Autocorrelation properties of channel encoded sequences-applicability to blind equalization

Many blind channel equalization/identification algorithms are derived assuming the transmitted information sequence to be white. In practical communication systems, redundancy is added to the source sequence in order to detect and correct symbol errors in the receiver. It is not obvious how channel encoding will affect the assumption of whiteness. The autocorrelation function of some commonly used channel codes is analyzed in order to study the validity of assumptions used in blind equalization. The codes are presented in terms of a Markov model for which the autocorrelation is analytically expressed. The various encoded sequences are used in a prediction error based blind equalizer, and the performance is empirically compared with the case of unencoded data. A blind equalization example using a practical GSM speech encoder combined with a convolutional channel encoder is also given.     

基于DDEA算法的短波信道Turbo均衡研究

针对数据引导均衡算法（DDEA）的缺陷,受到Turbo均衡中迭代思想的启发,提出一种基于数据引导均衡技术的短波迭代信道估计、均衡和译码算法,不仅均衡和译码之间互相传递软信息,信道估计器使用的也是译码器反馈的软信息,通过每次迭代时软信息质量的改善,提高系统的可靠性;通过多次迭代信道估计器输出的信道参数很接近当前帧的实际信...     

Joint Interference Cancellation and Channel Shortening in Multiuser-MIMO Systems

In this paper, a two-stage receiver structure for interference cancellation in multiuser spatially multiplexed multiple-antenna systems is presented. A space-time equalizer is used in the first stage for joint coantenna/cochannel-interference suppression and shortening of the effective channel for each transmit stream of the desired user. The channel shortening, combined with independent detection, helps reduce the complexity of the second stage Viterbi equalizer, which is used for separate intersymbol-interference equalization for each of the streams. Three objective functions are proposed for determining the coefficients of the space-time equalizer using a direct training data-based approach, which does not require estimation of the interferer's channel. Simulation results show good symbol error performance as compared to existing algorithms with asynchronous multiple-input multiple-output interferers     

A Recursive Blind Adaptive Equalizer for IIR Channels with Common Zeros

This paper considers the problem of blind adaptive equalization of infinite impulse response (IIR) channels without requiring the channel diversity condition. That is, the subchannels in the fractionally sampled model can have common factors. We analyze the case of two parallel channels, and develop an equalizer based on IIR prediction of the received signal. The predictor parameters are estimated by using the recursive extended least squares (RELS) algorithm. It is proved that with probability one the adaptive equalizer is globally stable, the parameter estimates are consistent, and the prediction error converges toward a scalar multiple of the input symbol sequence.     

Turbo均衡中的符号方差反馈均衡器

为了降低Turbo均衡中均衡器的复杂度,该文提出了符号方差反馈均衡算法(SVFE)。该算法是对精确的线性最小均方误差估计值(LMMSE)进行Taylor展开得到的。在该算法中,先利用时不变均衡器得到初步符号估计值,再根据先验符号方差对估计值加权,最后进行时不变滤波得到更佳的符号估计值。由于用到了时变的先验符号方差信息,其性能更接近精确的LMMSE均衡器。将所提算法用于Proakis C信道下的Turbo均衡处理,和时不变均衡算法进行仿真对比,所提算法将信噪比损失从0.83 dB降到了0.17 dB,并且仍可通过快速傅里叶变换降低为对数复杂度。     

Low-Complexity Block Turbo Equalization for OFDM Systems in Time-Varying Channels

We propose low-complexity block turbo equalizers for orthogonal frequency-division multiplexing (OFDM) systems in time-varying channels. The presented work is based on a soft minimum mean-squared error (MMSE) block linear equalizer (BLE) that exploits the banded structure of the frequency-domain channel matrix, as well as a receiver window that enforces this banded structure. This equalization approach allows us to implement the proposed designs with a complexity that is only linear in the number of subcarriers. Three block turbo equalizers are discussed: two are based on a biased MMSE criterion, while the third is based on the unbiased MMSE criterion. Simulation results show that the proposed iterative MMSE BLE achieves a better bit error rate (BER) performance than a previously proposed iterative MMSE serial linear equalizer (SLE). The proposed equalization algorithms are also tested in the presence of channel estimation errors.      

