Probabilistic constrained multicast beamforming in cognitive relay systems

Shengyu Li,Xiaomei Lu,Wenjun Xu,Jiaru Lin

doi:10.1186/s13638-015-0253-1

Abstract

AbstractIn this paper, multicast beamforming in cognitive relay systems is investigated with the consideration of imperfect channel state information at the transmitter (CSIT). We focus at the design of the optimal signal forwarding matrix at the cognitive relay in both centralized relay mode (CRM) and distributed relay mode (DRM). The problem is formulated aiming at minimizing the total consumed power at the relay node with suitable QoS guarantee for secondary users and strict interference control for primary users. Due to the uncertainty of transmission channel gains, constraints for QoS guarantee and interference control cannot be expressed in closed forms, making it extremely difficult to solve the problem directly. To circumvent this, we first employ the Bernstein-type inequality to convert the probabilistic constraints into closed-form expressions and then present both the semi-definite relaxation (SDR) algorithm and the penalty function (PenFun) algorithm to accomplish the non-convex problem optimization. Simulation results show that CRM is more resource efficient than DRM, and the PenFun algorithm can achieve a much better solution than the SDR algorithm at the cost of complexity. Meanwhile, compared with existing schemes which do not consider the CSIT error, the proposed schemes can support a much lower outage probability and enjoy perfect interference control for primary users.

Highlights

1 Introduction In recent years, along with the development of wireless communication technologies and the proliferation of multimedia services, multicast transmission has become an indispensable part of mobile communication systems, e.g., Multimedia Broadcast/Multicast Service (MBMS) in 3GPP [1], Broadcast and Multicast Service (BCMCS) in 3GPP2 [2], and Multicast and Broadcast Service (MBS) in IEEE 802.16 [3]
For distributed relay mode (DRM), we employ the Bernstein-type inequality to transform the probabilistic constraints into closed-form expressions and utilize the semi-definite relaxation (SDR)/penalty function (PenFun) method to optimize the diagonal vector
For centralized relay mode (CRM), we first derive the optimal structure of the forwarding matrix and jointly exploit the Bernsteintype inequality and the PenFun method to solve the transformed problem

Summary

Introduction

Along with the development of wireless communication technologies and the proliferation of multimedia services, multicast transmission has become an indispensable part of mobile communication systems, e.g., Multimedia Broadcast/Multicast Service (MBMS) in 3GPP [1], Broadcast and Multicast Service (BCMCS) in 3GPP2 [2], and Multicast and Broadcast Service (MBS) in IEEE 802.16 [3]. The CR technology and the cooperative multicast are jointly considered, and the multicast beamforming problem in cognitive relay systems is investigated. We pay attention to the design of the optimal multicast signal forwarding matrix at the multiantenna cognitive relay. Different from the model of perfect CSIT feedback, constraints for the SINR guarantee and the interference control are in probabilistic forms, instead of closed forms. This characteristic makes it difficult to solve the formulated problem as we cannot compute the probability directly. In CRM, we first prove that the optimal forwarding matrix is the combination of a matched-filter receiver and an adaptive beamformer and jointly exploit the Bernstein-type inequality and the PenFun method to accomplish the adaptive beamformer design

Notation

Imperfect CSIT feedback model

Detailed algorithm design

Conclusion