Decision feedback equalizer based on CMA1–2 and DD 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.

Adaptive blind equalization has gained widespread use in communication receivers that operate without training signals. In particular, the constant modulus algorithm (CMA) has become a favourite of practitioners due to its LMS-like complexity and desirable robustness properties. The desire for further reduction in computational complexity has motivated signed-error versions of CMA (SE-CMA) which have been found to lack the robustness properties of CMA. Alternatively a dithered signed-error of CMA (DSE-CMA) based on the judicious use of dither, has been proposed which results in algorithm with robustness properties nearly identical to those of CMA with the cost of the degradation in steady-state mean square error (MSE) performance. This paper presents a modified dithered signed-error version of CMA (MDSE-CMA) which is motivated by a reduction of the steady-state MSE of DSE-CMA without increase in its computational complexity.

Performance analysis of the deficient length augmented CLMS algorithm for second order noncircular complex signals

In digital communication system that the Modified Constant Modulus Algorithm (MCMA) reduced the use of the adaptive equalization algorithm to combat the Inter-symbol Interference (ISI). MCMA is relatively brief operation. The major point of MCMA that it only achieves moderate convergence rate and steady state mean square error (MSE). In this paper suggest, MCMA equalization improve the performance with parallel structure. It combines Modified Constant Modulus Algorithm(MCMA) and Modified Decision Directed(MDD) algorithm. By exploiting the inherent structural relationship between the 4-QAM signal's coordinates and 16-QAM signal's coordinates, another style of cost function for Modified Constant Modulus Algorithm(MCMA) is defined and If it happen to offset of received signals and MCMA is poor performance in order to overcome this because the paper combines apply for MCMA and MDD(Modified Decision Direct) algorithm. By computer simulation, we confirmed that the proposed PMCMA-MDD algorithm has the fater convergence rate and steady mean square error than the conventional MCMA.

The constant modulus algorithm (CMA) for blind equalization requires a separate carrier-recovery system for phase recovery. A modified CMA, called the multimodulus algorithm (MMA), which may perform joint blind equalization and carrier recovery without the need for a separate carrier-recovery system for quadrature amplitude modulation (QAM) signal constellations. This letter mathematically analyzes the steady-state mean square error (MSE) of MMA. Analysis results indicate that MMA produces 50% fewer steady-state MSE than CMA.

This paper presents two classes of adaptive blind algorithms based on second- and higher order statistics. The first class contains fast recursive algorithms whose cost functions involve second and third- or fourth-order cumulants. These algorithms are stochastic gradient-based but have structures similar to the fast transversal filters (FTF) algorithms. The second class is composed of two stages: the first stage uses a gradient adaptive lattice (GAL) while the second stage employs a higher order-cumulant (HOC) based least mean squares (LMS) filter. The computational loads for these algorithms are all linearly proportional to the number of taps used. Furthermore, the second class, as various numerical examples indicate, yields very fast convergence rates and low steady state mean square errors (MSE) and intersymbol interference (ISI). MSE convergence analyses for the proposed algorithms are also provided and compared with simulation results. >

The nonlinear decision feedback equalizer (DFE) provides significantly lower symbol error rates than a linear equalizer, but for the high speed digital transmission systems which shows more serious inter-symbol interference (ISI) the DFE suffers large steady-state mean square error (MSE) and slow convergence rate. So a new DFE is proposed, which consists of a feedforward filter based on T/2 fractionally-spaced structure and a feedback filter based on baud-spaced structure and uses a dual-mode algorithm. The efficiency of the method is proved by computer simulation.

Experimental performances of blind adaptive training algorithms have been evaluated in real-time WiMax (3.5GHz) radio channels in this paper. Inter Symbol Interference (ISI) cancellation and Mean Square Error (MSE) performances of the most commonly used blind equalization techniques, Constant Modulus Algorithm (CMA), and CMA based modified CMA (M-CMA) and normalized CMA (N-CMA) algorithms are investigated in study.

