New series representations for generalized Nuttall Q-function with applications

In this article, we derive six distinct series representations of the generalized Nuttall Q-function. Interestingly, some of these expressions generalise some of the recent results on series representation of the Marcum Q-function since the Marcum Q-function is a special case of the Nuttall Q-function. To the best of our knowledge, five of these representations are novel and the other one is included for the completeness of the article. The performances of these representations are compared using the magnitude of the truncation error which gives a measure of the accuracy and rate of convergence and allow us to show the strength of each representation. We then discussed the area of applications of our result. We showed that our Nuttall Q-function representations and their corresponding special case (Marcum Q-function) (though not limited to only these), can be used in (i) the computation of outage probability of wireless communication system with co-channel interferers, (ii) the evaluation of detection probability of energy detector over generalized fading channels in cognitive radio system, and (iii) the computation of cumulative distribution of selection diversity combining in correlated Nakagami-m fading channel. In all these areas of application, our solution has no restriction on any parameter of interest.