 
Summary: Loss of Continuity in Cellular Networks Under Stabilizing Transmit
Power Control
Vishwesh Kulkarni Vincent Fromion Tansu Alpcan Michael Safonov
Abstract Recently, passivitybased 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 ZamesFalb 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 ZamesFalb 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 setpoint
is varied with time: (i) the Nash equilibrium may cease to
exist, and (ii) vanishingly small changes in setpoints (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,
