Sum and difference of two squared correlated Nakagami variates in connection with the McKay distribution

General formulas for the probability density function of the sum and the difference of two correlated, not necessarily identically distributed, squared Nakagami variates (or equivalently, gamma variates) are derived. These expressions are shown to be in the form of the McKay "Bessel function" distributions. In addition, formulas for the moments of these distributions, in terms of the Gauss hypergeometric function, are provided. An application of these new results relevant to the calculation of outage probability in the presence of self-interference is discussed.