A Maximum-Likelihood Sequence Estimator with Decision-Feedback Equalization

A decision-feedback equalizer (DFE) is proposed as a prefilter which limits the complexity of a maximum-likelihood sequence estimator (MLSE) implemented by the Viterbi algorithm (VA) for channels having a long impulse response. By imbedding a DFE into the structure of the MLSE, the overall impulse response of the system is truncated to a short duration. With this practical receiver, a compromise may be made between performance and complexity by properly choosing the duration of a desired impulse response. A technique is also developed to estimate the performance of the receiver numerically, taking into account the effect of incorrect decision feedback on the VA. Analysis and computer simulation over a single-pole channel show that the proposed scheme can reduce the complexity of the MLSE while retaining much of its performance advantages.     

A robust noncoherent equalizer receiver for fading channels with short memory .I. Basic structure

Traditional equalizers are very sensitive to carrier frequency offsets between the transmitter and receiver. Coherent receivers with frequency estimation algorithms can remove the offset to prevent the equalizer breakdown, but with a penalty in receiver complexity. On the other hand, noncoherent receivers such as differential detectors are inherently robust to the frequency offsets but cannot employ standard equalization techniques due to their nonlinear front-end. We introduce a simple noncoherent equalizer receiver structure for fading channel environments with short memory (up to two-bit intervals). The receiver consists of a whitened matched filter followed by a differential detector and a maximum likelihood sequence estimation (MLSE) equalizer. We examine the performance of this noncoherent equalizer by both analysis and simulation. It is shown that despite the simplicity, this receiver structure is capable of significant performance improvement as compared to an ordinary differential detector while operating with receiver frequency offsets two orders of magnitude greater than a traditional MLSE equalizer. This structure offers an attractive solution for high-bit-rate cordless transmission systems such as Digital Enhanced Cordless Telecommunications (DECT) that use simple noncoherent receivers whose performance can be constrained by channel dispersion. Using DECT as a case study, we show that the equalizer's performance limits are caused by the receiver nonlinearity and can be improved by adaptation of this nonlinearity to channel conditions.     

MLSE and soft-output equalization for trellis-coded continuousphase modulation

This paper presents two equalizer structures for trellis-coded continuous phase modulation (TC-CPM) on multipath fading intersymbol interference (ISI) channels. An equivalent discrete-time (DT) model is developed by combining the tapped-delay-line (TDL) model of the frequency-selective channel and by oversampling at the receiver. The (noninterleaved) fractionally spaced maximum-likelihood sequence estimation (MLSE) equalizer performs continuous phase modulation (CPM) demodulation, trellis-coded modulation (TCM) decoding, and channel equalization by exploiting the finite state nature of the ISI-corrupted TC-CPM signal. Both simulation and analytical results show diversity-like improvement when performing joint MLSE decoding and equalization. For the interleaved soft-output equalizer, the soft symbol metric is delivered to the TCM decoder by using a forward and backward recursion algorithm. Three variants of the soft-output equalizer are examined. We conclude that the backward recursion is essential to partial response CPM schemes, and with moderate complexity, the soft-output equalizer can have a substantial advantage over a noninterleaved MLSE equalizer     

MLSE and MAP Equalization for Transmission Over Doubly Selective Channels

In this paper, equalization for transmission over doubly selective channels is discussed. The symbol-by-symbol maximum a posteriori probability (MAP) equalizer and the maximum-likelihood sequence estimation (MLSE) are discussed. The doubly selective channel is modeled using the basis expansion model (BEM). Using the BEM allows for an easy and low-complexity mechanism for constructing the channel trellis to implement the MLSE and the MAP equalizer. The MLSE and the MAP equalizer are implemented for single-carrier transmission and for multicarrier transmission implemented using orthogonal frequency-division multiplexing (OFDM). In this scenario, a complexity-diversity tradeoff can be observed. In addition, we propose a joint estimation and equalization technique for doubly selective channels. In this joint estimation and equalization technique, the channel state information (CSI) is obtained in an iterative manner. Simulation results show that the performance of the joint channel estimation and equalization approaches the performance when perfect CSI is available at the receiver.     

