Pilot-based secret key agreement for reciprocal correlated MIMÓME block fading channels

We consider a wireless communication scenario where two agents aim at agreeing on a secret key, while leaving a passive eavesdropper in the darkness. All terminals are equipped with multiple antennas resulting in a multiple input multiple output (MIMO) scenario with reciprocal correlated flat Rayleigh fading channels among antenna couples. Correlation properties are known to all agents. In order to limit complexity we focus only on pilot-based secret key agreement (SKA), resulting in a source model with wiretapper, where pilot sequences are known to all agents. The contribution of the paper is twofold: a) we derive closed form expressions of lower and upper bounds of the secret key achievable rates, and b) we address the training sequence optimization taking into account the spatial channel correlation. A reduced dimensionality problem is obtained when spatial correlation follows a Kronecker model and looser bounds are discussed. Numerical results in a cellular scenario, with reference to the cellular 3GPP MIMO channel model, show significant gains by the training sequence optimization.