TY - JOUR

T1 - Beamforming duality and algorithms for weighted sum rate maximization in cognitive radio networks

AU - Lai, I. Wei

AU - Zheng, Liang

AU - Lee, Chia Han

AU - Tan, Chee Wei

N1 - Publisher Copyright:
© 2014 IEEE.

PY - 2015/5/1

Y1 - 2015/5/1

N2 - 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.

AB - 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.

KW - Karush- Kuhn-Tucker conditions

KW - Optimization

KW - Perron-Frobenius theorem

KW - cognitive radio network

KW - convex relaxation

KW - nonnegative matrix theory

KW - quasi-invertibility

UR - http://www.scopus.com/inward/record.url?scp=84928714630&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928714630&partnerID=8YFLogxK

U2 - 10.1109/JSAC.2014.2361079

DO - 10.1109/JSAC.2014.2361079

M3 - Article

AN - SCOPUS:84928714630

SN - 0733-8716

VL - 33

SP - 832

EP - 847

JO - IEEE Journal on Selected Areas in Communications

JF - IEEE Journal on Selected Areas in Communications

IS - 5

M1 - 6913500

ER -