On The Compound MIMO Wiretap Channel with Mean Feedback

Compound MIMO wiretap channel with double sided uncertainty is considered under channel mean information model. In mean information model, channel variations is centered around its mean value which is fed back to the transmitter. We show that the worst case main channel is anti-parallel to the channel mean information resulting in an overall unit rank channel. Further, the worst eavesdropper channel is shown to be isotropic around its mean information. Accordingly, generalized eigenvector beamforming is known to be the optimal signaling strategy. We show that the saddle point property holds under mean information model, and thus, compound secrecy capacity equals to the worst case capacity over the class of uncertainty. Further, as the generalized eigenvector solution requires matrix inversion, we introduce null steering (NS) beamforming, that is, transmission in the direction orthogonal to the eavesdropper mean channel direction maintaining the maximum possible gain in mean main channel direction, as an alternative suboptimal solution. Extensive computer simulation reveals that NS performs extremely close to the optimal solution. It also verifies that, NS beamforming outperforms both maximum ratio transmission (MRT) and zero forcing (ZF) beamforming approaches over the entire SNR range. Finally, An equivalence relation with MIMO wiretap channel in Rician fading environment is established.