瑞利衰落信道下的Turbo均衡

Turbo均衡是一种将Turbo原理和均衡技术结合起来的技术。他通过反复均衡和信道译码来提高接收机性能。针时瑞利衰落信道，采用基于线性滤波器的软输入／软输出均衡器来消除码间干扰，其系数由最小均方误差准则确定。译码器采用最大后验概率算法时卷积码译码。考虑到瑞利衰落信道为随机信道，用非相干检测时信道进行估计。接收机通过联合均衡和译码以充分利用已经获得的信息，实现信道估计及信道均衡与信道译码的迭代更新。仿真结果表明其性能不仅远远优于非迭代系统．而且在信噪比高于4dB时几乎可以完全消除符号间干扰的影响，与MAPSE相比其复杂度大大降低。     

Blind equalization and channel estimation with partial responseinput signals

The problem of blind equalization and channel estimation for partial-response signals (PRS) is considered. Three approaches are investigated; two of them exploit the prior knowledge of the PR code, and the third approach does not. We propose a constrained optimization approach involving a quadratic cumulant matching criterion where the coding structure of the transmitted signal is assumed to be a priori known. The other two approaches exploit the Godard blind equalizer. Computer simulation results using 16-QAM signals, and duobinary and modified duobinary PR codes, show that the constrained optimization approach yields the best performance as measured via the probability of symbol detection error     

Matching pursuit-based tap selection technique for UWB channel equalization

In this letter, matching pursuit (MP) based tap selection technique is proposed and applied to ultra wideband (UWB) indoor channel equalization in the presence of inter symbol interference (ISI) and multiple access interference (MAI). Given the limited training sample support, quadratic constraint is incorporated into MP algorithm to insure the robustness for tap selection. The proposed method is shown to outperform the conventional minimum mean square error (MMSE) equalizer significantly given the same amount of training symbols.     

Performance analysis of linear MIMO equalizers for multitone DS/SS systems in multipath channels

In [11] the combination of multitone modulation with direct sequence spectrum spreading has been introduced. The performance of a correlation receiver has been evaluated for a multipath channel. In [12] the analysis has been extended to the presence of a multiple access interference. In the present paper we analyze the equalization problem of such a system for a single user scenario. In order to understand the potential of the system we first investigate the steady-state behavior of the MIMO equalizer for an MMSE design. The investigation is carried out for an equalizer following a receiver made of a bank of filters matched to both the symbol shape and the channel, which is a two-path channel. Assuming BPSK symbols an exact expression of the bit error probability before and after equalization is obtained in the form of an integral by means of the characteristic function method. Next adaptive LMS and RLS structures are proposed. The performance of the RLS algorithm is demonstrated.Part of this work has been presented at ICC '95, Seattle, June 1995.This author would like to thank the Belgian NSF for its financial support.This author is a Research assistant of FRIA.     

MIMO DFE equalization for multitone DS/SS systems over multipathchannels

The combination of multitone modulation with direct sequence spectrum spreading (DS/SS) has been introduced in the past. The performance of a correlation receiver has been evaluated for a multipath channel and in the presence of an additional multiple access interference. We analyze the problem of decision feedback equalization (DFE) for such a system. In order to understand the potential of the system with equalization, we first study the steady-state behavior of the equalizer for a minimum mean square error (MMSE) criterion. The investigation is carried out for a receiver made of a bank of filters matched to both the symbol shape and the channel, and for a two path channel. Assuming transmission of binary phase shift keying (BPSK) symbols, an exact expression of the bit error probability is obtained in the form of an integral. Then adaptive least mean square (LMS) and recursive least square (RLS) structures are derived. The performance of the adaptive RLS algorithm is demonstrated by means of computer simulations     

