Cross-layer Scheduling and Resource Allocation in Wireless Communication Systems

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1 Cross-layer Scheduling and Resource Allocation in Wireless Communication Systems Srikrishna Bhashyam Department of Electrical Engineering Indian Institute of Technology Madras 21 June 2011 Srikrishna Bhashyam (IIT Madras) 21 June / 44

2 Cellular Systems Time-varying channel Resource sharing Interference constraints Srikrishna Bhashyam (IIT Madras) 21 June / 44

3 Downlink Resource Allocation Problem User 1 Traffic Basestation User 2 User K Channel information Physical resources: power and bandwidth Total transmit power constraint Maximize system throughput Fairness or Quality of Service (QoS) constraints Srikrishna Bhashyam (IIT Madras) 21 June / 44

4 Dynamic Resource Allocation Periodic reallocation of resources User 1 User 2 User 3 Resources: Time, Bandwidth, Power Adaptation to channel and traffic conditions Dynamic resource allocation Reallocation period of the order of a millisecond Srikrishna Bhashyam (IIT Madras) 21 June / 44

5 Adapting to the Channel Srikrishna Bhashyam (IIT Madras) 21 June / 44

6 Adapting to the Channel: Maximizing Capacity Channel 1 User 1 Basestation Select the user with best channel Channel 2 User 2 Channel K User K Infinite backlog assumption All power and bandwidth resources to one user User with best achievable rate chosen: i = arg max R k, k where R k is the rate that can be supported by user k. Srikrishna Bhashyam (IIT Madras) 21 June / 44

7 Maximizing Capacity: Parallel Channels Parallel Channels to each user User 1 Basestation For each parallel channel Select the user with best channel User 2 User K Bandwidth resources split to achieve parallel channels For each channel n, user with best channel conditions chosen: Water-filling power allocation i n = arg max R k,n. k Srikrishna Bhashyam (IIT Madras) 21 June / 44

8 Fairness Proportional Fairness i = arg max k R k R k,av, where R k,av is the average rate that can be supported by user k. max k log (T k), where T k is the average long-term throughput of user k. Srikrishna Bhashyam (IIT Madras) 21 June / 44

9 Parallel Channels: OFDM User 1 Subcarriers User 2 User 3 Power Available resources: Subcarriers Transmit power Channel is frequency-selective subcarriers not identical. Srikrishna Bhashyam (IIT Madras) 21 June / 44

10 Fairness: Joint Subchannel and Power Allocation Proportional rate subcarrier allocation [Rhee] Proportional rate subcarrier allocation + power optimization [Shen] Joint subcarrier and power allocation Srikrishna Bhashyam (IIT Madras) 21 June / 44

11 Fairness: Joint Subchannel and Power Allocation Start Start Split power equally amongst subcarriers Split power equally amongst subcarriers Allocate all subcarriers to users Yes Check if all subcarriers are allocated Optimize power allocation with power Update each user s queue End No Allocate a subcarrier to a user Update each user s queue End Optimize power allocation with power Srikrishna Bhashyam (IIT Madras) 21 June / 44

12 Gradient Algorithm Stolyar (2005) General utility functions Multiuser scheduling at the same time PF is a special case Srikrishna Bhashyam (IIT Madras) 21 June / 44

13 Adapting to the Channel and Traffic Srikrishna Bhashyam (IIT Madras) 21 June / 44

14 Adapting to the Channel and Traffic Queues for each user Users Time-varying connectivity Servers Multi-Queue Multi-Server Model for each time slot Server: Subcarrier/Group of subcarriers/spreading code Srikrishna Bhashyam (IIT Madras) 21 June / 44

15 Resource Allocation/Cross-layer Scheduling Goals Scheduling Goals Stability and throughput optimality Stability: Average queue length finite Arrival rate of user 2 Stability region of policy 1 Stability region of policy 2 Stability region of throughput optimal policy Arrival rate of user 1 Packet delay constraints Fairness Srikrishna Bhashyam (IIT Madras) 21 June / 44

