Haiquan Zhao

Generalized Correntropy for Robust Adaptive Filtering

As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied in robust regression and filtering. The default kernel function in correntropy is the Gaussian kernel, which is, of course, not always the best choice. In this paper, we propose a generalized correntropy that adopts the generalized Gaussian density (GGD) function as the kernel, and present some important properties. We further propose the generalized maximum correntropy criterion (GMCC) and apply it to adaptive filtering. An adaptive algorithm, called the GMCC algorithm, is derived, and the stability problem and steady-state performance are studied. We show that the proposed algorithm is very stable and can achieve zero probability of divergence (POD). Simulation results confirm the theoretical expectations and demonstrate the desirable performance of the new algorithm.

Convergence of a Fixed-Point Algorithm under Maximum Correntropy Criterion

The maximum correntropy criterion (MCC) has received increasing attention in signal processing and machine learning due to its robustness against outliers (or impulsive noises). Some gradient based adaptive filtering algorithms under MCC have been developed and available for practical use. The fixed-point algorithms under MCC are, however, seldom studied. In particular, too little attention has been paid to the convergence issue of the fixed-point MCC algorithms. In this letter, we will study this problem and give a sufficient condition to guarantee the convergence of a fixed-point MCC algorithm.

Adaptive reduced feedback FLNN filter for active control of nonlinear noise processes

In actual nonlinear active noise control (NANC) systems, there often exist nonlinear distortions in such cases: the primary path may be nonlinear, the reference noise may exhibit nonlinear distortion, and the secondary path may have nonminimum-phase. To solve the problems of nonlinear distortions, two novel feedback adaptive filters based on the functional link neural network (FLNN) for NANC systems with low computational complexity are proposed in this paper, which are a feedback functional link neural network (FFLNN) and a reduced feedback functional link neural network (RFFLNN), respectively. To train the proposed nonlinear filters for NANC systems, a reduced complexity filtered-s least mean square (FSLMS) algorithm using filter bank approach is developed. The analysis of computational complexity shows that the RFFLNN adaptive filter involves less computation as compared to FFLNN and FLNN adaptive filters. Moreover, it is demonstrated through computer simulations for nonlinear noise processes that the RFFLNN adaptive filter outperforms FLNN and FFLNN in term of convergence speed and steady-state error. Furthermore, it is more effective in reducing nonlinear effects in NANC systems than other filters.

Adaptively Combined FIR and Functional Link Artificial Neural Network Equalizer for Nonlinear Communication Channel

This paper proposes a novel computational efficient adaptive nonlinear equalizer based on combination of finite impulse response (FIR) filter and functional link artificial neural network (CFFLANN) to compensate linear and nonlinear distortions in nonlinear communication channel. This convex nonlinear combination results in improving the speed while retaining the lower steady-state error. In addition, since the CFFLANN needs not the hidden layers, which exist in conventional neural-network-based equalizers, it exhibits a simpler structure than the traditional neural networks (NNs) and can require less computational burden during the training mode. Moreover, appropriate adaptation algorithm for the proposed equalizer is derived by the modified least mean square (MLMS). Results obtained from the simulations clearly show that the proposed equalizer using the MLMS algorithm can availably eliminate various intensity linear and nonlinear distortions, and be provided with better anti-jamming performance. Furthermore, comparisons of the mean squared error (MSE), the bit error rate (BER), and the effect of eigenvalue ratio (EVR) of input correlation matrix are presented.

Maximum correntropy Kalman filter

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm.

Functional link neural network cascaded with Chebyshev orthogonal polynomial for nonlinear channel equalization

Nonlinear intersymbol interference (ISI) leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel computationally efficient functional link neural network cascaded with Chebyshev orthogonal polynomial is proposed to combat nonlinear ISI. The equalizer has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomial and Chebyshev orthogonal polynomial. Due to the input pattern and nonlinear approximation enhancement, the proposed structure can approximate arbitrarily nonlinear decision boundaries. It has been utilized for nonlinear channel equalization. The performance of the proposed adaptive nonlinear equalizer is compared with functional link neural network (FLNN) equalizer, multilayer perceptron (MLP) network and radial basis function (RBF) along with conventional normalized least-mean-square algorithms (NLMS) for different linear and nonlinear channel models. The comparison of convergence rate, bit error rate (BER) and steady state error performance, and computational complexity involved for neural network equalizers is provided.

