PHYSICAL LAYER AND MEDIUM ACCESS CONTROL LAYER PROTOCOL DESIGN IN COGNITIVE RADIO NETWORKS CHEN QIAN NATIONAL UNIVERSITY OF SINGAPORE 2011 PHYSICAL LAYER AND MEDIUM ACCESS CONTROL LAYER PROTOCOL DESIGN IN COGNITIVE RADIO NETWORKS CHEN QIAN (M Eng., Xi’an Jiaotong University, China) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2011 Acknowledgement I would like to express my sincere gratitude and appreciation to my supervisors Professor Lawrence Wai-Choong Wong and Assoc Professor Mehul Motani for their valuable guidance and helpful technical support throughout my Ph.D course Had it not been for their advices, direction, patience and encouragement, this thesis would certainly not be possible I would like to thank Dr Ying-Chang Liang at Institute for Infocomm Research (I2 R), Agency for Science, Technology and Research (A-STAR), Dr Arumugam Nallanathan at King’s College London, and Dr Yan Xin at NEC Laboratories America, for many helpful discussions on my research work My thanks go to my colleagues in the ECE-I2 R Wireless Communications Laboratory at the Department of Electrical and Computer Engineering and Ambient Intelligence Lab at the Interactive and Digital Media Institute, and also go to the research group at I2 R A-STAR for their generous help and warm friendship during these years Last, I would like to thank my family, especially, my wife Xue Tian and my son Chen Xuesen Delmar, for their love and encouragement i Contents Acknowledgement i Contents ii Summary vii List of Figures ix List of Tables xii List of Notations xiii List of Abbreviations xiv Introduction 1.1 Spectrum Sensing Techniques 1.2 Spectrum Access Mechanisms 1.2.1 Opportunistic Spectrum Access Model 1.2.2 Spectrum Sharing Model 1.2.3 Overlay Model 1.3 Motivations and Challenges 1.4 Contributions and Organization of the Thesis 10 ii CONTENTS Existing Techniques and Literature Review 2.1 13 14 Cooperative Spectrum Sensing 15 Opportunistic Spectrum Access 16 2.2.1 Spatial OSA 17 2.2.2 Temporal OSA 17 Packet Scheduling 18 2.3.1 Guaranteed Access Model 18 2.3.2 2.4 Non-cooperative Spectrum Sensing 2.1.2 2.3 13 2.1.1 2.2 Spectrum Sensing Strategies Random Access Model 19 IEEE 802.11 MAC Protocol in WLAN and Multi-hop Networks 20 Cooperative Spectrum Sensing Strategies for Cognitive Radio Mesh Networks 24 3.1 Introduction 25 3.2 System Model 26 3.3 Cooperative Spectrum Sensing Strategies for Single-Relay Model 29 3.3.1 Overview of Non-Cooperative Spectrum Sensing Method 29 3.3.2 Performance of AR 31 3.3.3 Performance of DR 35 Cooperative Spectrum Sensing Strategies for Multi-Relay Model 36 3.4.1 AR for Multi-Relay Model 37 3.4.2 DR for Multi-Relay Model 39 3.4 3.5 Cooperative Spectrum Sensing Strategies with Known-CSI Condition 42 3.6 Simulation Results 44 3.6.1 Performance of Single-Relay Model 44 3.6.2 Performance of Multi-relay Model 47 iii CONTENTS 3.6.3 3.7 Effects of Known-CSI and Unknown-CSI Cases 49 Conclusions 50 A Two-Level MAC Protocol Strategy for Opportunistic Spectrum Access in Cognitive Radio Networks 51 4.1 Introduction 52 4.2 System Model 54 4.2.1 System Model 54 4.2.2 Spectrum Sensing method 55 4.2.3 Traffic Model and Assumptions 56 4.2.4 Spectrum Access Scheme 57 4.2.5 PU’s Activities and Performance Parameters 58 Slotted CR-ALOHA and its Performance 60 4.3.1 Slotted CR-ALOHA 60 4.3.2 Throughput Analysis 62 4.3.3 Delay Analysis 65 4.3.4 Optimal Spectrum Sensing Time 68 CR-CSMA and its Performance 68 4.4.1 CR-CSMA Protocol 68 4.4.2 Throughput Analysis 70 4.4.3 Delay Analysis 75 Simulation Results 76 4.5.1 Performance of slotted CR-ALOHA 76 4.5.2 Performance of CR-CSMA 81 4.5.3 Tradeoff between Performance and Interference 83 4.5.4 Tradeoff