Soft constraint satisfaction (SCS) blind channel equalization algorithms

We present a least squares (LS) algorithm for blind channel equalization based on a reformulation of the Godard algorithm. A transformation for the equalizer parameters is considered to convert the nonlinear LS problem inherent in the Godard algorithm to a linear LS problem. Unlike the Godard (1980) algorithm, the proposed LS approach does not suffer from ill-convergence to closed-eye local minima. Methods for extracting the equalizer parameters from their transformed version are developed. Offline and recursive implementations of the LS algorithm are presented. The algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis-a-vis the Godard algorithm. The channel input correlation does not impose any restriction on the application of the algorithm, as long as a weak sufficient-excitation condition is satisfied. Simulation examples are presented to demonstrate the LS approach and to compare it with the Godard algorithm.

In digital wireless communications, blind equalization without training sequence or any priori knowledge of the channel dynamics has become a topic problem, and one of its most important performance criterions is the convergence speed. Traditional constant modulus algorithm (CMA) with many advantages is a popular blind equalization approach, but its slower convergence rate is unsuitable for the compensation of the multipath fading wireless channels. In this paper, a novel blind channel equalization algorithm is presented by introducing a decorrelation factor into the equalization process. The improvement in convergence rate as well as residual MSE of the proposed algorithm is confirmed by computer simulation results.

The constant modulus algorithm (CMA) is an excellent technique for blind channel equalization. A signed error version of CMA (SE-CMA) and dithered signed error version (DSE-CMA) have been proposed which afford overall computational efficiency. We propose three different error functions for faster convergence. This would be essential for communication systems, which cannot afford a high startup delay or for systems, where the channel's impulse response is rapidly fluctuating. One of these algorithms relies on the idea of a variable step size, which increases the rate of convergence.

Blind channel equalization has gained great importance in the world of communications. Among a large number of available blind equalization algorithms, the CMA (constant modulus algorithm) enjoys widespread popularity because of its LMS-like complexity and robustness. Two important improvements on the CMA performance are the dithered signed-error CMA (DSE-CMA) and the pre-whitened CMA (PW-CMA). The DSE-CMA is an approach to reduce the computational complexity of the CMA while retaining its robustness and the PW-CMA aims at improving the convergence rate of the CMA in case of channels exhibiting large frequency response deviations. In this paper we review the two approaches and propose a new scheme combining the virtues of the two. The combined scheme is computationally simpler than the PW-CMA and provides better convergence than the DSE-CMA. It is particularly suited for the situations where ill-convergence needs to be treated with minimum additional complexity and without loss of robustness

A family of new MMSE blind channel equalization algorithms based on second order statistics are proposed. Instead of estimating the channel impulse response, we directly estimate the cross-correlation function needed in Wiener-Hopf filters. We develop several different schemes to estimate the cross-correlation vector, with which different Wiener filters are derived according to minimum mean square error (MMSE). Unlike many known subspace methods, these equalization algorithms do not rely on signal and noise subspace separation and are consequently more robust to channel order estimation errors. Their implementation requires no adjustment for either single or multiple user systems. They can effectively equalize single-input multiple-output (SIMO) systems and can reduce the multiple-input multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. The implementations of these algorithms on SIMO system are given and simulation examples are provided to demonstrate their superior performance over some existing algorithms.

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This paper addresses the problem radio mobile channel identification and equalization by blind algorithms. For this, we have proposed two algorithms, which are compared with: cumulants based algorithms, and adaptive filter algorithms (such us the constant modulus algorithm (CMA), Fractional Space CMA (FSCMA) and Sign Kurtosis Maximization Adaptive Algorithm (SKMAA)). However, The simulation results in noisy environment and for different SNR values with QPSK or 4QAM modulation shows that the proposed algorithms gives a good identification and equalization versus to the cumulants and the adaptive filter algorithms, for radio mobile channel.

Blind equalization is a technique for adaptive equalization of a communication channel without the aid of training sequences. This paper proposes a new blind equalization algorithm. The advantage of the new algorithm is that it has the lower residual error than the GA (proposed by Godard) and Sign_GA (proposed by Weerackody et al.). The superior performance of the proposed algorithm is illustrated for the 16-QAM signal constellation. A Rummler channel model is assumed as a transmission medium. The performance of the proposed algorithm is compared to the GA, Sign_GA and Stop & Go Algorithm (SGA). The simulation results demonstrate that an improvement in performance is achieved with the proposed equalization algorithm.

