Randomized Algorithms for Optimal Solutions of Double-Sided QCQP With Applications in Signal Processing
Quadratically constrained quadratic programming (QCQP) with double-sided constraints has plenty of applications in signal processing as have been addressed in recent years. QCQP problems are hard to solve, in general, and they are typically approached by solving a semidefinite programming (SDP) rela...
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| Published in | IEEE transactions on signal processing Vol. 62; no. 5; pp. 1093 - 1108 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.03.2014
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1053-587X 1941-0476 |
| DOI | 10.1109/TSP.2013.2297683 |
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| Abstract | Quadratically constrained quadratic programming (QCQP) with double-sided constraints has plenty of applications in signal processing as have been addressed in recent years. QCQP problems are hard to solve, in general, and they are typically approached by solving a semidefinite programming (SDP) relaxation followed by a postprocessing procedure. Existing postprocessing schemes include Gaussian randomization to generate an approximate solution, rank reduction procedure (the so-called purification), and some specific rank-one matrix decomposition techniques to yield a globally optimal solution. In this paper, we propose several randomized postprocessing methods to output not an approximate solution but a globally optimal solution for some solvable instances of the double-sided QCQP (i.e., instances with a small number of constraints). We illustrate their applicability in robust receive beamforming, radar optimal code design, and broadcast beamforming for multiuser communications. As a byproduct, we derive an alternative (shorter) proof for the Sturm-Zhang rank-one matrix decomposition theorem. |
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| AbstractList | Quadratically constrained quadratic programming (QCQP) with double-sided constraints has plenty of applications in signal processing as have been addressed in recent years. QCQP problems are hard to solve, in general, and they are typically approached by solving a semidefinite programming (SDP) relaxation followed by a postprocessing procedure. Existing postprocessing schemes include Gaussian randomization to generate an approximate solution, rank reduction procedure (the so-called purification), and some specific rank-one matrix decomposition techniques to yield a globally optimal solution. In this paper, we propose several randomized postprocessing methods to output not an approximate solution but a globally optimal solution for some solvable instances of the double-sided QCQP (i.e., instances with a small number of constraints). We illustrate their applicability in robust receive beamforming, radar optimal code design, and broadcast beamforming for multiuser communications. As a byproduct, we derive an alternative (shorter) proof for the Sturm-Zhang rank-one matrix decomposition theorem. |
| Author | Palomar, Daniel P. Yongwei Huang |
| Author_xml | – sequence: 1 surname: Yongwei Huang fullname: Yongwei Huang email: huang@math.hkbu.edu.hk organization: Dept. of Math., Hong Kong Baptist Univ., Kowloon, China – sequence: 2 givenname: Daniel P. surname: Palomar fullname: Palomar, Daniel P. email: palomar@ust.hk organization: Dept. of Electron. & Comput. Eng., Hong Kong Univ. of Sci. & Technol., Kowloon, China |
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| Keywords | Multiple access Downlink Matrix decomposition Quadratic programming Algorithm Data broadcast Information dissemination Beam forming Optimal design Constrained optimization Robust receive beamforming Multicast Relaxation homogeneous quadratically constrained quadratic program (QCQP) Randomization multicast downlink beamforming Optimal solution Radar Signal processing Optimal code Matrix method semidefinite programming (SDP) relaxation Approximate solution optimal radar waveform |
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| SubjectTerms | Algorithms Applied sciences Approximation Array signal processing Beamforming Coding, codes Decomposition Detection, estimation, filtering, equalization, prediction Exact sciences and technology Heuristic homogeneous quadratically constrained quadratic program (QCQP) Information, signal and communications theory Interference multicast downlink beamforming optimal radar waveform Optimization Radar Reduction Robust receive beamforming Robustness semidefinite programming (SDP) relaxation Signal and communications theory Signal processing Signal processing algorithms Signal, noise Telecommunications and information theory Theorems Vectors |
| Title | Randomized Algorithms for Optimal Solutions of Double-Sided QCQP With Applications in Signal Processing |
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