Competitive Optimization in Gaussian Frequency Selective Interference Channels Using Game Theory

The concept of cognitive radio such as sensing free frequency band and dynamic spectrum
access can achieve efficient use of the frequency band in future communication systems. One
of the important issues discussed in cognitive radio network is resource allocation. Given
the competitive character of the user, in this paper we model a cognitive radio network as a
non-cooperative game where secondary users compete intractably with each other in
frequency-selective channels, by maximizing their own information rates subject to the
total transmit power and peak transmit power in each frequency band. We express the
solution to the problem in Nash equilibrium form and investigate the existence and
uniqueness of the Nash equilibrium. Also, to achieve Nash equilibrium of the game, we use an
asynchronous distributed algorithm called smoothed asynchronous iterative water-filling
algorithm. This means that some users, among others, will have more opportunity to update
their own allocated power