On The Compound MIMO Wiretap Channel with Mean Feedback
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by
Amr Abdelaziz, C. Emre Koksal, Hesham El Gamal, Ashraf D. Elbayoumy
2017
Abstract
Compound MIMO wiretap channel with double sided uncertainty is considered
under channel mean information model. In mean information model, channel
variations are 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, we provide the capacity achieving beamforming
direction. 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. Moreover, capacity achieving beamforming
direction is found to require matrix inversion, thus, we derive the null
steering (NS) beamforming as an alternative suboptimal solution that does not
require matrix inversion. NS beamformer is in the direction orthogonal to the
eavesdropper mean channel that maintains the maximum possible gain in mean main
channel direction. Extensive computer simulation reveals that NS performs very
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.
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