Support vector machine techniques for nonlinear equalization

The emerging machine learning technique called support vector machines is proposed as a method for performing nonlinear equalization in communication systems. The support vector machine has the advantage that a smaller number of parameters for the model can be identified in a manner that does not require the extent of prior information or heuristic assumptions that some previous techniques require. Furthermore, the optimization method of a support vector machine is quadratic programming, which is a well-studied and understood mathematical programming technique. Support vector machine simulations are carried out on nonlinear problems previously studied by other researchers using neural networks. This allows initial comparison against other techniques to determine the feasibility of using the proposed method for nonlinear detection. Results show that support vector machines perform as well as neural networks on the nonlinear problems investigated. A method is then proposed to introduce decision feedback processing to support vector machines to address the fact that intersymbol interference (ISI) data generates input vectors having temporal correlation, whereas a standard support vector machine assumes independent input vectors. Presenting the problem from the viewpoint of the pattern space illustrates the utility of a bank of support vector machines. This approach yields a nonlinear processing method that is somewhat different than the nonlinear decision feedback method whereby the linear feedback filter of the decision feedback equalizer is replaced by a Volterra filter. A simulation using a linear system shows that the proposed method performs equally to a conventional decision feedback equalizer for this problem     

A DECISION FEEDBACK EQUALIZER FOR NON-LINEAR CHANNELS

A Simple and useful decision feedback equalizer used for non-linear channels with severe linear distortion and mild non-linear distortion is proposed. It is a combination of a nonlinear channel equalizer based on connectionist model and a common decision feedback equalizer for linear channels. For a typical non-linear channel model it is shown that the equalization performances of the proposed equalizer are improved significantly.     

A new adaptive functional-link neural-network-based DFE forovercoming co-channel interference

A new approach for the decision feedback equalizer (DFE) based on the functional-link neural network is described. The structure is applied to the problem of adaptive equalization in the presence of intersymbol interference (ISI), additive white Gaussian noise, and co-channel interference (CCI). It is shown through simulation results for a severe amplitude distorted co-channel system that the decision feedback functional-link equalizer (DFFLE) provides significantly superior bit-error rate (BER) performance characteristics compared to the conventional DFE, the linear transversal equalizer (LTE), the nonlinear radial basis function (RBF) neural-network-based structures and the feed-forward functional-link equalizer (FFLE)-based structures. The DFFLE is also shown to have a significantly simpler computational requirement relative to the RBF and the FFLE     

Adaptive Bayesian equalizer with decision feedback

A Bayesian solution is derived for digital communication channel equalization with decision feedback. This is an extension of the maximum a posteriori probability symbol-decision equalizer to include decision feedback. A novel scheme utilizing decision feedback that not only improves equalization performance but also reduces computational complexity greatly is proposed. It is shown that the Bayesian equalizer has a structure equivalent to that of the radial basis function network, the latter being a one-hidden-layer artificial neural network widely used in pattern classification and many other areas of signal processing. Two adaptive approaches are developed to realize the Bayesian solution. The maximum-likelihood Viterbi algorithm and the conventional decision feedback equalizer are used as two benchmarks to asses the performance of the Bayesian decision feedback equalizer     

改进的SC-FDE块迭代判决反馈均衡器

在单载波频域传输(SC-FDE)系统中,块迭代判决反馈均衡器(IBDFE)明显提升了传统线性频域均衡器的性能.未知发送信号与迭代判决信号的相关因子估计是其关键技术,直接影响均衡器的性能.首先对IBDFE相关因子估计算法进行了改进,同时提出一种基于独特字(UW)帧结构的估计方法.该方法利用独特字的已知性和恒包络性进行判决,基于此判决方式使相关因子得到更精准的估计.实验结果表明,两种方法对IBDFE的性能有较为明显的提升.     

