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Uniform Approximations for Wireless Performance in Fading Channels

We derive uniform approximations (UAs) for typical performance measures such as error probability, outage probability and capacity of wireless transmissions over flat fading channels impaired by noise. Uniform refers to the fact that these approximations are accurate over the whole range (low to high) of signal-to-noise ratio (SNR) values. First, the high-SNR results of Wang and Giannakis are generalized and unified for an arbitrary performance measure. Second, we develop a Mellin-transform-based procedure to construct low- and high-SNR asymptotics of error probability or outage. Specifically, these asymptotics are related to the left- and right-sided poles of a Mellin product with respect to its fundamental strip. Third, by using multiple low-SNR terms and a single high-SNR term, UAs for the error probability of coherent modulation are constructed for Rayleigh fading, maximal-ratio-combining (MRC), selection-combining (SC), dual hop relaying, and co-channel interference. UAs are also developed for the error probability of single- and multi-channel differential modulation, the product of two Q functions, and the miss probability of energy detection. By using a single low-SNR term and multiple high-SNR terms, the outage probability UA is also developed. Finally, since the capacity measure is not an exponentially decaying function, we derive a UA for an intermediate function which is based on the moment-generating function (MGF) and ultimately, the resulting approximation for the capacity.