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This paper focuses on the robust beamforming design for downlink multi‐cell multiple‐input multiple‐output (MIMO) nonorthogonal multiple access (NOMA) systems without having any restrictions on the number of users and cells. The beamforming matrices are designed by solving a sum rate maximization problem under imperfect channel state information (CSI) while satisfying transmission power constraints. In order to solve the proposed non‐convex optimization problem with infinite‐dimensional robust constraints, an iterative algorithm is provided to transform this problem into a convex form by utilizing diagonalization theory and introducing some auxiliary variables. Numerical results demonstrate that the proposed algorithm converges quickly, and the proposed robust NOMA design achieves strong robustness and acceptable performance. [ABSTRACT FROM AUTHOR]

The authors study robust beamforming and power allocation in cognitive relay networks using several relays in the secondary link. The channel state information is imperfect modelled by Gaussian random variables. First, minimisation of the total transmit power of relays and the secondary transmitter is considered with a constraint on the interference in the primary receiver. Also, a constraint is assumed on the received signal-to-interference plus noise ratio (SINR) in the secondary receiver. In the other scenario, maximisation of the SINR in the secondary receiver is investigated with a limit on the maximum transmit power of relays and the secondary transmitter. For each non-convex optimisation problem, an iterative and robust algorithm is derived. It is proved that the first proposed algorithm converges to the global optimum. Simulation results similarly show the convergence of both algorithms with a few number of iterations. The outperformance of the robust algorithms is shown compared with a non-robust design. [ABSTRACT FROM AUTHOR]