Asymptotically Exact Approximations for the Symmetric Difference of Generalized Marcum Q-Functions

作者：Lopez Martinez F Javier^*; Romero Jerez Juan M

来源：IEEE Transactions on Vehicular Technology, 2015, 64(5): 2154-2159.

DOI：10.1109/TVT.2014.2337263

• Asymptotic analysis
• cumulative distribution cdf)
• diversity reception
• Gaussian Q-function
• level crossing rate (LCR)
• Marcum Q-function
• Rice I-e-function

In this paper, we derive two simple and asymptotically exact approximations for the function defined as Delta Q(m)(a, b) = Q (Delta) under bar (m)(a, b) - Q(m)(b, a). The generalized Marcum Q-function Q(m)(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 Delta Q(m)(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 I-e-function.

• 出版日期2015-5