong Intersymbol Interference (ISI). However, their blind or Decision-Directed (DD) adaptation may endure the inherent limitation from blind equalization algorithm or DD algorithm, i.e., 1) the blind equalization such as Constant Modulus Algorithm (CMA) has the ¿eye-opened¿ ability, but moderate convergence rate and steady state Mean Square Error (MSE); 2) the DD algorithm has faster convergence rate and lower steady state MSE, but it always cannot work unless the MSE of received signals is very low. So for overcoming above disadvantages we study the geometrical relation between CMA1-2 and DD algorithm and obtain the method of soft switch between CMA1-2 and DD algorithm. Consequently a new DFE based on CMA1-2 and DD algorithm is proposed. Based on theoretical analysis and computer simulations, the proposed approach is shown to be much more effective than the conventional DFE.

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.