1. 111 Downlink Channel Assignment and Power Control for Cognitive Radio Networks Anh Tuan Hoang, Member, IEEE Ying-Chang Liang, Senior Member, IEEE Institute for Infocomm Research (I2R), Singapore IEEE Transactions on Wireless Communications 2008

2. 222 Outline Introduction Problem Definition Channel/Power Allocation with Global Knowledge of Active CPEs Channel/Power Allocation with Local Knowledge of Active CPEs Results Conclusions

3. 3 Cognitive Radio Networks The concept of opportunistic spectrum access allows secondary cognitive radio networks to opportunistically exploit the under-utilized spectrum The overall spectrum utilization can be improved Transmission from cognitive nodes can cause harmful interference to primary users of the spectrum Two important design criteria for cognitive radio networks maximize the spectrum utilization minimize interference caused to primary users

4. 4 Environment We consider a cognitive radio network that consists of multiple cells Within each cell, there is a base station (BS) supporting a set of customer premise equipments (CPEs) Each CPE can be either active or idle and a BS needs exactly one channel to support each active CPE The spectrum of interest is divided into a set of multiple orthogonal channels using FDMA We assume that the channel usage pattern of the PUs is fairly static over time cognitive radio network can carry out primary-user detection and thereby avoiding interfering with PU’s operation

5. 5 Goal and Constraints The objective is to maximize the number of active CPEs that can be supported, subject to the following conditions: R1: The total amount of interference caused by all cognitive transmissions to each PU must not exceed a predefined threshold. R2: For each supported CPE, the received signal to interference plus noise ratio (SINR) must be above a predefined threshold

6. 6 System Model Model K channels M primary users (PUs) N CPEs across B cells BS needs exactly one channel to support each active CPE only consider downlink scenario (BSs to CPEs) CPE is active with probability p a

7. 7 Notations

8. 8 Operational Requirements (1) SINR requirement for CPEs For a given channel c, the SINR at CPE i can be calculated by N o is the noise is the total interference caused by all primary transmissions on channel c to CPE i For reliable transmission toward CPE i can be the minimum SINR required to achieve a certain bit error rate (BER) performance at each CPE

9. 9 Operational Requirements (2) Protecting Primary Users For each PU, the total interference from all opportunistic transmissions does not exceed a predefined threshold ζ

10. 10 Joint Channel Assignment and Power Control Schemes (1) Let A be an N × K channel assignment matrix where Let P be an N × K power control matrix where

11. 11 Joint Channel Assignment and Power Control Schemes (2)

12. 12 Feasibility Check (1) Feasibility There exists a vector of positive transmit power levels such that all the SINR constraints of the m CPEs are met the interference caused to PUs operating on channel c does not exceed the acceptable threshold Because each BS can support at most one CPE on each given channel, we must have m CPEs i 1, i 2,..., i m associated with different BSs

13. 13 Feasibility Check (2) Define an m × 1 vector U c and an m × m matrix F c The SINR constraints of m CPEs i 1, i 2,..., i m can be written compactly as where I is the m × m identity matrix

14. 14 Feasibility Check (3) From the Perron-Frobenious theorem ([8], [11], [27], [28]), (7) has a positive component-wise solution P c if and only if the maximum eigenvalue of F c is less than one The Pareto-optimal transmit power vector is [ 8 ] J. Zander, “Performance of optimum transmitter power control in cellular radio systems,” IEEE Trans. Veh. Technol. 1992. [11] D. Mitra, “An asynchronous distributed algorithm for power control in cellular radio systems,” in Proc. 4th WINLAB Workshop on Third Generation Wireless Information Networks, Rutgers University, New Brunswick, NJ, Oct. 1993. [27] F. R. Gantmacher, The Theory of Matrices. Chelsea Publishing Company, 1959. [28] E. Seneta, Non-Negative Matrices. New York: John Wiley & Sons, 1973.

15. 15 Step 1 Check if the maximum eigenvalue of F c defined in (6) is less than one. If not, the assignment is not feasible otherwise, continue at Step 2 Step 2 Using (8), calculate the Pareto-optimal transmit power vector P c ∗ check if P c ∗ satisfies the constraints for protecting PUs in (3) and the maximum power constraints, i.e. P c ∗ ≤ P max If yes, conclude that the assignment is feasible and P c ∗ is the power vector to use Otherwise, the assignment is not feasible Two-step Feasibility Check Algorithm

16. 16 Channel/Power Allocation with Global Knowledge of Active CPEs (1) Without loss of generality, we assume that all N CPEs in the network are active The problem of maximizing the number of CPEs served can be formulated as the following mixed-integer linear programming (MILP)

17. 17 Channel/Power Allocation with Global Knowledge of Active CPEs (2)

18. 18 Dynamic Interference Graph Allocation (DIGA) (1) Construct interference graphs Vertex i represents CPE i Two vertices i and j will be connected by an edge if and only if CPE i and j cannot be simultaneously supported on channel c employ the Two-Step Feasibility Check to determine the existence of an edge between a pair of vertices Procedure start with no CPEs being assigned any channel allocate a channel to one CPE at a time, until either all CPEs are served, or there is no more feasible assignment At each step, construct an interference graph that represents the interference between pairs of unserved CPEs This interference graph must also take into account the aggregated interference caused by transmissions that have been allocated channels in previous steps

