Power Control for Underlay Cognitive Radio Networks with Full-duplex Transmissions by Ningkai Tang A thesis submitted to the Graduate Faculty of Auburn University in partial fulfillment of the requirements for the Degree of Master of Science Auburn, Alabama May 4, 2014 Keywords: Full-duplex Transmissions, Cognitive Radio, PID Controller Copyright 2014 by Ningkai Tang Approved by Shiwen Mao, Chair, McWane Associate Professor of Electrical and Computer Engineering Prathima Agrawal, Ginn Distinguished Professor of Electrical and Computer Engineering John Hung, Professor of Electrical and Computer Engineering Jitendra Tugnait, James B. Davis and Alumni Professor of Electrical and Computer Engineering Abstract Radio communication, one of core contents in wireless communication, is facing a great crisis of running out of resource. Unlike other energy crisis which can be solved by using all kinds of alternative energy, the only resource of radio communication is channel, in another word, spectrum. Rather than sticking on trying to achieve the rest one percent of capacity, more and more scholars start to realize that methods reuse the existing available channel such as cognitive radio and full-duplex transmission lead a much brighter future. Both cognitive radio (CR) and full duplex transmissions are effective means to enhance spectrum efficiency and network capacity. In this paper, we investigate the problem of power control in an underlay CR network where the CR nodes are capable of full-duplex (FD) transmissions. The objective is to guarantee the required quality of service (QoS) in the form of a minimum signal-to-interference-plus-noise (SINR) ratio at each CR user and keep the interference to primary users below a prescribed threshold. We design an effective distributed power control scheme that integrates a proportional-integral-derivative (PID) controller and a power constraint mechanism to achieve the above goals. We analyze the stability performance of the proposed scheme and develop a hybrid scheme that can switch between FD and half duplex modes. The proposed schemes are validated with extensive simulations. ii Acknowledgments In the beginning, I would like to express my deepest thanks to my committee chair and advisor Dr. Shiwen Mao, who has guided me over wireless communication area throughout my master life and inspired me of this idea. Without his support, I could have no chance to learn so much knowledge, not to mention to behave like a real researcher. I also would like to thank all the other committee members of mine. Dr. Prathima Agrawal has introduced a lot of new knowledge to me in her seminar; Dr. John Hung has shown me the basic concept of control theory which is very crucial to my thesis; And Dr. Jitendra Tugnait has get me through with lots of stochastic and channel problems. Sincerely thank you, for I could never have accomplished pursuing my master degree here. Then, I need to thank all the other professors who has taught me in Auburn University: Dr. Fa Dai, Dr. Bogdan Wilamowski and Dr. Chwan-Hwa Wu. Your knowledge has indeed broadened my view. Meanwhile, I need to thank Dr. Soo-Young Lee, without his help I would probably lose the opportunity to defense in time. In addition, I want to take this opportunity to appreciate the friendship and support from all my fellow colleagues in the Electrical and Computer Engineering at Auburn Uni- versity: Jing Ning, Yi Xu, Dr. Hui Zhou, Yu Wang, Zhifeng He, Zhefeng Jiang, Yu Wang (Same name), Xuyu Wang and Mingjie Feng. In addition, I want to thank our senior alumni Dr. Yingsong Huang for the knowledge he has generously offered me during my research. Finally, I would like to thank my dear parents and wife for their understand and support all these years, I really owe you a lot. I would also like to thank my future daughter, who is my strongest motivation during these days. I love them all forever! iii This work is supported in part by the US National Science Foundation (NSF) under Grants CNS-0953513, and through the NSF I/UCRC Broadband Wireless Access & Ap- plications Center (BWAC) site at Auburn University (Grant IIP-1266036). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF. iv Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Cognitive Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Software-defined Radio . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 The Birth and Definition of Cognitive Radio . . . . . . . . . . . . . . 2 1.1.3 Interoperability and Dynamic Spectrum Access . . . . . . . . . . . . 3 1.2 Full-duplex Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1 Definition of Full-duplex Wireless Transmission . . . . . . . . . . . . 9 1.2.2 Problem and Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Motivation for Our Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Background and Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 System Model and Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 15 2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Terms and Parameter Definition . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.1 Signal-to-Interference-plus-Noise Ratio . . . . . . . . . . . . . . . . . 17 2.2.2 Additive White Gaussian Noise Channel . . . . . . . . . . . . . . . . 17 2.2.3 Channel Capacity and Transmission Rate . . . . . . . . . . . . . . . . 17 2.2.4 Fading Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.5 Self-Interference Suppression Factor . . . . . . . . . . . . . . . . . . . 18 2.2.6 Mode Tuning Threshold . . . . . . . . . . . . . . . . . . . . . . . . . 18 v 2.3 Problem Statement and Equations . . . . . . . . . . . . . . . . . . . . . . . 18 3 Power Adjustment Schemes and System Analysis . . . . . . . . . . . . . . . . . 23 3.1 PID Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Power Adjustment Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Analysis of Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4 HD-FD Tuning Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4 Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.1 Simulation Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Control Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3 Throughput Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 vi List of Figures 1.1 SDR product [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Safety teams with different standard or operating frequency [22] . . . . . . . . . 4 1.3 Platform for inter-radio system switching with CR [10] . . . . . . . . . . . . . . 5 1.4 Frequency allocation charts for the United States [18] . . . . . . . . . . . . . . . 6 1.5 Spectrum measurement across the 928 to 948 MHz band on June 19, 2008 (Worcester, MA, USA) [22] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Full-duplex wireless transmission . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.7 Half-duplex wireless transmission . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.8 SIS design proposed in Mayank Jain et. al . . . . . . . . . . . . . . . . . . . . . 12 2.1 An FD underlay CR network considered in this paper. . . . . . . . . . . . . . . 16 3.1 The PID controller design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 System control block diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.1 Distribution of the TRs and DPs in the 100?100 network. . . . . . . . . . . . . 32 4.2 Evolution of the SINR at TR5 when ? = 0.1 and ? = 0.00005. . . . . . . . . . . 33 4.3 Evolution of the transmit power at TR5 when ? = 0.1 and ? = 0.00005. . . . . . 33 vii 4.4 Power adjustment u5(t) = min{z5(t),c5(t)} of TR5 when ? = 0.1 and ? = 0.00005. 34 4.5 PID controller adjustments z5(t) when ? = 0.1 and ? = 0.00005. . . . . . . . . . 35 4.6 PU protection constraint adjustments c5(t) when ? = 0.1 and ? = 0.00005. . . . 