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.

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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 zeroforcing 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.

Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied online. In this brief, we present a formulation that allows the tradeoff between the total squared error and the maximum deviation from the desired response in the passband and stopband. With this formulation, the maximum deviation can be reduced below the least-square solution with only a slight change in the performance of the total squared error. Similarly, the total squared error can be reduced below the minmax solution with a minor change in the maximum deviation from the minmax solution.

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