Wu-Sheng Lu

Impedance control with adaptation for robotic manipulations

Two adaptive impedance control algorithms are presented. In this treatment, it is assumed that some parameters in the manipulator dynamics may be uncertain, and the measurements from the wrist force sensor utilized are imprecise. By introducing the concept of target-impedance reference trajectory (TIRT), which characterizes a desired dynamic relation of the end-point with the environment and a refined Lyapunov approach, it is shown that the adaptation mechanisms previously suggested can be injected into N. Hogans (1987) conventional impedance control scheme. The two resulting algorithms are compared in terms of implementation feasibility as well as computation efficiency. Simulation results are presented to illustrate the proposed algorithms. >

A weighted least-squares method for the design of stable 1-D and 2-D IIR digital filters

We present a new approach to the least-squares design of stable infinite impulse response (IIR) digital filters. The design is accomplished by using an iterative scheme in which the denominator polynomial obtained from the preceding iteration is treated as a part of the weighting function, and each iteration is carried out by solving a standard quadratic programming problem that yields a stable rational function. When the iteration converges, a stable and truly least-squares solution is obtained. The method is then extended to address the least-squares design of stable IIR two-dimensional (2-D) filters. Examples are included to illustrate the proposed design techniques.

An improved weighted least-squares design for variable fractional delay FIR filters

Digital filters capable of changing their frequency response characteristics are often referred to as variable digital filters (VDFs) and have been found useful in a number of digital signal processing applications. An important class of VDFs is the class of digital filters with variable fractional delay. This paper describes an enhanced weighted least-squares design for variable-fractional-delay finite-impulse response filters, which offers improved performance of the filters obtained with considerably reduced computational complexity compared to a recently proposed weighted least-squares (WLS) design method. The design enhancement is achieved by deriving a closed-form formula for evaluating the WLS objective function. The formula facilitates accurate and efficient function evaluations as compared to summing up a large number of discrete terms, which would be time consuming and inevitably introduce additional errors into the design.

A New Peak-to-Average Power-Ratio Reduction Algorithm for OFDM Systems via Constellation Extension

Peak-to-average power-ratio (PAPR) reduction for OFDM systems is investigated in a probabilistic framework. A new constellation extension technique is developed whereby the data for each subcarrier are represented either by points in the original constellation or by extended points. An optimal representation of the OFDM signal is achieved by using a de-randomization algorithm where the conditional probability involved is handled by using the Chernoff bound and the evaluation of the many hyperbolic cosine functions involved is replaced by a tight upper bound for these functions. The proposed algorithm can be used by itself or be combined with a selective rotation technique described in the paper and with other known algorithms such as the coordinate descent optimization and selective mapping algorithms to achieve further performance enhancements at the cost of a slight increase in the computational complexity. When compared with other existing PAPR-reduction algorithms, the enhanced algorithm offers improved PAPR-reduction performance and improved computational complexity although, the transmit power is increased somewhat

A unified approach for the design of 2-D digital filters via semidefinite programming

This paper attempts to demonstrate that a modem optimization methodology known as semidefinite programming (SDP) can serve as the algorithmic core of a unified design tool for a variety of two-dimensional (2-D) digital filters. Representative SDP-based designs presented in the paper include minimax and weighted least-squares designs of FIR filters with continuous and discrete coefficients, and minimax design of stable separable-denominator IIR filters. Our studies are motivated by the fact that SDP as a subclass of convex programming can be solved efficiently using recently developed interior-point methods and, more importantly, constraints on amplitude/phase responses in certain frequency regions and on stability (for IIR filters), that are often encountered in many filter design problems, can be formulated in a natural way as linear matrix inequalities (LMI) which allow SDP to apply. Design examples for each class of filters are included to demonstrate that SDP-based methods can in many cases be useful in producing optimal or near-optimal 2-D filters with reduced computational complexity.

Synthesis of 2-D state-space fixed-point digital-filter structures with minimum roundoff noise

Based on a roundoff-noise analysis, a general synthesis procedure is developed which leads to an optimal local state-space 2-D digital-filter realization that minimizes the output-noise power due to roundoff subject to a scaling condition on the state variables. The outputnoise power and the signal scaling condition are closely related to two positive-definite matrices W and K . These matrices provide two sets of invariants, called the 2-D second-order modes of the filter, which play a crucial role in the minimization of the output-noise power. With the availability of matrices W and K , the 2-D similarity transformation that yields an optimal state-space realization can be obtained by solving separately two 1-D optimization problems so that the well-developed techniques for minimizing roundoff noise in 1-D state-space digital filters can also be used for minimizing roundoff noise in 2-D state-space digital filters.

Optimal design of IIR digital filters with robust stability using conic-quadratic-programming updates

In this paper, minimax design of infinite-impulse-response (IIR) filters with prescribed stability margin is formulated as a conic quadratic programming (CQP) problem. CQP is known as a class of well-structured convex programming problems for which efficient interior-point solvers are available. By considering factorized denominators, the proposed formulation incorporates a set of linear constraints that are sufficient and near necessary for the IIR filter to have a prescribed stability margin. A second-order cone condition on the magnitude of each update that ensures the validity of a key linear approximation used in the design is also included in the formulation and eliminates a line-search step. Collectively, these features lead to improved designs relative to several established methods. The paper then moves on to extend the proposed design methodology to quadrantally symmetric two-dimensional (2-D) digital filters. Simulation results for both one-dimensional (1-D) and 2-D cases are presented to illustrate the new design algorithms and demonstrate their performance in comparison with several existing methods.

Optimal design of frequency-response-masking filters using semidefinite programming

Since Lims paper (see IEEE Trans. Circuits Syst., vol.33, p. 357-364, Apr. 1986) on the frequency-response-masking (FRM) technique for the design of finite-impulse response digital filters with very small transition widths, the analysis and design of FRM filters has been a subject of study. In this paper, a new optimization technique for the design of various FRM filters is proposed. Central to the new design method is a sequence of linear updates for the design variables, with each update carried out by semidefinite programming. Algorithmic details for the design of basic and multistage FRM filters are presented to show that the proposed method offers a unified design framework for a variety of FRM filters. Design simulations are included to illustrate the proposed algorithms and to evaluate the design performance in comparison with that of several existing methods.

Joint Precoding Optimization for Multiuser Multi-Antenna Relaying Downlinks Using Quadratic Programming

This paper studies the optimization problem for joint precoding design in a multi-antenna downlink channel using relaying. We formulate the joint source and relay precoding design by aiming at sum capacity maximization. Since this problem is in general nonconvex, we first convert this problem into standard convex quadratic programs, and then propose an iterative joint precoding optimization algorithm by utilizing efficient quadratic programming approaches. We observe that the iterative method always yields optimal precoding matrices which diagonalize the compound channel of the backward (source-to-relay) and the forward (relay-to-destination) links at high SNR regimes. Motivated by this observation, we further develop an efficient structured precoding design. Simulation results are presented to verify the effectiveness of our proposed precoding schemes.

Efficient iterative design method for cosine-modulated QMF banks

An iterative algorithm for the design of multichannel cosine-modulated quadrature mirror-image filter (QMF) banks with near-perfect reconstruction is proposed. The objective function is formulated as a quadratic function in each step whose minimum point can be obtained using a closed-form solution. This approach has high design efficiency and leads to filter banks with high stopband attenuation and low aliasing and amplitude distortions. The proposed approach is then extended to the design of multichannel cosine-modulated QMF banks with low reconstruction delays, which are often required, especially in real-time applications. Several design examples are included to demonstrate the proposed algorithms, and some comparisons are made with existing designs.