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     

Global convergence of fractionally spaced Godard (CMA) adaptiveequalizers

The Godard (1980) or constant modulus algorithm (CMA) equalizer is perhaps the best known and the most popular scheme for blind adaptive channel equalization. Most published works on blind equalization convergence analysis are confined to T-spaced equalizers with real-valued inputs. The common belief is that analysis of fractionally spaced equalizers (FSEss) with complex inputs is a straightforward extension with similar results. This belief is, in fact, untrue. We present a convergence analysis of Godard/CMA FSEs that proves the important advantages provided by the FSE structure. We show that an FSE allows the exploitation of the channel diversity that supports two important conclusions of great practical significance: (1) a finite-length channel satisfying a length-and-zero condition allows Godard/CMA FSE to be globally convergent, and (2) the linear FSE filter length need not be longer than the channel delay spread. Computer simulation demonstrates the performance improvement provided by the adaptive Godard FSE     

Blind equalizer for constant-modulus signals based on Gaussian process regression

A new blind equalization method for constant modulus (CM) signals based on Gaussian process for regression (GPR) by incorporating a constant modulus algorithm (CMA)-like error function into the conventional GPR framework is proposed. The GPR framework formulates the posterior density function for weights using Bayes' rule under the assumption of Gaussian prior for weights. The proposed blind GPR equalizer is based on linear-in-weights regression model, which has a form of nonlinear minimum mean-square error solution. Simulation results in linear and nonlinear channels are presented in comparison with the state-of-the-art support vector machine (SVM) and relevance vector machine (RVM) based blind equalizers. The simulation results show that the proposed blind GPR equalizer without cumbersome cross-validation procedures shows the similar performances to the blind SVM and RVM equalizers in terms of intersymbol interference and bit error rate.     

On the convergence of blind adaptive equalizers for constantmodulus signals

This paper studies the behavior of the error sequence of stop-anti-go variants of two adaptive blind equalizers, namely CMA2-2 and Sato's (1975) algorithm. It is shown that for transmitted signals with constant modulus γ, the equalizer output can be made to lie within the circle of radius γ√c infinitely often, for some value of c that is only slightly larger than one     

Convergence analysis of the stop-and-go blind equalizationalgorithm

Unlike traditional trained channel equalizers, not much work has been done to theoretically characterize the convergence properties of blind channel equalizers due to their inherent nonlinearity. It is only recently that convergence properties of some well-known algorithms such as the generalised Sato algorithm (GSA) and the constant modulus algorithm (CMA) have been analytically derived. In this paper, the convergence properties of the stop-and-go algorithm proposed by Picchi and Prati (1987) are analyzed. The derived mean squared error and the coefficient trajectories are compared with simulation results to verify the validity of the analytical results     

Adaptive blind equalization for MIMO systems uadaptive blind equalization for MIMO systems under α-stable noise environmentnder α-stable noise environment

The presence of non-Gaussian impulsive noise in wireless system can degrade the performance of existing equalizers and signal detectors. In this paper, the problem of blind source separation and equalization for MIMO systems in heavy-tailed impulsive noise is studied. A generalized multiuser constant modulus cost function by employing the fractional lower-order statistic of the equalizer input signal is proposed. The associated adaptive blind equalization algorithm based on a stochastic gradient descent method is defined as fractional lower-order multi-user constant modulus algorithm (FLOS MU CMA). Computer simulations are presented to illustrate the performance of the new algorithm.     

Application of Recurrent Wavelet Neural Networks to the Digital Communications Channel Blind Equalization

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A dynamic convergence analysis of blind equalization algorithms

Blind equalizers do not require a training sequence to start up or to restart after a communications breakdown, making them particularly useful in applications such as broadcast and point-to-multipoint networks. We study in parallel the dynamic convergence behavior of three blind equalization algorithms: the multimodulus algorithm (MMA), the constant modulus algorithm (CMA), and the reduced constellation algorithm (RCA). Using a conditional Gaussian approximation, we first derive the theoretical mean-squared-error (MSE) trajectory for MMA. This analysis leads to accurate but somewhat cumbersome expressions. Alternatively, we apply a Taylor series approximation to derive MSE trajectories for MMA, CMA, and RCA. This approach yields simpler but somewhat less accurate expressions. For the steady-state operation, however we derive even simpler formulas that accurately predict the asymptotic MSE values. We finally study the convergence rates of the three blind algorithms using their theoretical MSE trajectories, computer simulations, and a laboratory experiment     

