Secure Wideband Beamforming Design for Two-Way MIMO Relaying Systems

In this paper, secure wideband beamforming design is investigated for two-way multiple-input multiple-output (MIMO) relaying systems with one eavesdropper. Due to the wideband signals exchanged by two sources via the relay, inter-symbol-interference (ISI) occurs inevitably and makes the beamforming design more challenging than the narrowband beamforming design. To sufficiently combat the ISI, the tapped delay lines are deployed at the relay. Besides, to reduce the computational complexity at the tapped delay lines based relay, the analog beamforming structure is also considered, and thus the MIMO relay beamforming can be distinctly partitioned into a transmit beamforming and a receive beamforming bridged by a single link. Joint optimization of the transmit and receive beamformings at both the relay and two sources is considered to maximize the secrecy sum rate (SSR) of the two-way MIMO relaying systems. Since the joint optimization is nonconvex and intractable, an iterative algorithm is proposed to decompose the original SSR maximization problem into four individual subproblems that can be reformulated as three types of convex problems, i.e., the generalized Rayleigh quotient problems, the polynomial time differential convex problem, and the semidefinite programming problem. A suboptimal solution for the secure transmit and receive beamformings at all nodes can then be obtained iteratively. Finally, numerical experiments are conducted to corroborate the effectiveness of our proposed iterative algorithm in terms of the achievable maximum SSR and ISI suppression.