Beamforming duality and algorithms for weighted sum rate maximization in cognitive radio networks

I. Wei Lai, Liang Zheng, Chia Han Lee, Chee Wei Tan

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


In this paper, we investigate the joint design of transmit beamforming and power control to maximize the weighted sum rate in the multiple-input single-output (MISO) cognitive radio network constrained by arbitrary power budgets and interference temperatures. The nonnegativity of the physical quantities, e.g., channel parameters, powers, and rates, is exploited to enable key tools in nonnegative matrix theory, such as the (linear and nonlinear) Perron-Frobenius theory, quasi-invertibility, and Friedland-Karlin inequalities, to tackle this nonconvex problem. Under certain (quasi-invertibility) sufficient conditions, we propose a tight convex relaxation technique that relaxes multiple constraints to bound the global optimal value in a systematic way. Then, a single-input multiple-output (SIMO)-MISO duality is established through a virtual dual SIMO network and Lagrange duality. This SIMO-MISO duality proved to have the zero duality gap that connects the optimality conditions of the primal MISO network and the virtual dual SIMO network. Moreover, by exploiting the SIMO-MISO duality, an algorithm is developed to optimally solve the sum rate maximization problem. Numerical examples demonstrate the computational efficiency of our algorithm, when the number of transmit antennas is large.

Original languageEnglish
Article number6913500
Pages (from-to)832-847
Number of pages16
JournalIEEE Journal on Selected Areas in Communications
Issue number5
Publication statusPublished - 2015 May 1
Externally publishedYes


  • Karush- Kuhn-Tucker conditions
  • Optimization
  • Perron-Frobenius theorem
  • cognitive radio network
  • convex relaxation
  • nonnegative matrix theory
  • quasi-invertibility

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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