# On The Compound MIMO Wiretap Channel with Mean Feedback

## TL;DR

This paper analyzes the compound MIMO wiretap channel with mean feedback, deriving capacity-achieving beamforming strategies and proposing a null steering approach that performs close to optimal and outperforms traditional methods.

## Contribution

It introduces the null steering beamforming as a practical alternative to matrix inversion for secure MIMO communication under mean feedback uncertainty.

## Key findings

- Null steering beamforming closely matches optimal capacity.
- NS outperforms MRT and ZF beamforming across SNR range.
- Capacity equals the worst case over the uncertainty class.

## 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.