50-Gb/sPAM-4调制NG-PON系统中的基于特征向量构建的改进型SVM均衡算法

本文针对低成本下一代无源光网络(NG-PON)传 输系统中带宽限制和光纤累计色散所产生的严重码间串扰问题,提出了一种基于特征向量 构建的改进型支持向量机(SVM)的均衡 算法。该算法充分考虑了码间串扰信号的特性,并在此基础上构建了新颖的特征向量,从而 适用于带限NG-PON系统中。此外,为了实现对PAM-4信号的多分类任务,该算法采用了 多对多(MVM)的方法训练三个独立SVM分类器。本文搭建了基于10-G 带宽光电器件的 50-Gb/sPAM-4信号传输实验来进一步验证本算法的可行性。实验结 果表明,相比于经典 前馈均衡器(FFE)和判决反馈均衡器(DFE),本算法可将接收灵敏度在HD-FEC门限下 (BER=3.8e－3)提高约1dB,从而使系统 在不使用任何放大器的情况下功率预算达到了20 dB。 此外,本方案对CDR定时偏移误差更稳定,可在相当大的偏移范围内保持可观的性能。因 此,该方案可被应用在NG-PON系统中用于更好的提升系统传输性性能。     

Low complexity soft-input soft-output block decision feedback equalization

A low complexity soft-input soft-output (SISO) block decision feedback equalizer (BDFE) is presented for turbo equalization. The proposed method employs a sub-optimum sequence-based detection, where the soft-output of the equalizer is calculated by evaluating an approximation of the sequence-based a posteriori probability (APP) of the data symbol. The sequence-based APP approximation is enabled by the adoption of both soft a priori information and soft decision feedback, and it leads to better performance and faster convergence compared to symbol-based detection methods as used by most other low complexity equalizers. The performance and convergence property of the proposed algorithm is analyzed by using extrinsic information transfer (EXIT) chart. Both analytical and simulation results show that the new equalizer can achieve a performance similar to that of trellis-based equalization algorithms, with a complexity similar to linear SISO minimum mean square error equalizers.     

Frequency domain decision feedback equalizer for time-reversal space-time block coding

In this paper,a frequency domain decision feedback equalizer is proposed for single carrier transmission with time-reversal space-time block coding (TR-STBC).It is shown that the diagonal decision feed...     

非线性信道判决反馈均衡器

本文针对严重线性失真、轻度非线性失真的信道提出了一种简单实用的非线性信道判决反馈均衡器。它是一个将关联模型非线性信道均衡器与线性信道判决反馈均衡器相结合的产物。对典型的非线性信道模型所做的模拟试验表明,该均衡器不仅简单实用、便于实时处理,而且均衡性能得到较大的改善。     

基于多小波双变换的非线性卫星信道盲均衡算法

针对非线性卫星信道Volterra盲均衡系统收敛缓慢、计算复杂高等不足,提出了基于多小波双变换的非线性卫星信道盲均衡算法.该算法用Wiener均衡器代替Volterra均衡器,减小了均衡器结构的复杂性;用平衡正交多小波对Wiener均衡器的输入信号进行变换,降低了输入信号的自相关性;在Wiener均衡器输出端增加一级判决反馈滤波器,同时对其输入信号作平衡多小波变换,又降低了判决反馈滤波器输出信号的自相关性.仿真结果验证了该算法的有效性.     

A decision feedback recurrent neural equalizer as an infiniteimpulse response filter

An adaptive decision feedback recurrent neural equalizer (DFRNE), which models a kind of an IIR structure, is proposed. Its performance is compared with the traditional linear and nonlinear equalizers with FIR structures for various communication channels. The small size and high performance of the DFRNE makes it suitable for high-speed channel equalization     

Adaptive noncoherent linear minimum ISI equalization for MDPSK andMDAPSK signals

A novel noncoherent linear equalization scheme is introduced and analyzed. In contrast to previously proposed noncoherent equalization schemes, the proposed scheme is not only applicable for M-ary differential phase-shift keying (MDPSK) but also for M-ary differential amplitude/phase-shift keying (MDAPSK). The novel scheme minimizes the variance of intersymbol interference (ISI) in the equalizer output signal. The optimum equalizer coefficients may be calculated directly from an eigenvalue problem. For an efficient recursive adaptation of the equalizer coefficients, a modified least-mean-square (LMS) and a modified recursive least-squares (RLS) algorithm are proposed. It is shown that the corresponding cost function has no spurious local minima that ensures global convergence of the adaptive algorithms. Simulations confirm the good performance of the proposed noncoherent equalization scheme and its robustness against frequency offset     

A note on the modified Kalman filter for channel equalization

An application of the Kalmsn filter to equalization of a digital communication Chmnnel is described. The resultant modified Kalman equalizer (KE) is a nonlinear system in which the channel tap gain are estimated via a decision feedback approach and the state variable is estimated by a prediction process.     

