Young-June Choi and Saewoong Bahk Seoul National University, Korea

1. Multichannel Wireless Scheduling underLimited Terminal Capability Young-June Choi and Saewoong Bahk Seoul National University, Korea IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS2008

2. Outline • Introduction • System model • Opportunistic Multichannel Scheduling • Numerical results • Conclusions

3. Introduction • Emerging systems like OFDMA and MIMO systems require • multichannel scheduling over a wireless link. • Wireless channels change over time in unpredictable ways due to • location environments, user movement, or other interferences. • Considering various factors, they are generally characterized by • large-scale and small-scale propagation effects.

4. Introduction • For the emerging multichannel systems like OFDMA and MIMO • antenna systems, the opportunistic scheduling can be easily extended. • Some previous approaches have dealt with multichannel scheduling. • Typically in MIMO systems, the number of antennas of an MT (Mobile • Terminal) is smaller than that of a BS. • The MT cannot use all the channels available in the system. •  limited-matching <-> unlimited-matching

5. Introduction • Motivation • The limited-matching scheduling is an NP-complete problem that needs an • exhaustive searching. • To solve it easily, we can use the Hungarian algorithm • Its complexity is still too high • Goal • To propose a suboptimal algorithm that follows a heuristic and greedy manner.

6. System model a1 Downlink User 1 Scheduler Data 1 a2 Data 2 Packet Arrival User 2 . . . . . . . . . am Data m User k Channel estimation Uplink Feedback information Mobile Terminal Base Station

7. System model The unlimited-matching scheduler assigns each channel to a user with larger gain.

8. System model The unlimited-matching scheduler assigns each channel to a user with larger gain. The limited-matching scheduler assigns only a channel to each user at the cost of throughput degradation.

9. Opportunistic Multichannel Scheduling Unlimited-matching Let A(i) indicate the assigned user for channel i (i = 1, · · · ,N). The unlimited scheduling can be expressed as

10. Opportunistic Multichannel Scheduling Limited-matching Let A(i) indicate the assigned user for channel i (i = 1, · · · ,N). The limited scheduling can be expressed as The unlimited scheduler is applied to each channel independently, the optimal allocation for limited scheduler needs exhaustive searching to maximize the sum of N channel gains.

11. Opportunistic Multichannel Scheduling - Overview Channel User 1 1 1 3 4 5 6 2 2 2 1 3 2 2 3 3 3 4 1 5 2 4 4 5 Each worker has different efficiency for each job. The optimal assignment problem is to assign n jobs to n workers.

12. Opportunistic Multichannel Scheduling - Overview Channel User 1 1 1 3 4 5 6 2 2 2 1 3 2 2 3 3 3 4 1 5 2 4 4 5 This problem can be solved by Hungarian algorithm using weighted bipartite matching graphs.

13. Opportunistic Multichannel Scheduling An example of Hungarian algorithm: Channel User 1 1 1 5 6 2 2 4 1 5 2 3 3 2 4 4 4

14. Opportunistic Multichannel Scheduling An example of Hungarian algorithm: Channel User 1 1 1 5 6 2 2 4 1 5 2 3 3 2 4 4 4 Total channel gains: 11

15. Opportunistic Multichannel Scheduling An example of Hungarian algorithm: Channel User 1 1 1 5 6 2 2 4 1 5 2 3 3 2 4 4 4 Total channel gains: 15

16. Opportunistic Multichannel Scheduling An example of Hungarian algorithm: Channel User 1 1 1 5 6 2 2 4 1 5 2 3 3 2 4 4 4 Total channel gains: 16

17. Opportunistic Multichannel Scheduling An example of Hungarian algorithm: Channel User 1 1 1 5 6 2 2 4 1 5 2 3 3 2 4 4 4 The complexity of the Hungarian algorithm is O(K3) in the K × N bipartite graph.

18. Opportunistic Multichannel Scheduling An example of Heuristic greedy algorithm: Channel User 1 1 1 5 K: user 6 4 2 2 N: channel 1 5 3 2 3 2 4 4 4

19. Opportunistic Multichannel Scheduling An example of Heuristic greedy algorithm: Channel 1) Choose the best gain from the gain matrix, and delete the corresponding row and column. 2) repeat this until further choices are not available User 1 1 1 5 K: user 6 4 2 2 N: channel 1 5 3 2 3 2 4 4 4

20. Opportunistic Multichannel Scheduling An example of Heuristic greedy algorithm: Channel 1) Choose the best gain from the gain matrix, and delete the corresponding row and column. 2) repeat this until further choices are not available User 1 1 1 5 K: user 6 4 2 2 N: channel 1 5 3 2 3 2 4 4 4

21. Opportunistic Multichannel Scheduling An example of Heuristic greedy algorithm: Channel 1) Choose the best gain from the gain matrix, and delete the corresponding row and column. 2) repeat this until further choices are not available User 1 1 1 5 K: user 6 4 2 2 N: channel 1 5 3 2 3 2 4 4 4 Total channel gains: 15

22. Opportunistic Multichannel Scheduling Complexity comparison among Exhaustive Searching, Hungarian Algorithm, AARR Algorithm, and Heuristic Algorithm (N≤ K) Heuristic algorithmachieves lower complexity than the Hungarian algorithm. AARR algorithm is the simplest, but it gives lowerthroughput.

23. Numerical results • Users with the same channel condition • (average data rate of 538kbps at −0.6dB). • A cell with six hexagonal neighboring cells. • Each cell has a BS at its center and covers a radius of 1Km. • The downlink queues for active users always have packets to transmit.

24. Numerical results

25. Numerical results

26. Numerical results

27. Numerical results

28. Numerical results

29. Conclusions • They proposed a heuristic algorithm that reduces the algorithm • complexity while obtaining almost the same cell throughput as the • optimal one. • The limited-matching scheduler can significantly reduce the amount • of feedback information with a slight throughput degradation.

30. Thank you!