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Loss of Continuity in Cellular Networks Under Stabilizing Transmit Power Control
 

Summary: Loss of Continuity in Cellular Networks Under Stabilizing Transmit
Power Control
Vishwesh Kulkarni Vincent Fromion Tansu Alpcan Michael Safonov
Abstract-- Recently, passivity-based techniques to control the
transmit power of mobile nodes have been proposed to ensure
the finite gain stability of a class of cellular CDMA networks.
These techniques implement the Zames-Falb multipliers at the
mobile node and at the base stations. The finite gain stability
of such a cellular network follows as a consequence of the fact
that the Zames-Falb multipliers preserve positivity of monotone
memoryless nonlinearities. In this note, we show that such
a cellular network may not be a continuous system. Hence,
the following undesirable scenarios may occur if the set-point
is varied with time: (i) the Nash equilibrium may cease to
exist, and (ii) vanishingly small changes in set-points (such
as the target SINR values) may cause the system trajectory
to jump from one equilibrium point to another, leading to
nonvanishingly small variations in the mobile transmit powers
and the actual SINR values across such networks.
Index Terms-- CDMA, power control, Nash equilibrium,

  

Source: Alpcan, Tansu - Deutsche Telekom Laboratories & Technische Universitšt Berlin

 

Collections: Engineering