A robust noncoherent equalizer receiver for fading channels with short memory . II. Modified structure

For pt. I see ibid., vol.5, no.5, p.1040-54 (2002). In Part I, we introduced a robust noncoherent maximum likelihood sequence estimation (MLSE) equalizer receiver structure applicable to radio channels with impulse responses spanning less than two bit intervals. The distinct characteristic of this receiver was its robustness to carrier frequency offsets. However, due to the differential operation prior to the MLSE equalization, we observed some performance degradation, resulting in a delay spread range significantly smaller than an equivalent coherent MLSE equalizer. We propose techniques to significantly improve the performance of the noncoherent equalizer by using a second, complementary differential processor. The performance assessment of the new receiver is presented. In particular, using the Digital Enhanced Cordless Telecommunications system as an example, it is shown that the modified receiver's dispersive channel operation range is almost twice as much as the basic structure, with a multipath diversity gain comparable to a coherent equalizer receiver. On the other hand, unlike coherent structures, it retains low sensitivity to both frequency offsets and modulation index drifts. Finally, we introduce an approach to further extend the receiver's frequency offset tolerance to that of a standard differential detector receiver.     

A new adaptive equalizer with channel estimator for mobile radiocommunication

For unknown mobile radio channels with severe intersymbol interference (ISI), a maximum likelihood sequence estimator, such as a decision feedback equalizer (DFE) having both feedforward and feedback filters, needs to handle both precursors and postcursors. Consequently, such an equalizer is too complex to be practical. This paper presents a new reduced-state, soft decision feedback Viterbi equalizer (RSSDFVE) with a channel estimator and predictor. The RSSDFVE uses maximum likelihood sequence estimation (MLSE) to handle the precursors and truncates the overall postcursors with the soft decision of the MLSE to reduce the implementation complexity. A multiray fading channel model with a Doppler frequency shift is used in the simulation. For fast convergence, a channel estimator with fast start-up is proposed. The channel estimator obtains the sampled channel impulse response (CIR) from the training sequence and updates the RSSDFVE during the bursts in order to track changes of the fading channel. Simulation results show the RSSDFVE has nearly the same performance as the MLSE for time-invariant multipath fading channels and better performance than the DFE for time-variant multipath fading channels with less implementation complexity than the MLSE. The fast start-up (FS) channel estimator gives faster convergence than a Kalman channel estimator. The proposed RSSDFVE retains the MLSE structure to obtain good performance and only uses soft decisions to subtract the postcursor interference. It provides the best tradeoff between complexity and performance of any Viterbi equalizers     

带判决反馈的盲最大似然序列估计

本文提出了一种新型的带有判决反馈的减小状态最大似然序列估计ＲＳＳＤＦＰＳＰ,新算法带有两个信道估值器并且可以工作在盲环境下．使用最大似然序列估计（ＭＬＳＥ）来处理信道冲激响应的前导干扰及主径,反馈滤波器处理后尾干扰,并且用ＰｅｒＳｕｒｖｉｖｉｎｇＰｒｏｃｅｓｉｎｇ（ＰＳＰ）算法来得到ＭＬＳＥ部分的信道冲激响应,信道估值器２得到后尾干扰．计算机模拟表明,这种ＲＳＳＤＦＰＳＰ方案在减小ＭＬＳＥ的计算复杂度的同时能最大限度地得到ＭＬＳＥ的性能,是ＭＬＳＥ在计算复杂度与性能之间的较好折中．     

Detection for a statistically known, time-varying dispersivechannel

Detection for the statistically known channel (SKC) is aimed at obtaining good performance in situations where our statistical knowledge of a time-varying channel is good, and where other equalization/detection schemes are either too complex to implement, or their performance is limited due to the rapidity of channel fading, or where we are simply unable to perform channel estimation. By using a statistical characterization of the channel, we develop a new detector that performs maximum-likelihood sequence estimation (MLSE) (given the channel model) on blocks of N symbols. Both symbol-spaced and fractionally spaced samples are used, to obtain two different detectors, that are generalizations of those devised for optimal block schemes on nondispersive channels. The detector that uses fractionally spaced samples is shown to outperform the detector that uses symbol-spaced samples. The performance of both appears to approach that of the corresponding known channel (KC) detector as the block length increases. We also numerically evaluate the SKC detector performance under conditions where the channel parameters (statistics) are incorrectly estimated, and show that the fractionally spaced detector is fairly robust to modeling errors. Finally, we devise a sliding block algorithm, for use when transmitting more than N symbols     

