We consider a robust downlink beamforming optimization problem for secondary multicast transmission in a multiple-input multiple-output (MIMO) spectrum sharing cognitive radio (CR) network. The minimization of transmit power is formulated subject to both quality-of-service (QoS) constraints on the secondary receivers and interference temperature constraints on the primary users, under the assumption of imperfect channel state information (CSI). The problem is a nonconvex quadratically constrained quadratic program (QCQP), and in general it is hard to achieve the global optimality. As a compromise, we present two randomized approximation algorithms for the problem via convex optimization techniques. Apart from the general setting of the robust beamforming problem, we identify one interesting special case, the robust problem of which can be solved efficiently. Simulation results are presented to demonstrate the performance gains of the proposed algorithms over an existing robust design.
Bibliographical noteFunding Information:
Manuscript received January 08, 2011; revised May 30, 2011 and August 24, 2011; accepted August 31, 2011. Date of publication September 22, 2011; date of current version December 16, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Min Dong. This work is supported by a General Research Fund awarded by Research Grant Council, Hong Kong (Project No. CUHK415908), a Direct Grant awarded by the Chinese University of Hong Kong (Project Code 2050489), and an RC-Start-Up Grant awarded by Hong Kong Baptist University (Project Code 38-40-064). Part of this work was presented at the Thirty-Sixth International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Prague, Czech Republic, May 22-27, 2011.
- Imperfect channel state information
- MIMO cognitive radio networks
- robust multicast beamforming
- semidefinite programming relaxation
- spectrum sharing