Generalized Channel Probing and Generalized Pre-Processing for Secret Key Generation

The paper considers secret key generation (SKG) from a channel between Alice and Bob against Eve all with multiple antennas. A generalized channel probing (GCP) method and a generalized pre-processing (GPP) method are proposed as two major steps before quantization, information reconciliation and privacy amplification for SKG. The degree-of-freedom (DoF) of the secret key capacity (SKC), relative to power or signal-to-noise ratio, based on the data sets at Alice, Bob and Eve after the execution of GCP is shown. The SKC-DoF is also shown to be the same as that based the new data sets after the application of GPP except for modifications chosen for computational efficiency. In particular, if Eve has a less number of antennas than either Alice and/or Bob, the SKC-DoF grows with the number of random transmissions from either Alice and/or Bob within each channel coherence period. This SKC-DoF property for GCP and GPP does not require the reciprocity of the channel. A reciprocal channel simply adds a product of the numbers of antennas at Alice and Bob towards the total SKC-DoF. Also shown in this paper is GCP with embedded public pilots, which results in no loss of SKC-DoF. Two prior methods for channel probing are also reviewed, and it is shown that none of them has the above mentioned SKC-DoF property despite previous claims. The potential application areas of GCP and GPP include both wireless and wireline networks.