35 4.7 Maximum measured interference among all the DPs when ? = 0.1 and ? = 0.00005. 36 4.8 Maximum measured interference among all the DPs when ? = 0.3 and ? = 0.00005. 37 4.9 Evolution of the SINR at TR5 when ? = 0.3 and ? = 0.00005. . . . . . . . . . . 37 4.10 Evolution of the SINR at TR5 under varying ?. . . . . . . . . . . . . . . . . . . 39 4.11 Evolution of the SINR at TR5 under varying ?. . . . . . . . . . . . . . . . . . . 39 4.12 Maximum measured interference among all the DPs under varying ?. . . . . . . 40 4.13 Distribution of the TRs and DPs in the 1000?1000 network. . . . . . . . . . . . 40 4.14 Average throughput of the FD, HD, and hybrid modes for different values of ?. 41 4.15 Average throughput of the FD, HD, and hybrid modes for different values of ?2. 42 viii List of Tables 4.1 Setting of ?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 ix Chapter 1 Introduction 1.1 Cognitive Radio In recent years, an unprecedented increase in wireless data has been observed, largely due to the proliferation of smartphones, tablets and other wireless devices. The exploding wireless data calls for effective technologies for enhancing spectrum utilization and wireless network capacity. To this end, cognitive radios (CR) have been recognized as one of the key technologies to meet this grand challenge on wireless network capacity. As an effective means of sharing spectrum among licensed (i.e., primary) users (PU) and unlicensed (i.e., secondary) users (SU), CR has been demonstrated to achieve high utilization of the scarce spectrum resource [23,24]. Due to the rapidly running out of spectrum over available frequency in communication, CR has become a promising solution to reuse frequency resource. CR was motivated by recent spectrum measurements by the Federal Communication Commission (FCC), where temporal and geographical variations in the utilization of assigned spectrum are found to range from 15% to 85%, and a significant amount of the spectrum remains unutilized. A CR is an advanced radio device that enables dynamic spectrum access (DSA). It represents a paradigm change in spectrum regulation and access, from exclusive use by primary users to shared spectrum and dynamic access for secondary users, to enhance spectrum utilization and achieve high throughput capacity. CR has profound impact on how future wireless networks will be designed and operated and has become one of the suggested key concept of 5G criterion. 1 Figure 1.1: SDR product [2] 1.1.1 Software-defined Radio Before saying something about CR, we need to acquire the concept about one of its key predecessor technology software-defined radio (SDR) first. With the development of wireless communication and microelectronics technology, SDR has been officially introduced to the public in 1991. With its presence, it is defined as ?A radio platform of which the functionality is at least partially controlled or implemented in software? [22]. According to the definition, if certain kind of waveform has been saved in the memory of SDR product, it should be able to be employed on any frequency. Thanks to the industriousness of manufactures, the hardware needed for SDR has be- coming quite affordable for commercial use. This also induced more attention about this technology and caused a virtuous cycle. Nowadays, SDR product like what is shown in Fig. 1.1 is quite common to see and benefits a lot of ensuing works. 1.1.2 The Birth and Definition of Cognitive Radio Joseph Mitola III [1], who is now a professor at Stevens Institute of Technology, is well known as the father of CR technology. In 2000 he finished his doctoral defense with 2 dissertation ?Cognitive radio?An integrated agent architecture for software defined radio? and defined CR for the first time. At first, CR is seen as a ?intersection of personal wireless technology and computational intelligence? and should be defined as ?A really smart radio that would be self-aware, RF- aware, user-aware, and that would include language technology and machine vision along with a lot of high-fidelity knowledge of the radio environment?. However, just like Hamlet in eys of different people, this definition is too large for a single technology and has caused various understandings. In ?Cognitive radio: Brain-empowered wireless communication? [11], Simon Haykin redefined CR as ?an intelligent wireless communication system that is aware of its surrounding environment, and uses the methodology of understanding-by- building to learn from the environment and adapt its internal states to statistical variations in the incoming RF stimuli by making corresponding changes in certain operating parameters in real-time, with two primary objectives in mind: highly reliable communications whenever and wherever needed; efficient utilization of the radio spectrum.? To simplify the conclusion, he used six words to represent the characteristcs of CR: ?awareness, intelligence, learning, adaptivity, reliability, and efficiency?. Due to the blossom of CR research, U.S. FCC has proposed their official and strict definition of CR which is ?A Cognitive Radio is a radio that can change its transmitter parameters based on interaction with the environment in which it operates. The majority of cognitive radios will probably be SDR but neither having software nor being field pro- grammable are requirements of a cognitive radio?. From then on, this definition becomes a recognized meaning for CR. 1.1.3 Interoperability and Dynamic Spectrum Access For its all kinds of capabilities, CR has enabled a list of applications. However, the most well-known and widely used two implementations are Interoperability and DSA. 3 Figure 1.2: Safety teams with different standard or operating frequency [22] Interoperability How to understand interoperability? Let us start froma existing tragedy first: InAugust 2005, The Hurricane Katrina struck New Orlean, caused mass casualty and property loss. After the disaster, a lot of people has blamed government for reacting too slow. Not everyone knows that, but one important reason for the problem is the lacking of interoperability. The communication equipment used by local rescue teams (For instance, police and hospital) has different specifications so that they cannot cooperate with each other efficiently, like Fig. 1.2. Imagine, if they can communicate with each team smoothly, how many lives can be saved? Although set their equipments all in a united frequency at the beginning is not possible due tofeasibility andsecurity problems, we couldstill solve theproblem by benefiting from interoperability of CR. As we have discussed in the former parts, CR has the ability of adaptivity and is fully capable of dealing this. CR may reconfigure all the existing standards in a single form, thus to allow them communicating with everyone. 