Xian-Da Zhang

Nonorthogonal Joint Diagonalization Free of Degenerate Solution

The problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications. For nonorthogonal joint diagonalization based on the weighted least-squares (WLS) criterion, the trivial (zero) solution can simply be avoided by adopting some constraint on the diagonalizing matrix or penalty terms. However, the resultant algorithms may converge to some undesired degenerate solutions (nonzero but singular or ill-conditioned solutions). This paper discusses and analyzes the problem of degenerate solutions in detail. To solve this problem, a novel nonleast-squares criterion for approximate nonorthogonal joint diagonalization is proposed and an efficient algorithm, called fast approximate joint diagonalization (FAJD), is developed. As compared with the existing nonorthogonal diagonalization algorithms, the new algorithm can not only avoid the trivial solution but also any degenerate solutions. Theoretical analysis shows that the FAJD algorithm has some advantages over the existing nonorthogonal diagonalization algorithms. Simulation results are presented to demonstrate the efficiency of this papers algorithm

Secure Relay Beamforming With Imperfect Channel Side Information

In this paper, we study the robust relay beamformer design problem in the relay-eavesdropper network with imperfect knowledge of the eavesdroppers channel. In this network, the half-duplexing relay is equipped with multiple antennas and employs the amplify-and-forward (AF) relaying protocol. Assuming static legitimate links, we consider the relay beamforming problem under two models for the eavesdroppers channel: 1) the Rician fading channel model, where only statistical information of the eavesdroppers channel is known by the legitimate nodes; and 2) the deterministic uncertainty model, where the uncertainty region of the eavesdroppers channel vector is modeled as a sphere. As for the optimization criteria, we use an approximation of the ergodic secrecy rate under the Rician fading model and the worst-case secrecy rate under the deterministic uncertainty model. Under both models, the optimal rank-1, match-and-forward (MF), and zero-forcing (ZF) beamformers are developed, and the equivalence of the optimal rank-1 beamformer and the optimal MF beamformer is also established. Under the Rician fading model, it is shown that the optimal ZF beamformer may have a rank greater than 1 and, therefore, could outperform the optimal MF beamformer, whereas under the deterministic uncertainty model, the optimal ZF beamformer must be rank-1. Numerical results are presented to verify the effectiveness of the proposed relay beamformers.

A Family of Generalized Constant Modulus Algorithms for Blind Equalization

By generalizing the definition of complex modulus, this letter presents a family of generalized constant modulus algorithms whose special examples includes not only the well-known constant modulus algorithm, but also the recently proposed sign Godard algorithm, square contour algorithm (SCA), generalized SCA, and sign SCA

Superimposed Training Based Channel Estimation for OFDM Modulated Amplify-and-Forward Relay Networks

In this paper, we consider the channel estimation for the classical three-node relay networks that employ the amplify-and-forward (AF) transmission scheme and the orthogonal frequency division multiplexing (OFDM) modulation. We propose a superimposed training strategy that allows the destination node to separately obtain the channel information of the source→relay link and the relay→destination link. Specifically, the relay superimposes its own training signal over the received one before forwarding it to the destination. The proposed training strategy can be implemented within two transmission phases and is thus compatible with the two-phase data transmission scheme, i.e., the training can be embedded into data transmission. We also derive the Cramér-Rao bound for the random channel parameters, from which we compute the optimal training sequence as well as the optimal power allocation. Since the optimal minimum mean square error (MMSE) estimator and the maximum a posteriori (MAP) estimator cannot be expressed in closed-form, we propose to first obtain the initial channel estimates from the low complexity linear estimators, e.g., linear minimum mean-square error (LMMSE) and least square (LS) estimators, and then resort to the iterative method to improve the estimation accuracy. Simulation results are provided to corroborate the proposed studies.

Singular value decomposition-based MA order determination of non-Gaussian ARMA models

Singular-value-decomposition (SVD)-based moving-average (MA) order determination of non-Gaussian processes using higher-order statistics is addressed. It is shown that the MA order determination of autoregressive moving-average (ARMA) models is equivalent to the rank determination of a certain error matrix, and a SVD approach is proposed. Its simplified form is applied to pure MA models. To improve the robustness of the order selection, a combination of the SVD and the product of diagonal entries (PODE) test is proposed. Some interesting applications of the two SVD approaches are presented, and simulations verify their performance. >

A fast recursive total least squares algorithm for adaptive FIR filtering

This work develops a new fast recursive total least squares (N-RTLS) algorithm to recursively compute the total least squares (TLS) solution for adaptive infinite-impulse-response (IIR) filtering. The new algorithm is based on the minimization of the constraint Rayleigh quotient in which the first entry of the parameter vector is fixed to the negative one. The highly computational efficiency of the proposed algorithm depends on the efficient computation of the gain vector and the adaptation of the Rayleigh quotient. Using the shift structure of the input data vectors, a fast algorithm for computing the gain vector is established, which is referred to as the fast gain vector (FGV) algorithm. The computational load of the FGV algorithm is smaller than that of the fast Kalman algorithm. Moreover, the new algorithm is numerically stable since it does not use the well-known matrix inversion lemma. The computational complexity of the new algorithm per iteration is also O(L). The global convergence of the new algorithm is studied. The performances of the relevant algorithms are compared via simulations.

Prefiltering-based ESPRIT for estimating sinusoidal parameters in non-Gaussian ARMA noise

Addresses the ESPRIT algorithm for estimating sinusoidal parameters in non-Gaussian ARMA noise. The authors show that after prefiltering the output data via the estimated AR polynomial of the noise model, a new ESPRIT based on some extensions of ESPRIT can be used to estimate sinusoidal parameters. >

Adaptive RLS algorithm for blind source separation using a natural gradient

By using the natural gradient on the Stiefel manifold to minimize a nonlinear principle component analysis criterion, this letter proposes a new adaptive recursive-least-squares (RLS) algorithm with prewhitening for blind source separation (BSS), which makes full use of the orthogonality constraint of the separating matrix. Simulations show that the new natural-gradient-based RLS algorithm has faster convergence than the existing least-mean-square algorithms and RLS algorithm for BSS.

A Gabor atom network for signal classification with application in radar target recognition

A Gabor atom neural network approach is proposed for signal classification. The Gabor atom network uses a multilayer feedforward neural network structure, and its input layer constitutes the feature extraction part, whereas the hidden layer and the output layer constitute the signal classification part. From the physics point of view, it is shown that the time-shifted, frequency-modulated, and scaled Gaussian function is available for a basic model for the signal of high-resolution radar. Two experiment examples show that the Gabor atom network approach has a higher recognition rate in radar target recognition from range profiles as compared with several existing methods.

FIR system identification using higher order statistics alone

This paper focuses on FIR system identification in Gaussian ARMA noise using higher order cumulants alone. Two new types of cumulant-based normal equations are established, and two algorithms are proposed for MA parameter estimation. Simulations verify the high performance of the new developments. >