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.     

Decision feedback equalization

As real world communication channels are stressed with higher data rates, intersymbol interference (ISI) becomes a dominant limiting factor. One way to combat this effect that has recently received considerable attention is the use of a decision feedback equalizer (DFE) in the receiver. The action of the DFE is to feed back a weighted sum of past decision to cancel the ISI they cause in the present signaling interval. This paper summarizes the work in this area beginning with the linear equalizer. Three performance criteria have been used to derive optimum systems; 1) minimize the noise variance under a "zero forcing" (ZF) constraint i.e., insist that all intersymbol interference is cancelled, 2) minimize the mean-square error (MMSE) between the true sample and the observed signal just prior to the decision threshold, and 3) minimize the probability of error (Min Pe). The transmitter can be fixed and the receiver optimized or one can obtain the joint optimum transmitter and receiver. The number of past decisions used in the feedback equalization can be finite or infinite. The infinite case is easier to handle analytically. In addition to reviewing the work done in the area, we show that the linear equalizer is in fact a portion of the DFE receiver and that the processing done by the DFE is exactly equivalent to the general problem of linear prediction. Other similarities in the various system structures are also shown. The effect of error propagation due to incorrect decisions is discussed, and the coaxial cable channel is used as an example to demonstrate the improvement available using DFE.     

A class of block-iterative equalizers for intersymbol interferencechannels: fixed channel results

A new and efficient class of nonlinear equalizers is developed for intersymbol interference (ISI) channels. These -"iterated-decision equalizers” use an optimized multipass algorithm to successively cancel ISI from a block of received data and generate symbol decisions whose reliability increases monotonically with each iteration. These equalizers have an effective complexity comparable to the decision-feedback equalizer (DFE), yet asymptotically achieve the performance of maximum-likelihood sequence detection (MLSD). We show that, because their structure allows cancellation of both precursor and postcursor ISI, iterated-decision equalizers outperform the minimum mean-square error DFE by 2.507 dB on severe ISI channels even with uncoded systems. Moreover, unlike the DFE, iterated-decision equalizers can be readily used in conjunction with error-control coding, making them attractive for a wealth of applications     

Adaptive DFE for GMSK in indoor radio channels

We simulate the performance of an equalized Gaussian minimum shift keying (GMSK) signal in an indoor radio environment with fading, noise, imperfect carrier recovery, cochannel interference (CCI), and intersymbol interference (ISI). We show that data rates of 20 Mb/s at bit error rates (BER) ⩽10^-4 are possible with root mean square (RMS) delay spreads up to 25 ns using a simple limiter-discriminator-integrator (LDI) receiver and a (6, 4) decision feedback equalizer (DFE). In environments with larger RMS delay spreads, coherent detection is required for the same performance. We show that using a decision-directed second-order digital carrier synchronizer with time varying loop filters, frequency offsets up to 200 kHz can be corrected with negligible performance degradation. This paper utilizes a DFE structure which compensates for both modulator and channel ISI, and yet requires no power-intensive multiplication operations in the feedback section. A DFE (8, 8) with two-level switched (selection) diversity is shown to allow 20 Mb/s data transfer at a BER⩽10^-4 for RMS delay spreads under 150 ns, with CCI. A light BCH (26, 31) code allows error-free reception of over 90% of packets with RMS delay spreads under 150 ns, and up to 70% of packets with RMS delays of 150 ns     

Error-rate evaluation of linear equalization and decision feedbackequalization with error propagation

We propose applying an approximate Fourier series to evaluate efficiently the bit-error-rate (BER) performance of finite-length linear equalization (LE) and decision feedback equalization (DFE). By extending the Fourier series, we enable BER calculations for quadrature phase-shift keying (QPSK) transmission on complex channels with in-phase and crosstalk intersymbol interference (ISI). The BER calculation is based on determining the residual ISI samples and background Gaussian noise variance at the equalizer output for static channels or for realizations of quasi-static fading channels. A simple bound on the series error magnitude in terms of the Fourier series parameters ensures the required accuracy and precision. Improved state transition probability estimates are derived and verified by simulation for an approximate Markov model of the DFE error propagation for the case in which residual ISI exists even when the previous decisions stored in the feedback filter (FBF) are correct. We demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs. Our analysis includes symbol-spaced and fractionally spaced minimum mean-square error (MMSE)-LE, zero-forcing (ZF)-LE, and MMSE-DFE (with and without error propagation) on static ISI channels and multipath channels with quasi-static Rayleigh fading; a comparison between suboptimum and optimum receiver filtering in conjunction with equalization; and an assessment of the accuracy of some widely used equalization BER approximations and bounds     