4 Figure 1.3: Platform for inter-radio system switching with CR [10] Interoperability even have other practical use in commercial usage. Fig. 1.3 shows the design of inter-radio system with cognitive radio system. In the figure, a cognitive radio basestation has the ability to ?translate? all kinds of wireless standards so users will be able to connect with each other even they used to be in a different network. Still fearing about phones cannot be used in a foreign country? That is an old story. Dynamic Spectrum Access Spectrum is now considered as a valuable resource in wireless communication, and re- source is always accompanied with allocation problem. International Telecommunication Union (ITU) has provided a general plan for global spectral use and FCC is in charge of regulating spectrum use in the U.S.. As shown in Fig. 1.4, spectrum is allocated mostly for licensed users. Licensed user pays considerable money for occupying certain band in order to guarantee their QoS. 5 Figure 1.4: Frequency allocation charts for the United States [18] 6 Figure 1.5: Spectrum measurement across the 928 to 948 MHz band on June 19, 2008 (Worcester, MA, USA) [22] As we all know, spectrum is limited, with most of the spectrum occupied by licensed user, the usage of radio communication seems to be ?dead? too. However, the efficiency of the current allocation mechanism has been challenged by more and more surveys. As a matter of fact, these surveys indicate considerable waste in the usage of licensed spectrum, like Fig. 1.5. Frequency around 800Hz is usually seen as one the best range since it is both good for wall-piercing and transmission. Knowing the value of such spectrum forces people rethink about current allocation. Upholding the idea of saving and basing on the possible technology, FCC prompts the concept of DSA. DSA encourage unlicensed user to ?borrow? spectrum from licensed users. Quite obvious, the CR platform is facing two problems here: The needing of being environmentally aware and the needing of rapidly reconfigurable. With the progress of CR technology, the idea of DSA which needs unlicensed user accessing to licensed spectrum while 7 protecting primary user (PU) is completely realizable. For a secondary user (SU), usually there are two approaches to accomplish such task: Overlay and underlay. In overlay approach, CR will try to find out some random, small idle bands rather than a single wode spectrum. This shows the ?aggregate?ability of overlay CR. Figuratively, overlay CR is working like pouring sand into the crevice of stones. Stones are like SUs who has filled in the space, and sand like overlay SUs can fully utilize the rest resource. The main idea of overlay CR technology is to reuse all the unused spectrum, since there is no PU using it, it should never collide with PU. In another word, it is temporarily playing the role of a PU. One representative application for overlay is opportunistic spectrum access (OSA), which usually goes hand in hand with multicarrier modulations schemes and spectrum sensing technology. Overlay may sometimes offense the right of PUs due to false spectrum sensing. Although overlay is solving the problem, it sometimes has to face the pain of lacking stability. To the opposite, underlay uses another way of thinking. While overlay is surely a great idea and is making good use of wasted spectrum, underlay is even astonishing and shows the ability of utilizing spectrum which is still in use. Rather than the sand in the crevice, underlay technology is more like the cream on a cup of Mocha. Coffee and cream stays in different layer, they never collide with each other and can stay together in peace. To achieve such characteristics, underlay technology has to apply power control technology and remain in a low interference. Underlay technology is capable of using any band due to its characteristic, however it also has problems like being unable to transmit in long distance due to low transmission power and its high frequency carrier wave. In CR networks, the most important design factor is to balance the tension between PU protection and SU spectrum access gains [23]. On one hand, the capacity of SUs should be maximized to ?squeeze? the most out of the spectrum. On the other hand, the adverse impact to PUs, resulting from sharing spectrum with SUs, should be kept below a tolerable level. Obviously, these are two conflicting goals that should be balanced in the design of CR networks. In the so-called overlay CR networks, PU protection is achieved by spectrum 8 Figure 1.6: Full-duplex wireless transmission sensing and spectrum access only when the PUs are sensed absent [23]. In the so-called underlay CR networks, both PU and SU transmissions coexist in the same spectrum band, and PU protection is achieved by carefully controlling the power of the SU transmitters [17]. 1.2 Full-duplex Transmission Recently, a breakthrough in wireless communications is FD transmission [5?7,14]. Tra- ditionally, wireless communications are all half duplex (HD) due to the large path loss typical in wireless transmissions. If FD transmission is allowed, the self-interference will be so strong (like the sun) and the weak received signal from a remote transmitter (like stars) will be completely overwhelmed and cannot be decoded. Recently, encouraging results have been reported on enabling FD wireless transmissions in both single link and a network set- ting [5?7,14]. The enabler of HD is the recent advances in self-interference suppression (SIS). Various effective SIS techniques have been proposed and tested, such as antenna separation [7], antenna cancellation [6], signal inversion and adaptive cancellation [14], and combined optimal antenna placement and analog cancellation [20]. In [20], the author showed a practical implementation that can suppress self-interference (SI) for up to 80 dB, which should be sufficient for many application environments [3]. 1.2.1 Definition of Full-duplex Wireless Transmission FD wireless transmission is defined as a wireless transmission which is communicating in both directions simultaneously, as shown in Fig. 1.6. 9 Figure 1.7: Half-duplex wireless transmission FD is quite common in wired communication equipments, such as Ethernet. The tech- nology is quite simple too: It simply enables connections work by making simultaneous use of two physical pairs of twisted cable, one pair for receiving packets the other is used for sending packets. However, when things come to single channel wireless network, everything has changed. 1.2.2 Problem and Ideas Until today, most wireless equipments still remains in the half-duplex (HD) age like Fig. 1.7 Unlike the wired communication, wireless has some innate problem in implementing FD on a single channel: The direction of signal cannot be guided. For a wireless equipment, the self-issued signal is always omnidirectional and will also be received by the receiver of its own, with little path loss due to extremely near distance. Meanwhile, the desired signal coming from the other equipment is nearly negligible comparing to the signal transmitted by itself. As we may all know, a signal with too low SINR could not be decoded. And that is the problem of FD on a single channel: SI adds a destructive impact on its own receiving antenna. 10 After locking on the problem, some idea to solve the problem has already emerged, and they are all classified into SIS technology. Radio Frequency Cancellation Radio Frequency (RF) cancellation is a chip based SIS method [19]. Since we must know transmitted signal and received signals. So we could use them as inputs and take the difference of the received signal with the SI (the transmitted signal) as the output. By changing the amplitude and phase of the interference reference signal we can try to match the interference in the received signal. An RF splitter is also used to give the transmit signal to the cancellation circuit as the interference reference. Digital Cancellation Digital cancellation is another key technology for SIS. As for now, there are two well- known way for digital cancellation. First one is decode and cancellation. The transmitted packets are all marked with special symbol first. After receiving the original signal, the receiver decodes it, pick out all interference packets and then the packets are clean. The other digital cancellation is called coherent detection, which use a detector to correlates the incoming signal with the transmitted signal. Since the detector have full knowledge about the transmitted signal, it is capable to estimate the delay and phase shift of the received signal, so it can use the transmit signal to correlate with the interference. The second method need no modulation of the signal and is backwards compatible so this technique is somehow seen as a better one. Antenna Cancellation Antenna cancellation is maybe the most important technique of the three because it re- ally has shown a significant ability in SIS. The idea of this method is using pairs of transmit- ters to destroy their effect on the receiver. As we all know, radio is a kind of electromagnetic 11 Figure 1.8: SIS design proposed in Mayank Jain et. al wave and it has crest and trough, so by properly placed we can add crest with trough on the receiver?s location so they will cancel each other. Although efficient, antenna cancellation is usually deployed together with other two method to ensure a better result, like the design in 1.8. 