Hai Huyen Heidi Dam

Iterative method for the design of DFT filter Bank

Multirate adaptive filters have numerous advantages such as low computational load, fast convergence, and parallelism in the adaptation. Drawbacks when using multirate processing are mainly related to aliasing and reconstruction effects. These effects can be minimized by introducing appropriate problem formulation and employing sophisticated optimization techniques. In this paper, we propose a formulation for the design of a filter bank which controls the distortion level for each frequency component directly and minimizes the inband aliasing and the residual aliasing between different subbands. The advantage of this problem formulation is that the distortion level can be weighted for each frequency depending on the particular practical application. A new iterative algorithm is proposed to optimize simultaneously over both the analysis and the synthesis filter banks. This algorithm is shown to have a unique solution for each iteration. For a fixed distortion level, the proposed algorithm yields a significant reduction in both the inband aliasing and the residual aliasing levels compared to existing methods applied to the numerical examples.

Variable Digital Filter With Group Delay Flatness Specification or Phase Constraints

In this paper, we consider the design of finite-impulse response variable digital filters (VDFs) with variable cutoff frequency or variable fractional delay. We propose the design of VDFs with minimum integral squared error and constraints on the maximum error deviation in conjunction with flatness group delay specification or phase constraints. These specifications allow the VDFs to have approximately linear phase, especially in the passband. As these specifications are required to be satisfied for all the filters generated by the VDF with controllable spectral characteristics, the linear constraints resulting from the flatness specification are relaxed to inequality constraints. To make the optimization problem tractable for the phase constrained problem, suitable approximations are employed in the paper. The design problem is formulated as an optimization problem with a quadratic cost function and infinite number of constraints. A numerical scheme with adaptive grid step size is proposed for solving the optimization problem.

Interior point method for optimum zero-forcing beamforming with per-antenna power constraints and optimal step size

This paper proposes a new computational procedure for solving the optimal zero-forcing beamforming problem in multiple antenna channels that maximizes user achievable rate with restriction on the per-antenna element power constraints. An interior point method with optimal step size procedure is developed in which the step size for the line search in the Newton search direction is calculated exactly for each iteration. This significantly enhances the efficiency associated with the line search. Design examples show that the proposed algorithm converges rapidly to the optimal solution with low computational complexity. HighlightsThis paper proposes a new computational procedure for optimal zero-forcing beamforming problem.An optimal step size procedure is developed for the interior point method for solving the problem.Design examples show that the proposed algorithm is efficient with low complexity.

A Parallel Low Complexity Zero-Forcing Beamformer Design for Multiuser MIMO Systems Via a Regularized Dual Decomposition Method

Zero-forcing beamforming under per-antenna power constraint (PAPC) is considered in this paper, and the objective is to maximize the minimum user information rate. A parallel low complexity zero-forcing beamformer design is proposed in this paper for MU-MIMO systems by introducing a regularized dual decomposition method. The idea of this method is to solve the problem via solving its dual problem. Since the dual objective is not differentiable, a Tikhonov regularization is introduced. The regularized problem can be solved by using a gradient-based method in a parallel manner. Moreover, the optimal solution of the Lagrangian is in a closed form. The smoothness properties of the regularized dual function are investigated. We also estimate the error bound between the optimal function value of the primal problem and that of the regularized dual problem. Corresponding convergence analysis and convergence rate of the proposed algorithm are established. Computational complexity analysis is carried out to compare the complexity of the proposed method with that of state-of-the-art interior point method. Simulation results are provided to show the effectiveness of the proposed method.

A First-Order Optimal Zero-Forcing Beamformer Design for Multiuser MIMO Systems via a Regularized Dual Accelerated Gradient Method

A first-order zero-forcing beamformer design is proposed in this letter for MU-MIMO systems under per-antenna power constraints (PAPC). By forming the regularized dual problem, first-order methods can be applied. To achieve the limit convergence rate of first-order methods, an accelerated method is introduced to solve the regularized dual problem. Simulation results are provided to show the effectiveness of the proposed method.

Digital Laguerre filter design with maximum passband-to-stopband energy ratio subject to peak and Group delay constraints

In this paper, we formulate a general design of transversal filter structures with maximum relative passband-to-stopband energy ratio subject to complex frequency response constraints in the passband and the stopband as well as additional constraints such as null constraints. These null constraints are important for applications where the suppression of noise at certain frequencies are important. Additional constraints are introduced allowing approximately linear phase and constant group delay in the passband. For a given set of basis functions, the design problem can be formulated as a semi-infinite quadratic optimization problem in the filter coefficients, which are the decision variables to be optimized. In this paper, we focus on the design of digital Laguerre filter and digital finite impulse response (FIR) filter structures. A modified bridging algorithm is developed for searching for the optimum pole of the Laguerre filters. Design examples are given to demonstrate the effectiveness of the proposed algorithm.

Second-Order Blind Signal Separation for Convolutive Mixtures Using Conjugate Gradient

This letter presents a new computational procedure for the second-order gradient-based blind signal separation (BSS) problem with convolutive mixtures that has improved convergence characteristics over the steepest descent algorithm. The BSS problem is formulated as a constrained optimization problem with complex unmixing weight matrices where the constraints are formulated to overcome the permutation effects. This problem is then transformed into an unconstrained optimization problem, so that the conjugate gradient algorithm can be applied. The convergence of the proposed procedure is compared with the steepest descent algorithms in real and simulated environments.

Design of Allpass Variable Fractional Delay Filter with Powers-of-Two Coefficients

In this letter, we develop an algorithm for the design of allpass variable fractional delay filter with powers-of-two coefficients as a means of achieving low complexity and efficient hardware implementation. The algorithm includes an efficient procedure to obtain the objective function in the neighborhood of a search point, which significantly reduces the complexity associated with the global optimization approach. Design examples show that significant improvement is obtained by using the proposed method over existing methods.

Some interesting properties for zero-forcing beamforming under per-antenna power constraints in rural areas

Providing broadband services in the rural area is a challenging work. Multi-user multiple-input multiple-output (MU-MIMO) systems can be applied to increase spectral efficiency. One of the most commonly used method in MU-MIMO broadcast channel is zero-forcing beamforming (ZFBF) since it provides a good trade off between complexity and performance. In this paper, we consider the ZFBF under the per-antenna power constraints. Particularly, a deterministic line-of-sight modeling of the downlink channels is adopted. To reduce the computational complexity, we consider the problem in which all the equality constraints are eliminated. By examining the KKT optimality conditions and the properties of the channel, some interesting properties are revealed.

Variable Fractional Delay FIR Filter Design with a Bicriteria and Coefficient Relationship

This brief investigates a tradeoff between the integral squared error and the peak deviation error for a variable fractional delay (VFD) filter with a coefficient relationship. The integral squared error is minimized subject to additional constraints on the peak deviation error. The problem is solved by utilizing second-order cone programming. In addition, the performance of the VFD filter with discrete coefficients is investigated, in which the filter coefficients are expressed as the sum of power-of-two terms to reduce the filter operations to shifts and adds. Design examples show that the peak deviation error can be significantly reduced from the least squares solution while maintaining approximately the same integral squared error. Similarly, the integral squared error can be significantly reduced from the minimax solution while maintaining approximately the same peak deviation error. Furthermore, the tradeoff filters are less sensitive with respect to quantization than the least squares and minimax solutions.