We address a new blind equalizer incorporating both the good initial convergence characteristic of the dual-mode modified constant modulus algorithm (MCMA) and the low residual error characteristic after convergence of the decision-directed (DD) algorithm. In the proposed scheme, a convergence detector is employed to help switching from the dual-mode MCMA to the DD algorithm. We have observed that the proposed scheme exhibits a good overall performance in comparison with the CMA, MCMA, and dual-mode MCMA.KeywordsMean Square ErrorChannel Impulse ResponseSteady State ModeNormalize Little Mean SquareConstant Modulus AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, an efficient blind equalization with two‐stage single/multilevel modulus and decision directed (DD) least mean square (LMS)‐like algorithm is proposed for high‐order QAM (64/256/1024QAM) cable modem systems. In wire‐lined cable systems, it seems that the cable channel may display a nearly invariant multi‐path effect over a considerable time, and then the blind equalizer can have the capability to recover the received high‐order QAM symbols on wired cables. The proposed blind equalization algorithm applies a two‐stage convergence scheme, which results from the multi‐modulus algorithm (MMA), sometimes called the modified constant modulus algorithm (MCMA), and the DD LMS‐like method. In the first equalization stage, the joint MMA and DD LMS‐like methods are applied for the purpose of fast convergence. When the convergence process reaches an acceptably steady condition, the convergence detector changes the process into the second stage. In the second equalization stage, the enhanced DD LMS‐like method with the generalized multi‐modulus is applied to reduce the mean square error (MSE) of equalizations further. For high‐order QAM cable systems, the proposed method performs faster than the previous well‐known blind methods do. Simultaneously, the proposed algorithm also provides less MSE and lower symbol error rate (SER) than the other blind methods do at the same signal‐to‐noise ratio (SNR).

A least mean square (LMS) algorithm with clipped data is studied for use when updating the weights of an adaptive filter with correlated Gaussian input. Both stationary and nonstationary environments are considered. Three main contributions are presented. The first, corresponding to the stationary case, is a proof of the convergence of the algorithm in the case of a M-dependent sequence of correlated observation vectors. It is proven that the steady state mean square misalignment of the adaptive filter weights has an upper bound proportional to the algorithm step size mu . The second contribution, also belonging to the stationary case, is the derivation of the expressions of convergence time N/sub c/ and steady state mean square excess estimation error epsilon . It is shown that N/sub c/ is proportional to 1/( mu lambda ), with lambda being the minimum eigenvalue of the input covariance matrix. It is also shown that the product N/sub c/ epsilon is independent of mu . For a given epsilon , the convergence time increases with the eigenvalue spread of the input covariance matrix and the filter length, as well as its input noise power. The range of mu that achieves tolerable values of N/sub c/ and epsilon is determined. The third contribution is concerned with the nonstationary case. It is shown that the mean square excess estimation error is the sum of the two terms with opposite dependencies on mu . An optimum value of mu is derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new super-exponential decision feedback blind equalization algorithm is proposed in this paper. In comparison with the conventional SEI-DFE equalization algorithm, the proposed algorithm presents a new fast convergence weight update error function. Therefore, phase compensation ability and steady-state Mean Square Error (MSE) performance have been increased, but they don't significantly increase the computational complexity. At the same time, a second order digital phase-locked loop is introduced in order to track and compensate phase rotation. The MSE and carrier recovery performance of the proposed algorithm are better than that of the SEI-DFE algorithm, which is verified by computer simulation. In addition, the MULAN Lake experiment shows that the performance of the proposed algorithm is better than that of the SEI-DFE algorithm in terms of Bit Error Rate (BER) by comparing the influences causing filter weight vector length, step size and Q matrix size.

The paper investigates the application of the multilayer perceptron structure to the packet wise adaptive decision feedback equalization of a M-ary QAM signal through a TDMA indoor radio channel in the presence of intersymbol interference (ISI) and additive Gaussian noise. Since the multilayer neural networks are capable of producing complex decision regions with arbitrarily nonlinear boundaries, this would greatly improve the performance of conventional decision feedback equalizer (DFE), where the decision boundaries of conventional DFE's are linear. Nevertheless, the applications of the traditional multilayer neural networks have been limited to real valued signals. To tackle this difficulty, a neural based DFE is proposed to deal with the complex QAM signal over the complex valued fading multipath radio channel without performing time consuming complex valued backpropagation training algorithms, while maintaining almost the same computational complexity as the original real valued training algorithm. Moreover, this neural based DFE trained by packet wise backpropagation algorithm would approach an ideal equalizer after receiving a sufficient number of packets. Results 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.

Distributed sparse diffusion estimation based on set membership and affine projection algorithm

A convex combination LMS (least mean square) algorithm based on Krylov subspace transform is proposed in this paper. In this approach, impulse response of the unknown system is firstly transformed into Krylov subspace, in which the system structure is changed into sparse. Then an improved proportionate normalized LMS (IPNLMS) algorithm and a variable tap-length normalized LMS (VTNLMS) algorithm are combined. Simulations are performed to show the convergence performance of the combined algorithm. The results show that both a fast convergence rate and small steady state mean square deviation (MSD) are obtained.