1.3 Motivation for Our Work The high potential of FD has attracted substantial interest. However, the mainstream FD research nowadays has only focused on feasible physical layer techniques or the per- formance analysis for certain utilization. Although some advances have been made, the important problem of guaranteeing overall system performance is yet to be studied. Since the compelling objective of FD transmission for fully utilizing the limited resource of wire- less networks meets the core purpose of CR technique, we propose to combine FD with CR. Thus, certain problems such as ?If FD transmission could also improve the performance in CR networks under certain circumstances?? remains to be answered . Unlike HD trans- mission which mostly cares about distance as the fading parameter, FD transmission has to take more consideration of a set of much more complex data such as SI suppression factor 12 and SINR ratio. Their relationship and impact are highly important for our research, and could lead a revolution to the new communication criterion. 1.4 Background and Related Work FD transmission is a new technology to push the limit of single channel communications. In [6], the authors proposed basic concepts such as RF and digital cancellations and discusses potential MAC and network gains with full-duplexing. In [20], the authors presented the design and implementation of a real-time 64-subcarrier 10 MHz full-duplex OFDM physical layer, and demonstrated up to 80 dB SI suppression with experiments. In [14], the authors presented a full duplex radio design using signal inversion and adaptive cancellation, as well as a full duplex MAC design and evaluation results with a testbed of 5 prototype FD nodes. In [5], a MIMO FD design was presented, while FD cellular networks have been investigated in some recent papers [8,21]. CR has been recognized as an important technology for enhancing spectrum access efficiency [23,24]. In the class of overlay CR networks, SUs sense the spectrum and access the spectrum when PUs are absent. In the class of underlay CR networks, SUs coexist with PUs in the same spectrum conditioned on limited interference to the PUs. Both techniques can be transparent to PUs [23]. In a recent work [3], the authors proposed to combine FD with CRs. The FD capability can be utilized to allow current two-way transmissions for the SUs, as well as enabling SUs to transmit while sensing. Feedback control has found wide application in communication and networking systems. A modern overview of functionalities and tuning methods for PID controllers was presented in [4]. In [12], a proportional (P) controller was developed for streaming videos to stabilize the received video quality as well as the bottleneck link queue, for both homogeneous and heterogeneous video systems. A modern overview of functionalities and tuning methods for PID controllers was presented in [4]. In [9], the author presented a PID based power 13 adjustment algorithm that was later extended in [17], which developed a PID control for power control in underlay CR networks. In this paper, we investigate several control model based on single channel full duplex cognitive radio, which is different from previous work. By taking interference cancellation factor into consideration we can surely acquire a better throughput and more accurate conse- quence. This work is inspired by the recent idea about single channel full duplex transmission and has utilized the model listed in [17]. Some math proofs may come after the previous work which has been finished in [16] and [3]. 14 Chapter 2 System Model and Problem Formulation 2.1 System Model Consider an underlay CR network as illustrated in Fig. 2.1. There is a primary network with active transmissions using a licensed spectrum band. A co-located secondary network consists of (s + 1) secondary users (SU), termed TRi, i = 1,2,??? ,s + 1, where s is an odd number. The SUs are paired to form (s + 1)/2 FD transmission links, i.e., TRi is transmitting to, and simultaneously receiving from TRi+1, while i is an odd index. Due to the underlay spectrum sharing policy, the SUs are allowed to use the same spectrum band as the primary network. For protection of the primary network, there are p detection points (DP) in the primary work that measure the interference from the secondary transmissions. Such interference should be kept below a threshold at the DP locations by effectively controlling the power of the secondary transmitters. In Fig. 2.1, gij denotes the channel gain from TRi to DPj; hij represents the channel gain from TRi to TRj; and ?2i is the sum of the total interference from primary transmissions and the noise power at TRi. To simplify notation, we assume channel reciprocity, i.e., hij (or gij) is equal to hji (or gji) for all i, j. For each FD link, the SI is Pi(t)h2ii, where Pi(t) is the transmit power of TRi and hii is the channel gain from TRi?s transmitting antenna to the receiving antenna. We assume that each TRi utilizes SIS, and the residual SI is reduced to ?Pi(t)h2ii, where ? is a constant in [0,1] depending on the specific SIS design. When ? = 0, it is the perfect case where the SI can be completely canceled; when ? = 1, it is the worst case without SIS and FD transmission is not possible. Usually ? is a small number, e.g., at least 45 dB across a 40 MHz band and up to 73 dB for a 10 MHz OFDM signal [14]. 15 2 s? g 1 g 2 g1 g g g g , +1 g g , +1 Detection point 1 TR1 TR2 TR TR +1 TR TR +1 h , +1 = h +1, 2 1+s? h h +1, +1 2 i? h , +1 = h +1, 2 1+i? h h +1, +1 2 1? h12 = h21 2 2? h11 h22 h 1 h 2 h h , +1 h h , +1 Detection point j Detection point p... ... Figure 2.1: An FD underlay CR network considered in this paper. 16 2.2 Terms and Parameter Definition Since this theis contains a lot of terms and parameters, this section aims to clarify the confusion for what each term or parameter stands for. 2.2.1 Signal-to-Interference-plus-Noise Ratio Signal-to-interference-plus-noise ratio, or SINR is defined as the power of a certain signal of interest divided by the sum of the interference power and the power of noise. According to the value of interference power and noise power, SINR may also stand for Signal-to- interference ratio (SIR) or Signal-to-noise ratio (SNR). In the thesis, we use ? to represent SINR. 2.2.2 Additive White Gaussian Noise Channel Additive white Gaussian noise channel, as know as AWGN channel, express a certain kind of channel model. Here, the additive noise has a uniform power across the frequency band and is normal distributed in the time domain. In the thesis, we assume the whole system is using AWGN channel. 2.2.3 Channel Capacity and Transmission Rate Channel capacity is defined as the upper bound on the rate of information that can be reliably transmitted over a communications channel. According to Shannon, the channel capacity of AWGN channel is C = Blog2(1 + SNR) (2.1) Here, B is the bandwidth of channel. 