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This paper considers the designs of the periodic window functions in the filter window banks. First, the filter window bank with the constant synthesis periodic window functions is considered. The total number of the nonzero coefficients in the impulse responses of the analysis periodic window functions is minimized subject to the near perfect reconstruction condition. This is an \begin{document}$ L_0 $\end{document} norm optimization problem. To find its solution, the \begin{document}$ L_0 $\end{document} norm optimization problem is approximated by the \begin{document}$ L_1 $\end{document} norm optimization problem. Then, the column of the constraint matrix corresponding to the element in the solution with the smallest magnitude is removed. Next, it is tested whether the feasible set corresponding to the new \begin{document}$ L_0 $\end{document} norm optimization problem is empty or not. By repeating the above procedures, a solution of the \begin{document}$ L_0 $\end{document} norm optimization problem is obtained. Second, the filter window bank with the time varying synthesis periodic window functions is considered. Likewise, the design of the periodic window functions in both the analysis periodic window functions and the synthesis periodic window functions is formulated as an \begin{document}$ L_0 $\end{document} optimization problem. However, this \begin{document}$ L_0 $\end{document} norm optimization problem is subject to a quadratic matrix inequality constraint. To find its solution, the set of the synthesis periodic window functions is initialized. Then, the set of the analysis periodic window functions is optimized based on the initialized set of the synthesis periodic window functions. Next, the set of the synthesis periodic window functions is optimized based on the found set of the analysis periodic window functions. Finally, these two procedures are iterated. It is shown that the iterative algorithm converges. A design example of a filter window bank with the constant synthesis periodic window functions and a design example of a filter window bank with the time varying synthesis periodic window functions are illustrated. It is shown that the near perfect reconstruction condition is satisfied, whereas this is not the cases for the nonuniform filter banks with the conventional samplers and the conventional block samplers.

This paper investigates the design of non-uniform cosine modulated filter bank (CMFB) with both finite precision coefficients and infinite precision coefficients. The finite precision filter bank has been designed to reduce the computational complexity related to the multiplication operations in the filter bank. Here, non-uniform filter bank (NUFB) is obtained by merging the appropriate filters of an uniform filter bank. An efficient optimization approach is developed for the design of non-uniform CMFB with infinite precision coefficients. A new procedure based on the discrete filled function is then developed to design the filter bank prototype filter with finite precision coefficients. Design examples demonstrate that the designed filter banks with both infinite precision coefficients and finite precision coefficients have low distortion and better performance when compared with other existing methods.

Compressive speech enhancement makes use of the sparseness of speech and the non-sparseness of noise in time-frequency representation to perform speech enhancement. However, reconstructing the sparsest output may not necessarily translate to a good enhanced speech signal as speech distortion may be at risk. This paper proposes a two level optimization approach to incorporate objective quality measures in compressive speech enhancement. The proposed method combines the accelerated proximal gradient approach and a global one dimensional optimization method to solve the sparse reconstruction. By incorporating objective quality measures in the optimization process, the reconstructed output is not only sparse but also maintains the highest objective quality score possible. In other words, the sparse speech reconstruction process is now quality sparse speech reconstruction. Experimental results in a compressive speech enhancement consistently show score improvement in objectives measures in different noisy environments compared to the non-optimized method. Additionally, the proposed optimization yields a higher convergence rate with a lower computational complexity compared to the existing methods.

In this paper, we consider the zero-forcing beamforming (ZFBF) under the per-antenna power constraints (PAPC). Our objective is to maximize the minimum user information rate. Traditionally, ZFBF under PAPC with a max-min performance measure can be transformed into a second order cone problem and then solved by applying the interior point method. However, it is expensive to realize this design in practice due to high computational complexity per iteration. An alternative low complexity zero-forcing beamformer design is proposed for MU-MIMO systems by applying a dual gradient method. Different from the step size rule in the literature, a backtracking line search is adopted. A numerical example is provided to show the effectiveness of the proposed method.

In this paper, we investigate a zero-forcing beamformer design with signed power-of-two coefficients for rural applications. In this design, the minimum user information rate is taken as the performance measure, while a practical system design constraint, the per-antenna power constraint, is imposed. The problem is formulated as a constrained zero-one integer programming problem. Based on a transform between two different integer spaces, the problem is transformed into an equivalent constrained integer programming problem. A global optimal two-stage design is proposed for solving the problem. In the first stage, a polynomial time quantization method is applied to obtain an initial design. In the second stage, an auxiliary function method is used to find the global optimal design. For illustration, numerical examples under several different scenarios are studied and the results are compared with those obtained by an existing method. Furthermore, the impact of the mutual interference terms in the performance measure is also studied.