A game-theoretic approach to power allocation in frequency-selective gaussian interference channels

This paper defines a rate maximization power allocation game in a frequency selective Gaussian interference channel, after assuming a suboptimal but pragmatic multi-user coding scheme. We show that the Nash equilibrium always exists in this game. We consider a distributed power allocation scheme [l, Section IV.], and provide a sufficient condition for the convergence of the distributed algorithm. The condition for the convergence is also a sufficient condition under which the Nash equilibrium is unique. I. PROBLEM FORMULATION Current communication channels are both frequency selective and interference-limited, with a Gaussian thermal noise at the receiver end. Coordinating all the users is costly and physically impossible in a fast-fading channel. Hence, a frequency selective Gaussian interference channel well describes a multiuser channel [I, 21. When Discrete Multi-Tone (DMT) is assumed, the channel can be modeled as a set of N parallel independent frequencyflat channels. A Gaussian interference channel per frequency tone is modeled as a linear channel between the M transmitters and M receivers with a thermal noise. For the mth user at the nth tone, the received signal to interference plus noise ra-P(m,n) tio (SINR) is SINR(m,n) =