Outage probability with transmit and receive diversity in a shadowing environment

We study the effects of lognormal shadowing on systems employing transmit and receive diversity. We derive a closed form formula for the average outage probability of a cellular system with M transmit antennas and N receive antennas. Two cases are considered: (i) all M × N channels are affected by the same shadowing environment, and (ii) all channels face independent shadowing. We validate the formulas that are derived by Monte-Carlo simulations. The results show that the outage probability of the independent-shadowing channels is less than the case in which all channels face the same shadowing.