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Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

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3 Author(s)
Wei, D. ; Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA ; Sestok, C.K. ; Oppenheim, A.V.

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.

Published in:

Signal Processing, IEEE Transactions on  (Volume:61 ,  Issue: 4 )