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In this paper, we study the statistical characterization of the sum of thesquared $\kappa-\mu$ shadowed random variables with correlated shadowingcomponents. The probability density function (PDF) of this sum is obtained inthe form of a power series. The derived PDF is utilized for obtaining theperformance results of the maximal ratio combining (MRC) scheme over correlated$\kappa-\mu$ shadowed fading channels. First, we derive the moment generatingfunction (MGF) of the received signal-to-noise ratio of the MRC receiver. Byusing the derived MGF expression, the analytical diversity order is obtained;it is deduced on the basis of this analysis that the diversity of the MRCreceiver over correlated $\kappa-\mu$ shadowed channels depends upon the numberof diversity branches and $\mu$ parameter. Further, the analytical average biterror rate of the MRC scheme is also derived, which is applicable for $M$-PSKand $M$-QAM constellations. The Shannon capacity of the correlated $\kappa-\mu$shadowed channels is also derived in the form of the Meijer-G function.

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