19. 19 Dynamic Interference Graph Allocation (DIGA) (2) At each step, given the prior channel allocation matrix A, for each unserved CPE i, we calculate its degree corresponding to channel c as follows D(i, c, A)= ∞ if it is not feasible to assign channel c to CPE i while supporting all prior assignments The feasibility can be checked using the two-step procedure If it is feasible to assign channel c to CPE i, then D(i, c, A) is the total number of unserved CPEs that can not be assigned channel c anymore when this channel is assigned to CPE i The algorithm then picks a CPE-channel pair [i ∗, c ∗ ] that minimizes D(i, c, A) and assigns channel c ∗ to CPE i ∗

20. 20 Dynamic Interference Graph Allocation (DIGA) (3)

21. 21 Other Algorithms Power Control Scheduling Algorithm (PCSA) [18] An interference graph is first constructed The problem is then converted into the problem of finding a maximum independent set of the interference graph The interference graph cannot account for the aggregated interference effect, a clean-up step is needed at the end to remove some links and make the set feasible Minimum Incremental Power Allocation (MIPA) [19] Allocate subchannels to interfering links so that their rate requirements are met while the total transmit power is minimized [18] A. Behzad and I. Rubin, “Multiple access protocol for power-controlled wireless access nets,” IEEE Trans. Mobile Comput., vol. 3, no. 4, pp.307–316, Oct.-Dec. 2004 [19] G. Kulkarni, S. Adlakha, and M. Srivastava, “Subcarrier allocation and bit loading algorithms for OFDMA-based wireless networks,” IEEE Trans. Mobile Comput 2005.

22. 22 Channel/Power Allocation with Local Knowledge of Active CPEs Assume a centralized power controller to coordinate transmit powers of all BSs to protect PUs Two-Phase Resource Allocation (TPRA) scheme Phase 1 - Global Allocation channels and transmit powers are allocated to BSs so that the interference caused to each PU is below a tolerable threshold at the same time, we aim to cover as many CPEs as possible  do not care whether a CPE is active or idle

23. 23 Phase 1 - Global Allocation (1) Intuition for allocation decision making A BS that is near any PU receiving on channel c should transmit at low power to reduce interference A BS faraway from all PUs receiving on channel c can transmit at higher power The K channels are processed one at a time For channel c, define denotes the channel gain from base station b to primary user p on channel c

24. 24 Phase 1 - Global Allocation (2) Allocation procedure Sort the base stations in the ascending order of The BSs will be processed one at a time in this order For base station b n, determine a particular CPE i n that b n should cover Given the set of CPEs being covered by base stations Let be the set of all CPEs i in the cell of b n such that is feasible on channel c Then i n is the CPE that has the weakest channel gain from b n

25. 25 Phase 1 - Global Allocation (3) After processing all BSs, using (8), determine the transmit power to serve each of these CPEs i.e. Finally, based on, determine the N × K coverage matrix C where C(i, c)=1 means CPE i can be served by the corresponding BS on channel c

26. 26 Phase 2 - Local Allocation (1) Based on the coverage matrix C obtained in Phase 1, channel allocation can be carried out within each cell, independent to what happens in the rest First, determine all active CPEs in the cell Next, form a bipartite graph represent the set of active CPEs as a set of vertices which are connected to another set of vertices representing the available channels  an edge exists between CPE i and channel c if and only if C(i, c)=1 Maximizing the number of active CPEs served is equivalent to maximizing the number of disjoint edges in the newly-formed bipartite graph This is the maximal bipartite matching problem

27. 27 Phase 2 - Local Allocation (2)

28. 28 Phase 2 - Local Allocation (3) Berge’s Theorem: A matching is maximum if and only if there is no more augmenting path Step 1: Start with the empty match For a particular match, if an edge is in the corresponding set of disjoint edges, then we say the edge is occupied, otherwise, the edge is free Step 2: Find an augmenting path for the current match The edges within the path must alternate between occupied and free The path must start and end with free edges If there is no augmenting path, the current match is maximal Step 3: Flip the augmenting path found in Step 2 Change free edges to occupied and occupied edges to free to get a better matching After flipping, the number of matches will be increased by 1 Go back to Step 2

29. 29 Square area: 1000× 1000 m 2 divided into B adjacent cells, B =4 or 9 a BS is deployed at the center of each cell Total number of CPEs: N = 100 active with probability p a = 0.1 or 0.2 PUs: M = 5 ~ 20 Channels: K = 8 Power maximum transmit power of BS: P max =50 mW noise: No = −100 dBm required SINR for each CPE: 15 dB maximum tolerable interference for each PU: −110 dBm Simulation Environment

30. 30 Performance of Different Schemes with Global Knowledge (1) p a = 0.1 p a = 0.2 4 BS

31. 31 Performance of Different Schemes with Global Knowledge (2) p a = 0.1 p a = 0.2 9 BS

32. 32 Percentage of CPEs being Covered

33. 33 Performance of Different Schemes with Local Knowledge p a = 0.1 p a = 0.2 4 BS

34. 34 Conclusions A control framework is formulated to protect primary users from excessive interference and to guarantee reliable communications for cognitive nodes Global knowledge of active subscribers is available formulate the optimization problem as a mixed-integer linear programming propose a suboptimal allocation scheme based on a dynamic interference graph Only local knowledge of active subscribers is available propose a scalable two-phase channel/power allocation scheme that achieves good performance