A Formal Approach to Analysis and Design of SelfConfiguring Wireless Ad Hoc Networks

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A Formal Approach to Analysis and Design of
Self-Configuring Wireless Ad Hoc Networks

• Tara Javidi
• Electrical and Computer Engineering
• UCSD
• Graduate Student Jennifer Price (Funded by AFOSR)

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Outline

• Introduction
• Self-Configuring Ad-Hoc Networks
• Desirable Global Properties
• An Example Time Division and CDMA
• Joint Power, Time-Slot and Rate Assignment
• Problem Decomposition
• Distributed Algorithms
• Power and Slot Assignment
• Rate Adaptation
• Properties and Performance
• Conclusions

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Self-Configuring Ad-Hoc Networks

• Scenario A set of devices which are compatible
  at the physical layer are randomly dropped into
  an area and remain there for some length of time
  (quasi-static)
• Task Use locally available information at each
  node to self-configure a feasible network
  architecture (leader-follower control hierarchy,
  MAC)
• Goal Develop a set of rules which, when
  implemented locally at each node, result in a
  network with desirable global properties

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Motivation (I)Coordinated Control (AFOSR with
K. Morgansen, UW Seattle)

• Network in support of coordinated control
• Robotic-fish Schools
• The communication is needed over a control-driven
  logical graph
• Leader-Follower cliques with particular graph
  structure
• Each clique communication can be regulated
• Maintain synchronization
• Contention-based access is too costly

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Motivation (II)Medium Access Infrastructure

• Complete link scheduling into future is
  BW-efficient
• Needs knowledge of average throughput demand on
  links
• Cannot be decentralized
• Random access is fully distributed
• Avoiding contention can be inefficient
• The right trade-off application-dependent!

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Motivation (II)PHY gains sustained over longer
period

• Quasi-Static Access Control Infrastructure
• Some level of schedule/synch
• Handle interference management signals

Detect Changes
Slot Assgnmnt
Slot Assgnmnt
Adjust Rates for Minor Environment Variations
Neighbor ID
Neighbor ID

• time

Significant change in environment
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Desired Global Properties
We are interested in decentralized selection of
MAC and physical layer parameters (such as
transmit power, transmission rate, time-slot
assignment, beam and directional antenna angle,
etc) that guarantee the following desirable
network properties
C1 Efficient Quasi-static Transmission
Schedule C2 Connectivity C3 Interference
Management
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An Example TD-CDMA

• Elevating modulation schemes for multi-access
  (direct-sequence, multi-carrier, etc)
• CDMA allows simultaneous reception
• Save on contention-avoidance overhead/inefficiency
  
• Rate Adaptation manages interference (by adapting
  to variations in demand)
• The interference is kept low enough
• Requires some notion of link (time) scheduling as
  well as infra-structure to manage interference
• Appropriate when traffic is heavy on all links
• Increases bandwidth efficiency

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Ad-Hoc Time-Scheduled CDMA

• Network Parameters
• M number of mobiles T number of slots
• Physical Layer Parameters
• W chip bandwidth Rb pilot rate
• Network Variable
• gij path gain (time varying)
• Variables at Each Node
• P0i pilot power for user i
• ?i transmit rate for user i
• ?it indicator function for node i transmitting
  in slot t
• Uit rate utility of node i (time varying)

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Feasible TD-CDMA Network Desirable Network
Properties
Definition A tuple of pilot power, time-slot,
and rate assignment vectors (P0, ?, s) belongs to
the feasible region ? if and only if they satisfy
the following conditions
C1
C2 Every node has at least X neighbors
C3
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Optimal Resource Allocation

• Problem P Find the pilot power, time-slot, and
  rate assignment vectors that solve the following

Note that we are interested in maximizing the MAC
layer transmission capacity in a fair manner
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Distributed Algorithms - Problem Decomposition
Problem P
Suboptimal but Elegant decomposition
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Slot Assignment Algorithm
Increase Pilot Signal Transmit Power
yes
Access Control Channel?
Response from Transmitted Pilot Signal?
no
yes
no
Execute Rule from Slot Assignment Algorithm
no
Fix Pilot Signal Transmit Power Yield
Control Channel
Ni gt X?
yes
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Rate Assignment Algorithm
Transmitting Node?
Start of Time Slot t
Receive Packets Measure Interference
Calculate ?j(t) Transmit PPS
no
yes
Transmit Packets
Receive pi Calculate New Transmisison Rate
Previously developed auctioning mechanisms known
to converge to optimum fast
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Tt transmit, Rt listen
Rt transmit, Tt listen
Information Packets
Pilot Signal
Prices
frames
Time slot
1
T
1
1
T
T
time
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Main Result
Self-Stabilizing System A system which is
guaranteed to reach a feasible state from any
initial condition after a finite number of steps
Theorem When run simultaneously, the power,
slot, and rate algorithms constitute a
self-stabilizing system whose equilibrium point
solves AP1 and AP2
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Possible Extension

• Generalization of proposed schedules
• Allow users to transmit over several slots

• Fairness issues will arise

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Conclusions

• To trade-off BW-efficiency/decentralization, an
  access infra-structure is needed
• Self-configuration is (must be) essential to
  setting up of this infra-structure
• Self-configuration problem heavily depends on the
  application and the PHY technology
• Notions of desired networking infrastructure
• Notions of interference and its management

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Future Research Goals

• Examine the result of our research from a
  cross-layer perspective
• Incorporating outing information into both slot
  and rate assignment algorithms
• Optimizing E2E performance measure
• Incorporate various physical layer technologies
  into the model
• Exploit modulation techniques at the MAC
• Examine the pros and cons of such solutions