17 In the thesis, we use R to represent the transmission rate, the transmission rate is ideal rate when there is no error possibility during transmission and has been normalized with B = 1Hz. 2.2.4 Fading Distance Since wireless signal will lose power during transmission, we usually use maths model with distance to evaluate the path loss. The distance is what we call fading distance. In the thesis, we use dij or di,j to represent the fading distance. 2.2.5 Self-Interference Suppression Factor In FD technology, the transceiver is capable to suppress its own transmission signal in the receiving antenna in order to enable FD transmission. However, the transmission signal cannot be cancelled completely so we use a SIS factor to denote the capability of suppression. It is defined as the power of processed SI divided by the power of orignial SI. In the thesis, SIS factor is written as chi. 2.2.6 Mode Tuning Threshold In our design, we propose a hybrid mode which would select HD or FD mode automat- ically in order to gain optimal throughput. The factor that decide the mode selection is the mode tuning threshold. In the thesis, mode tuning threshold is represented with T. 2.3 Problem Statement and Equations For the FD CR network to work properly, two conditions should be satisfied by control- ling the transmit power of the TRj?s. The first condition is primary user protection. That is, the measured interference from secondary transmissions should be kept below a prescribed tolerance level Dj at each DPj. The second condition is guaranteeing the QoS of SUs. That 18 is, the SINR at the TRi?s should be kept above a prescribed threshold ?, such that the SUs can be guaranteed with a minimum data rate. We assume that time is slotted. To achieve these goals, in each time slot t, a centralized power control algorithm updates the transmit power of each TRi, denoted as Pi(t), according to the measured radio environment, as Pi(t+ 1) = Pi(t) + ui(t), (2.2) where ui(t) is the increment (positive or negative) of power at TRi in time slot t. We assume that the DPs can detect the interference from the SUs. For example, if the channel gains and the transmit powers from the primary transmitters are known, the DP can estimate the interference from primary transmissions. Alternatively, a quiet period as in IEEE 802.22 WRANs could be enforced for the SUs [13]. Since there is no secondary transmissions in the quiet period, the DPs can measure the interference from primary trans- missions. Once the primary interference is known, a DP can estimate secondary interference by subtracting the primary interference from the total interference it receives. As shown in Fig. 2.1, the total interference from the TRi?s to a detection point DPj is yj(t) = s+1summationdisplay k=1 Pk(t)g2kj, j = 1,2,??? ,p. (2.3) Then the primary user protection constraint becomes yj(t) ? Dj, j = 1,2,??? ,p. (2.4) For time slot t + 1, the secondary interference yj(t + 1) caused by the updated transmit powers should also satisfy (2.4), i.e., yj(t+ 1) ? Dj, j = 1,2,??? ,p. (2.5) 19 For the second constraint on guaranteeing the QoS of SUs, the SINR at the receiving antenna of TRi can be written as ?i(t) = ?? ? ?? Pi+1(t)h2i+1,isummationtext s+1 j=1,jnegationslash=i Pj(t)h 2 ji+?iPi(t)h 2 ii+? 2 i (t) , i is odd Pi?1(t)h2i?1,isummationtext s+1 j=1,jnegationslash=i Pj(t)h 2ji+?iPi(t)h2ii+?2i (t), i is even, (2.6) where ?j is the SIS factor [3]. Recall that ui(t) = Pi(t + 1) ? Pi(t). From the control point of view, (2.6) can be regarded as the state equation and ui(t) the input. The updated state is ?i(t+ 1) = ? ??? ??? ? ??? ??? ?? ?i(t) + h2i+1,iIi(t) ui(t)+ Pi(t+1)h2i+1,i[Ii(t)?Ii(t+1)] Ii(t)Ii(t+1) , i is odd ?i(t) + h2i?1,iIi(t) ui(t)+ Pi(t+1)h2i?1,i[Ii(t)?Ii(t+1)] Ii(t)Ii(t+1) , i is even, (2.7) where Ii(t) = s+1summationdisplay j=1,jnegationslash=i Pj(t)h2ji + ?iPi(t)h2ii + ?2i (t). (2.8) It is shown that generally Ii(t)?Ii(t+1) is much smaller than Ii(t)Ii(t+1) [15]. It follows that (2.7) can be approximated as ?i(t + 1) = ? ?? ?? ?i(t) + h2i,i+1Ii(t) ui(t), i is odd ?i(t) + h2i,i?1Ii(t) ui(t), i is even. (2.9) Let ? denote the minimum required SINR for SU TRi. The SU QoS constraint is ?i(t) ? ?. (2.10) 20 The updated ?i(t + 1) should also satisfy condition (2.10), i.e., ?i(t+ 1) ? ?. (2.11) Define parameters a and b as a = ?? ? ?? [ui(t) + Pi(t)]h2i+1,i, i is odd [ui(t) + Pi(t)]h2i?1,i, i is even. (2.12) b = s+1summationdisplay j=1,jnegationslash=i [uj(t) + Pj(t)]h2ji + ?i[ui(t) + Pi(t)]h2ii+ ?2i (t+ 1),i = 1,2,??? ,s + 1. (2.13) From (2.2), (2.5), and (2.11), we derive the following system of equations that can be solved for ui(t). ? ??? ? ??? ? a/b = ?, i = 1,2,??? ,s + 1 [ui(t) + Pi(t)]g2ij +summationtexts+1k=1,knegationslash=i[uk(t)+ Pk(t)]g2kj ? Dj, j = 1,2,??? ,p. (2.14) If the channel gains vary over time (e.g., in a mobile SU network), we can defined parameters a? and b? as a? = ? ?? ?? [ui(t) + Pi(t)]h2i+1,i(t+ 1),i is odd, [ui(t) + Pi(t)]h2i?1,i(t+ 1),i is even. (2.15) b? = s+1summationdisplay j=1,jnegationslash=i [uj(t) + Pj(t)]hji(t+ 1)2 + ?i[ui(t)+ Pi(t)]hii(t + 1)2 + ?2i (t + 1),i = 1,??? ,s+ 1. (2.16) 21 A similar system of equations can be solved to determine ui(t) as ? ??? ? ??? ?? a?/b? = ?,i = 1,2,??? ,s + 1 [ui(t) + Pi(t)]g2ij(t + 1) +summationtexts+1k=1,knegationslash=i[uk(t)+ Pk(t)]g2kj(t + 1) ? Dj,j = 1,2,??? ,p. (2.17) 22 Chapter 3 Power Adjustment Schemes and System Analysis In this chapter, we develop a power control scheme for adapting the transmit power of the secondary users [9]. The goal is to achieve the SU QoS requirement while satisfying PU protection constraint as given in (2.14). In the rest part of the chapter, we are going to discuss about the stability of our controller and find out our tuning point for FD and HD modes. 3.1 PID Controller Design First, we consider the SU QoS constraint, while ignoring the PU protection constraint. The goal is to drive ?i(t) to converge to the the SU QoS requirement ?, for all i. The difference between these two parameters should be considered and should be reduced as small as possible. Another consideration is that the error signal ei(t) should be related to the power Pi(t), which is the parameter that we need to determine for each TRi. Therefore Pi(t) is used as the reference input. As we can see, the ratio of ? and ?i(t) can be an indicator for the control error, and ?i(t) ? Pi(t) if all other parameters remain the same. Thus, we could use ?? i(t) Pi(t) as the feedback. The error ei(t) should be the difference of feedback and Pi(t) and we have the diagram of the PID controller as in Fig. 3.1. The PID controller collects the SINR of each TR at every time slot and uses it as feedback for the controller. For each time slot, let zi(t) denote the power increment from 23 ? 1)-?(t?  -WH.3  -W[.,   ---WHWH.' + W3L + + + +  -WH W]L + )(tPi - ? ? Figure 3.1: The PID controller design. Pi(t) to Pi(t+ 1). With feedback ?? i(t) Pi(t), the PID controller controls the system as ei(t?1) = braceleftbigg ? ?i(t?1) ?1 bracerightbigg Pi(t) (3.1) xi(t?1) = xi(t?2) + ei(t?1) (3.2) zi(t) = KPei(t?1)+ KIxi(t?1) + KD |ei(t?1)?ei(t?2)|, (3.3) where ei(t?1), xi(t?1) and |ei(t?1)?ei(t?2)| represent the proportional, integral and derivative parts, respectively; Kp, KI, and KD are the corresponding coefficients. Proper co- efficients should be designed to achieve a stable and convergent control process for adjusting the Pi(t)?s to achieve the required minimum SINR ? for each SU [4]. 