一种用于水声通信的快速自适应均衡器设计

信道均衡是现代水声通信系统中克服码间干扰的重要手段,根据时变水声信道需进行信道均衡的要求,设计了一种判决反馈盲均衡器。针对恒模算法在固定步长下存在收敛速度与剩余误差的矛盾缺陷,提出了一种基于剩余误差的变步长恒模算法,并对改进算法进行了计算机仿真及试验测试,结果表明,改进算法无论是在收敛性能还是在均衡效果上都有大幅提高,在实际水声通信中具有较好的应用价值。     

Adaptive blind source separation and equalization formultiple-input/multiple-output systems

In this paper, we investigate adaptive blind source separation and equalization for multiple-input/multiple-output (MIMO) systems. We first analyze the convergence of the constant modulus algorithm (CMA) used in MIMO systems (MIMO-CMA). Our analysis reveals that the MIMO-CMA equalizer is able to recover one of the input signals, remove the intersymbol interference (ISI), and suppress the other input signals. Furthermore, for the MIMO finite impulse response (FIR) systems satisfying certain conditions, the MIMO-CMA FIR equalizers are able to perfectly recover one of the system inputs regardless of the initial settings. We then propose a novel algorithm for blind source separation and equalization for MIMO systems. Our theoretical analysis proves that the new blind algorithm is able to recover all system inputs simultaneously regardless of the initial settings. Finally, computer simulation examples are presented to confirm our analysis and illustrate the effectiveness of blind source separation and equalization for MIMO systems     

On fractionally spaced blind adaptive equalization under symboltiming offsets using Godard and related equalizers

The problem of fractionally spaced (FS) blind adaptive equalization under symbol-timing-phase offsets is considered. In the case of trained (nonblind) equalizers, the performance of FS equalizers is known to be independent of the timing-phase unlike that of baud-rate equalizers. Moreover, trained FS equalizers synthesize optimal filters in the minimum mean-square error sense, and hence are superior to baud-rate trained equalizers. It is an open question whether such properties hold true for FS Godard blind equalizers. We present a simulation example where such advantages do not materialize. We also present a solution based upon a parallel multimodel Godard baud-rate filter bank approach which yields a performance almost invariant w.r.t. symbol-timing-phase and superior to that of baud-rate equalizers     

Multichannel Algorithms for Simultaneous Equalization and Interference Suppression

This paper proposes techniques for simultaneous cancellation of intersymbol and interchannel or multi-access interference (ISI and ICI) that shows up in several multi-input, multi-output (MIMO) communication channels. Correlation and kurtosis based optimization criteria are derived for multi-channel decision feedback equalizers (MC-DFE) and compared with the popular Godard algorithm (CMA) and the minimum mean-square error in a decision directed mode (MMSE-DD). The proposed adaptive algorithms are easily extended to a scenario with more than two users with the computational complexity increasing linearly with the number of inputs. Simulation results show that the algorithms converge to the global minimum in a blind environment with channels that introduce moderate distortion.     

Nonsingular Constant Modulus Equalizer for PDM-QPSK Coherent Optical Receivers

Adaptive electronic equalizers using the constant modulus algorithm (CMA) algorithm often converge to a singular coefficient matrix that produces the same signal at multiple outputs. We address this issue in the context of optical communications systems with polarization-division multiplexing and coherent receivers. We study, by computer simulation, the performance of multiuser CMA equalizer, an enhanced CMA equalizer initially proposed for use in wireless multiuser and later multiple-input/multiple-output communications systems. We show that the proposed adaptive electronic equalizer does not exhibit singularities and, therefore, is superior to the commonly used CMA equalizer.     

