Bounds on the Lambert function and their application to the outage analysis of user cooperation

Abstract

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.

4 pages, accepted for publication in the IEEE Communications Letters

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