Adaptive combined DFE/MLSE techniques for ISI channels

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     

Adaptive array processing MLSE receivers for TDMA digitalcellular/PCS communications

Array processing is a promising approach for improving quality, coverage, and capacity in digital cellular communication systems. By combining array processing with maximum likelihood sequence estimation (MLSE), intersymbol interference (ISI) introduced by multipath propagation can be mitigated as well. Novel symbol-spaced and fractionally spaced adaptive array processing MLSE receivers are developed for both diversity and phased array antenna configurations. The practical issues of synchronization and channel estimation are addressed. A novel approach to automatic frequency error correction (AFC) is proposed and is shown to be critical when cancelling cochannel interference. Performance is evaluated for the reverse link of the IS-136 TDMA-based digital cellular system. Substantial improvements are obtained over conventional antenna configurations for receiver sensitivity (2.5-4 dB) and over traditional antenna combining when cochannel interference is present (0.5-25 dB)     

Adaptive MLSE for DPSK in time- and frequency-selective channels

An adaptive equalizer structure based on a state space formulation and maximum likelihood sequence estimation (MLSE) is developed for a time-varying, frequency-selective channel. Differential phase shift keying (DPSK) is assumed at the transmitter and effective differential decoding is performed at the receiver. The standard models of a time-varying linear channel and the Karhunen-Lo`eve (KL) expansion underpin the receiver structure. Analytical and simulation results for the receiver are shown. The resulting receiver is a per-survivor structure.     

自适应均衡算法在信道均衡技术中的应用研究

文中描述了两种非线性均衡器分别为判决反馈均衡器(DFE)和最大似然序列估计(MLSE)均衡器.所用信道模型为加性白高斯噪声信道,在DFE和线性均衡器(LE)中都是使用递归最小二乘(RLS)算法和最小均方(LMS)算法对数据进行分块处理.MLSE均衡器中使用了维特比最佳译码算法.就误比特性能来做以比较,DFE远好于LE,MLSE均衡器又明显优于DFE,并且它能达到几乎最优的性能.     

A suboptimal approach to channel equalization based on the nearestneighbor rule

Applications of clustering and neural network techniques to channel equalization have revealed the classification nature of this problem. This paper illustrates an implementation of a global system for mobile communications (GSM) receiver in which channel equalization and demodulation are realized by means of the nearest neighbor (NN) classifier algorithm. The most important advantage in using such techniques is the significant reduction in terms of the computational complexity compared with the maximum likelihood sequence estimation (MLSE) equalizer. The proposed approach involves symbol-by-symbol interpretation and the knowledge of the channel is embedded in the mapping process of the received symbols over the symbols of the training sequence. This means that no explicit channel estimation need be carried out, either with correlative blocks or using neural networks thus speeding up the entire process. The performance of the proposed receiver, evaluated through a channel simulator for mobile radio communications, is compared with the results obtained by means of a 16-state Viterbi algorithm and other suboptimal receivers. It is shown that the presented algorithm increases the bit error rate (BER) compared with the MLSE demodulator, but the performance degradation, despite the simplicity of the receiver, is kept within the limits imposed by the GSM specifications     

Adaptive MLSE equalizers with parametric tracking for multipathfast-fading channels

We use the parametric channel identification algorithm proposed by Chen and Paulraj (see Proc. IEEE Vehicular Technology Conf., p.710-14, 1997) and by Chen, Kim and Liang (see IEEE Trans. Veh. Technol., p.1923-35, 1999) to adaptively track the fast-fading channels for the multichannel maximum likelihood sequence estimation (MLSE) equalizer using multiple antennas. Several commonly-used channel tracking schemes, decision-directed recursive least square (DD/RLS), per-survivor processing recursive least square (PSP/RLS) and other reduced-complexity MLSE algorithms are considered. An analytic lower bound for the multichannel MLSE equalizer with no channel mismatch in the time-varying specular multipath Rayleigh-fading channels is derived. Simulation results that illustrate the performance of the proposed algorithms working with various channel tracking schemes are presented, and then these results are compared with the analytic bit error rate (BER) lower bound and with the conventional MLSE equalizers directly tracking the finite impulse response (FIR) channel tap coefficients. We found that the proposed algorithm always performs better than the conventional adaptive MLSE algorithm, no matter what channel tracking scheme is used. However, which is the best tracking scheme to use depends on the scenario of the system     