基于线性化因子更新的频域迭代判决反馈均衡

迭代块判决反馈均衡(Iterative Block Decision Feedback Equalization,IBDFE)是单载波频域均衡中一种行之有效的非线性均衡算法,但算法计算复杂度随迭代次数增加而增大。本文针对传统IBDFE算法的不足提出一种基于线性因子更新的频域迭代判决反馈均衡算法,利用了线性因子更新来降低均衡器复杂度,并引入修正因子计算反馈滤波器系数以避免性能损失。仿真结果表明,所提出算法性能与传统IBDFE算法相比复杂度降低且在误比特率为10-5时有0.12 dB的性能增益,与已有的低复杂度算法(Low-Complexity IBDFE,LC-IBDFE)相比有0.1 dB的性能增益。      

Fast initialization of equalizers for VSB-based DTV transceivers in multipath channel

This paper proposes a fast initialization technique for equalization of 8-VSB-based digital television (DTV) signal in severe multipath channels. We consider the use of a modified decision feedback equalizer (MDFE) , for fast initialization. The feedback filter (FBF) of the MDFE can be initialized simply by estimating the channel impulse response and only the feedforward filter (FFF) of the MDFE need training for initialization. To overcome the shortage of the training sequence in the VSB DTV signal, we propose a new initialization method by generating a virtual training signal to initialize the FFF of the MDFE. Simulation results show that the proposed scheme can fast initialize the equalizer using less than 5000 symbols, while providing the receiver performance comparable to that of conventional schemes.     

Adaptive decision feedback equalization for digital satellitechannels using multilayer neural networks

This paper introduces an adaptive derision feedback equalization using the multilayer perceptron structure of an M-ary PSK signal through a TDMA satellite radio channel. The transmission is disturbed not only by intersymbol interference (ISI) and additive white Gaussian noise, but also by the nonlinearity of transmitter amplifiers. The conventional decision feedback equalizer (DFE) is not well-suited to detect the transmitted sequence, whereas the neural-based DFE is able to take into account the nonlinearities and therefore to detect the signal much better. Nevertheless, the applications of the traditional multilayer neural networks have been limited to real-valued signals. To overcome this difficulty, a neural-based DFE is proposed to deal with the complex PSK signal over the complex-valued nonlinear MPSK satellite channel without performing time-consuming complex-valued back-propagation training algorithms, while maintaining almost the same computational complexity as the original real-valued training algorithm. Moreover, a modified back-propagation algorithm with better convergence properties is derived on the basis of delta-bar-delta rule. Simulation results for the equalization of QPSK satellite channels show that the neural-based DFE provides a superior bit error rate performance relative to the conventional mean square DFE, especially in poor signal-to-noise ratio conditions     

应用于LTE上行链路的D-MMSE-FE 均衡算法

为克服线性均衡性能的局限性及避免传统判决反馈均衡器的高复杂度,提出了一种判决反馈均衡算法D-MMSE-FE。该均衡器先是分析线性MMSE均衡的结果成分,并根据最小均方误差准则计算出均衡器的前、后向传递函数,形成反馈链路,提高均衡器性能。将该种均衡器应用于TDD-LTE 1×2 SIMO上行链路中,在协议中常用的信道下进行了计算机仿真,仿真结果表明,TDD-LTE 1×2 SIMO均衡器相对于线性均衡器使系统性最多可提高达2 dB。     

A Comparison of Compromise Viterbi Algorithm and Standard Equalization Techniques Over Band-Limited Channels

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.     

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.