Consider a network consisting of two independent single-antenna sources, a single-antenna destination and a helping multiple-antenna relay. This network is called a dual-hop multiple access relay network (MARN). In this network, sources transmit to the relay simultaneously in the first time slot. The relay retransmits the received sum-signal to the destination using a linear beamforming scheme in the second time slot. In this paper, we characterize the achievable rate region of MARN under linear beamforming. The achievable rate region characterization problem is first transformed to an equivalent "corner point" optimization problem with respect to linear beamforming matrix at the relay. Then, we present an efficient algorithm to solve it via only semi-definite programming (SDP). We further derive the mathematical close-forms of the maximum individual rates and the sum-rate. Finally, numerical results demonstrate the performance of the proposed schemes.
Keywords: achievable rate region; beamforming; multiple-access relay network (MARN); semi-definite programming; semi-definite relaxation.