A simpler form of the Craig representation for the two-dimensional joint Gaussian Q-function

We derive a simpler form for the Craig (1991) representation of the two-dimensional joint Gaussian Q-function which dispenses with the trigonometric factor that precedes the exponentials in the integrands and furthermore results in an exponential argument that is precisely in the same simple form as that in the Craig representation of the one-dimensional Gaussian Q-function. As such, the entire dependence on the correlation parameter now appears only in the limits of integration. The resulting single integral form is particularly useful in evaluating the outage probability for dual diversity selection combining over correlated identically and nonidentically distributed log normal channels.