Blind, Adaptive Channel Shortening Equalizer Algorithm Which Can Provide Shortened Channel State Information (BACS-SI)

Channel shortening equalization plays an important role in multicarrier modulation (MCM) systems. In this paper, we propose a blind channel shortening equalizer structure named blind, adaptive channel shortening equalizer which can provide the shortened channel state information (BACS-SI). The algorithm depends on the minimization of a cost function defined as the sum-squared difference of the autocorrelations of the shortened channel impulse response (CIR) and a target impulse response. The surface is proven to be multimodal; however, minima are shown to be related to each other in a certain way. A two-phase approach is proposed. In the first phase, the cost function is minimized by a stochastic gradient descent algorithm in order to find an arbitrary minimum. In the second phase using the relation between minima, genetic algorithms are employed to find the best minimum according to a fitness function. The algorithm can both successfully shorten the channel and also explicitly provides shortened CIR which is a necessary information for the proper operation of a MCM receiver, in contrast to many other algorithms proposed in the literature which cannot directly provide this information.      

MIMO系统中的非常数模半盲均衡方案

在多输入多输出(Multiple-Input Multiple-Output, MIMO)无线通信中,信道衰落、随机噪声、空间多径效应和共信道干扰等因素会产生符号间干扰,造成接收端信号严重失真。为提高MIMO系统传输性能,有效减少信道中相位失真,提出了一种改进的非常数模半盲均衡方案(Non-constant Modulus Algorithm, NCMA)。该方案结合了MIMO信道先验知识对半盲均衡器的初始值进行预设,采用变步长迭代更新均衡器权系数,寻找到最小目标函数值。仿真结果表明,改进后的算法能通过控制变步长减小剩余稳态误差,加快收敛速度,改善信道均衡效果。     

A family of low-complexity blind equalizers

Two important topics in equalizer design are its complexity and its training. We present a family of blind equalizers which, by incorporating a decomposition finite-impulse response filtering technique, can reduce the complexity of the convolution operation therein by about one half. The prototype algorithm in this equalizer family employs the prevalent Godard cost function. Several simplified algorithms are proposed, including a sign algorithm which eliminates multiplications in coefficient adaptation and a few delayed versions. We also study the convergence properties of the algorithms. For the prototype algorithm, we show that, in the limit of an infinitely long equalizer and under mild conditions on signal constellations and channel characteristics, there are only two sets of local minima on the performance surface. One of the sets is undesirable and is characterized by a equalized channel response. The other corresponds to perfect equalization, which can be reached with proper equalizer initialization. For the simplified algorithms, corresponding cost functions may not exist. Some understanding of their convergence behaviors are obtained via examination of their adaptation equations. Simulation results are presented to demonstrate the performance of the algorithms.     

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.      

Fast and low complexity blind equalization via subgradient projections

We propose a novel blind equalization method based on subgradient search over a convex cost surface. This is an alternative to the existing iterative blind equalization approaches such as the Constant Modulus Algorithm (CMA), which often suffer from the convergence problems caused by their nonconvex cost functions. The proposed method is an iterative algorithm called SubGradient based Blind Algorithm (SGBA) for both real and complex constellations, with a very simple update rule. It is based on the minimization of the l/sub /spl infin// norm of the equalizer output under a linear constraint on the equalizer coefficients using subgradient iterations. The algorithm has a nice convergence behavior attributed to the convex l/sub /spl infin// cost surface as well as the step size selection rules associated with the subgradient search. We illustrate the performance of the algorithm using examples with both complex and real constellations, where we show that the proposed algorithm's convergence is less sensitive to initial point selection, and a fast convergence behavior can be achieved with a judicious selection of step sizes. Furthermore, the amount of data required for the training of the equalizer is significantly lower than most of the existing schemes.     

Interior point least squares estimation: transient convergenceanalysis and application to MMSE decision-feedback equalization

In many communication systems, training sequences are used to help the receiver identify and/or equalize the channel. The amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization. In this paper, we propose the use of a new adaptive filtering method called interior point least squares (IPLS) for adaptive equalization. First, we show that IPLS converges exponentially fast in the transient phase. Then, we use the IPLS algorithm to update the weight vector for a minimum-mean-square-error decision-feedback equalizer (MMSE-DFE) in a CDMA downlink scenario. Numerical simulations show that when training sequences are short IPLS consistently outperforms RLS in terms of system bit-error-rate and packet error rate. As the training sequence gets longer IPLS matches the performance of the RLS algorithm     

