Noncoherent Capacity of Secret-Key Agreement With Public Discussion

We study the noncoherent capacity of secret-key agreement with public discussion over independent identically distributed (i.i.d.) Rayleigh fading wireless channels, where neither the sender nor the receivers have access to instantaneous channel state information (CSI). We present two results. At high signal-to-noise ratio (SNR), the secret-key capacity is bounded in SNR, regardless of the number of antennas at each terminal. Second, for a system with a single antenna at both the legitimate and the eavesdropper terminals and an arbitrary number of transmit antennas, the secret-key capacity-achieving input distribution is discrete, with a finite number of mass points. Numerically we observe that at low SNR, the capacity achieving distribution has two mass points with one of them at the origin.