Optimal Downlink Training Sequence for Massive MIMO Secret-Key Generation

In this paper, the secret-key capacity is max-imized by optimizing the downlink training sequence in a time division duplexing (TDD) massive multiple-input-multiple-output (MIMO) scenario. Both single-user and multiple user cases are considered. As opposed to previous works, the optimal training sequence and the related secret-key capacity is characterized in closed-form in the single-user case and the large antenna multiple-user case. Designs taking into account a constraint on the maximal number of pilots are also proposed. In the multiple-user case, both the max-min and the sum capacity criteria are considered, including potential user priorities. In the end, it is shown that massive MIMO boosts the secret-key capacity by leveraging: i) spatial dimensionality gain and ii) array gain. Moreover, in the large antenna case, the multiple-user capacity is obtained with no extra pilot overhead as compared to the single-user case.