Opportunistic Scheduling for Multiuser Multicarrier Systems

1
Opportunistic Scheduling for Multi-user
Multi-carrier Systems

• Prof. Song Chong
• Network Systems Lab.
• EECS, KAIST
• song_at_ee.kaist.ac.kr

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Outline

• Multi-user Opportunistic Communication
• Long-term Capacity Region
• Network Utility Maximization
• Maximization of Sum of Weighted Rates
• Gradient-based Scheduling
• OFDMA Downlink Problem
• Throughput-optimal Scheduling Flow Control
• Opportunistic Feedback
• References

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Multi-user Opportunistic Communication

• Multi-user diversity
• In a large system with users fading
  independently, there is likely to be a user with
  a very good channel at any time.
• Long-term total throughput can be maximized by
  always serving the user with the strongest
  channel.

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Multi-user Diversity An Insightful Look

• Independent fading makes it likely that users
  peak at different times.
• In the downlink, channel tracking can be done via
  a strong pilot amortized between all users.
• Challenge is to share the benefit among the users
  in a fair way.

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Long-term Capacity Region

• Time-varying achievable rate region
• Long-term rate region

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Network Utility Maximization (NUM)

• Long-term NUM
• Utility function Mo00

a0 throughput maximization a1 proportional
fairness (PF) a?8 max-min fairness
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Sum of Weighted Rates (SWR)

• Maximization of sum of weighted rates
• Both problems yield an unique and identical
  solution if we set , where is
  the optimal solution of the long-term NUM
  problem.

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Gradient-based Scheduling

• Assuming stationarity and ergodicity, one can
  show that
• where rate of user i at state s
• capacity region at state s
• The long-term NUM problem can be solved if we
  solve with at
  each state s.
• The resource allocation problem during slot t
• where is the average rate of user i up to time t
  and is the replacement of which is unknown
  a priori
• Convergence of to can be proved by
  stochastic approximation theory Kush04 or fluid
  limit technique Stol05.

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OFDMA Downlink Problem

• Joint optimization of subcarrier and power
  allocation at each time t Lee07
• Mixed integer nonlinear programming

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Suboptimal Algorithm

• Observations on the problem
• For fixed p, subcarrier allocation problem
• Scheduling over each subcarrier
• For fixed x, power allocation problem
• Convex optimization (water-filling)
• Each problem is easy
• Algorithm (frequency-selective power allocation)

Equal power allocation
Initialization
Equal power allocation
Subcarrier allocation for given power allocation
While subcarrier allocation is changing
Power allocation for given subcarrier allocation
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Frequency-selective vs Equal Power Allocation

• Simulation setup M50, N512, B5MHz/20MHz
• Frequency-selective power allocation has
  significant benefit in OFDMA downlink scheduling

B5MHz
B20MHz
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Throughput-optimal Scheduling and Flow Control

• Joint scheduling and flow control
• Stabilize the system whenever the long-term input
  (demand) rate vector lies within the capacity
  region
• Stabilize the system while achieving throughput
  optimality even if the long-term input (demand)
  rate vector lies outside of the capacity region
• Long-term NUM for arbitrary input rates Nee05

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Single-carrier Downlink Problem

• Virtual queue

Flow Control
Base Station
fading channel
demands
Scheduling
feedback achievable rates
Virtual flow
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Single-carrier Downlink Problem

• Scheduling
• Flow control
• Virtual flow control

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Lyapunov Optimization

• Lyapunov function and its drift
• Drift bound
• Minimizing the bound will maximize network
  utility while guaranteeing network stability
• Performance bound
• Tradeoff between utility and delay

Stability
Optimality
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Opportunistic feedback

• SNR thresholding scheme Ges04
• Can we reduce the amount of feedback and still
  preserve the scheduler performance?
• Each user compares its own channel quality to a
  predetermined threshold.
• Normalized thresholding scheme Yang04
• The study in Gest04 was limited to the scenario
  in which all the users have identical average
  channel quality.
• When we assume that the scheduling is based on
  the relative SNR,

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Opportunistic feedback

• Random access-based feedback protocolTang05
• Feedback Design
• In every minislot, each active user attempts to
  send back to the AP a data package containing its
  ID with a probability pjk.
• The AP randomly selects one of the successful
  users.
• The AP polls the selected user and requests it to
  feed back its actual channel information.

ltpossible framing structuregt
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Opportunistic feedback

• Efficiency based feedback reduction Jeon07
• Feedback reduction scheme for multicarrier
  system.
• Define the feedback efficiency of the kth user
  as the avg. of allocated subbands, , to
  the of feedback, .
• For the predetermined target efficiency factor e,
  each user own of feedback as following.
• The can be updated using exponential
  weighted lowpass filter.

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Opportunistic feedback

• Performance comparison under a-proportional fair
  scheduler

Advantage 1 does not distort the property of the
scheduler.
Advantage 2 total feedback load can be
controlled to a target level.
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References

• Mo00 J. Mo and J. Walrand, Fair End-to-End
  Window-Based Congestion Control, IEEE/ACM Trans.
  Networking, Vol. 8, No. 5, pp. 556-567, Oct.
  2000.
• Kush04 H. J. Kushner and P. A. Whiting,
  Convergence of Proportional-Fair Sharing
  Algorithms Under General Conditions, IEEE Trans.
  Wireless Comm., vol. , no., 2004.
• Stol05 A. L. Stolyar, On the Asymptotic
  Optimality of the Gradient Scheduling Algorithm
  for Multiuser Throughput Allocation, Operations
  Research, vol. 53, no. 1, pp. 12-25, Jan. 2005.
• Lee07 H. W. Lee and S. Chong, "Downlink
  Resource Allocation in Multi-Carrier Systems
  Frequency-Selective vs. Equal Power Allocation,"
  IEEE WoWMoM 2007, Helsinki, Finland, June 2007.
• Nee05 M. J. Neely et al., Fairness and Optimal
  Stochastic Control for Heterogeneous Networks,
  IEEE INFOCOM 2005.

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References

• Ges04 D. Gesbert and M. S. Alouini, How much
  feedback is multi-user diversity really worth?,
  IEEE ICC 2004.
• Yang04 L. Yang, M. S. Alouini and D. Gesbert,
  Further Results on Selective Multiuser
  Diversity, ACM MSWiM 2004.
• Tang05 T. Tang and R. W. Heath, Jr.,
  Opportunistic Feedback for Downlink Multiuser
  Diversity, IEEE Communications Letters, vol. 9,
  no. 10, Oct. 2005.
• Jeon07 J. H. Jeon, K. H. Son, H. W. Lee and S.
  Chong, Efficiency Based Feedback Reduction,"
  IEEE ICC 2007.