Contents

1. EE726 Optimization in Communication Networks-Workshop-Throughput Maximization in Cognitive NetworkKiSong LeeChungWoon Park JaeGwang Lee 2009. 12. 23.

2. Contents 01 Introduction and motivation……………………………… 3 02 System model description…………………. 4 03 Problem formulation……………………… 5 04 Algorithm/analysis/simulation results……………………… 6 05 Big picture about the chosen papers………… 12 06 Criticism and conclusion………………… 13 07 Reference……15

3. Introduction and motivation • What is Cognitive Radio?

4. Introduction and motivation • What issues are in CR network? • User detection • Spectrum sharing • Access • Resource allocation • In this report • Focus on the throughput maximization of the secondary users • Motivation • CR is quite a recent technology • To taxonomize the way of solving the optimization problem in CR

5. System model description • System model description

6. Problem formulation • Problem formulation

7. Algorithm/analysis/simulation results Opportunistic Scheduling with Reliability Guarantees in Cognitive Radio Networks [1] • System model (check points) • Distributed cognitive network • One sub channel is allocated to only one CU • Assume imperfect sensing • Assume no infinite backlog • Mobility model • PU-static • CU-mobile • Problem formulation • CNC Algorithm • Flow control • Scheduling • Theorem 1.1 and 1.2 • Prove queue stability A fixed control parameter Maximize total admitted data in queue of SU Larger queue backlog Low collision queue Maximum collision constraint with PU

8. Algorithm/analysis/simulation results Opportunistic Scheduling with Reliability Guarantees in Cognitive Radio Networks [1] • Theorem 1.3 • Prove throughput optimality by using Lyapunov function and drift • Theorem 2. • The Lyapunov drift satisfies • then, we have • Simulation results

9. Algorithm/analysis/simulation results Weighted Sum Rate Optimization for Cognitive Radio MIMO Broadcast Channels[2] • System model (check points) • Centralized cognitive network • One sub channel is shared by multiple cognitive users • Assume perfect sensing • Assume infinite backlog • Problem formulation • TX-RX signal model BS-SUi • . • SIPA Algorithm • BC-MAC duality + DIPA • BC-MAC Maximize the weighted sum rate of SU Interference Power Constraints Sum power constraint

10. Algorithm/analysis/simulation results Weighted Sum Rate Optimization for Cognitive Radio MIMO Broadcast Channels[2] • DIPA • The achievable rate MIMO MAC • Objective Function • Dual Objective Function • Equivalent to the min. problem • Subgradient algorithm • Simulation results

11. Algorithm/analysis/simulation results Exploiting Multi-Antennas for Opportunistic Spectrum Sharing in Cognitive Radio Networks [3] • System model (check points) • Centralized cognitive network • One sub channel is shared by multiple cognitive users • Assume perfect sensing • Assume infinite backlog • Problem formulation • TX-RX signal Model SU-PU&SU • Single-Antenna PU receiver • The eigenvalue decomposition of S where • D-SVD : • MIMO channel • Equivalent problem and multilevel WF solution Maximize Transmit Rate Transmit-power constraint Total interference-power constraints

12. Algorithm/analysis/simulation results Exploiting Multi-Antennas for Opportunistic Spectrum Sharing in Cognitive Radio Networks [3] • P-SVD : • MIMO Channel • Multiple Primary Antenna • Hybrid D-SVD/P-SVD • The secondary users’MIMO channel is first projected into the null space of some selected subspace of as opposed to the whole space spanned by in the P-SVD. • D-SVD algorithm to obtain transmit precoding matrix as well as power allocations. • Simulation results

13. Algorithm/analysis/simulation results Opportunistic Spectrum Access in Cognitive Radio Networks[4] • System model (check points) • Distributed cognitive network • One sub channel is shared by multiple cognitive users • Assume perfect sensing • Assume infinite backlog • K<N • The set of utilized channels for CR link i as Si • Power vector of CR link i over channels is denoted by • Pi = [Pi(1), Pi(2) ,…, Pi(K)], • Problem formulation • where Max. power constraint for CU Max. power constraint to give no disturbance to PU Price function

14. Algorithm/analysis/simulation results Opportunistic Spectrum Access in Cognitive Radio Networks[4] • Analysis • Compare Lagrangian and KKT condition of both optimal problem and proposed problem • KKT condition • Power allocation • Simulation results

15. Algorithm/analysis/simulation results Stable Throughput of Cognitive Radios With and Without Relaying Capability[5] • System model (check points) • Distributed cognitive network • One sub channel is shared by multiple cognitive users • Assume imperfect sensing • Assume no infinite backlog • Mobility model • PU-static • CU-static • Two source-destination links • Independent & stationary packet arrival process, λP,λS • Rayleigh flat-fading in each slot • Problem formulation • Analysis Stable throughput maximization of SU given PU’s average throughput Queue stability constraint Loyne’s theorem: Under the assumption that arrival and departure rates of a queuing system are stationary, if the average arrival rate λi is less than the average departure rate μi, λi < μi, then the ith queue is stable. Little’s law:L = λW

16. Algorithm/analysis/simulation results Stable Throughput of Cognitive Radios With and Without Relaying Capability[5] • Analysis (Continued) • Proposition 1 (Conditions for PS such that the PU’s queue is stable) • (Proof) • Proposition 2 (Stable throughput maximization problem with power constraint such that the queue of both PU and SU is stable) • (Proof) • - Same manner as in Proposition 1 with Little’s law • Simulation results Original system transform Dominant system Loynes’ theorem cannot be applicable Has the same stability property as the original and Loynes’ theorem can be applicable

