Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 66, Issue 14, Pages 3824-3837Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2018.2841887
Keywords
Beamforming; l(infinity)-minimization; steering vector mismatch; alternating direction method of multipliers (ADMM); proximity operator
Categories
Funding
- National Natural Science Foundation of China [61601284, 61602317]
- Fundamental Research Funds for the Central Universities
- Natural Science Foundation of Guangdong Province [2016A030310066]
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In this paper, linearly constrained and robust l(infinity)-norm beamforming techniques are proposed for non-Gaussian signals. A conventional approach for l(infinity)-minimization needs to solve a linear programming (LP) or second-order cone programming (SOCP). However, this strategy is computationally prohibitive for big data because the existing algorithms for LP or SOCP, such as simplex method or interior point method, can only solve small or medium-scale problems. In this paper, the alternating direction method of multipliers (ADMM) is devised for large-scale l(infinity)-beamforming problems, where the core subproblems can be formulated concisely as a linearly or second-order cone constrained least squares and the proximity operator of the l(infinity)-norm in each iteration. Remarkably, a linear-time complexity algorithm is devised that efficiently computes the l(infinity)-norm proximity operator. Simulation results verify the high efficiency of the ADMM and the superiority of the l(infinity)-norm beamforming techniques over several representative beamformers, indicating that its performance can approach the optimal upper bound.
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