Resource allocation for secret transmissions over MIMOME fading channels

For a communication where agent Alice aims at transmitting to agent Bob a message which must be kept secret to a third agent Eve, we consider terminals equipped with multiple antennas, obtaining the multiple-input multiple-output multiple-output-eavesdropper (MIMOME) channel. In this scenario, we assume that Alice knows the instantaneous channel conditions of the Alice-Bob channel before transmission, while knowing only the statistics of the Alice-Eve channel. For Rayleigh fading channels there is a non-zero probability that Eve gets a better channel than Bob, thus obtaining some information on the secret message (secrecy outage probability). We derive a closed form expression of the secrecy outage probability and then we consider the problem of allocating the power among the space streams, in order to maximize the total rate of the secret message under a constraint on the secrecy outage probability.