24 3.2 Power Adjustment Constraint Next we take into account the PU protection constraint. The objective of this constraint is to prevent the SU transmission powers from violating the interference tolerance at the DPs. This constraint actually represents a relationship between Pi(t) and Dj, for all i and j. We first introduce the following two parameters. Dmin = min j=1,2,???,p Dj (3.4) ymax(t?1) = max j=1,2,???,p yj(t?1). (3.5) Dmin is the minimum tolerance value among all the DPs, and ymax(t) is the maximum measured interference among all DPs. Since Dmin is a constant and ymax(t?1) ? Pi(t?1), the additional power constraint should also be proportional Pi(t ? 1). We follow a similar approach as in prior work [17] to introduce the following additional constraint on the power adjustment zi(t). ci(t) = ?(t)Pi(t?1)?Pi(t), (3.6) where, ?(t) = Dminy max(t?1) . (3.7) According to (3.6) and (3.7), once the maximum interference ymax(t ? 1) exceeds the minimum tolerance Dmin, the constraint will reduce the transmit power with a proportion of ?(t), which will drive the maximum interference back to Dmin. Eqn. (3.6) enforces an additional constraint to the power increment zi(t) for the SUs, so as to satisfy the PU protection constraint as given in (2.4). Because the PU protection is a fundamental condition for spectrum sharing, the the constraint ci(t) cannot be exceeded. 25 TR TR +1 ConstraintConstraintConstraintonstraint PID ConstraintConstraintConstraintonstraint PID 2 i? p ( )h +1 =1, ? 2 1+i? p ( )h , +1 +1 =1, ? +1 -- ? ++ ? ( ? 1) ? + 1 ( ? 1) z ( ) z +1( ) u ( ) ++ P ( +1) P ( ) ++ P +1( +1) P +1( ) DP1 g1 g1, +1 DP g g , +1 DP g g , +1 , u +1( ) Figure 3.2: System control block diagram. Therefore, we have the final allowed power increment ui(t) in time slot t for TRi as ui(t) = min{zi(t),ci(t)}, i = 1,2,??? ,s + 1. (3.8) With such adjustment, the transmit power can be limited in a safe range that does not lead to severe interference to the primary network, while trying to achieve the minimum required SINR for the SUs. The overall diagram of the proposed power controller is illustrated in Fig. 3.2. 26 3.3 Analysis of Stability It is important to analyze the stability performance of the proposed power control scheme. The stability of the PID controller (i.e., without considering FD and the PU pro- tection constraint (3.6)) has been studied in [9]. The stability of the overall scheme depends on the parameter settings. In the following, we examine two cases when each of the two constraints, i.e., zi(t) and ci(t), becomes the dominant factor at the beginning stage. Case I: zi(t) > ci(t) Initially From (3.1), (3.2) and (3.3), we have Pi(0) = Pi(1) = Pi(2), and xi(0) = ei(0) = 0 for the initial time slots. There is no power adjustment in the first time slot, and the first power adjustment occurs at t = 2, as zi(2) = (KP + KI + KD)ei(1). (3.9) If zi(2) > ci(2), from (3.8) we have ui(2) = ci(2) and ?? ? ?? Pi(3) = ?(2)Pi(1) Pi(4) = ?(3)Pi(2). (3.10) After the power adjustment in time slot 2, the detected total SU interference at DP j in time slot 3 is yj(3) = s+1summationdisplay i=1 Pi(3)g2ij = s+1summationdisplay i=1 ?(2)Pi(1)g2ij = Dminy max(1) s+1summationdisplay i=1 Pi(1)g2ij. 27 The maximum measured interference among all the DPs is ymax(3) = max j=1,???,p yj(3) = Dminy max(1) max j=1,???,p s+1summationdisplay i=1 Pi(1)g2ij = Dminy max(1) ymax(1) = Dmin. (3.11) Therefore the maximum measured interference will remain at Dmin and the constraint ci(t) will remain at 0 starting from time slot 3. According to (3.8), ui(t) will also remain at 0 after time slot 3. All the transmit powers converge to the steady value and the primary goal of PU protection is satisfied. However, there is no guarantee that the target SU QoS requirement can be achieved by the converged TR powers. If ?i(3) < ?, the SU QoS requirement cannot be satisfied since the transmit powers cannot be adjusted anymore. If zi(t) remains non-negative, ui(t) will always be 0 since ci(t) = 0 for all t ? 3. All the TR powers will remain the same and the maximum measured interference remains at Dmin. Otherwise, if zi(t) < 0 due to some disturbance, the TRi power will be reduced with zi(t), until the target SINR ? is reached. However, if the above two situations both happens during the control process, we can predict that there will be oscillation and the system will enter a bounded oscillation state. Therefore, the system can be called bounded-in-bounded- out (BIBO) stable. In summary, for all the three cases discussed above, the system will be stabilized by the proposed power control scheme. Case II: zi(t) < ci(t) Initially On the other hand, if the control function is initially dominated by the PID controller adjustment zi(t), the pattern changes. If the transmit powers to achieve the desired SINR cause a smaller measured interference than the Dj?s, that is, if the primary network has high interference tolerance Dj?s, the additional constrain enforced by ci(t) can be ignored, and the power control will become a stable PID control process. The stability of such a system has been demonstrated in [9]. 28 However, if the desired SINR ? cannot be achieved due to a small Dmin, the PU pro- tection constraint will take over the control during the process and will drive the TR powers to the maximum allowed value. The other situation is that due to the impact of some disturbance, the control process may enter the same BIBO state as discussed in Section 3.3. 3.4 HD-FD Tuning Point Recall that the SIS factor ? depends on the particular SIS design and is a small value in [0,1]. Clearly, ?, along with other network dynamics such as the channel gains, the number and locations of SUs and DPs, and the prescribed control goals (i.e., ? and Dj?s), all have big impact on the system performance. So in a practical underlay CR network, it is not true that FD transmissions will always achieve a better performance; when ? is large, the residual SI will be so large that HD transmissions will be a better choice. Therefore, a hybrid scheme that can switch between FD and HD modes depending on the system parameters and states would be highly desirable. In the following, we investigate the condition under which a switching between HD and FD modes should be made. We use Shannon?s capacity to approximate the throughput of an SU, i.e., C = Blog2(1+ SINR). Since bandwidth B is a constant for all SUs, we use the spectrum efficiency log2(1+ SINR) for comparing the efficiency of the two operation modes in the following. Let ?FDi and ?HDi denote the SINRs of TRi in the FD mode and HD mode, respectively. We can derive the average throughput for the SU pair in the HD mode, denoted as RHDi , as follows. RHDi = ?? ? ?? 1 2 bracketleftbiglog 2(1 + ? HD i ) + log2(1 + ? HD i+1) bracketrightbig, i is odd 1 2 bracketleftbiglog 2(1 + ? HD i ) + log2(1 + ? HD i?1) bracketrightbig, i is even, (3.12) where, ?HDi = ?? ? ?? Pi+1(t)h2i+1,isummationtext s+1 j=1,jnegationslash=i Pj(t)h 2 ji+? 2 i (t) , i is odd Pi?1(t)h2i?1,isummationtext s+1 j=1,jnegationslash=i Pj(t)h 2 ji+? 2 i (t) , i is even. (3.13) 29 In the FD mode, the throughput for the SU pair is RFDi = ? ?? ?? log2(1 + ?FDi ) + log2(1 + ?FDi+1), i is odd log2(1 + ?FDi ) + log2(1 + ?FDi?1), i is even, (3.14) where ?FDi is given in (2.6). In each time slot t, we estimate the expected throughput for each SU pair in both the FD and HD modes and decide which mode to adopt for the time slot. The cross-over point for the two modes is derived by solving the following equation. RHDi = RFDi . (3.15) It can be seen that (3.15) can be rewritten as ? ??? ??? ? ??? ??? ?? radicalBig (1+ ?HDi )(1 + ?HDi+1) = (1 + ?FDi )(1+ ?FDi+1), i is oddradicalBig (1+ ?HDi )(1 + ?HDi?1) = (1 + ?FDi )(1+ ?FDi?1), i is even. (3.16) Define a ratio T as follows. Ti = ?? ? ?? ? (1+?HDi )(1+?HDi+1) (1+?FDi )(1+?FDi+1) , i is odd? (1+?HDi )(1+?HDi?1) (1+?FDi )(1+?FDi?1) , i is even. (3.17) Thus, we have the following proposition for determining the operation mode for TRi in the hybrid scheme. Proposition 1. A TRi should operate in the HD mode if Ti ? 