16 Stability in a general wireless network [Tassiulas et al 1992, Georgiadis et al 2006] Dynamic backpressure policy b 1 (b 1 b 3)r 13 b 1r 14 b3 (b 2 b 1)r 21 b 3r 34 b 2 b 2r 24 Destination node Interference model: Only certain links can be activated simultaneously Scheduling problem: Which links will you activate? Solution: Activate those links such that the sum of their weights is maximum. Srikrishna Bhashyam (IIT Madras) 21 June / 44

17 Dynamic back-pressure policy for our setting Max-Weight Scheduling b 1(t) Users b 1C 11 Servers b 2(t) b 1C 12 b 2 C 21 b 2C 22 Only one link per server to be activated. Which links to activate? Solution: Make the servers as destination nodes. Assign the weights for each link as in back-pressure policy. Activate those links such that the sum of their weights is maximum. max k b n C nk b n : Backlog of user n, C nk : Capacity of user n on server k Srikrishna Bhashyam (IIT Madras) 21 June / 44

18 Two Throughput Optimal Policies b 1 Users b 1 C 11 Servers b 1 C 12 b 2 C 21 b 2 b 2 C 22 b 3 b 3 C 31 b 3 C 32 Policy 1: Max-Weight Scheduling Policy 2: Improving delay performance Update queue information after each server is scheduled Srikrishna Bhashyam (IIT Madras) 21 June / 44

19 Joint Server and Power Allocation Finite number of power levels Max-weight scheduling Joint subcarrier and power allocation Joint optimization Sub-optimal solutions Srikrishna Bhashyam (IIT Madras) 21 June / 44

20 Max. arrival rate for less than 0.5% packets dropped Srikrishna Bhashyam (IIT Madras) 21 June / 44 Results: Max. Arrival Rate vs. Transmit Power Homogenous rate users CAO+FPA CAO+FPA+PAO CAO+JSPA MLWDF CAQA+FPA CAQA+JSPA Arrival rate (Mbps) P total in dbw

21 Results: Delay Performance P total = 8dBW Arrival rate = 3 Mbps Homogenous rate users CAO+FPA CAO+FPA+PAO CAO+JSPA MLWDF CAQA+FPA CAQA+JSPA P(delay>x) delay (time slots) Best and worst delay performance among users plotted Srikrishna Bhashyam (IIT Madras) 21 June / 44

22 Fairness and Utility Maximization Arrival rate vector outside stability region Support a fraction of the traffic Optimize utility based on long term throughput Flow control to get stabilizable rates + stabilizing policy Fairness based on choice of utility function Proportional fairness Srikrishna Bhashyam (IIT Madras) 21 June / 44

23 Fairness and Utility Maximization Flow control + stabilizing policy Maximize utility subject to stability max [Vf k (r k ) b k r k ] {r k } k Srikrishna Bhashyam (IIT Madras) 21 June / 44

24 Adapting with Partial Information Srikrishna Bhashyam (IIT Madras) 21 June / 44

25 Using Delayed Information b(t 1), C(T 1) b(2t 1), C(2T 1) Slot T First Interval T Second Interval T Third Interval Time-slots are grouped into intervals Channel and queue information available only once in T slots Srikrishna Bhashyam (IIT Madras) 21 June / 44

26 Channel model USER 1 s CHANNEL USER 2 s CHANNEL PACKETS PACKETS SERVERS SERVERS C nk : channel capacity of user n on server k. C nk {0, 1, 2, 3}. Srikrishna Bhashyam (IIT Madras) 21 June / 44

27 Loss model Packets sent Rate R nk 0 R nk <= C nk R nk > C nk Capacity R nk : number of packets user n transmits on server k. C nk (lt 1): channel information available at the start of l th interval. Srikrishna Bhashyam (IIT Madras) 21 June / 44