between Performance and Agility 84 4.5.5 Optimal Frame Length 84 4.3 4.4 4.5 iv CONTENTS 4.5.6 4.6 Effects of PU’s Activities 89 Conclusions 92 MAC Protocol Design and Performance Analysis for Multi-hop Cognitive Radio Networks 93 5.1 Introduction 94 5.2 System Model 96 5.2.1 System Model 96 5.2.2 Spectrum Sensing and PU Protection 97 5.2.3 PTS/RTS/CTS Access Mechanism 98 5.2.4 Exponential Backoff and Blocking Mechanisms 101 5.3 Queueing Model for CR-CSMA/CA 102 5.3.1 5.3.2 Markov Chain Model for Packet Transmission Probability τ 110 5.3.3 Packet Service Time Ts 113 5.3.4 Queue Empty Probability P0 122 5.3.5 Performance Metrics for G/G/1 Queueing Model 123 5.3.6 5.4 The Packet Transmission Process 102 Performance Metrics for M/G/1 Queueing Model 126 Simulation Results 126 5.4.1 5.4.2 Performance of CR-CSMA/CA for WLAN 135 5.4.3 Performance Comparisons 135 5.4.4 5.5 Performance of CR-CSMA/CA for multi-hop CRN 128 Effects of Spectrum Utilization of Primary Network 140 Conclusions 142 Conclusions and Future Work 143 6.1 Conclusions 143 6.2 Future Work 145 v CONTENTS 6.2.1 Spectrum Sensing Technique in Transmission Process 145 6.2.2 Multi-Channel Access Mechanism 145 6.2.3 Security Problem under CRN 146 6.2.4 Cross-Layer Protocol Design for CRN 146 A Appendices to Chapter 147 A.1 Proof of Theorem 3.2 147 A.2 Proof of Theorem 3.3 147 A.3 Proof of Theorem 3.4 148 B Appendices to Chapter 150 B.1 Proof of Lemma 4.1 150 B.2 Proof of Lemma 4.2 151 B.3 Proof of Lemma 4.3 151 C Appendices to Chapter 153 C.1 Derivation of B (1) and B (1) 153 C.2 Derivation of U p 154 Bibliography 168 List of Publications 170 vi Summary Cognitive radio (CR) communication technique is proposed to relieve the spectrum scarcity problem, which allows the unlicensed secondary users (SUs) to use the spectrum bands originally allocated to the licensed primary users (PUs) Generally, SUs have lower access priority and must operate in a transparent manner without interfering the PUs’ work Thus, the coexistence of SUs and PUs at the same frequency bands brings the challenges for the protocol design of the secondary network on both physical (PHY) layer and medium access control (MAC) layer In this thesis, we focus on cognitive radio networks (CRN) and aim to improve the spectrum sensing performance at the PHY layer and to solve the access contention problem at the MAC layer Thus, the performance of the secondary network is optimized, while the primary network also can be adequately protected To improve detection performance, two cooperative spectrum sensing strategies called amplify-and-relay (AR) and detect-and-relay (DR) using data fusion policy are proposed to work at the PHY layer of CR mesh networks Considering the single-relay and multi-relay models with the conditions of known and unknown channel state information (CSI), closed-form expressions of the performance metrics, e.g., false alarm probability and detection probability, are derived for each strategy Then, the comparisons between our proposed strategies and an exiting method or the non-cooperative spectrum sensing method are provided In addition, the effect of the number of relay users on detection performance is also investigated vii Summary To solve the channel access contention problem at the MAC layer, a two-level OSA strategy is proposed, and two MAC protocols called Slotted CR-ALOHA and CR-CSMA, are developed accordingly Moreover, closed-form expressions of network metrics -normalized throughput and average packet delay are derived, respectively For various frame lengths and different number of SUs, the optimal performances are analyzed Meanwhile, using the interference factor and the agility factor, the