Semi-Blind Key-Agreement over MIMO Quasi-Static Channels

We analyze the fundamental limits of secret-key agreement over MIMO quasi-static fading channels. We establish closed-form expressions for secret-key capacity, in the low-power and high-power regimes,. In the former case, we show that the optimal signaling strategy is independent of the eavesdropper's fading realization, as the secret-key capacity is achieved by transmitting along the direction corresponding to the maximal eigenvalue of the legitimate channel. By combining this signaling strategy with reconciliation and privacy amplification, one obtains a semi-blind key-distillation strategy in which the knowledge of the eavesdropper's fading is required for privacy amplification alone. We also show that in the high-power regime every transmission strategy achieves the secret-key capacity, provided that power is transmitted over all the available directions.