28 Scheduling with infrequent measurements Retain throughput optimality of dynamic backpressure policy Two policies: Policy 1 and Policy 2 Comparison with KLS policy [Kar et al 2007] Srikrishna Bhashyam (IIT Madras) 21 June / 44

29 Policy 1 & Policy 2 b 1 Users b 1 C 11 Servers b 1 C 12 b 2 C21 b 2 b 2 C22 b 3 b 3 C31 b 3 C 32 Define C nk = max E [T nk (t) C nk (lt 1)] = max r Pr{r C nk C nk (lt 1)} r Policy 1 is the dynamic back pressure policy for our setting Assignment changes every slot Policy 2: Update queue information after each server is scheduled Srikrishna Bhashyam (IIT Madras) 21 June / 44

30 KLS Policy b 11 Users b 11 Ĉ 11 Servers b 21 b 31 b 12 b 22 b 21 Ĉ 21 b 31 Ĉ 31 b 12 Ĉ 12 Virtual queue for each user-server pair Define Ĉ nk (lt ) as (l+1)t 1 1 T E C nk (t) C nk (lt 1) t=lt Assignment changes once in T slots b 22 Ĉ 22 b 32 b 32 Ĉ 32 Srikrishna Bhashyam (IIT Madras) 21 June / 44

31 Simulation setup Truncated Poisson arrivals 128 users and 16 servers Markov fading channel with probability transition matrix Backlog and delay are used as metrics for comparison Simulations for both symmetric and asymmetric arrivals Symmetric case shown here Srikrishna Bhashyam (IIT Madras) 21 June / 44

32 Average backlog comparison: Slow fading, T = 8 Average backlog in packets/timeslot/user KLS Policy Policy 1 Policy Net arrival rate All the policies have similar stability region. Srikrishna Bhashyam (IIT Madras) 21 June / 44

33 Average backlog comparison for low traffic 180 Average backlog in packets/time slot/user KLS Policy Policy 1 Policy Net arrival rate At low traffic, proposed policies outperform KLS policy. Srikrishna Bhashyam (IIT Madras) 21 June / 44

34 Delay comparison 10 0 Probability that delay is > d 10 1 min(delay) policy 2 max(delay) policy 2 min(delay) policy 1 max(delay) policy 1 min(delay) KLS policy max(delay) KLS policy delay d in seconds Net arrival rate = 25.6, T = 4 Srikrishna Bhashyam (IIT Madras) 21 June / 44

35 Average backlog comparison vs T for Policy 2 Average backlog in packets/timeslot/user T=1 T=2 T=4 T=8 T= Net arrival rate Srikrishna Bhashyam (IIT Madras) 21 June / 44

36 Average backlog comparison for different policies Average backlog in packets/timeslot/user KLS Policy Policy 1 Policy Net arrival rate Srikrishna Bhashyam (IIT Madras) 21 June / 44

37 Comparison of stability regions: Fast fading Average backlog in packets/timeslot/user Policy 1 KLS Policy Policy Net arrival rate 2 queues, 1 server, T = 2, states are {0, 1} [ δ 1 δ Probability transition matrix: 1 δ δ ], δ = 0.1 Srikrishna Bhashyam (IIT Madras) 21 June / 44

38 Possible Extensions Srikrishna Bhashyam (IIT Madras) 21 June / 44

39 More Physical Layer Options Multiple antennas Power allocation across resources (servers) Interference processing vs. Interference avoidance Multi-cell scenario: Centralized vs. Distributed methods Srikrishna Bhashyam (IIT Madras) 21 June / 44

40 Approximate Solutions Lower complexity/approximate solutions to optimization problem Appropriate reduction search space of physical layer modes Srikrishna Bhashyam (IIT Madras) 21 June / 44

41 Summary Adapting to the channel Adapting to the channel and traffic Max-weight Scheduling Adapting to partial information Conditional expected rate Possible extensions Approximate lower complexity solutions Appropriate choice of physical layer modes Srikrishna Bhashyam (IIT Madras) 21 June / 44

