Yingbo Hua

Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise

A study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and/or undamped sinusoids in noise is presented. Comparison of this method to a polynomial method (SVD-Prony method) shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes. It is found through perturbation analysis and simulation that, for signals with unknown damping factors, the pencil method is less sensitive to noise than the polynomial method. An expression of the Cramer-Rao bound for the exponential signals is presented. >

Optimal Design of Non-Regenerative MIMO Wireless Relays

Given a multiple-antenna source and a multiple-antenna destination, a multiple-antenna relay between the source and the destination is desirable under useful circumstances. A non-regenerative multiple-antenna relay, also called non-regenerative MIMO (multi-input multi-output) relay, is designed to optimize the capacity between the source and the destination. Without a direct link between the source and the destination, the optimal canonical coordinates of the relay matrix are first established, and the optimal power allocations along these coordinates are then found. The system capacity with the optimal relay matrix is shown to be significantly higher than those with heuristic relay matrices. When a direct link is present, upper and lower bounds of the optimal system capacity are discussed.

Generalized pencil-of-function method for extracting poles of an EM system from its transient response

A generalized pencil-of-function (GPOF) method is developed for extracting the poles of an electromagnetic system from its transient response. The GPOF method needs the solution of a generalized eigenvalue problem to find the poles. Subspace decomposition is also used to optimize the performance of the GPOF method. The GPOF method has advantages over the Prony method in both computation and noise sensitivity, and approaches the Cramer-Rao bound when the signal-to-noise ratio (SNR) is above threshold. An application of the GPOF method to a thin-wire target is presented. >

Estimating two-dimensional frequencies by matrix enhancement and matrix pencil

A new method, called the matrix enhancement and matrix pencil (MEMP) method, is presented for estimating two-dimensional (2-D) frequencies. In the MEMP method, an enhanced matrix is constructed from the data samples, and then the matrix pencil approach is used to extract out the 2-D sinusoids from the principal eigenvectors of the enhanced matrix. The MEMP method yields the estimates of the 2-D frequencies efficiently, without solving the roots of a 2-D polynomial or searching in a 2-D space. It is shown that the MEMP method can be faster than a 2-D FFT method if the number of the 2-D sinusoids is much smaller than the data set. Simulation results are provided to show that the accuracy of the MEMP method can be very close to the Cramer-Rao lower bound. >

A Unified Framework for Optimizing Linear Nonregenerative Multicarrier MIMO Relay Communication Systems

In this paper, we develop a unified framework for linear nonregenerative multicarrier multiple-input multiple-output (MIMO) relay communications in the absence of the direct source-destination link. This unified framework classifies most commonly used design objectives such as the minimal mean-square error and the maximal mutual information into two categories: Schur-concave and Schur-convex functions. We prove that for Schur-concave objective functions, the optimal source precoding matrix and relay amplifying matrix jointly diagonalize the source-relay-destination channel matrix and convert the multicarrier MIMO relay channel into parallel single-input single-output (SISO) relay channels. While for Schur-convex objectives, such joint diagonalization occurs after a specific rotation of the source precoding matrix. After the optimal structure of the source and relay matrices is determined, the linear nonregenerative relay design problem boils down to the issue of power loading among the resulting SISO relay channels. We show that this power loading problem can be efficiently solved by an alternating technique. Numerical examples demonstrate the effectiveness of the proposed framework.

Blind system identification

Blind system identification (BSI) is a fundamental signal processing technology aimed at retrieving a systems unknown information from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation, and blind image restoration. This paper reviews a number of recently developed concepts and techniques for BSI, which include the concept of blind system identifiability in a deterministic framework, the blind techniques of maximum likelihood and subspace for estimating the systems impulse response, and other techniques for direct estimation of the system input.

On SVD for estimating generalized eigenvalues of singular matrix pencil in noise

Several algorithms for estimating generalized eigenvalues (GEs) of singular matrix pencils perturbed by noise are reviewed. The singular value decomposition (SVD) is explored as the common structure in the three basic algorithms: direct matrix pencil algorithm, pro-ESPRIT, and TLS-ESPRIT. It is shown that several SVD-based steps inherent in the algorithms are equivalent to the first-order approximation. In particular, the Pro-ESPRIT and its variant TLS-Pro-ESPRIT are shown to be equivalent, and the TLS-ESPRIT and its earlier version LS-ESPRIT are shown to be asymptotically equivalent to the first-order approximation. For the problem of estimating superimposed complex exponential signals, the state-space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first-order approximation. The second-order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal. An improved state-space algorithm is found to be the most robust to noise. >

Combating synchronization errors in cooperative relays

Cooperative relays have recently been proposed and studied for mobile ad hoc networks. It has been shown that under perfect symbol synchronization, parallel relays with space-time modulation can yield more than 10 dB power savings over conventional serial relays in a highly mobile environment. We analyze the effect of synchronization errors on the performance of parallel relays, and also study several effective methods to reduce the negative impact of synch errors. Our study shows that when the synch errors are much smaller than a symbol interval, the performance of parallel relays deteriorates gracefully. We have also found that well designed space-time coding techniques, such as TR-STC and ST-OFDM, can be highly effective in combating large synch errors with only marginal reduction of data rate.

An L-shaped array for estimating 2-D directions of wave arrival

A simple structured 2-D array, the L-shaped array, is presented. The L-shaped array consists of two uniform linear arrays (ULA) connected orthogonally at one end of each ULA. It is shown that the Cramer-Rao bounds (CRB) of the estimated wave directions based on the L-shaped array are about 37% smaller than those for the cross array. The CRB indicates the accuracy potential because it is the (reachable) lower bound on the variance of any unbiased estimate. An efficient maximum likelihood algorithm is developed utilizing the ULA structure inherent in the L-shaped array. >

Fast orthonormal PAST algorithm

Subspace decomposition has proven to be an important tool in adaptive signal processing. A number of algorithms have been proposed for tracking the dominant subspace. Among the most robust and most efficient methods is the projection approximation and subspace tracking (PAST) method. This paper elaborates on an orthonormal version of the PAST algorithm for fast estimation and tracking of the principal subspace or/and principal components of a vector sequence. The orthonormal PAST (OPAST) algorithm guarantees the orthonormality of the weight matrix at each iteration. Moreover, it has a linear complexity like the PAST algorithm and a global convergence property like the natural power (NP) method.