Distributed Rate Assignments for Broadband CDMA Networks

1
Distributed Rate Assignments for Broadband CDMA
Networks

• Tara Javidi
• Electrical Computer Engineering
• University of California, San Diego

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Multi-Cell Single Hop CDMAMotivation

• Wideband CDMA network with variable rates
• Mobiles communicate directly with the base
  station
• Base stations are connected directly to the
  traditional IP network

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Rate Assignment Problem

• Limited by congestion constraints in the wired
  network
• Limited by interference constraints in the
  wireless network
• Objective Maximize the global network utility in
  a distributed adaptive manner

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Philosophically Related Works
Wired Networks 1 F. Kelly. Mathematical
Modeling of the Internet. B. Enquist and W.
Schmid, editors. Mathematics Unlimited 2001
and Beyond, pages 685-702. Springer-Verlaq,
2001. 2 J. Mo and J. Walrand. Fair End-to-End
Window-Based Congestion Control. IEEE/ACM
Transactions on Networking, 8(5)555-567,
2000. 3S.H. Low and D.E. Lapsley. Optimization
Flow Control I Basic Algorithm and Convergence.
IEEE/ACM Transactions on Networking,
7(6)861-874, 1999. Wireless Networks 3 T.
Javidi Distributed Rate Assignment in
Multi-sector CDMA. Global Telecommunications
Conference, 2003. 4 M. Chiang and R. Man.
Jointly Optimal Congestion Control and Power
Control in Wireless Multihop Networks. Global
Telecommunications Conference, 2003. 5 X. Lin
and N.B. Shroff. The Impact of Imperfect
Scheduling on Cross-Layer Rate Control in
Wireless Networks. INFOCOM 2005.
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Cross-Layer Design One-Shot

• One-shot and joint design of a rate assignment
  protocol (merging MAC and transport layers)
• Wireless and wired networks generate feedback
  based on their respective system constraints
• This feedback allows for dynamic adaptation to
  slowly varying network conditions

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Iterative Methods and Convergence
If the Lagrange multipliers are computed using a
gradient projection method, the rate assignment
becomes an iterative algorithm that uses feedback
from the network
Theorem Given an appropriate choice of
step-size, the distributed system will converge
to the solution to the primal problem
(cross-layer optimal)
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Related Work

• 1 X. Lin and N.B. Shroff. Joint rate control
  and scheduling in multi-hop wireless networks.
  CDC04
• 2 M. Neely, E. Modiano, and C. Li. Fairness and
  Optimal Stochastic Control for Heterogeneous
  Networks. Infocom05
• Due to structure of the problem, we get truly
  distributed solutions (little overhead comm)
• Such solutions require a fundamental re-doing of
  the protocol stack in general and transport layer
  in particular

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Cross-Layer Design Modular

• MAC and transport layer protocols are separate
• MAC chooses rate using feedback from wireless
• The transport layer chooses rate based on end-end
  feedback following a dual controller
• Can this be optimal in a cross-layer sense?
• If no wired core, the answer is yes
• 1 A. Eryilmaz and R. Srikant. Fair Resource
  Allocation in Wireless Using Queue-based
  Scheduling and Congestion Control

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Outline

• Motivation and Overview
• One-Shot Rate Assignments
• Modular Rate Assignments
• The Problem with Dual Methods
• Practical Implementation Cross-Layer
  Coordination
• Observations, Conclusions, Future Work

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Notation

• CDMA uplink
• dynamic power and spreading gain control
  (distributed)
• Network Parameters
• M number of nodes N of them wireless
  
• L number of sectors J number of
  (wired) links
• Cj capacity of link j ?ij routing
  function
• W chip bandwidth gil channel power
  gain
• K acceptable interference b(i) mobile is
  sector
• Node Variables
• Pi transmit power for user i
• ai transmit rate for user i at MAC
• xi transmit rate for user i at transport

