A Geometrical Description of the SINR Region of the Gaussian   Interference Channel: the two and three-user case
  This paper addresses the problem of computing the achievable rates for two (and three) users sharing a same frequency band without coordination and thus interfering with each other. It is thus primarily related to the field of cognitive radio studies as we look for the achievable increase in the spectrum use efficiency. It is also strongly related to the long standing problem of the capacity region of a Gaussian interference channel (GIC) because of the assumption of no user coordination (and the underlying assumption that all signals and interferences are Gaussian). We give a geometrical description of the SINR region for the two-user and three-user channels. This geometric approach provides a closed-form expression of the capacity region of the two-user interference channel and an insightful of known optimal power allocation scheme. 
Abdoulaye Bagayoko and Patrick Tortelier