Adaptive turbo reduced-rank equalization for MIMO channels

An adaptive iterative (turbo) decision-feedback equalizer (DFE) for channels with intersymbol interference (ISI) is presented. The filters are computed directly from the soft decisions and received data to minimize a least-squares (LS) cost function. Numerical results show that this method gives a substantial improvement in performance relative to a turbo DFE computed from an exact channel estimate, assuming perfect feedback. Adaptive reduced-rank estimation methods are also presented, based on the multistage Wiener filter (MSWF). The adaptive reduced-rank turbo DFE for single-input/single-output channels is extended to multiple-input/multiple-output (MIMO) channels with ISI and multiple receive antennas. Numerical results show that for MIMO channels with limited training, the reduced-rank turbo DFE can perform significantly better than the full-rank turbo DFE.     

Detection of coded modulation signals on linear, severely distortedchannels using decision-feedback noise prediction with interleaving

On linear bandlimited Gaussian noise channels with sufficiently high SNR, channel capacity can be approached by combining powerful coded modulation schemes designed for Nyquist channels with the equalization power of decision-feedback equalization (DFE). However, this combination may not be realized in a straightforward manner, since, in general, DFE requires delay-free decisions for feedback, and in a coded system such decisions are not sufficiently reliable. A technique is proposed that combines periodic interleaving with noise-predictive DFE, so that delayed reliable decisions can be used for feedback. When sufficient delay in the interleavers can be tolerated, this technique can attain the DFE performance. On severely distorted channels, modest delays can be sufficient to obtain respectable gains over linear equalization     

Antenna diversity combining and finite-tap decision feedbackequalization for high-speed data transmission

The next-generation wireless communication systems are expected to support high-speed data transmission. Associated with high transmission rates, however, is the problem of multipath intersymbol interference (ISI) due to frequency-selective fading. Decision feedback equalization (DFE) and antenna diversity combining are two practical techniques for combating multipath ISI. Through simulations we investigate the performance of diversity combining, together with DFE, under various numbers of antenna branches and equalization taps, in a quasistationary frequency-selective fading environment with additive white Gaussian noise (AWGN) and cochannel interference (CCI). We consider joint optimization combining and power selection diversity combining. We simulate the combiner, using quaternary phase shift keying (QPSK) modulation with up to four antenna branches. Our results show that using antenna diversity and DFE with joint optimization combining provides performance improvement with lower computational complexity, as compared to that of using either DFE or diversity combining alone for combating ISI     

运用误差反馈的判决反馈均衡器的性能分析

判决反馈均衡器（Decision Feedback Equalizer，DFE）能补偿具有严重符号间干扰（Inter Symbol Interference，ISI）的信道，且不存在线性均衡器增强噪声的影响。而在其基础上改进的运用误差反馈的DFE，可利用误差反馈滤波器来减少传统DFE中存在的误差信号的相关性，同时其硬件实现的复杂度没有明显提高。理论分析和仿真表明，这种方法比传统的DFE更有效，特别是针对信道有严重符号间干扰的情况。     

A New Class of Efficient Block-Iterative Interference Cancellation Techniques for Digital Communication Receivers

A new and efficient class of nonlinear receivers is introduced for digital communication systems. These iterated-decision receivers use optimized multipass algorithms to successively cancel interference from a block of received data and generate symbol decisions whose reliability increases monotonically with each iteration. Two variants of such receivers are discussed: the iterated-decision equalizer and the iterated-decision multiuser detector. Iterated-decision equalizers, designed to equalize intersymbol interference (ISI) channels, asymptotically achieve the performance of maximum-likelihood sequence detection (MLSD), but only have a computational complexity on the order of a linear equalizer (LE). Even more importantly, unlike the decision-feedback equalizer (DFE), iterated-decision equalizers can be readily used in conjunction with error-control coding. Similarly, iterated-decision multiuser detectors, designed to cancel multiple-access interference (MAI) in typical wireless environments, approach the performance of the optimum multiuser detector in uncoded systems with a computational complexity comparable to a decorrelating detector or a linear minimum mean-square error (MMSE) multiuser detector.     