tradeoffs between the achievable performance of the secondary network and the protection effects on the primary network are studied, and the optimal frame length problem is also addressed accordingly In addition, the performance comparisons between slotted CR-ALOHA and CR-CSMA are provided, and the effects of the spectrum utilization of the primary network on the performance of the secondary network are also considered To address the problem of MAC protocol design for a multi-hop network, we consider the hidden terminal problem and the spectrum sensing technique, and then extend the traditional RTS/CTS mechanism to the PTS/RTS/CTS mechanism which involves an asynchronous spectrum sensing technique to perform detection during the process of the transmission link establishment Based on this mechanism, a new MAC protocol, namely, CR-CSMA/CA, is proposed to coordinate the channel access for the secondary network and avoid interference to the primary network Using the discrete time G/G/1 queuing model with the assumption of unsaturated network condition, the performance of CR-CSMA/CA is analyzed, and closed-form expressions of the performance metrics are also derived, viz., packet successful transmission probability, normalized throughput, average packet service time, average buffer queue size, etc In addition, the achievable performance of the secondary network are studied for both multi-hop CRN and WLAN, in consideration with the number of neighboring SUs, the offered traffic load, and the spectrum utilization of the primary network viii 5.4 Simulation Results (Fig 4.6) or CR-CSMA (Fig 4.11) for various number of SUs On the other hand, the packet delay D defined in Chapter actually refers to the packet service time Ts in this chapter Therefore, as compared Fig 5.11(e) with Fig 4.8 and Fig 4.12, we can easily verify that the average packet service time of CR-CSMA/CA outperforms that of slotted CR-ALOHA and CR-CSMA 5.4.4 Effects of Spectrum Utilization of Primary Network Now, we consider the effects of the spectrum utilization of PUs PH1 , which is equal to − PH0 , on S and T s under the assumption of a saturated network As seen in Fig 5.12(a), the normalized throughput S monotonically increases as PH0 increases This is because the channel access probability V of the SU increases and the probability that the SU is blocked decreases Therefore, larger V makes the packets of the SU have more chances to be successfully transmitted, which eventually results in the better performance of S For average packet service time T s , the curves monotonically decrease for small number of SUs or increase at the beginning phase, but later on, monotonically decreases with the increase of PH0 for large number of SUs, which are shown in Fig 5.12(b) From Eq (5.49), we know that the packet service time Ts consists of three parts: 1) the data transmission time of a successful transmission without being dropped, 2) the total deferring time during the backoff process, and 3) the total transmission time of unsuccessful attempts Obviously, the first part almost has no change with the values of PH0 Thus, at the beginning of increasing PH0 , the second part dominates the value of Ts since the interference from the neighboring SUs increases However, if PH0 continues to increase, each packet has more chance to be transmitted, thus the corresponding time cost on unsuccessful transmission attempts sharply decreases, which becomes the dominating part of Ts The above reasons clearly 140 5.4 Simulation Results 0.8 Mc = 5, M = 3, N = Mc = 9, M = 5, N = Normalized Throughput S 0.7 Mc = 17, M = 9, N = 0.6 Mc = 33, M = 17, N = Mc = 65, M = 33, N = 16 0.5 0.4 0.3 0.2 0.1 0 0.2 