TY - CHAP

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

AU - Wei Lai, I.

AU - Zheng, Liang

AU - Lee, Chia-Han

AU - Tan, Chee Wei

PY - 2018/1

Y1 - 2018/1

N2 - In this chapter, 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 condition, a tight convex relaxation technique can relax 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. By exploiting the SIMO-MISO duality, we present an algorithm to optimally solve the sum rate maximization problem.

AB - In this chapter, 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 condition, a tight convex relaxation technique can relax 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. By exploiting the SIMO-MISO duality, we present an algorithm to optimally solve the sum rate maximization problem.

KW - Cognitive radio network

KW - Convex relaxation

KW - Karush-kuhn-tucker conditions

KW - Nonnegative matrix theory

KW - Optimization

KW - Perron-frobenius theorem

KW - Quasi-invertibility

UR - http://www.scopus.com/inward/record.url?scp=85048427033&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:85048427033

SN - 9781536130683

SP - 153

EP - 183

BT - Cognitive Radio Networks

PB - Nova Science Publisher Inc.

ER -