利用无约束函数的QAM信号自适应盲均衡方法

本文针对正交幅度调制(QAM)信号的盲均衡与载波相位恢复问题,首先在对现有的基于功率最大化盲均衡算法分析的基础上,依据向量范数间的关系,给出了一种QAM信号盲均衡与载波相位恢复的无约束代价函数;然后对代价函数的收敛性和解的唯一性进行严格论证,证明代价函数在取得最优解时能够同时实现盲均衡与载波相位恢复;之后将其转化为采用随机梯度法实现的自适应算法。相对CMA、MMA等其他自适应算法,新算法可获得更好的性能,通过对高阶QAM信号的均衡仿真,进一步验证了算法的有效性。      

含软方向判决的修正CMA盲均衡新算法

提出了一种新颖的盲均衡算法MCMA SDD,它一方面在代价函数中同时包含了幅度和相位的信息,另一方面,增加了并行的软方向判决(SDD)盲均衡算法,使得MCMA SDD算法无需载波跟踪环就能够纠正相位的失真;在低信噪比条件下具有较快的收敛速度和较低的稳态均方误差。     

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     

An adaptive algorithm for differentially coherent detection in the presence of intersymbol interference

An adaptive equalization method is proposed for use with differentially coherent detection of M-ary differential phase-shift keying (DPSK) signals in the presence of unknown carrier frequency offset. A decision-feedback or a linear equalizer is employed, followed by the differentially coherent detector. The equalizer coefficients are adjusted to minimize the post-detection mean squared error. The error, which is a quadratic function of the equalizer vector, is used to design an adaptive algorithm of stochastic gradient type. The approach differs from those proposed previously, which linearize the post-detection error to enable the use of least mean squares (LMS) or recursive least squares (RLS) adaptive equalizers. The proposed quadratic-error (Q) algorithm has complexity comparable to that of LMS, and equal convergence speed. Simulation results demonstrate performance improvement over methods based on linearized-error (L) algorithm. The main advantages of the technique proposed are its simplicity of implementation and robustness to carrier frequency offset, which is maintained for varying modulation level.     

一种适用于稀疏多径信道的自适应均衡算法

针对传统的自适应均衡算法在稀疏多径信道下性能表现不佳的问题,提出了一种基于基追踪降噪的自适应均衡算法。该算法利用稀疏多径信道下均衡器权值的稀疏性,将自适应均衡器的训练过程看作压缩感知理论中稀疏信号对字典的加权求和,并利用重构算法直接对稀疏权值进行求解,解决了迭代参数设置和收敛慢的问题。采用基追踪降噪作为重构算法并选用变量分离近似稀疏重构对该最优化问题进行求解,既提高了权值的重构精度又降低了计算的复杂度。仿真结果表明,所提算法能够以较低的计算量和较少的训练序列达到更优性能,这对提升系统的通信性能具有参考价值。     

组合半盲均衡算法及其在半盲均衡中的应用

针对传输正交幅度调制信号的多输入多输出卷积通信系统中的码间干扰和共信道干扰问题,利用软决策算法的选择性以及QAM信号星座图的几何特征,提出一种组合的半盲均衡算法。该算法不仅克服了传统恒模算法,多模算法在稳态下的误调问题,而且避免了SDD算法在高阶QAM系统中运算量急剧增加的问题。采用梯度牛顿法优化CSBEA算法代价函数,与常用的梯度类算法相比,其具有收敛速度快,稳态性能好的特点。通过仿真实验证明了所提算法的有效性。     

Blind equalization for short burst wireless communications

In this paper, we propose a dual mode blind equalizer based on the constant modulus algorithm (CMA). The blind equalizer is devised for short burst transmission formats used in many current wireless TDMA systems as well as future wireless packet data systems. Blind equalization is useful for such short burst formats, since the overhead associated with training can be significant when only a small number of bits are transmitted at a time. The proposed equalizer overcomes the common problems associated with classic blind algorithms, i.e., slow convergence and ill-convergence, which are detrimental to applying blind equalization to short burst formats. Thus, it can eliminate the overhead associated with training sequences. Also, the blind equalizer is extended to a two branch diversity combining blind equalizer. A new initialization for fractionally spaced CMA equalizers is introduced. This greatly improves the symbol timing recovery performance of fractionally spaced CMA equalizers with or without diversity, when applied to short bursts. Through simulations with quasi-static or time-varying frequency selective wireless channels, the performance of the proposed equalizer is compared to selection diversity and conventional equalizers with training sequences. The results indicate that its performance is far superior to that of selection diversity alone and comparable to the performance of equalizers with short training sequences. Thus, training overhead can be removed with no performance degradation for fast time-varying channels, and with slight performance degradation for static channels     

MIMO通信系统中QAM信号的快速半盲均衡算法研究

该文针对传输正交幅度调制(QAM)信号的多输入多输出(MIMO)系统的均衡问题,结合方环算法(SCA)的简单性和软决策(SDD)算法的精确性,提出了一种既比较精确又简单的算法(SCA+SDD)。在优化该算法的代价函数过程中,首先用很少的训练序列(等于接收天线数)得到均衡器权向量的一个粗略估计,然后提出利用共轭梯度法进行迭代优化该代价函数的方法,该算法具有近似的二次收敛性,与传统梯度类算法相比较,该方法有非常快的收敛速度和较少的计算量。最后通过误码率(BER)和收敛速度分析该算法的可靠性和有效性,并且通过计算机仿真证明了该算法的良好性能。     

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.     