A modified CMA equalizer for the removal of length dependent localminima in AR channels

Finite-length CMA equalizers contain undesired minima termed length dependent local minima (LDLM), we note that for autoregressive (AR) channels, the equalizer output is correlated with a delayed input at these minima, this property is then used to modify the CMA cost function and remove the LDLM in AR channels     

Bussgang盲均衡器

文中描述了基带均衡通信系统的信号模型,研究了基于此模型的三个典型的Bussgang均衡器：恒模算法（CMA）,Sato和直接判决（DD）均衡器。给出了与算法相关的性能仿真结果。仿真结果展示了CMA均衡器可以提供更好的BER性能及比Sato和DD均衡器更快的收敛速度。     

CMA Performance in CDMA Transmit Diversity System

1IntroductionThe capacity and performance of CDMAare largelyaffected by disturbances ,and Multi-Access Interference( MAI) is the main disturbance factor whenthe numberof user is large . Blind adaptive Multi-User Detection(B-MUD)is aneffectivetechniquetoreduce MAI[1 ~2].In many advanced and convergence faster algorithms ,Constant Mode Algorithm ( CMA) is an efficient B-MUDand has better systemperformance .Refs .[3 ~6]depict the CMAin details .The channel of mobile communications p…     

Low complexity concurrent constant modulus algorithm and soft decision directed scheme for blind equalisation

The recently introduced concurrent constant modulus algorithm (CMA) and decision-directed (DD) scheme provides a state-of-the-art low-complexity blind equalisation technique for high-order quadrature amplitude modulation (QAM) channels. At a small cost of slightly more than doubling the complexity of the standard CMA blind equaliser, this concurrent CMA and DD blind equaliser achieves a dramatic improvement in equalisation performance over the CMA. In the paper, a new blind equalisation scheme is proposed based on concurrent CMA and a novel soft decision-directed (SDD) adaptation. The proposed concurrent CMA and SDD blind equaliser has simpler computational requirements than the concurrent CMA and DD algorithm. Extensive simulation shows that it has the same steady-state equalisation performance as the concurrent CMA and DD algorithm and a faster convergence speed over the latter scheme     

Blind Multiuser Detection in Frequency Domain for MC-CDMA Systems Using Particle Swarm Optimization

In digital communication systems, the constant modulus algorithm (CMA) for blind multiuser detector has some disadvantage such as slow convergence speed and weight phase rotation. In this paper, we put forward a novel receiver, which combines CMA blind adaptive multiuser detection and particle swarm optimization (PSO) technique in frequency domain for multi-carrier direct sequence code division multiple access (MC DS-CDMA) systems. By this approach we present an adaptive multistage structure based on PSO technique. In this structure, the weights are obtained by PSO technique between the received signal and its estimate through a CMA. The resulting weights contain reliability information for the hard decisions made in the previous stage. The simulation results show that BER performance of the PSO-based CMA blind multiuser detector is superior to that of steepest decreasing constant modulus algorithm (SDCMA), linearly constrained constant modulus algorithm (LCCMA), CMA based multiuser detection and is worthy due to its significant detection performance to achieve desirable improvement in convergence speed and tractability.     

A Supervised Constant Modulus Algorithm for Blind Equalization

Blind equalization is a technique for adaptive equalization of a communication channel without the aid of the usual training sequence. Although the Constant Modulus Algorithm (CMA) is one of the most popular adaptive blind equalization algorithms, it suffers from slow convergence rate. A novel enhanced blind equalization technique based on a supervised CMA (S-CMA) is proposed in this paper. The technique is employed to initialize the coefficients of a linear transversal equalizer (LTE) filter in order to provide a fast startup for blind training. It also presents a computational study and simulation results of this newly proposed algorithm compared to other CMA techniques such as conventional CMA, Normalized CMA (N-CMA) and Modified CMA (M-CMA). The simulation results have demonstrated that the proposed algorithm has considerably better performance than others.     

Blind per tone equalization of multilevel signals using support vector machines for OFDM in wireless communication

We present an efficient support vector machine (SVM)-based blind per tone equalization for OFDM systems. Blind per tone equalization using constant modulus algorithm (CMA) and multi-modulus algorithm (MMA) are used as the comparison benchmark. The SVM-based cost function utilizes a CMA-like error function and the solution is obtained by means of an iterative re-weighted least squares algorithm (IRWLS). Moreover, like CMA, the error function allows to extend the method to multilevel modulations. In terms of bit error rate (BER), simulation experiments show that the blind per tone equalization using SVM performs better than blind per tone equalization using CMA and MMA.