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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 -1 , 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.
Ioannis Chatzigeorgiou (2013) studied this question.