  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.
