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López-Martínez, Francisco Javier Romero-Jerez, Juan Manuel López-Martínez, Francisco Javier 2017-07-27T10:05:01Z 2017-07-27T10:05:01Z 2015 F. J. Lopez-Martinez and J. M. Romero-Jerez, "Asymptotically Exact Approximations for the Symmetric Difference of Generalized Marcum $Q$-Functions," in IEEE Transactions on Vehicular Technology, vol. 64, no. 5, pp. 2154-2159, May 2015. 0018-9545 http://hdl.handle.net/10630/14395 In this paper, we derive two simple and asymptotically exact approximations for the function defined as ΔQm(a, b) =Δ Qm(a, b) - Qm(b, a). The generalized Marcum Q-function Qm(a, b) appears in many scenarios in communications in this particular form and is referred to as the symmetric difference of generalized Marcum Q-functions or the difference of generalized Marcum Q-functions with reversed arguments. We show that the symmetric difference of Marcum Q-functions can be expressed in terms of a single Gaussian Q-function for large and even moderate values of the arguments a and b. A second approximation for ΔQm(a, b) is also given in terms of the exponential function. We illustrate the applicability of these new approximations in different scenarios: 1) statistical characterization of Hoyt fading; 2) performance analysis of communication systems; 3) level crossing statistics of a sampled Rayleigh envelope; and 4) asymptotic approximation of the Rice Ie-function. eng open access by-nc-nd Análisis funcional Asymptotically Exact Approximations for the Symmetric Difference of Generalized Marcum-Q Functions journal article