0.4 0.6 0.8 P H (a) S vs PH0 Average packet service time Ts (sec) Mc = 5, M = 3, N = 0.9 Mc = 9, M = 5, N = 0.8 Mc = 17, M = 9, N = 0.7 Mc = 33, M = 17, N = Mc = 65, M = 33, N = 16 0.6 0.5 0.4 0.3 0.2 0.1 0 0.2 0.4 0.6 0.8 P H (b) T s vs PH0 Figure 5.12: Effects of the spectrum utilization of the primary network on the performance of the secondary network 141 5.5 Conclusions explain the variations of T s in Fig 5.12(b) In addition, when PH0 goes to 0, the packet transmission failure is more likely due to being blocked Conversely, when PH0 goes to 1, most of the failures occur due to the collisions Therefore, we conclude that the time costs on being blocked and collisions determine the performance of Ts Generally, the predefined blocking time TB is set larger than Tsuc in order to avoid inference to the primary network, thus it is reasonable that Ts at higher PH0 would be smaller than that at lower PH0 for small M However, as M increases, Ts at higher PH0 becomes greater than that at lower PH0 since the time cost on collisions dramatically increases in this case 5.5 Conclusions In this chapter, we have proposed a new MAC protocol called CR-CSMA/CA for multi-hop CRN Using the discrete time G/G/1 queuing model with the assumption of unsaturated network condition, we have developed a framework to analyze the performance of our proposed MAC protocol, and have derived closed-form expressions of the network metrics accordingly, viz, packet successful transmission probability, normalized throughput, average packet service time, average buffer queue size, etc In addition, based on multi-hop CRN and WLAN, simulation results have been provided to evaluate the performance of CR-CSMA/CA for various number of SUs, traffic load and spectrum utilization of primary network, respectively 142 Chapter Conclusions and Future Work In this chapter, we summarize the main contributions of this thesis, and present some suggestions for the future work 6.1 Conclusions In this thesis, we have focused on the PHY and MAC protocol design and performance analysis in cognitive radio networks and aimed to improve the detection performance at the PHY layer and to solve the access contention problem at the MAC layer In addition, we have also considered the influence on performance between the secondary network and the primary network to optimize system performance of the secondary network, and meanwhile, to protect the operation of primary network In Chapter 3, we have considered the detection performance improvement problem and have proposed two cooperative spectrum sensing strategies, namely, AR and DR, using data fusion policy under a CR mesh networks The frame structure has been appropriately designed, arranging AR or DR to be performed in the spectrum sensing phase before the data transmission Based on the single-relay and multi-relay models with known-CSI and unknown-CSI conditions, we have derived 143 6.1 Conclusions closed-form expressions of the false alarm probability and the detection probability, respectively The simulation results have shown that our proposed strategies can achieve better performance as compared with the method proposed in [38, 39] and the non-cooperative (or non-relay) spectrum sensing method We also note that, given a target false alarm probability, the detection probability dramatically increases as the number of relay SUs increases, and the performance for the known-CSI case is better than that for the unknown-CSI case In Chapter 4, we have focused on the MAC protocol design for a CR WLAN A two-level OSA strategy has been proposed and two MAC protocols, namely, Slotted CR-ALOHA and CR-CSMA for CRN, are developed based on the random