TY - GEN
T1 - SDR approximation bounds for the robust multicast beamforming problem with interference temperature constraints
AU - Wu, Sissi Xiaoxiao
AU - Yue, Man Chung
AU - Man-Cho So, Anthony
AU - Ma, Wing Kin
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/16
Y1 - 2017/6/16
N2 - In this work, we consider the robust beamforming design for secondary downlink multicasting channels, where primary users are present with norm-bounded channel errors. In particular, the max-min-fair formulation is considered and the resulting design problem is a quadratically constrained quadratic program (QCQP) with a set of semi-infinite constraints, which is NP-hard in general. As a remedy, we apply the semidefinite relaxation (SDR) technique and S-lemma to approximate the problem into a tractable form. The key contribution of this paper is to study the approximation quality. Our analytical results show that, the SDR solution achieves an objective value that is at least ω(1/MN log J) times the optimal objective value, where M is the number of secondary users, J is the number of primary users, and N is the number of antennas at the secondary base station. This is a fundamentally new result for SDR applied to robust QCQPs. Practically, it provides a performance guarantee for the robust beamforming design. All these results are verified by our numerical simulations.
AB - In this work, we consider the robust beamforming design for secondary downlink multicasting channels, where primary users are present with norm-bounded channel errors. In particular, the max-min-fair formulation is considered and the resulting design problem is a quadratically constrained quadratic program (QCQP) with a set of semi-infinite constraints, which is NP-hard in general. As a remedy, we apply the semidefinite relaxation (SDR) technique and S-lemma to approximate the problem into a tractable form. The key contribution of this paper is to study the approximation quality. Our analytical results show that, the SDR solution achieves an objective value that is at least ω(1/MN log J) times the optimal objective value, where M is the number of secondary users, J is the number of primary users, and N is the number of antennas at the secondary base station. This is a fundamentally new result for SDR applied to robust QCQPs. Practically, it provides a performance guarantee for the robust beamforming design. All these results are verified by our numerical simulations.
KW - approximation bounds
KW - Robust beamforming
KW - S-lemma
KW - semidefinite relaxation (SDR)
KW - ϵ-net
UR - http://www.scopus.com/inward/record.url?scp=85023749879&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2017.7952918
DO - 10.1109/ICASSP.2017.7952918
M3 - Conference article published in proceeding or book
AN - SCOPUS:85023749879
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4054
EP - 4058
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -