Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms
Author(s)Wei, Dennis; Sestok, Charles K.; Oppenheim, Alan V.
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This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signal-to-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
IEEE Transactions on Signal Processing
Institute of Electrical and Electronics Engineers (IEEE)
Wei, Dennis, Charles K. Sestok, and Alan V. Oppenheim. “Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms.” IEEE Transactions on Signal Processing 61, no. 4 (February 2013): 857–870.
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