Robust Power Allocation For OFDM

With the fast development of wireless applications,the demand on radio spectrum has been significantly increasing in recent years.Although majority of the spectrum has been assigned for various applications,a large portion of the licensed spectrum is still under-utilized,which leads to significant waste of the scarce spectrum resources.Cognitive Radio(CR)is expected to solve the spectrum scarcity problem by allowing Secondary Users(SUs)to share the licensed spectrum in a dynamic or opportunistic manner.Orthogonal Frequency Division Multiplexing(OFDM)has been widely used in CR Networks(CRNs)due to its flexibility in Power Allocation(PA)to protect Primary Users(PUs).CRNs may consist of various uncertainties,such as channel uncertainty,noise uncertainty,and interference power uncertainty.Robust PA design is thus of significant importance for OFDM-based CRNs.In previous research,the probability distribution or the region of uncertainty are typically required for robust power allocation in CRN.Once the thresholds of these parameters are not well chosen,these methods may fail to work or introduce negative effect.Furthermore,in these works,the problems are solved by the optimization theory but the inherent transient behavior of the system has not been studied,which is an important characteristic of CRN.Therefore,power allocation in CRN still has large potential to improve.On the other hand,in the area of control theory,the controller design for systems has been studied for decades and many methods for system control have been very well designed,which are mature,robust and practical.Therefore,it is promising to conduct research in allocating transmit power using control theory.In this dissertation,we conduct our research in robust power allocation in OFDM-based CRN considering the unavoidable uncertainties(channel perturbation and varying environment)and delay.In detail,a controller is designed for a dynamic model which describes the inherent transient behavior of the system based on Lyapunov stability theory and LMI.Furthermore,a robust power allocation is designed by the controller through tracking a reference target.We summarize our main contributions in this dissertation as follows:1.To design a common controller based on control theory,first,two uniformed optimal models are formulated under two different scenarios in CRN.Second,it is transformed into a distributed and static Variational Inequality(VI)model.Third,a distributed Projected Dynamic System(PDS)model based on the VI model to describe the dynamic property of the CR system is proposed for further use.Finally,a SAS from PDS model is derived after reducing the complexity of discontinuous projection operation in PDS.With this model,control theory on the basis of feed-back principle is used to handle the channel perturbations and the change of dynamic environment.2.Based on the constructed SAS,we propose a control target by considering the acceptable transmit power related to the maximum allowable interference power to protect PU,which is very important for the robust feed-back controller design to make the transmit power of SUs converge to its target.To reduce the affect from uncertainties and proctect PU away from interference,we propose three realistic tracking targets for the designed controller: 1)a transmit power target to protect Pus,2)a Signal to Interference plus Noise Ratio(SINR)target to achieve an accepted Qo S,3)a SINR target related to the maximum permissible interference power to achieve an acceptable QoS under the protection of Pus.3.According to SAS and the above designed target,we define a Lyapunov function and propose a Linear Matrix Inequality(LMI)controller to keep the first-order derivative of this function negative and realize the robust PA in the sense of convergence to the equilibrium point as fast as possible.The convergence of the designed controller is guaranteed by Lyapunov stability theorem and LMI.A total transmit power adjustment is proposed to guarantee the controller converges to the the SINR target.Under the consideration of time-varying delay,a robust controller for power allocation is obtained by adjusting the received outdated information.We evaluate our proposed algorithms in simulation environments.The simulation results demonstrate the robustness and effectiveness of our approaches in comparison with the Iterative Water Filling Algorithm(IWFA)and worst-case method.