In this paper, we study slotted Spread Spectrum Aloha with Successive Interference Cancelation 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 Cancelation process leads to a constant signal to noise plus interference ratio for all users. We consider both perfect and imperfect interference cancellation.
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