Optimal Channel Estimation in Beamformed Systems for Common-Randomness-Based Secret Key Establishment

Establishing secret keys from the commonly-observed randomness of reciprocal wireless propagation channels has recently received considerable attention. We consider such key establishment between two multiantenna nodes that use beamforming for communication, showing that the upper bound on the number of key bits that can be generated from the channel observations can be maximized by properly probing the channel. Specifically, we demonstrate that the eigenvectors of the channel spatial covariance matrix should be used as beamformer weights during channel estimation and we optimize the energy allocated to channel estimation for each beamformer weight under a total energy constraint. Finally, by assuming that the channel covariance is separable, we illustrate implementation of the technique for practical beamforming systems and more advanced signal models that incorporate antenna mutual coupling.