1, and it should operate in the FD model if Ti < 1. 30 Chapter 4 Simulation and Analysis 4.1 Simulation Configuration To evaluate the performance of the proposed power control scheme for FD underlay CR networks, we conduct extensive simulations using a MATLAB implementation. We use one network in a 100?100 area and another network in a 1000?1000 area. The outdoor channel model h = 40log10(d)+10 dB is used in all the simulations, where d is the distance between the transmitter and receiver. In each simulation, the noises powers ?2 are i.i.d. random variables evenly distributed in a fixed range, while the range may change in different simulations. As discussed, the performance of FD systems are greatly affected by ?. We choose ? = 0.00005 in most of the simulations, unless otherwise specified. There are eight TRs and four DPs in the network. The location of the TRs and DPs are shown in Fig. 4.1 and Fig. 4.13. We assume each TR can communicate with all the DPs through a control channel to obtain information about detected interference level at the DPs (i.e., ymax(t?1)). The control goals ? and Dj?s are prescribed and is known to all the TRs. Such information is used as input to the control scheme executed at each TR to adjust its transmit power. 4.2 Control Performance Analysis In this section, we evaluate the performance of the proposed controller in the FD and HD modes. First, we simulate the 100?100 network under fixed ? and fixed ?. We set ? = 0.1 and ? = 0.00005 in the simulation. Noise ?2 is uniform distributed in [1.2?10?6,2.4?10?8] W. DP?s tolerance limit is set as Dj = 5?10?10W for all j. 31 0 20 40 60 80 1000 10 20 30 40 50 60 70 80 90 100 x y TR location Location of TR5 Detection point location Figure 4.1: Distribution of the TRs and DPs in the 100?100 network. Take TR5 as an example. The evolutions of its SINR ?5(t) and transmit power P5(t) are plotted in Fig. 4.2 and Fig. 4.3, respectively. It can be seen that both the SINR and power curves quickly converge to the neighborhood of the stable values, and then fluctuate around the stable values. In Fig. 4.2, the HD SINR is slightly higher than that of HD. However this does not mean that the throughput of an FD link is lower than that of an HD link, since the FD link throughput is the sum of that of the two end TRs. In Fig. 4.3, it can be seen that a higher transmit power is used in the FD mode to overcome the residual SI in order to achieve the target SINR value ?. Due to the parameters used, in the HD mode the power adjustment of TR5 is initially dominated by the PU protection constraint (3.6), and then controlled by the SU QoS con- straint (3.3). In the FD case the control of the power adjustment is jointly done by both constraints. This can be witnessed by comparing u5(t) = min{z5(t),c5(t)}, z5(t), and c5(t) as plotted in Fig. 4.4, Fig. 4.5, and Fig. 4.6, respectively. In a few time slots the control 32 0 50 100 150 2000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Time SINR of TR5 ? FD mode HD mode Figure 4.2: Evolution of the SINR at TR5 when ? = 0.1 and ? = 0.00005. 0 50 100 150 2000 0.2 0.4 0.6 0.8 1 x 10 ?3 Time Power of TR5 (w) FD mode HD mode Figure 4.3: Evolution of the transmit power at TR5 when ? = 0.1 and ? = 0.00005. 33 0 20 40 60 80 100 120 140 160 180 200?10 ?8 ?6 ?4 ?2 0 2 4 x 10 ?4 Time Power adjustment of TR5 (W) FD mode HD mode Figure 4.4: Power adjustment u5(t) = min{z5(t),c5(t)} of TR5 when ? = 0.1 and ? = 0.00005. process u5(t) reaches the stable value 0 and achieves the optimal SINR with the given D for TR5. In Fig. 4.7, we demonstrate the PU protection performance by plotting the PU inter- ference tolerant D and the maximum measure interference at the DPs for the FD and HD modes. It can be seen that with the proposed power control scheme, the maximum DP detected interference ymax defined in (3.7) quickly drops below D after a few time slots. Therefore the PU protection goal is well achieved by the proposed power control scheme. In the meantime, the controlled power remains around 0.4 W for the FD mode and 0.2 W for the HD mode (see Fig. 4.3), which are sufficient to satisfy the required SINR ? = 0.1 for TR5, as shown in Fig. 4.2. Since the controlled power of TR5 has achieved both PU protection and SU QoS goals, the power adjustment u5(t) will stay within a narrow range around 0. Next we try a large value of ? = 0.3 in the simulation to evaluate the case of an overly high QoS requirement of the SUs that cannot be supported in the underlay CR network. That is, there is no feasible solution to satisfy both PU protection and SU QoS constraints 34 0 50 100 150 200?4 ?3 ?2 ?1 0 1 2 3 4 5 x 10 ?4 Time PID increment of TR5 (W) FD mode HD mode Figure 4.5: PID controller adjustments z5(t) when ? = 0.1 and ? = 0.00005. 0 20 40 60 80 100 120 140 160 180 200?10 ?8 ?6 ?4 ?2 0 2 4 x 10 ?4 Time PU protection increment of TR5 (W) FD mode HD mode Figure 4.6: PU protection constraint adjustments c5(t) when ? = 0.1 and ? = 0.00005. 35 0 50 100 150 2000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 x 10 ?8 Time Maximum DP detected interference (W) DP tolerance D FD mode HD mode Figure 4.7: Maximum measured interference among all the DPs when ? = 0.1 and ? = 0.00005. in this case. In this case, the power control scheme will try to achieve PU protection as a primary goal, as the prerequisite condition for spectrum sharing, and then try to maximize the SINR of the SUs as a secondary goal. The maximum DP detected interferences to PUs are plotted in Fig. 4.8 for the FD and HD modes. It can be seen that the proposed power control scheme can effectively guarantee that the interference to PUs is below the tolerance D. The achieved SINR for TR5 is also plotted for the FD and HD modes in Fig. 4.9. It can be seen that the SINR of TR5 is stabilized around 0.17 for the HD mode and 0.1 for the FD mode, although the desired SINR for TR5 is 0.3. Since the maximum allowed interference has been reached (i.e., D = 5 ? 10?10 W as in Fig. 4.8), the power of TR5 cannot be further increased to reach the target SINR level ? = 0.3. Note that although the HD mode achieves a higher SINR than the FD mode as in Fig. 4.9, this does not necessarily mean the HD throughput is higher than that of the FD model. We will examine the throughput performance in Section 4.3. 36 0 20 40 60 80 100 120 140 160 180 2000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 x 10 ?8 Time Maximum DP detected interference (W) DP tolerance D FD mode HD mode Figure 4.8: Maximum measured interference among all the DPs when ? = 0.3 and ? = 0.00005. 0 20 40 60 80 100 120 140 160 180 2000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Time SINR of TR5 ? FD mode HD mode Figure 4.9: Evolution of the SINR at TR5 when ? = 0.3 and ? = 0.00005. 37 Table 4.1: Setting of ?. Time slot (t) 1-50 51-100 101-150 151-200 Fig. 4.10 ? 0.1 0.05 0.05 0.1 Fig. 4.11 ? 0.05 0.1 0.15 0.2 Finally, we demonstrate the performance of the proposed power controller under vary- ing SU QoS requirements. In particular, we vary the SU SINR requirement ? as given in Table 4.2. In Fig. 4.10, the required SINR is with the range such that the proposed controller can achieve both PU protection and SU QoS goals. It can be seen that the SINR can be stabilized around the target SINR for the full range. In Fig. 4.11, the SINR is continuously increased, from the feasible range to the infeasible range both goals cannot be met simul- taneously. In Fig. 4.11, the HD SINR curve is controlled well and the SINR of TR5 can quickly follow ? from 0.05 to 0.2. On the other hand, the FD SINR curve cannot follow the increased ? byond 0.1, because of a larger power is required to combat the residual SI in order to achieve the same SINR, which, however, is not allowed since the primary constraint of PU protection will be violated. In Fig. 4.12, the maximum measured interference among the DPs is also plotted. It can be seen that the primary goal of PU protection is always achieved by the proposed scheme. 