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.

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Millimeter wave beam alignment (BA) is a challenging problem especially for large number of antennas. Compressed sensing (CS) tools have been exploited due to the sparse nature of such channels. This paper presents a novel deterministic CS approach for BA. Our proposed sensing matrix which has a Kronecker-based structure is sparse, which means it is computationally efficient. We show that our proposed sensing matrix satisfies the restricted isometry property (RIP) condition, which guarantees the reconstruction of the sparse vector. Our approach outperforms existing random beamforming techniques in practical low signal to noise ratio (SNR) scenarios.Index Terms-MIMO, Millimeter Wave, beam alignment, compressed sensing.

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