稀疏多径信道的T/2间隔CFE均衡器研究

完全反馈均衡器(Complete Feedback Equalizer, CFE)是判决反馈均衡器(DFE)的改进。该文提出了一种T/2分数间隔稀疏CFE(T/2 Sparse CFE, T/2-SCFE)结构,以避免接收机对于符号定时误差的敏感性,并有效利用长时延扩展多径信道的稀疏性来降低均衡器的复杂度。理论分析与基于实测信道的计算机仿真表明, T/2-SCFE均衡器对符号定时误差保持了稳健性,总体性能优于符号间隔CFE及分数间隔DFE。     

Multichannel MLSE equalizer with parametric FIR channelidentification

We propose a parametric finite impulse response (FIR) channel identification algorithm, apply the algorithm to a multichannel maximum likelihood sequential estimation (MLSE) equalizer using multiple antennas, and investigate the improvement in the overall bit error rate (BER) performance. By exploring the structure of the specular multipath channels, we are able to reduce the number of channel parameters to provide a better channel estimate for the MLSE equalizer. The analytic BER lower bounds of the proposed algorithm as well as those of several other conventional MLSE algorithms in the specular multipath Rayleigh-fading channels are derived. In the derivation, we consider the channel mismatch caused by the additive Gaussian noise and the finite-length channel approximation error. A handy-to-use simplified BER lower bound is also derived. Simulation results that illustrate the BER performance of the proposed algorithm in the global system for mobile communications (GSM) system are presented and compared to the analytic lower bounds     

Adaptive maximum-likelihood sequence estimation by means ofcombined equalization and decoding in fading environments

This paper proposes an adaptive maximum-likelihood sequence estimation (MLSE) by means of combined equalization and decoding, i.e., adaptive combined MLSE, which employs separate channel estimation for respective states in the Viterbi algorithm. First, an approximate metric including channel estimation is derived analytically for this proposed adaptive combined MLSE. Secondly, procedures to accomplish blind equalization are investigated for the proposed MLSE. Finally, its excellent BER performance on fast time-varying fading channels is confirmed by computer simulation, when the proposed MLSE operates as a blind equalizer     

A channel estimation using sliding window approach and tuningalgorithm for MLSE

A simultaneous sliding window channel estimation and timing adjustment method is proposed for adaptive maximum-likelihood sequence equalizer (MLSE) in the global system for mobile communication (GSM) system, and also a tuning scheme based on least mean squared (LMS) algorithm is presented in order to improve the performance of equalizer. Simulation results show that the proposed channel estimation technique is effective for channel estimation of the adaptive equalizer     

MLSE equalization and decoding for multipath-fading channels

The performance of a receiver using a combined MLSE (maximum likelihood sequence estimation) equalizer/decoder and D-diversity reception is analyzed for multipath Rayleigh fading channels. An upper bound on the (decoded) bit error probability is derived. Comparisons to simulation results show that this upper bound is quite tight when the system has a high signal-to-noise ratio or when diversity reception is used. The upper bound involves an infinite series that must be truncated at a point where the remainder can be safely assumed to be small. An algorithm based on a one-directional stack algorithm is proposed for this calculation because it makes efficient use of computer memory     

Performance analysis of an adaptive receiver structure for digital mobile communications

In this paper we investigate the performance of a combined estimation/equalization technique for the mobile radio channel, assuming a GSM-recommended transmission format (narrowband TDMA with midamble, recommendation 5.04) and MSK modulation scheme. Channel estimation is performed via correlation of the received signal with a suitably modulated replica of the transmitted midamble. Equalization is then obtained by means of a maximum likelihood sequence estimation (MLSE) scheme in the form of a so-called Viterbi equalizer. Our analysis provides theoretical results concerning the bit error rate (BER) attained by the receiver for a given stationary multipath channel model. Simulation results are also presented in order to integrate and validate the theory.