The Concept of Adaptive Equalization is to counter Intersymbol Interference (ISI) which severely degrades the performance of a Communication System. Adaptive Equalization can be classified into Supervised/Trained Equalization and Unsupervised/Blind Equalization. Supervised Equalization is carried out with the aid of a training sequence and Blind Equalization is done without the aid of a training sequence. Godard's Constant Modulus Algorithm (CMA) was the very first blind equalization algorithm that could be used in two dimensional digital communication systems. It requires the knowledge of statistical properties of the transmitted data symbols to perform channel equalization. Picchi and Prati by modifying the standard Decision-Directed Algorithm proposed a new Blind Equalization Algorithm known as "Stop-and-Go" Decision-Directed Algorithm. This paper compares the performance of Blind Equalization algorithms: CMA and Stop-and-Go. Simulation results indicate faster convergence rate of Stop-and-Go than CMA for 16 and 64 Quadrature Amplitude Modulated (QAM) transmitted constellations. The results also indicate negligible difference between the MSE's of Stop-and-Go after convergence and supervized equalizer.

All existing blind equalization algorithms rely on the non-Gaussianity of the input sequence. In recent years, a technique called shaping has been used in data transmission, in order to approach the capacity of Gaussian channels. The transmitted signal then has a Gaussian-like distribution and this will affect blind equalization algorithms. In this paper, we address the problem of blind equalization where the input of the unknown system is a shaped data signal. In particular, we demonstrate the effects of shaping on some of the widely known blind equalization schemes. Our results point to the need for more powerful blind equalization algorithms for shaped signals.

The paper proposes a concurrent constant modulus algorithm (CMA) and soft decision-directed (SDD) scheme for low-complexity blind equalization of high-order quadrature amplitude modulation channels. Simulation using a fractionally spaced equalization setting is used to compare the proposed scheme with the recently introduced state-of-art concurrent CMA and decision-directed (DD) scheme. The proposed CMA+SDD blind equalizer is shown to have simpler computational complexity per weight update, faster convergence speed, and slightly improved steady-state equalization performance, compared with the CMA+DD blind equalizer.

The project of ant colony algorithm optimization neural network combining blind equalization algorithm is proposed. The better initial weights of neural networks are provided because of the randomness, ergodicity and positive feedback of the ant colony algorithm. And then, a combination of optimal weights are found through BP algorithm, which is fast local search speed. Thus blind equalization performance is improved. Computer simulation show that, the novel blind equalization algorithm speeds up the convergence rate, reduces the remaining steady-state error and bit error rate, which is compared with the Neural Network Blind Equalization Algorithm(NNBE) and Genetic Algorithm optimization Neural Network Blind Equalization Algorithm(GA-NNBE) .

A blind equalization algorithm may switch to a decision-directed (DD) equalization mode in order to speed up the convergence rate and improve the steady-state performance. The crux for this kind of equalization is the control of the switches between the two equalization mode. A new blind equalization scheme is proposed which automatically controls the switches between the blind equalization mode and DD equalization mode according to the estimated error variance, and the blind equalization mode used in the proposed scheme is the modified constant modulus algorithm. Simulation results shows that the proposed blind equalization scheme can present significant improvements in the convergence rates along with steady-state performance

Blind adaptive channel equalizers are important devices to remove channel distortion in high data-rate, bandlimited digital communication systems when the transmission of a training sequence is impractical or very costly. Traditional blind equalization algorithms adapt the equalizer parameters to minimize some specially designed non-MSE cost functions. These algorithms can experience local convergence problems and can thereby result in insufficient or no removal of channel distortion. We present a new quadrature amplitude modulated blind equalization scheme that is globally convergent in the equalizer parameter space to a compact set containing the desired ideal equalizer parameter setting. Our new algorithm is based on a convex cost function and a linear constraint on the equalizer parameters. For a generic class of channels, this new algorithm results in the equalizer parameter convergence to a unique global minimum achieving intersymbol interference suppression and carrier phase error removal. Different implementation approaches are assessed and simulation results are shown to confirm the theoretical global convergence of the new algorithm.

Among the useful blind equalization algorithms, there are stochastic-gradient iterative equalization algorithms. Because these algorithms basically use a linear FIR filter except to adopt a memoryless nonlinear function of the equalizer output to generate the desired response, only linear channel distortion can be corrected well. To overcome nonlinear channel distortion two new blind equalization schemes using the structure of the complex multi-layer perceptron that can deal with signals of any constellation size are proposed. One is a modification of the constant modulus algorithm (CMA), the most widely used blind algorithm. The other is a modification of the radius-directed equalization (RDE) algorithm with multiple constant modulus that is more suitable for the node activation function having a multi-saturated output region. The experimental results show that the proposed schemes have very low MSE in the steady state and at the same time can recover the arbitrary phase rotation due to the channel when the major channel distortion is both linear and nonlinear.