This work focuses on the beamforming design for downlink multiple-input single-output (MISO) nonorthogonal multiple access (NOMA) systems. The beamforming vectors are designed by solving a total transmission power minimization (TPM) problem with quality-of-service (QoS) constraints. In order to solve the proposed nonconvex optimization problem, we provide an efficient method using semidefinite relaxation. Moreover, for the first time, we characterize the optimal beamforming in a closed form with quasi-degradation condition, which is proven to achieve the same performance as dirty-paper coding (DPC). For the special case with two users, we further show that the original nonconvex TPM problem can be equivalently transferred into a convex optimization problem and easily solved via standard optimization tools. In addition, the optimal beamforming is also characterized in a closed form and we show that it achieves the same performance as the DPC. In the simulation, we show that our proposed optimal NOMA beamforming outperforms OMA schemes and can even achieve the same performance as DPC. Our solutions dramatically simplifies the problem of beamforming design in the downlink MISO NOMA systems and improve the system performance.

中文翻译：

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下行链路 MISO NOMA 系统的优化波束成形设计

这项工作的重点是下行链路多输入单输出 (MISO) 非正交多址 (NOMA) 系统的波束成形设计。波束成形矢量是通过解决具有服务质量 (QoS) 约束的总传输功率最小化 (TPM) 问题来设计的。为了解决所提出的非凸优化问题，我们提供了一种使用半定松弛的有效方法。此外，我们首次在具有准退化条件的封闭形式中表征了最佳波束成形，这被证明可以实现与脏纸编码（DPC）相同的性能。对于有两个用户的特殊情况，我们进一步表明，原始的非凸 TPM 问题可以等效地转换为凸优化问题，并且可以通过标准优化工具轻松解决。此外，最佳波束成形也以封闭形式表征，我们表明它实现了与 DPC 相同的性能。在模拟中，我们表明我们提出的最优 NOMA 波束成形优于 OMA 方案，甚至可以达到与 DPC 相同的性能。我们的解决方案极大地简化了下行链路 MISO NOMA 系统中的波束成形设计问题，并提高了系统性能。