Wireless Operators in a Shared Spectrum

1
Wireless Operators in a Shared Spectrum

• Mark Felegyhazi, Jean-Pierre Hubaux
• EPFL, Switzerland
• Infocom06, Barcelona, Spain
• April 26, 2006

2
Spectrum utilization
measured power dB
frequency GHz
D. Cabric, S. M. Mishra, D. Willkomm, R. W.
Brodersen, and A. Wolisz, A Cognitive Radio
Approach for Usage of Virtual Unlicensed
Spectrum, 14th IST Mobile and Wireless
Communications Summit, June 2005.
3
Problem formulation

• today, cellular operators own separate
  frequencies
• operate wireless / cellular networks in an
  unlicensed spectrum
• BUT, problem of interference
• power control of the pilot signal

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System model (1/2)

• two operators A and B
• set of base stations BA and BB
• base stations are placed on the vertices of a
  grid
• each base station of A has the same radio range
  rA (relaxed later), same for B
• base stations emit pilot signals on the same
  channel, with the radio ranges rA, rB
• full coverage by combination of the two
  operators coverage
• maximum power limit PMAX ? RMAX
• if
• devices have omnidirectional antennas

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System model (2/2)

• a set of users uniformly distributed in the area
• free roaming
• users attach to the base station with the best
  pilot signal
• operators want to cover the largest area with
  their pilot signal

where the channel gain
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Power control game

• static game G (P, S, U)
• operators ? Players
• pilot signal radio range ? Strategy
• Utility coverage area of their own pilot signal
  minus the interference area

• where ?i is the cooperation parameter of player
  i
• cooperativeness
• agreement
• power price

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Definitions

• Let
• Best response of player i to strategy sj of
  player j
• Nash equilibrium
• Nash equilibrium strategies are mutual best
  responses to each other.

Pareto-superiority A strategy profile
is Pareto-superior to a strategy profile
if for any player i we have with strict
inequality for at least one player.
M. Felegyhazi and J.-P. Hubaux, Game Theory in
Wireless Networks A Tutorial, EPFL Technical
report LCA-REPORT-2006-002, April 2006.
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Best response values
best response of player i
radio range of player j (rj)
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Mutual best responses Nash equilibria
radio range of player i (ri)
Nash equilibrium
radio range of player j (rj)
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Pareto-superior Nash equilibria

• (NEMAX)
• (NEMIN)
• (NEMIN,A,B)
• (NEMIN,A,B0)

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Repeated game (1/3)

• Punisher strategy Play RMIN in the first time
  step. Then for each time step
• play RMIN, if the other player played RMIN
• play RMAX for the next ki time steps, if the
  other player played anything else

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Repeated game (2/3)

• cooperation utility
• deviation gain
• defection utility

utility of player j (Uj)
time steps (t)
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Repeated game (3/3)

• Cooperation is enforceable A Nash equilibrium
  based on RMIN is enforceable using the Punisher
  strategy if
• If the above condition holds, the punishment
  interval is defined by

where ? is the discounting factor
Note Similar result to the Folk-Theorem
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Generalization of the problem
? base station might have different positions and
ranges

• Hardness result Finding the maximum utility of a
  player for general values of radio ranges is
  NP-complete.

Corollary Finding Nash equilibria in the power
control game for general values of radio ranges
is NP-complete.
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Conclusion

• Coexistence is a main problem in shared spectrum
  networks
• Power control of the pilot signal to cope with
  interference
• Single stage game
• various Nash equilibria in the grid scenario,
  depending on ?A and ?B
• Repeated game
• RMIN (cooperation) is enforceable with
  punishments
• General scenario arbitrary ranges
• the problem is NP-complete

http//winet-coop.epfl.ch