This paper investigates so-called diagonally correlated multiple input-multiple output (MIMO) channels, which provide higher ergodic capacity than independent and identically distributed (i.i.d.) fading channels. The presented analysis details physical scenarios leading to such channels, some properties of the channel matrix, and an analytical expression for its ergodic capacity.
Oezcelik, H., & Oestges, C. (2005). Some remarkable properties of diagonally correlated MIMO channels. IEEE Transactions on Vehicular Technology, 54(6), 2143-2145. https://doi.org/10.1109/TVT.2005.858193 (Original work published 2005)