Abstract
Secret sharing over the fast-fading MIMO wiretap channel is considered. A source and a destination try to share secret information over a fast-fading MIMO channel in the presence of an eavesdropper who also makes channel observations that are different from but correlated to those made by the destination. An interactive, authenticated public channel with unlimited capacity is available to the source and destination for the secret sharing process. This situation is a special case of the "channel model with wiretapper" considered by Ahlswede and Csiszár. An extension of their result to continuous channel alphabets is employed to evaluate the key capacity of the fast-fading MIMO wiretap channel. The effects of spatial dimensionality provided by the use of multiple antennas at the source, destination, and eavesdropper are then investigated.
Highlights
The wiretap channel considered in the seminal paper [1] is the first example that demonstrates the possibility of secure communications at the physical layer
Our result indicates that the key capacity is always positive, no matter how large the channel gain of the eavesdropper’s channel is; in addition this holds even if the destination and eavesdropper channel state information (CSI) is available only at the destination and eavesdropper, respectively
We show that the spatial dimensionality advantage that the eavesdropper has over the destination has exactly the same effect as the channel gain advantage of the eavesdropper
Summary
The wiretap channel considered in the seminal paper [1] is the first example that demonstrates the possibility of secure communications at the physical layer. Other approaches to employ feedback have been recently considered [22,23,24] It is shown in [22] that positive secrecy capacity can be achieved for the modulo-additive discrete memoryless wiretap channel and the modulo-Λ channel if the destination is allowed to send signals back to the source over the same wiretap channel and both terminals can operate in full-duplex manner. We show that the limiting key capacity is positive only if the eavesdropper has fewer antennas than the source The results in these scenarios confirm that spatial dimensionality can be used to combat the eavesdropper’s gain advantage, which was already observed for the MIMO wiretap channel. Perhaps more surprisingly, this is achieved with neither the source nor destination needing any eavesdropper CSI
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