access model Moreover, an appropriate frame structure has been designed, and closed-form expressions of network metrics - normalized throughput and average packet delay have been derived, respectively For various frame lengths and different number of SUs, the optimal performances of SUs can be achieved at the same spectrum sensing time Using interference factor and agility factor, we have shown that there exists a tradeoff between the achieved performance of the secondary network and the protection effects on the primary network, and the optimal frame length also has been determined accordingly In addition, we have found that the performance of slotted CR-ALOHA or CR-CSMA degrades due to the activities of PUs In Chapter 5, we have considered the MAC protocol design for a mutli-hop CRN Considering the hidden terminal problem and the asynchronous spectrum sensing technique, we have developed the PTS/RTS/CTS mechanism to establish the transmission link and have proposed the blocking mechanism working together with the existing exponential backoff mechanism Based on these mechanisms, a new MAC protocol called CR-CSMA/CA has been proposed to coordinate channel access for the secondary network and avoid interference to the primary network Furthermore, using the discrete time G/G/1 queuing model with the assumption of unsaturated 144 6.2 Future Work network condition, we have developed a framework to analyze the performance of our proposed MAC protocol and have derived closed-form expressions of the performance metrics, viz., packet successful transmission probability, normalized throughput, average packet service time, average buffer queue size, etc In addition, based on multi-hop CRN and WLAN, simulation results have been provided to evaluate the performance of CR-CSMA/CA for various number of SUs, traffic load and spectrum utilization of primary network, respectively 6.2 Future Work In the future, we can extend our work to the following aspects 6.2.1 Spectrum Sensing Technique in Transmission Process In this thesis, our proposed cooperative spectrum sensing strategies are only designed to perform in a specified spectrum sensing phase before the data transmission However, if PUs suddenly wake up during the transmission phase, SUs will definitely interfere with the ongoing operation of the primary network In this case, we need to develop a spectrum sensing technique that can work in the transmission phase Whenever PUs become active, SUs should be aware of these changes in their surrounding spectrum environment and agilely vacate the channel in time 6.2.2 Multi-Channel Access Mechanism In this thesis, the proposed PHY and MAC protocols are designed only for a single channel Actually, multiple spectrum bands are available for utilization, e.g in IEEE 802.11b/g/n, there are 14 channels designated at the 2.4 GHz spaced MHz apart Therefore, we must consider the issue of how to extend the single channel MAC 145 6.2 Future Work protocol to the multi-channel case under CRN Although the existing methods [84–87] proposed for the conventional multi-channel scenario indeed give us some clues, CR still brings many difficulties for protocol design under multi-channel CRN The issues such as channel choice, channel handoff, access contention, hidden terminal problem, interference avoidance, etc, still remain to be solved in future 6.2.3 Security Problem under CRN Security problem [88–94] is an interesting research area in future work This issue arises from the fact that some intended attackers would imitate the PU’s working scheme so as to obstruct normal transmissions of SUs In this case, the SU must have the ability to distinguish these impersonators from