42 References R. Knopp, P. Humblet, Information Capacity and power control in single cell multiuser communications, in Proc. IEEE ICC, Seattle, WA, vol. 1, pp , June D. N. C. Tse, Optimal power allocation over parallel Gaussian channels, in Proc. IEEE ISIT, Ulm, Germany, pp. 27, June E. F. Chaponniere, P. Black, J. M. Holtzman, and D. Tse, Transmitter directed multiple receiver system using path diversity to equitably maximize throughput, U. S. Patent No , September P. Viswanath, D. N. C. Tse, R. Laroia, Opportunistic beamforming using dumb antennas, IEEE Transactions on Information Theory, vol. 48, no. 6, pp , June C. Y. Wong, R. S. Cheng, K. B. Letaief, R. D. Murch, Multiuser OFDM with Adaptive Subcarrier, Bit, and Power Allocation, IEEE Journal on Selected Areas in Communications, vol. 17, no. 10, pp , October J. Jang, K. B. Lee, Transmit power adaptation for multiuser OFDM systems, IEEE Journal on Selected Areas in Communications, vol. 21, no. 2, pp , February W. Rhee, J. M. Cioffi, Increase in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation, Proceedings of the 51st IEEE Vehicular Technology Conference, Tokyo, vol. 2, pp , Spring Z. Shen, J. G. Andrews, B. L. Evans, Adaptive Resource Allocation in Multiuser OFDM Systems with Proportional Rate Constraints, IEEE Transactions on Wireless Communications, vol. 4, no. 6, pp , November C. Mohanram, S. Bhashyam, A sub-optimal joint subcarrier and power allocation algorithm, IEEE Communications Letters, vol. 9, no. 8, pp , August Srikrishna Bhashyam (IIT Madras) 21 June / 44

43 References L. Tassiulas, A. Ephremides, Stability properties of constrained queueing systems and scheduling for maximum throughput in multihop radio networks, IEEE Transactions on Automatic Control, vol. 37, no. 12, pp , December L. Georgiadis, M. J. Neely, L. Tassiulas, Resource allocation and cross-layer control in wireless networks, Foundations and Trends in Networking, vol. 1, no. 1, pp , M. Andrews, K. Kumaran, K. Ramanan, A. L. Stolyar, R. Vijayakumar, P. Whiting, Providing quality of service over a shared wireless link, IEEE Communications Magazine, vol. 39, no. 2, pp , Feb A. L. Stolyar, On the asymptotic optimality of the gradient scheduling for multi-user throughput allocation, Operations Research, vol. 53, no. 1, pp , S. Kittipiyakul, T. Javidi, Resource allocation in OFDMA with time-varying channel and bursty arrivals, IEEE Communication letters, vol. 11, no. 9, September C. Mohanram, S. Bhashyam, Joint subcarrier and power allocation in channel-aware queue-aware scheduling for multiuser OFDM, IEEE Transactions on Wireless Communications, vol. 6, no. 9, September K. Kar, X. Luo, S. Sarkar, Throughput-optimal scheduling in multichannel access point networks under infrequent channel measurements, IEEE Transactions on Wireless Communications, vol. 7, no. 7, pp , July C. Manikandan, S. Bhashyam, R. Sundaresan, Cross-layer scheduling with infrequent channel and queue measurements, IEEE Transactions on Wireless Communications, vol. 8, no. 12, pp , December P. Chaporkar, K. Kar, X. Luo, S. Sarkar, Throughput and Fairness Guarantees through maximal scheduling in wireless networks, IEEE Transactions on Information Theory, vol. 54, no. 2, pp , February Srikrishna Bhashyam (IIT Madras) 21 June / 44

44 Acknowledgements Rajesh Sundaresan Chandrashekar Mohanram C. Manikandan Parimal Parag Department of Science and Technology Srikrishna Bhashyam (IIT Madras) 21 June / 44

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