A Novel Adaptive Nonlinear Filter-Based Pipelined Feedforward Second-Order Volterra Architecture

Due to the computational complexity of the Volterra filter, there are limitations on the implementation in practice. In this paper, a novel adaptive joint process filter using pipelined feedforward second-order Volterra architecture (JPPSOV) to reduce the computational burdens of the Volterra filter is proposed. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the feedforward second-order Volterra (SOV), and a linear combiner performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the nonlinear and linear combiner subsections, respectively. Moreover, the analysis of theory shows that these adaptive algorithms based on the pipelined architecture are stable and convergence under a certain condition. To evaluate the performance of the JPPSOV, a series of simulation experiments are presented including nonlinear system identification and predicting of speech signals. Compared with the conventional SOV filter, adaptive JPPSOV filter exhibits a litter better convergence performance with less computational burden in terms of convergence speed and steady-state error.

Memory proportionate APA with individual activation factors for acoustic echo cancellation

An individual-activation-factor memory proportionate affine projection algorithm (IAF-MPAPA) is proposed for sparse system identification in acoustic echo cancellation (AEC) scenarios. By utilizing an individual activation factor for each adaptive filter coefficient instead of a global activation factor, as in the standard proportionate affine projection algorithm (PAPA), the adaptation energy over the coefficients of the proposed IAF-MPAPA can achieve a better distribution, which leads to an improvement of the convergence performance. Moreover, benefiting from the memory characteristics of the proportionate coefficients, its computational complexity is less than the PAPA and improved PAPA (IPAPA). In the context of AEC and stereophonic AEC (SAEC) for highly sparse impulse responses, simulation results indicate that the proposed IAF-MPAPA outperforms the PAPA, IPAPA, and memory IPAPA (MIPAPA) in terms of the convergence rate and tracking capability when the unknown impulse response suddenly changes.

A New Normalized Subband Adaptive Filter Algorithm with Individual Variable Step Sizes

Proposed is a novel variable step size normalized subband adaptive filter algorithm, which assigns an individual step size for each subband by minimizing the mean square of the noise-free a posterior subband error. Furthermore, a noniterative shrinkage method is used to recover the noise-free priori subband error from the noisy subband error signal. Simulation results using the colored input signals have demonstrated that the proposed algorithm not only has better tracking capability than the existing subband adaptive filter algorithms, but also exhibits lower steady-state error.

Pipelined Chebyshev Functional Link Artificial Recurrent Neural Network for Nonlinear Adaptive Filter

A novel nonlinear adaptive filter with pipelined Chebyshev functional link artificial recurrent neural network (PCFLARNN) is presented in this paper, which uses a modification real-time recurrent learning algorithm. The PCFLARNN consists of a number of simple small-scale Chebyshev functional link artificial recurrent neural network (CFLARNN) modules. Compared to the standard recurrent neural network (RNN), those modules of PCFLARNN can simultaneously be performed in a pipelined parallelism fashion, and this would lead to a significant improvement in its total computational efficiency. Furthermore, contrasted with the architecture of a pipelined RNN (PRNN), each module of PCFLARNN is a CFLARNN whose nonlinearity is introduced by enhancing the input pattern with Chebyshev functional expansion, whereas the RNN of each module in PRNN utilizing linear input and first-order recurrent term only fails to utilize the high-order terms of inputs. Therefore, the performance of PCFLARNN can further be improved at the cost of a slightly increased computational complexity. In addition, due to the introduced nonlinear functional expansion of each module in PRNN, the number of input signals can be reduced. Computer simulations have demonstrated that the proposed filter performs better than PRNN and RNN for nonlinear colored signal prediction, nonstationary speech signal prediction, and chaotic time series prediction.