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Robust Transceiver Design for Broadband Multiuser Multi-Relay Networks

In this paper, we study the robust design of the relay beamforming (rBF) and destination equalization (dEQ) filters for broadband multiuser multi-relay networks employing single-carrier frequency-division multiple access (SC-FDMA) and orthogonal frequency-division multiple access (OFDMA). Thereby, we consider the realistic case where only imperfect channel state information is available for rBF and dEQ filter optimization. Our goal is to maximize a lower bound for the weighted achievable bit rate (ABR) of the network, subject to either individual relay power constraints (Ind-PCs) or an aggregate relay power constraint (Agg-PC). We first derive the optimal dEQ filters and the phases of the optimal rBF filter coefficients, which are independent of the power constraints. For the Agg-PC, the amplitude optimization of the rBF filter coefficients is decomposed into two subproblems, which correspond to the optimization of the power allocation across the relays and the power allocation across the users and subcarriers, respectively. We obtain a closed-form structural solution for the first subproblem by fixing the powers across users and subcarriers, and the global optimal solution for the second subproblem. For the Ind-PCs, the corresponding optimization problem is formulated as a reverse-convex problem with convex constraints. Subsequently, the constrained convex concave procedure is applied to approximate the original non-convex problem with a sequence of convex problems, which can be efficiently solved using convex optimization techniques. Simulation results validate the excellent performance of the proposed robust rBF and dEQ filter designs and show their superiority compared to conventional non-robust and naive relaying schemes.