A blind decision feedback equalizer incorporating fixed lagsmoothing

A new type of blind decision feedback equalizer (DFE) incorporating fixed lag smoothing is developed in this paper. The structure is motivated by the fact that if we make full use of the dependence of the observed data on a given transmitted symbol, delayed decisions may produce better estimates of that symbol. To this end, we use a hidden Markov model (HMM) suboptimal formulation that offers a good tradeoff between computational complexity and bit error rate (BER) performance. The proposed equalizer also provides estimates of the channel coefficients and operates adaptively (so that it can adapt to a fading channel for instance) by means of an online version of the expectation-maximization (EM) algorithm. The resulting equalizer structure takes the form of a linear feedback system including a quantizer, and hence, it is easily implemented. In fact, because of its feedback structure, the proposed equalizer shows some similarities with the well-known DFE. A full theoretical analysis of the initial version of the algorithm is not available, but a characterization of a simplified version is provided. We demonstrate that compared to the zero-forcing DFE (ZF-DFE), the algorithm yields many improvements. A large range of simulations on finite impulse response (FIR) channels and on typical fading GSM channel models illustrate the potential of the proposed equalizer     

Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems

Conventional equalization and carrier recovery algorithms for minimizing mean-square error in digital communication systems generally require an initial training period during which a known data sequence is transmitted and properly synchronized at the receiver. This paper solves the general problem of adaptive channel equalization without resorting to a known training sequence or to conditions of limited distortion. The criterion for equalizer adaptation is the minimization of a new class of nonconvex cost functions which are shown to characterize intersymbol interference independently of carrier phase and of the data symbol constellation used in the transmission system. Equalizer convergence does not require carrier recovery, so that carrier phase tracking can be carried out at the equalizer output in a decision-directed mode. The convergence properties of the self-recovering algorithms are analyzed mathematically and confirmed by computer simulation.     

Adaptive MAPSD algorithms for symbol and timing recovery of mobileradio TDMA signals

Dual-mode adaptive algorithms with rapid convergence properties are presented for the equalization of frequency selective fading channels and the recovery of time-division multiple access (TDMA) mobile radio signals. The dual-mode structure consists of an auxiliary adaptive filter that estimates the channel during the training cycle. The converged filter weights are used to initialize a parallel bank of filters that are adapted blindly during the data cycle. When the symbol timing is known, this filter bank generates error residuals that are used to perform approximate maximum a posteriori symbol detection (MAPSD) and provide reliable decisions of the transmitted signal. For channels with timing jitter, joint estimation of the channel parameters and the symbol timing using an extended Kalman filter algorithm is proposed. Various methods are described to reduce the computational complexity of the MAP detector, usually at the cost of some performance degradation. Also, a blind MAPSD algorithm for combining signals from spatially diverse receivers is derived. This diversity MAPSD (DMAPSD) algorithm, which can be easily modified for the dual-mode TDMA application, maintains a global set of MAP metrics even while blindly tracking the individual spatial channels using local error estimates. The performance of these single-channel and diversity MAPSD dual-mode algorithms are studied via computer simulations for various channel models, including a mobile radio channel simulator for the IS-54 digital cellular TDMA standard     

A suboptimum linear receiver based on a parametric channel model

A suboptimum, linear, minimum mean-squared error (MMSE) data communication receiver that is based on a parametric model for a linear, time-invariant, or slowly time-varying channel is shown to perform well at reasonable input signal-to-noise ratios (SNRs) and for short training periods. The receiver makes use of a fractionally spaced equalizer (FSE) design whose time span is a single symbol period. It is assumed that a parametric model, with parameter estimates that are obtainable from a training sequence prior to data acquisition, is adequate for representing the impulse response of the equivalent baseband channel     

Trellis-coded CPFSK and soft-decision feedback equalization for micro-cellular wireless applications

In this paper, trellis-codedM-ary CPFSK with noncoherent envelope detection and adaptive channel equalization are investigated to improve the bit error rate (BER) performance of microcellular digital wireless communications systems. For the same spectral efficiency, the trellis-coded modulation (TCM) schemes studied outperform minimum shift keying (MSK) with noncoherent or differentially coherent detection in Rayleigh fading channels. For the case of frequency-selective fading channels, adaptive channel equalization is applied to mitigate the time-variant intersymbol interference (ISI). A new equalizer structure is proposed which, in its feedback path, makes use of fractionally spaced signal samples instead of symbol-spaced hard decisions on transmitted symbols. Computer simulation results indicate that the soft-decision feedback equalizer (SDFE) can significantly improve the system's performance.     

