Efficient Power Control Via Pricing in Wireless Data Networks

1
Efficient Power Control Via Pricing in Wireless
Data Networks

• Cem U. Saraydar, Narayan B. Mandayam and David J.
  Goodman
• Presented by
• Ramesh Mishra

2
The Incentive for Power Control

• Need for QoS for a wireless terminal.
• Need for Efficient use of radio resources.
• Need for a mechanism that maximizes the overall
  utility of the system.

3
Some Basic Concepts

• Utility Function
• It refers to the level of satisfaction the
  decision taker gets as a result of its actions.

4
System Model

• Single Cell System.
• Each user transmits L information bits in
  packets of size M gt L.
• The Rate of Transmission is R and power used is
  p.
• The probability of correct reception of a frame
  is Pc (FSR) which is a function of SIR.

5
Continued

• FSR( Frame Success Rate) is defined as
• Pc ( 1 - Pe )M. where Pe is the bit error
  rate.
• Under these definitions the utility function is
  defined as
• u (L R Pc/Mp) bits/joule

6
Degenerate Solution and Efficiency Function

• We have a degenerate solution when p 0.
• Efficiency function that closely follows the
  behavior of the original function is introduced
• f(y) (1-2Pe)M.

7
(No Transcript)
8
Non-Cooperative Power Control Game

• Let G N, Pj, uj(.) denote a
  non-cooperative power control game(NPG).
• The utility of user j obtained by expending power
  pj can be expressed as

9
NPG A Formal Look

• Formally the Power Control Game can be expressed
  as

10
Nash Equilibrium in NPG

• At Nash Equilibrium, no user can improve its
  utility, given the power level of other users.
• The power level chosen by a rational user
  constitutes its best response.

11
(No Transcript)
12
Some Results

• The Nash Equilibrium exists in NPG, G N, Pj,
  uj(.).
• The NPG has a unique Equilibrium.

maximizer
13
Inefficiency of NPG and Pareto Dominance.

• The power allocation can be made more efficient
  (Pareto dominant) if we can increase the utility
  of some of the terminals without hurting others.
• The NPG equilibrium is inefficient.

14
Pareto Dominance
15
Non-Cooperative Power Control with Pricing.

• Pricing is motivated by two objectives.
• Generates revenues for the system.
• Encourages players to use system resources more
  efficiently.
• Many possible pricing schemes eg (flat rate,
  access based, usage based, priority based etc).
• Efficiency in power control can be promoted by a
  usage-based pricing scheme strategy where the
  penalty is proportional to its transmit power.

16
NPGP- A Formal Look

• Let Gc N, Pj, ucj (.) denote an N
  player non-cooperative Game with pricing.
• Utility is defined as

17
Linear Pricing scheme is of the form
Where c and aj are positive scalars.
18
Supermodularity and NPGP

• A Theorem
• The set of Nash Equilibrium of a super modular
  game is nonempty. Furthermore, the Nash set has a
  largest and smallest element.
• A Definition
• A Game Ge with exogenous parameter e is said to
  be supermodular, or it is a parameterized game
  with complementarities if

has NDD in (pj,p-j) and (pj,e) for all j.
19
Theorems Continued
20
Algorithm for generating a sequence of powers.
21
Algorithm(Network)
22
Numerical Results
23
(No Transcript)
24
(No Transcript)