BER improvement of PRCPM in mobile radio channels withdiscriminator detection using decision feedback equalization

The authors investigate the bit error rate (BER) improvement of partial-response continuous-phase modulation (PRCPM) signals in mobile radio channels, when decision feedback equalization (DFE) to cancel the effect of intersymbol interference (ISI) of one adjacent bit is added to the limiter discriminator. A closed-form expression for the average probability of error as a function of the Doppler shift is derived for discriminator detection with decision feedback. Numerical results are presented to compare the BER performance of discriminator detection with and without feedback equalization     

RLS Algorithm with Variable Fogetting Factor for Decision Feedback Equalizer over Time-Variant Fading Channels

In a high-rate indoor wireless personal communication system, the delay spread due to multipath propagation results in intersymbol interference (ISI) which can significantly increase the transmission bit error rate (BER). Decision feedback equalizer (DFE) is an efficient approach to combating the ISI. Recursive least squares (RLS) algorithm with a constant forgetting factor is often used to update the tap-coefficient vector of the DFE for ISI-free transmission. However, using a constant forgetting factor may not yield the optimal performance in a nonstationary environment. In this paper, an adaptive algorithm is developed to obtain a time-varying forgetting factor. The forgetting factor is used with the RLS algorithm in a DFE for calculating the tap-coefficient vector in order to minimize the squared equalization error due to input noise and due to channel dynamics. The algorithm is derived based on the argument that, for optimal filtering, the equalization errors should be uncorrelated. The adaptive forgetting factor can be obtained based on on-line equalization error measurements. Computer simulation results demonstrate that better transmission performance can be achieved by using the RLS algorithm with the adaptive forgetting factor than that with a constant forgetting factor previously proposed for optimal steady-state performance or a variable forgetting factor for a near deterministic system.     

Mitigating error propagation effects in a decision feedbackequalizer

We present an approximate analysis approach to the computation of the probability of error and mean burst error length for a decision feedback equalizer (DFE) that takes into account feedback of decision errors. The method uses a reduced-state Markov model of the feedback process and is applicable to linear modulation formats. We use this technique to analyze a DFE design that mitigates the effects of feedback error by incorporating a soft decision device into the feedback path and a norm constraint on the feedback filter weights. We apply the DFE design and analysis approach to a dispersive multipath propagation environment     

Adaptive Decision Feedback Space–Time Equalization With Generalized Sidelobe Cancellation

In wireless communications, cochannel interference (CCI) and intersymbol interference (ISI) are two main factors that limit system performance. Conventionally, a beamformer is used to reduce CCI, whereas an equalizer is used to compensate for ISI. These two devices can be combined into one as space–time equalizer (STE). A training sequence is usually required to train the STE prior to its use. In some applications, however, spatial information corresponding to a desired user is available, but the training sequence is not. In this paper, we propose an adaptive decision feedback STE to cope with this problem. Our scheme consists of an adaptive decision feedback generalized sidelobe canceller (DFGSC), a blind decision feedback equalizer (DFE), and a channel estimator. Due to the feedback operation, the proposed DFGSC is not only superior to the conventional generalized sidelobe canceller but also robust to multipath channel propagation and spatial signature error. Theoretical results are derived for optimum solutions, convergence behavior, and robustness properties. With the special channel-aided architecture, the proposed blind DFE can reduce the error propagation effect and be more stable than the conventional blind DFE. Simulation results show that the proposed STE is effective in mitigating both CCI and ISI, even in severe channel environments.      