Blind equalization using least-squares lattice prediction

Second-order statistics of the received signal can be used to equalize a communication channel without knowledge of the transmitted sequence. Blind zero-forcing (ZF) and minimum mean-square error (MMSE) equalization can be achieved with linear prediction error filtering. The equivalence with the equalizers derived by Giannakis and Halford (see ibid., vol.45, p.2277-92, 1997) is shown, and adaptive predictors that result in a lattice filtering structure are applied. The required channel coefficient vector is obtained with adaptive eigen-pair tracking. Either forward or backward prediction errors can be used. The performance of the blind equalizer is examined by simulations. The MMSE of the optimum FSE is approached, and the algorithm exhibits robustness to channels with common subchannel zeros     

Iterative nonlinear detection for SFBC SC–FDMA uplink MIMO transmission systems

Single‐carrier frequency division multiple access (SC‐FDMA) systems with space frequency block coding (SFBC) transmissions achieve both spatial and frequency diversity gains in wireless communications. However, SFBC SC‐FDMA schemes using linear detectors suffer from severe performance deterioration because of noise enhancement propagation and additive noise presence in the detected output. Both issues are similar to inter‐symbol‐interference (ISI). Traditionally, SC‐FDMA system decision feedback equalizer (DFE) is often used to eliminate ISI caused by multipath propagation. This article proposes frequency domain turbo equalization based on nonlinear multiuser detection for uplink SFBC SC‐FDMA transmission systems. The presented iterative receiver performs equalization with soft decisions feedback for ISI mitigation. Its coefficients are derived using minimum mean squared error criteria. The receiver configuration study is Alamouti's SFBC with two transmit and two receive antennas. New receiver approach is compared with the recently proposed suboptimal linear detector for SFBC SC‐FDMA systems. Simulation results confirm that the performance of the proposed iterative detection outperforms conventional detection techniques. After a few iterations, bit‐error‐rate performance of the proposed receiver design is closely to the matched filter bound. Copyright © 2016 John Wiley & Sons, Ltd.     

An efficient decision feedback equalizer for the ATSC DTV receiver

In this paper an efficient decision feedback equalizer is presented for the equalization of the received signal in the eight level vestigial sideband, Advanced Television Systems Committee, digital television system, adopting a novel detection rule for symbol detection at the output of the equalizer. The conventional hard limiter is replaced by an efficient symbol detection algorithm, based on the underlying trellis coded modulated coding of the transmitted symbols. The proposed decision device has a marginal computational cost and it can be implemented using simple combinatorial and sequential logic circuitry. When the equalizer operates in the decision directed mode, the normalized least mean squared algorithm is utilized for the adaptation of the equalizer coefficients, in a “stop-and-go” like mode, triggered by a reliability signal associated to the detected symbols. The performance of the proposed method is illustrated by typical computer simulation.     

带有循环前缀的单载波通信系统中干扰抵消辅助的频域均衡技术

在单载波通信系统中,循环前缀(简称CP)的存在不仅能减轻由于多径信道造成的传输数据块间信号干扰(简称IBI),而且可以采用频域均衡(简称FDE)技术来补偿由多径信道引起的频率选择性信号衰落.本文主要分析了带有循环前缀的单载波通信系统(简称CP-SC)中广泛应用的基于线性最小均方误差(简称LMMSE)准则的FDE技术中的残余信号间干扰(RISI)问题,提出了一种干扰抵消辅助的LMMSE-FDE接收机结构,它能很好的消除RISI,改善系统性能.