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Problems formulated in terms of logarithmic or exponential equations often use the Lambert W function in their solutions. Expansions, approximations and bounds on W have been derived in an effort to gain a better understanding of the relationship between equation parameters. In this paper, we focus on one of the branches of W, denoted as W<sub>-1</sub>, we derive tractable upper and lower bounds and we illustrate their usefulness in identifying conditions under which user cooperation can yield a lower outage probability than non-cooperative transmission.

Bounds on the Lambert Function and Their Application to the Outage Analysis of User Cooperation