Maximising the minimum achievable secrecy rate of two‐way relay networks using the null space beamforming method

Abstract

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.

Secure transmission in AF satellite system based on FH‐MWFRFT and null space beamforming

“…5 and 6 with the comparison to the method in [30]. According to these two figures, the secrecy capacity acquired by the proposed method outperforms the method in [30] and both of them reach a same upper bound when . As for the situation of , the secrecy capacity of the proposed method is higher when is small, and is lower with the increasing of than the method in [30].…”

“…The secrecy capacity of proposed method under one‐way scenario is depicted in Figs. 5 and 6 with the comparison to the method in [30]. According to these two figures, the secrecy capacity acquired by the proposed method outperforms the method in [30] and both of them reach a same upper bound when .…”

“…Comparison of computing time versus secrecy capacity and maximum power at the satellite between the proposed scheme and the transmission scheme in [30]…”

“…According to (15), the optimisation problem with NSBF can be given by Since this optimisation is non‐convex, the regular solution is to transform the original problem to a semi‐definite programming problem [30] or a second‐order cone programming problem [36]. Even the SVD is utilised during the designment of the beamforming vector, a optimisation method is still needed if a optimum performance is expected (structured beamforming).…”

“…It was demonstrated that the underlying achievable secrecy rate optimisation problem of a two‐way relay network could be simplified by adopting NSBF [29]. The sum secrecy rate constraint was taken into account to reside the obtained rates inside the secrecy rate region in a MIMO non‐regenerative relay system with SWIPT [30]. The null space vectors of useful signal and the orthogonal subspace vectors of the interference signal were combined in [31] to propose two types of beamforming methods to cancel the inter‐link interference and maximise the spectral efficiency in a three node AF relay network.…”