Efficient algorithm for nonconvex minimization and its application to PM regularization

In image processing, nonconvex regularization has the ability to smooth homogeneous regions and sharpen edges but leads to challenging computation. We propose some iterative schemes to minimize the energy function with nonconvex edge-preserving potential. The schemes are derived from the duality-based algorithm proposed by Bermúdez and Moreno and the fixed point iteration. The convergence is proved for the convex energy function with nonconvex potential and the linear convergence rate is given. Applying the proposed schemes to Perona and Malik's nonconvex regularization, we present some efficient algorithms based on our schemes, and show the approximate convergence behavior for nonconvex energy function. Experimental results are presented, which show the efficiency of our algorithms, including better denoised performance of nonconvex regularization, faster convergence speed, higher calculation precision, lower calculation cost under the same number of iterations, and less implementation time under the same peak signal noise ratio level.     

Low Complexity Joint Blind Equalization and CFO Estimation for MC-CDMA System

Based on the orthogonality between the used and the unused spreading codes (excess codes) subspaces in one hand and on the restoration of guard interval redundancy of Multicarrier Code Division Multiple Access signal in other hand, we propose joint Carrier Frequency Offset and time domain equalizer estimators. A major difficulty arises from the highly complexity of these methods. Use of an approximation method or an adaptive algorithm has been popular approach to ease problem solving. Our derived methods are found to be good in terms of estimation accuracies, computation complexity, and convergence speed when compared to the block processing algorithms.     

时域自适应均衡技术的分析与应用

概述了频率选择性衰落信道的传输特性,论述了采用均衡技术的必要性。通过对各种均衡器结构和自适应均衡算法在抵抗符号间干扰能力、收敛速度以及运算复杂度等方面的分析与比较,选择了判决反馈作为均衡器结构、最小均方自适应算法作为自适应准则的均衡器方案。仿真及试验结果证实了设计的时域自适应均衡器不仅具有较强的抵抗符号间干扰能力,而且能够获得隐分集增益,在频率选择性衰落信道中具有良好的应用效果。     

RLS-based adaptive algorithms for generalized eigen-decomposition

The aim of this paper is to develop efficient online adaptive algorithms for the generalized eigen-decomposition problem which arises in a variety of modern signal processing applications. First, we reinterpret the generalized eigen-decomposition problem as an unconstrained minimization problem by constructing a novel cost function. Second, by applying projection approximation method and recursive least-square (RLS) technique to the cost function, a parallel adaptive algorithm for a basis for the r-dimensional (r>0) dominant generalized eigen-subspace and a sequential algorithm based on deflation technique for the first r-dominant generalized eigenvectors are derived. These algorithms can be viewed as counterparts of the extended projection approximation subspace tracking (PAST) and PASTd algorithms, respectively. Furthermore, we modify the parallel algorithm to explicitly estimate the first r-generalized eigenvectors in parallel, not the generalized eigen-subspace. More important, the modified parallel algorithm can be used to extract multiple generalized eigenvectors of two nonstationary sequences, while the proposed sequential algorithm lacks this ability because of slow convergence of minor generalized eigenvectors due to error propagation of the deflation technique. Third, following convergence analysis methods for PAST and PASTd, we prove the asymptotic convergence properties of the proposed algorithms. Finally, computer simulations are performed to investigate the accuracy and the speed advantages of the proposed algorithms.     

Static and dynamic convergence behavior of adaptive blindequalizers

This paper presents a theoretical analysis of the static and dynamic convergence behavior for a general class of adaptive blind equalizers. We first study the properties of prediction error functions of blind equalization algorithms, and then, we use these properties to analyze the static and dynamic convergence behavior based on the independence assumption. We prove in this paper that with a small step size, the ensemble average of equalizer coefficients will converge to the minimum of the cost function near the channel inverse. However, the convergence is not consistent. The correlation matrix or equalizer coefficients at equilibrium are determined by a Lyapunov equation. According to our analysis results, for a given channel and stepsize, there is an optimal length for an equalizer to minimize the intersymbol interference. This result implies that a longer-length blind equalizer does not necessarily outperform a shorter one, which is contrary to what is conventionally conjectured. The theoretical analysis results are confirmed by computer simulations