Stochastic Power Allocation with Outage-Expectation Constraints in Lognormal Fading Wireless Channels

This paper concerns stochastic power allocation in lognormal fading wireless channels. We consider an outage-based quality of service (QoS) specification which requires that, for each channel, the outage expectation (i.e., the average probability/time that a transmitter/receiver pair experiences any outage due to fading) is kept below a given level. The problem of finding an optimal power allocation to achieve this QoS goal over lognormal fading wireless channels (with statistically independent fadings) can be posed as a specific type of stochastic posynomial programming with lognormally distributed random coefficients. We show that this expectation-based stochastic posynomial program (with lognormal variations) can be reformulated as a conventional (i.e., deterministic) posynomial program, which can be furthered solved by the very efficient interior-point method.