Second-Order Analysis of Secret-Key Capacity From a MIMO Channel

This paper presents an analysis of Maurer-Ahlswede-Csiszar (MAC) bounds on secret-key capacity (SKC) based on a MIMO channel probing scheme between two multi-antenna nodes against a multi-antenna eavesdropper (Eve). To reveal useful insights into SKC, we consider the regime of high signal powers or high signal-to-noise ratios (SNR) where SKC consists of a first-order term (FoT) which is proportional to the logarithm of signal power, and a second-order term (SoT) which is invariant to signal power. Applying random-matrix theory for large numbers of antennas on all nodes, this paper shows the FoT and SoT of a lower MAC bound on SKC. While the FoT is consistent with prior work, which vanishes if none of the two nodes has more antennas than Eve and the channel is not perfectly reciprocal, the SoT shows a positive secrecy that increases linearly with the length of random transmissions from one node to another during channel probing even if Eve has many more antennas than the legitimate nodes.