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One-Shot Problem Formulation
Bench Mark cross-layer optimal
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Iterative Methods and Convergence
If the Lagrange multipliers are computed using a
gradient projection method, the rate assignment
becomes an iterative algorithm that uses feedback
from the network
Theorem Given an appropriate choice of
step-size, the distributed system will converge
to the solution to the primal problem
(cross-layer optimal)
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Modular Problem Formulation
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Dual Controller Fails

• Question What happens when we try to use the
  dual controller/gradient projection?
• Answer The dual controller fails to converge to
  solution of the optimization problem
• We need to maximize a function that is strictly
  concave over all the primal variables

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Modular Utility Functions
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A New Modular Problem Formulation
subject to
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Economic Interpretation of the Dual
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Iterative Methods and Convergence
If the Lagrange multipliers are computed using a
gradient projection method, the rate assignment
becomes an iterative algorithm that uses feedback
from the network
Theorem Given an appropriate choice of
step-size, the distributed system will converge
to the solution to the primal problem
(cross-layer optimal)
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Wired Network Prices

• Individual Lagrange multipliers are generated
  using gradient projection
• This has a well known physical interpretation
  queuing delay!
• Aggregate price qi can be interpreted as
  end-to-end queuing delay, which can be measured
  by each user

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Wireless Network Prices

• We can construct a signaling mechanism under
  which the
• aggregate price pi becomes closely related to
  forward link
• SINR on the pilot signal

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Cross-Layer Coordination Signal

• Again, individual Lagrange multipliers are
• generated using gradient projection

• Each equality is broken into two inequalities
• For each inequality two multipliers computed

• These equations are similar to the equations
• representing delay in queues!

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Cross Layer Coordination Signal

• Two imaginary queues whose associated delays are
  ?i and ?i-
• Queue 1 is our MAC-layer buffer, and Queue 2 is
  our token bucket
• Token bucket is not used to regulate service
  rate, but to keep track of the mismatch between
  transport and MAC layer rates

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The Role of the New Buffers

• Non-zero delay in the MAC-layer buffer
  corresponds to a wireless bottleneck
• The price from the actual link prevents the
  transport layer from out-running the MAC layer
• Non-zero delay in the token bucket corresponds to
  a wired bottleneck
• The price from the token bucket prevents the
  MAC layer from out-running the transport layer
• Generally only one of the queues is nonempty
  (i.e. only one of the constraints is active) at a
  time
• Without the use of a token bucket, the solution
  will converge but not to the desired equilibrium
  when wired bottle-neck

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Transport Layer Profit Maximization

• Information about the interference levels in the
  wireless network is now incorporated into the
  end-to-end queuing delay (qi?i) minus the token
  bucket delay (?i-)
• Allows the transport layer to take interference
  levels into account without any major
  modification of current protocols
• add the token bucket delay to the propagation
  delay

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Mac Layer Profit Maximization

• Wireless sources now receive credit for long
  data queues (i.e. large ?i) and are penalized
  for long token buckets (i.e. large ?i-)
• Prioritize wireless users based on their backlog
• (De)Prioritize wireless users based on received
  service so far

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Simulations
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Dynamical Behavior

• Convergence
• Since we wish to interpret the Lagrange
  multipliers as delay, the step size must be
  chosen as ?t/C
• Convergence is dependent upon the step size being
  small enough, hence the algorithm being run
  fast enough
• Nested Feedback Loops
• Decoupling of the MAC and transport layer allows
  for the corresponding feedback loops to be run at
  different time scales aid in convergence and/or
  robustness?
• Interaction of three separate feedback loops
  (MAC, transport, and power control) plays a
  significant role in dynamic situations
• Choice of parameters s and K play an important
  role

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Future Work

• Provide a stability analysis
• Use the concept of Markov chain stability for
  queue lengths
• Understand the impact of realistic arrival
  statistics on the system
• How does statistical multiplexing impact the
  transient behavior of the system?
• Determine whether these results can be extended
  to other MAC protocols
• Does the addition of the MAC-layer queue and
  token bucket provide sufficient coordination for
  other MAC schemes?