On the equivalence of the simultaneous and separate MMSEoptimizations of a DFE FFF and FBF

There is great interest in the use of decision feedback equalization (DFE) to mitigate the effects of intersymbol interference (ISI) on wireless multipath fading channels. The coefficients of a DFE feedforward filter (FFF) and feedback filter (FBF) are usually adjusted based on the minimum mean square error (MMSE) criterion. The equalizer coefficients can be calculated by recursive adaptation or by direct computation based on a channel estimate. The equivalence of the simultaneous and separate MMSE optimization of the FFF and FBF of a finite-length DFE is established     

一种用于背板互连的10 Gbit/s接口电路

基于SMIC 40 nm CMOS工艺,提出了一种用于背板互连的10 Gbit/s I/O接口电路。该接口电路由前馈均衡器(FFE)、接收机前端放大器和判决反馈均衡器(DFE)组成。FFE对发射端信号进行预加重,DFE消除较大的残余码间干扰。重点分析了FFE和DFE在消除码间干扰时存在的问题。使用改进的FFE减少对发射端信号的衰减,保证信号到达接收端时具有较大幅度,实现接收机对信号的正确判决,降低系统的误码率。测试结果表明,系统数据率为10 Gbit/s,传输信道在Nyquist频率(即5 GHz)处的衰减为22.4 dB。在1.1 V电源电压下,判决器Slicer输入端信号眼图的眼高为198 mV,眼宽为83 ps。FFE的功耗为31 mW,接收机前端放大器的功耗为1.8 mW,DFE的功耗为5.4 mW。     

Adaptive algorithms for channel equalization with soft decisionfeedback

A new approach based on joint entropy maximization (JEM) is taken and adaptive algorithms are developed for channel equalization with a decision feedback equalizer (DFE). The proposed work generalizes the existing algorithms for DFE with a hard decision device. Previous research has shown that when the hard decisions in a DFE are replaced with soft decisions, the performance of the adaptive algorithms [e.g., minimum mean square error (MMSE)] improves dramatically. The soft decisions can be introduced naturally via the viewpoint taken here. Additionally, constant modulus and other (blind) algorithms for DFE with soft decisions can be derived from this JEM approach     

Dual diversity combining and decision feedback equalizer in indoor millimetre‐wave channel

Wideband communication characteristics of wireless indoor millimetre‐wave channel for arched and rectangular buildings are investigated. The impulse responses of arched and rectangular buildings for any transmitter–receiver location are computed by shooting and bouncing ray/image (SBR/Image) techniques. By using the impulse responses of these multipath channels, the impact of shapes of building is presented and the bit error rate performance of binary phase shift keying (BPSK) system with phase and timing recovery circuits are also calculated. Moreover, dual space antenna diversity technique and decision feedback equalizer (DFE) with four forward and three feedback taps are used to combat the multipath fading. Numerical results show that the mean root mean square (rms) delay spread for the arched building is smaller than that for the rectangular building. In addition, it is also found that the transmission rate can be up to 20 Mbps for indoor millimetre‐wave channel of these two buildings by using dual space diversity and DFE. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive Techniques for Joint Optimization of XTC and DFE Loop Gain in High‐Speed I/O

High‐speed I/O channels require adaptive techniques to optimize the settings for filter tap weights at decision feedback equalization (DFE) read channels to compensate for channel inter‐symbol interference (ISI) and crosstalk from multiple adjacent channels. Both ISI and crosstalk tend to vary with channel length, process, and temperature variations. Individually optimizing parameters such as those just mentioned leads to suboptimal solutions. We propose a joint optimization technique for crosstalk cancellation (XTC) at DFE to compensate for both ISI and XTC in high‐speed I/O channels. The technique is used to compensate for between 15.7 dB and 19.7 dB of channel loss combined with a variety of crosstalk strengths from 60 mV_p‐p to 180 mV_p‐p adaptively, where the transmit non‐return‐to‐zero signal amplitude is a constant 500 mV_p‐p.     

网络编码在无线通信网络中的应用

网络编码是一种可以逼近网络容量传输理论极限的有效方法,在无线网络环境。中有着广泛的应用前景。在无线中继网络中采用网络编码技术,可以使中继节点同时为多个用户转发数据,从而获得较高的转发效率。网络编码在无线中继网络中的典型应用方案包括噪声中继采用置信传播算法实现网络编码,复数域网络编码算法以及信道编码和网络编码联合设计方法,它们均可在获得较高网络吞吐量的同时实现完全分集。在多用户协作通信网络中采用网络编码技术,可获得更高的分集增益以及更低的符号错误概率。