17. Algorithm/analysis/simulation results Joint Beamforming and Power Allocation for Multiple Access Channels in Cognitive Radio Networks[6] • System model (check points) • Centralized cognitive network(performed at the BS) • One sub channel is allocated to only one CU • Assume imperfect sensing • Assume no infinite backlog • Problem formulation • TX-RX signal model SUs-BS • CML water-filling algorithm(PU1) • Lagrangian Function • KKT Conditions • Power Allocation SUi Maximize the Sum Rate of the SUs Individual peak transmission power const. Interference power constraints

18. Algorithm/analysis/simulation results Joint Beamforming and Power Allocation for Multiple Access Channels in Cognitive Radio Networks[6] • Lemma 3 : If the two inequalities, and , are satisfied simultaneously, then the globally optimal power vector must simultaneously satisfy the interference constraints given with equality. • Power allocation(KKT, Lagrargian func.) • Extended Case with N(N>2) • Recursive Decoupled Power Allocation Algorithm • Theorem 1: The optimal power allocation • Extended to Multiple PU constraints • 2 PU->generalized algorithm • Decouple the original problem • Lemma 1: The two inequalities, and ,cannot be satisfied simultaneously. • Lenmma 2: If , then p(2) is the globally optimal solution. Similarly, if , then p(2) is the globally optimal solution.

19. Algorithm/analysis/simulation results Maximizing Throughput of Cognitive Radio Networks with Limited Primary Users' Cooperation[7] • System model (check points) • Centralized cognitive network • One sub channel is allocated to only one CU • Assume perfect sensing • Assume infinite backlog • Cognitive network consists of a BS serving a set of N CPEs • SINRs at PU and CU • Problem formulation • Power controls for PU and CU • Channel assignment Binary channel assignment SINR requirement for PU

20. Algorithm/analysis/simulation results Maximizing Throughput of Cognitive Radio Networks with Limited Primary Users' Cooperation[7] • MDCA Algorithm • Distributed power control • i) Initialization : > • ii) Power updating • iii)Termination : one node approaches max. power constraint • Centralized channel assignment • the weighted bipartite graph • Prove three propositions • i) The power updating process will be terminated after a finite number of iterations, • ii) If the initial transmit and are selected as at then • iii) The SINR of each CPE increases after each power updating step. • Simulation results

21. Algorithm/analysis/simulation results Optimal and Suboptimal Power Allocation Schemes for OFDM-based Cognitive Radio Systems [8] • System model (check points) • Centralized cognitive network • One sub channel is allocated to only one CU • Assume perfect sensing • Assume infinite backlog • Mobility model • PU-static • CU-static • OFDM-based(non-orthogonal subcarriers) • Problem formulation • Analysis • Consider two interferences which are related to the spectral distance (due to non-orthogonality) • : • : Total transmission rate maximization Interference limit constraint SU PU PU SU

22. Algorithm/analysis/simulation results Optimal and Suboptimal Power Allocation Schemes for OFDM-based Cognitive Radio Systems [8] • Analysis (Continued) • Theorem: The total transmission capacity is maximized by • (Proof) • - Establish Lagrange dual problem • - Use KKT conditions • The power allocation policy above is indeed an water-filling type • More power should be allocated to the subcarrier which has relatively better channel quality and is relatively far away from the PU’s band • Simulation results

23. Big picture about the chosen papers Secondary User Throughput Maximization In CR NETWORK Opportunistic Scheduling Power Allocation Lyapunov Optimization Technique Optimization Approach in MIMO/ not MIMO Queuing Analsys Probabilistic Approach

24. Criticism and conclusion

25. References • References • Rahul Urgaonkar and Michael J. Neely, ‘Opportunistic Scheduling with Reliability Guarantees in Cognitive Radio Networks’ IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 6, JUNE 2009 • Lan Zhang, Yan Xin, and Ying-Chang Liang, ‘Weighted Sum Rate Optimization for Cognitive Radio MIMO Broadcast Channels’ IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 6, JUNE 2009 • Rui Zhang and Ying-Chang Liang, ‘Exploiting Multi-Antennas for Opportunistic Spectrum Sharing in Cognitive Radio Networks’ IEEE JOURNAL OF SELECTED TOPIC IN SIGNAL PROCESSING, VOL. 2, NO. 1, FEBRUARY 2008 • Senhua Huang Xin Liu Zhi Ding,’ Opportunistic Spectrum Access in Cognitive Radio Networks’ IEEE INFOCOM 2008 • Osvaldo Simeone, Yeheskel Bar-Ness, and Umberto Spagnolini, ‘Stable Throughput of Cognitive Radios With and Without Relaying Capability’ IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 55, NO. 12, DECEMBER 2007 • Lan Zhang, Ying-Chang Liang, and Yan Xin, ‘Joint Beamforming and Power Allocation for Multiple Access Channels in Cognitive Radio Networks’, IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 1, JANUARY 2008. • Anh Tuan Hoang, Ying-Chang Liang, Islam, M.H., ‘Maximizing Throughput of Cognitive Radio Networks with Limited Primary Users' Cooperation’, IEEE ICC 2008. • Gaurav Bansal, Md. Jahangir Hossain and Vijay K. Bhargava, ‘Optimal and Suboptimal Power Allocation Schemes for OFDM-based Cognitive Radio Systems’, IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 11, NOVEMBER 2008.