  In this paper, we study slotted Spread Spectrum Aloha with Successive
Interference Cancellation at the receiver over a Gaussian channel. We consider
a decentralized power control setting in which each user chooses its transmit
power independently at random according to a power distribution with continuous
support. In this setting, we derive an analytical expression for the expected
interference power experienced by a user. This allows us to derive analytically
the power distribution that, during the Successive Interference Cancellation
process leads to a constant signal to noise plus interference ratio for all
users. We consider both perfect and imperfect interference cancellation.
