On the Sum of Correlated Squared $\kappa-\mu$ Shadowed Random Variables and Its Application to Performance Analysis of MRC

In this paper, we study the statistical characterization of the sum of the squared κ-μ shadowed random variables with correlated shadowing components. The probability density function of this sum is obtained in the form of a power series. The derived pdf is utilized for obtaining the performance results of the maximal ratio combining (MRC) scheme over correlated κ-μ shadowed fading channels. First, we derive the moment-generating function (mgf) of the received signal-to-noise ratio of the MRC receiver. By using the derived mgf expression, the analytical diversity order is obtained; it is deduced on the basis of this analysis that the diversity of the MRC receiver over correlated κ-μ shadowed channels depends upon the number of diversity branches and μ parameter. Further, the analytical average bit error rate of the MRC scheme is also derived, which is applicable for M-ary phase shift keying and M-ary quadrature amplitude modulation constellations. The Shannon capacity of the correlated κ-μ shadowed channels is also derived in the form of the Meijer-G function.