  This paper concerns maximizing the minimum achievable secrecy rate of a
two-way relay network in the presence of an eavesdropper, in which two nodes
aim to exchange messages in two hops, using a multi-antenna relay. Throughout
the first hop, the two nodes simultaneously transmit their messages to the
relay. In the second hop, the relay broadcasts a combination of the received
information to the users such that the transmitted signal lies in the null
space of the eavesdropper's channel; this is called null space beamforming
(NSBF). The best NSBF matrix for maximizing the minimum achievable secrecy rate
is studied, showing that the problem is not convex in general. To address this
issue, the problem is divided into three sub-problems: a close-to-optimal
solution is derived by using the semi-definite relaxation (SDR) technique.
Simulation results demonstrate the superiority of the proposed method w.r.t.
the most well-known method addressed in the literature.
