The Nuttall Q function - its relation to the Marcum Q function and its application in digital communication performance evaluation

The Nuttall (1972) Q function is introduced and, for the case where the sum of its two order indices is odd, a closed-form expression is derived for it in terms of the Marcum (1950) Q function and modified Bessel functions of the first kind. Alternatively, a finite-range integral expression is also given for it, which has the identical form to that of the generalized Marcum Q function. Finally, digital communication performance applications involving the Nuttall Q function are presented to justify the value of the results.