4.3 Throughput Performance In this section, we evaluate the achievable throughput by the proposed power control scheme. We focus on the proposed hybrid scheme in the simulations, with which the operat- ing mode for each TR is determined as given in Section 3.4. The large 1000?1000 network with eight TRs and four DPs is used in the following simulations, as shown in Fig. 4.13. In the simulation, we increase ? from 0.000005 to 0.005 with step size of 0.000005. With each ? value, we simulate the system for 200 time slots each with a random noise level, which has been shown to be sufficient long for convergence in our previous simulations. We plot 38 0 50 100 150 2000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Time SINR of TR5 ? FD mode HD mode Figure 4.10: Evolution of the SINR at TR5 under varying ?. 0 20 40 60 80 100 120 140 160 180 2000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Time SNR of TR5 ? FD mode HD mode Figure 4.11: Evolution of the SINR at TR5 under varying ?. the average throughput of the 200 time slots for each ? value in the figure for the FD, HD and hybrid schemes. 39 0 50 100 150 2000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 x 10 ?8 Time Maximum DP detected interference (W) DP tolerance D FD mode HD mode Figure 4.12: Maximum measured interference among all the DPs under varying ?. 0 200 400 600 800 10000 100 200 300 400 500 600 700 800 900 1000 x y TR location Detection point location Figure 4.13: Distribution of the TRs and DPs in the 1000?1000 network. 40 0 1 2 3 4 5 x 10?3 0 0.5 1 1.5 2 2.5 ? Average Throughput (bits/sec/Hz) FD mode HD mode Hybrid mode Figure 4.14: Average throughput of the FD, HD, and hybrid modes for different values of ?. It can be seen in Fig. 4.14 that the hybrid scheme achieves the highest throughput for the entire range of ?. In particular, when ? ? 3.43?10?4, SIS is very effective and most of the TRs operate in the FD mode. The hybrid scheme achieves the same throughput as FD, which is higher than that of HD. As ? is increased, the advantage of FD transmissions diminishes and HD begins to achieve higher throughput than FD. When 3.43?10?4 ? ? ? 1.3?10?3, some TRs operate in the FD mode and some others in the HD mode. When ? ? 1.3?10?3, all the TRs operate in the HD mode since the residual SI is so strong, there is no benefit for using FD transmissions. The proposed hybrid scheme compares the gains of FD and HD, and always chooses the better operating mode to achieve the highest throughput for the entire range of ?. Finally, we investigate the impact of noise level. In the simulation, we set ? to 0.0005 and increase the noise power ?2 from 10?6W to 10?3W. The throughput results for the three schemes are presented in Fig. 4.15. As expected, the hybrid scheme achieves the highest throughput among the three, and the throughput decreases when noise is increased 41 0 0.2 0.4 0.6 0.8 1 x 10?3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Average Noise (W) Average Throughput (bits/sec/Hz) FD mode HD mode Hybrid mode Figure 4.15: Average throughput of the FD, HD, and hybrid modes for different values of ?2. for all the three schemes. However, the influence of noise on throughput is different for the three schemes. As shown in (2.6), the FD mode has one extra interference source, i.e., the residual SI, making it less sensitive to the varying noise power. This is why the throughput of HD decreases faster than FD. The hybrid scheme can use FD instead of HD even though the ? value is larger in this simulation. The hybrid scheme always achieves the highest throughput in all the scenarios simulated. 42 Chapter 5 Conclusions and Future Work 5.1 Conclusion In this paper, we investigate the design of effective power controllers for single channel underlay CR networks, where FD transmissions are exploited to improve the network capac- ity. Taking the SIS factor into consideration, we investigate the design of a PID controller and a hybrid FD-HD scheme to achieve the dual goals of PU protection and SU QoS provi- sioning. The stability performance of the proposed scheme is analyzed and evaluated with simulations. In the previous chapters, we developed a hybrid mode power controlled transmission system over underlay CR network, which enables SUs achieving optimum throughput while remaining undetected from CR PUs. Our research includes PID controller design, network optimization, performance analysis and simulation validation. In the begining of Chapter 2 we explicitly stated our system, which is very practical in reality. In the following, we also discussed the problem, which is a underlay CR network based power control and throughput optimization quest. Then, we designed our general PID controller in Chapter 3 to control transmission power in order to gain optimal throughput. However the PID controller could not guarantee the control systems stealth ability, so we set a constraint to every power adjustment to enable such function. Then, during researching on our system, we analyzed the stability of the system. Mean- while we found simply using FD or HD mode would not provide us with optimal performance, or in another word, throughput. So we also tackled with this more challenging problem and 43 found the tuning point of the two modes. Finally we combined our former proposed system with the hybrid mode to gain a better throughput than any of the former two modes. In the end, we had lots of detailed and accurate simulations under different environments in Chapter 4. The results which has been shown by the results suggested both stability and undoubtable superior performance of our system. 5.2 Future Work Although our proposed system has already shown considerable advantages comparing to original CR network, there are still many topics to be explored which can make our system even better. For example, maybe we could design an optimization algorithm to allocate the transmission power for each SU to gain a even better, organized overall throughput; We could also do more work on the constraint, which may degrade the performance of PID controller. The optimization and the reestablishment of constraint could even be studied together to create a dynamic condition which assures better efficiency of the system. Also, certain validation may still be needed. Since we have only simulated the system using software, the real performance may not be guaranteed. Thus, further verification like testbed based hardware simulation should be performed in order to check the availability in reality. Throughout the booming development of FD hardware, testbed validation which is much more convincing should definitely be our next target. Last but not the least, our proposed system shows some potential ability of combining with other technology. For instance, relay network, which need fairness as well as optimal throughput. The problem of general optimization we?ve mentioned before could be studied together with relay network and may generate some interesting tradeoff during researching. If such kind of tasks we have listed before can be accomplished, we are sure that the system will present an even better availability and efficiency. 44 Bibliography [1] Joseph Mitola III. http://web.it.kth.se/~maguire/jmitola/. 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