Da-Zheng Feng

Total least mean squares algorithm

Widrow (1971) proposed the least mean squares (LMS) algorithm, which has been extensively applied in adaptive signal processing and adaptive control. The LMS algorithm is based on the minimum mean squares error. On the basis of the total least mean squares error or the minimum Raleigh quotient, we propose the total least mean squares (TLMS) algorithm. The paper gives the statistical analysis for this algorithm, studies the global asymptotic convergence of this algorithm by an equivalent energy function, and evaluates the performances of this algorithm via computer simulations.

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.

Matrix-Group Algorithm via Improved Whitening Process for Extracting Statistically Independent Sources From Array Signals

This paper addresses the problem of blind separation of multiple independent sources from observed array output signals. The main contributions in this paper include an improved whitening scheme for estimation of signal subspace, a novel biquadratic contrast function for extraction of independent sources, and an efficient alterative method for joint implementation of a set of approximate diagonalization-structural matrices. Specifically, an improved whitening scheme is first developed by estimating the signal subspace jointly from a set of diagonalization-structural matrices based on the proposed cyclic maximizer of an interesting cost function. Moreover, the globally asymptotical convergence of the proposed cyclic maximizer is analyzed and proved. Next, a novel biquadratic contrast function is proposed for extracting one single independent component from a slice matrix group of any order cumulant of the array signals in the presence of temporally white noise. A fast fixed-point algorithm that is a cyclic minimizer is constructed for searching a minimum point of the proposed contrast function. The globally asymptotical convergence of the proposed fixed-point algorithm is analyzed. Then, multiple independent components are obtained by using repeatedly the proposed fixed-point algorithm for extracting one single independent component, and the orthogonality among them is achieved by the well-known QR factorization. The performance of the proposed algorithms is illustrated by simulation results and is compared with three related blind source separation algorithms

Neural network learning algorithms for tracking minor subspace in high-dimensional data stream

A novel random-gradient-based algorithm is developed for online tracking the minor component (MC) associated with the smallest eigenvalue of the autocorrelation matrix of the input vector sequence. The five available learning algorithms for tracking one MC are extended to those for tracking multiple MCs or the minor subspace (MS). In order to overcome the dynamical divergence properties of some available random-gradient-based algorithms, we propose a modification of the Oja-type algorithms, called OJAm, which can work satisfactorily. The averaging differential equation and the energy function associated with the OJAm are given. It is shown that the averaging differential equation will globally asymptotically converge to an invariance set. The corresponding energy or Lyapunov functions exhibit a unique global minimum attained if and only if its state matrices span the MS of the autocorrelation matrix of a vector data stream. The other stationary points are saddle (unstable) points. The globally convergence of OJAm is also studied. The OJAm provides an efficient online learning for tracking the MS. It can track an orthonormal basis of the MS while the other five available algorithms cannot track any orthonormal basis of the MS. The performances of the relative algorithms are shown via computer simulations.

A locally adaptive filter of interferometric phase images

We propose an adaptive filtering approach for interferograms, which is a modification to the Lee adaptive complex filter. Based on local frequency estimates, we compute the normal orientation of local phase fringes. A directionally dependent filtering window is aligned perpendicular to the normal orientation of local phase fringes (i.e., along local phase fringes) by interpolation, making the pixels included in the filtering window have approximately more homogeneous values. Moreover, the computation of the filter parameter does not require local phase unwrapping in the real plane. This filter minimizes the loss of signal and reduces the level of noise. By using two sets of simulated data, its effectiveness can be seen in terms of the fidelity to noise-free phases, fringe preservation, and residue reduction.

A neural network learning for adaptively extracting cross-correlation features between two high-dimensional data streams

This paper proposes a novel cross-correlation neural network (CNN) model for finding the principal singular subspace of a cross-correlation matrix between two high-dimensional data streams. We introduce a novel nonquadratic criterion (NQC) for searching the optimum weights of two linear neural networks (LNN). The NQC exhibits a single global minimum attained if and only if the weight matrices of the left and right neural networks span the left and right principal singular subspace of a cross-correlation matrix, respectively. The other stationary points of the NQC are (unstable) saddle points. We develop an adaptive algorithm based on the NQC for tracking the principal singular subspace of a cross-correlation matrix between two high-dimensional vector sequences. The NQC algorithm provides a fast online learning of the optimum weights for two LNN. The global asymptotic stability of the NQC algorithm is analyzed. The NQC algorithm has several key advantages such as faster convergence, which is illustrated through simulations.

An efficient multistage decomposition approach for independent components

In this paper, we present an efficient off-fine algorithm for sequentially extracting one independent component from simultaneously mixed data corrupted by the spatially colored noises. For this purpose, this paper develops a new criterion and its efficient search algorithm to achieve the extraction of an independent component. The algorithm is an efficient, off-line update approach, and can find the global optimal solution of the cost function defined in this paper. By the systematic multistage decomposition and multistage reconstruction, we can get all the independent components. This algorithm uses only the second-order statistics of the source signals and suited particularly to separate the temporally colored signals. The main advantage of this algorithm over the conventional jointly approximated diagonalization of eigenmatrices (JADE) is its ability to separate sources from the simultaneously mixed data with the spatially colored noises.

Minimax robust transmission waveform and receiving filter design for extended target detection with imprecise prior knowledge

It is well known that optimal extended target detection for wideband radar in the presence of colored Gaussian noise and signal-dependent interference can be implemented, based on the prior information of target impulse response, by transmit-receiver design via maximizing the output signal-to-interference plus noise ratio (SINR). However, the prior knowledge of the target is usually imprecise. The target impulse response is very sensitive to target-radar orientation, and the initial phase of target echo is a function of target-radar distance, namely, the exact target impulse response cannot be obtained in transmission waveform design. Additionally, the transmission waveform is desired to be of constant modulus for power efficiency. In this paper, we propose a robust method to jointly design the transmission waveform with constant modulus constraint and the receiving filters. The cost function is established by maximizing the worst-case output SINR and an iterative procedure is presented based on modified sequential quadratic programming. Numerical results show that the proposed method can increase the worst-case output SINR significantly.

Fast communication: Two-sided minimum-variance distortionless response beamformer for MIMO radar

In this letter, we propose a novel two-sided minimum-variance distortionless response (TS-MVDR) beamformer applicable to multi-input multi-output (MIMO) radar systems. For this purpose, a new bi-quadratic cost function is introduced, whose minimum point can be efficiently found by a bi-iterative algorithm (BIA). The convergence of the BIA is analyzed by the well-known LaSalle invariance principle. It is shown via experimental results that the proposed TS-MVDR beamformer can achieve relatively good performance.

A novel algorithm for two-dimensional frequency estimation

This paper addresses the two-dimensional (2-D) frequency estimation embedded in additive Gaussian noise. By use of the biorthogonality of matrices and rotational invariance property, we construct an interesting cost function and propose a novel iterative algorithm for 2-D frequency estimation, which obtains one column of the Vandermonde matrix containing 1-D frequencies and the corresponding column of the Vandermonde matrix containing the other 1-D frequencies at each stage. Therefore, the proposed algorithm can pair the 2-D frequencies automatically. The convergence of the proposed iterative algorithm is also proven. Moreover, all the columns of the frequency matrices can be obtained by systematically multistage decomposition and multistage reconstruction. Simulation results are provided to show the good performance of the proposed algorithm.