  In this letter, we consider a multiple-input multiple-output two-way
cognitive radio system under a spectrum sharing scenario, where primary and
secondary users operate on the same frequency band. The secondary terminals
aims to exchange different messages with each other using multiple relays where
each relay employs an amplify-and-forward strategy. The main objective of our
work is to maximize the secondary sum rate allowed to share the spectrum with
the primary users by respecting a primary user tolerated interference
threshold. In this context, we derive a closed-form expression of the optimal
power allocated to each antenna of the terminals. We then discuss the impact of
some system parameters on the performance in the numerical result section.