the real PUs, regardless of whether the attacks are periodic or intermittent 6.2.4 Cross-Layer Protocol Design for CRN Combining the PHY layer, the MAC layer and the upper layers together, there will be a cross-layer design problem [95–97] to optimize the end-to-end traffic rate in CRN The entire network elements can be considered to be cognitive, therefore the network can perceive the current network states firstly, and then plan, decide and act based on the states information, as proposed in [98] The application layer users can implement this learning and decision model through the artificial intelligent (AI), expert system or some other techniques 146 Appendix A Appendices to Chapter A.1 Proof of Theorem 3.2 For bi > a0 , b0 i = 1, · · · , M , we have a0 a0 + a1 + · · · + aM > b0 + b1 + · · · + bM b0 (A.1) Since we have assumed that only Ui with the higher SNR is eligible to help U0 , Ei /Ni > E0 /N0 can be attained Now, we set that a0 = E0 +N0 , b0 = N0 = βi (Ei +Ni )gi , and bi = βi Ni gi , thus (1) the lefthand side in (A.1) is the corresponding Γ0 for AR strategy, and the righthand side refers to the non-cooperative spectrum sensing case Therefore, Theorem 3.2 is proved A.2 Proof of Theorem 3.3 From (3.42), for given the conditions Pf,i → and Pd,i → 1, we have (2) Γ0 = M i=1 N0 + E0 + N0 + M i=1 147 ˆ E θi|H1 Ei ˆ E θi|H0 Ei A.3 Proof of Theorem 3.4 = > M i=1 N0 + E0 + M i=1 N0 + N0 + E0 + N0 + Pd,i Ei Pf,i Ei M i=1 βi (Ni M i=1 βi Ni + Ei ) (1) = Γ0 , (A.2) where θi|Hj denotes Ui ’s decision results under Hj Moreover, the inequality in (A.2) holds due to Ei = βi (Ni + Ei ) which is calculated from (3.8), (3.11) and (3.22) Thus, it follows that Theorem 3.3 is proved A.3 Proof of Theorem 3.4 (1) For AR strategy with the known-CSI condition, Γ0 is attained by (3.50) (1) Γ0 = > = N0 + M i=1 M i=1 N0 + N0 + M i=1 M i=1 βi Ni + E0 + βi Ni + E0 + M i=1 N0 + N0 + E0 + N0 + M i=1 βi (Ni M i=1 βi Ni βi /d3 pi Es βi Ni M i=1 βi /d3 pi Es βi Ni + Ei ) (A.3) (1) Obviously, the last equation given in (A.3) refers to the value of Γ0 for the unknown-CSI case In a similar way, from (3.53), for given the conditions Pf,i → and Pd,i → 1, (2) Γ0 for DR strategy with known-CSI is given by M ˆ i=1 θi|H1 N0 + E0 + E (2) Γ0 = M ˆ i=1 θi|H0 N0 + E = M i=1 N0 + E0 + N0 + M i=1 Pd,i Pf,i 148 Ei Ei Ei Ei 2 2 A.3 Proof of Theorem 3.4 > M i=1 N0 + E0 + N0 + M i=1 Pd,i Ei Pf,i Ei , (A.4) (2) where the last equation denotes the value of Γ0 for the unknown-CSI case in (3.42) From the derivation process in (A.3) and (A.4), we see that Theorem 3.4 is proved 149 Appendix B Appendices to Chapter B.1 Proof of Lemma 4.1 In this case, since BP starts at time x during β and it consists of exactly k TPs, the length of this BP and UP are given by B0 |k,x = β − x + k(1 + α) + (k − 1)/M β and N N U0 |k,x = z1 −1 +(k − − (k − 1)/M ) N (1−z2 )z2 −1 /(1−z)+ (k − 1)/M N (1− N z3 )z3 −1 /(1 − z), respectively, where z1 = Z(β − x), z2 = Z(1 + α) and z3 = Z(1 + α + β) By removing the conditions of k and x, we have B0 = β β ∞ β − x + k(1 + α) + k=1 k−1 β z(1 − z)k−1 dx, M (B.1) and U0 = β + β ∞ k=1 k−1 M N N (1 − z2 )z2 −1 1−z N k − N (1 − z3 )z3 −1 z(1 − z)k−1 dx M 1−z It is easily verified that ∞ k=1 N z1 −1 + k − − ∞ k=1 z(1 − z)k−1 = 1, ∞ k=1 (B.2) kz(1 − z)k−1 = 1/z, and (k + j − 1)/M z(1 − z)k−1 = (1 − z)M −i / − (1 − z)M , therefore Eqs (4.32) and (4.33) in Lemma 4.1 hold 150 B.2 Proof of Lemma 4.2 B.2 Proof of Lemma 4.2 In a similar way, we obtain B j and U j , j = 1, · · · , M − 1, as Bj = 1+α β+j(1+α) ∞ k+j−1 x−β σ − (x − β) + k(1 + α) + β σ M β+(j−1)(1+α) k=1 ∞ k−1 · z(1 − z) + j(1 + α) − k=M −j+1 x−β σ z(1 − z)k−1 dx, σ (B.3) and Ij = 1+α β+j(1+α) ∞ β+(j−1)(1+α) k=1 ∞ k−1 · z(1 − z) N z4 −1 k+j−1 − PH0 M + k=M −j+1 + k+j−1 + k−1− M N N (1 − z2 )z2 −1 1−z N N (1 − z3 )z3 −1 1−z N PH0 N (1 − z5 )z5 −1 z(1 − z)k−1 dx, 1−z (B.4) where the variables z4 and z5 are given by z4 = Z ( (x − β)/σ σ − (x − β)) and z5 = Z (β + (j + 1)(1 + α) − (x − β)/σ σ), respectively Moreover, we note that and β+i(1+α) β+(j−1)(1+α) β+i(1+α) z N −1 β+(j−1)(1+α) dx = (1 + α)(1 − e−GV0 σ )/(GV0 σ), N N (1 − z5 )z5 −1 dx ≈ [1 + α + β + 1/(GV0 )]e−GV0 (1+α+β) − [2 + 2α + β + 1/(GV0 )]e−GV0 (2+2α+β) From (B.3) and (B.4), it follows that Lemma 4.2 is proved B.3 Proof of Lemma 4.3 The proof process is similar to Lemma B.1 and B.2 In this case, we obtain BM = 1+α β+l ∞ β + l − x + k(1 + α) + β+l−(1+α) k=1 · z(1 − z)k−1 dx, k+M −1 β M (B.5) 151 B.3 Proof of Lemma 4.3 and UM = 1+α β+l ∞ β+l−(1+α) k=1 N N z6 −1 V0 + (N − 1)(1 − z6 )z6 −2 (1 − V0 ) PH0 N k+M −1 N (1 − z2 )z2 −1 + k− + M 1−z N N (1 − z3 )z3 −1 · z(1 − z)k−1 dx 1−z k+M −1 − PH0 M (B.6) where z6 = Z(l − x + β) Solving (B.5) and (B.6), we see that (4.36) and (4.37) in Lemma 4.3 are verified 152 Appendix C Appendices to Chapter C.1 Derivation of B (1) and B (1) Taking the first-order and second-order derivatives of G(z) in (5.42), Mi (z) in (5.43) and F (z), respectively, we have † G (1) = Pb† TT b + Ps† Tsuc + Pc† TRc + Po TV t + Pi† TX , † G (1) = Pb† TT b (TT b − 1) + Ps† Tsuc (Tsuc − 1) + Pc† TRc (TRc − 1) + Po TV t (TV t − 1) TU , Ki (1) = (Wi − 1)Wi TX /2, Ki (1) = (Wi − 1)Wi G (1)/2 + TX (Wi − 2)(Wi − 1)Wi /3, F (1) = PT b (TT b + TB ) + PRf TRf + PP f TP f + PRb (TRb + TB ) + PDf TDf + PAf TAf TY , F (1) = PT b (TT b + TB )(TT b + TB − 1) + PRf TRf (TRf − 1) + PP f TP f (TP f − 1) + PRb (TRb + TB )(TRb + TB − 1) + PDf TDf (TDf − 1) + PAf TAf (TAf − 1) TV (C.1) 153 C.2 Derivation of U p Then, the first-order and second-order derivatives of Hi (z) in (5.44) are given by i Hi (z) = K0 (z) F (z)Kj (z) [F (z)K1 (z)] + W0 j=1 Wj W1 F (z) [F (z)Ki (z)] + Wi F (z) F (z)Kj (z) Wj j=0 K0 (z) F (z)Kj (z) [F (z)K1 (z)] + W0 j=1 Wj W1 F (z) [F (z)Ki (z)] + Wi F (z) +2 F (z)Kj (z) + ··· Wj j=0,j=1 i−1 i Hi (z) = i i F (z)Kj (z) + ··· Wj j=0,j=1 i−1 F (z)Kj (z) K (z) [F (z)K1 (z)] +2 Wj W0 W1 j=0 K0 (z) [F (z)K2 (z)] W0 W2 i F (z)Kj (z) Wj j=2 i F (z)Kj (z) + ··· Wj j=1,j=2 [F (z)Ki−1 (z)] [F (z)Ki (z)] +2 Wi−1 Wi F (z) i−2 F (z)Kj (z) Wj j=0 (C.2) Given z = 1, substituting (C.1) into (C.2) yields (2i+1 − 1)W0 − (i + 1) , (2i+1 − 1)W0 − (i + 1) Hi (1) = TV i(1 − Psuc )i−1 + TU (1 − Psuc )i Hi (1) = (1 − Psuc )i−1 iTY + (1 − Psuc )TX + TY i(i − 1)(1 − Psuc )i−2 + TX TY i(1 − Psuc )i−1 (2i+1 − 1)W0 − (i + 1) (22(i+1) − 1)W0 /3 − 3(2i+1 − 1)W0 + 2(i + 1) i+1 i+1 i+1 2(2 − 1)(2 − 2)W0 /3 − 2i(2 − 1)W0 + i(i + 1) + + TX (1 − Psuc )i (C.3) Therefore, taking the fist-order and second-order derivatives of B(z) in (5.45) at z = and using (C.1) and (C.3), B (1) and B (1) are obtained in (5.49) and (5.58), respectively C.2 Derivation of U p Since the length of UP is independent of the service order of arrivals in a BP, we can assume that the last-in-first-out (LIFO) discipline has been adopted Let Ci ’s be the 154 ... both physical (PHY) layer and medium access control (MAC) layer In this thesis, we focus on cognitive radio networks (CRN) and aim to improve the spectrum sensing performance at the PHY layer and. .. Sensing Strategies for Cognitive Radio Mesh Networks Chapter Cooperative Spectrum Sensing Strategies for Cognitive Radio Mesh Networks In this chapter, we consider cooperative spectrum sensing for. .. Random Access Model 19 IEEE 802.11 MAC Protocol in WLAN and Multi-hop Networks 20 Cooperative Spectrum Sensing Strategies for Cognitive Radio Mesh Networks 24 3.1 Introduction