本論文考慮一個多用戶無線通訊系統的下行鏈波束成形設計問題，目標於分別最大化用戶的頻譜效益(Spectrum Efficiency)與系統的能量效益(Energy Efficiency)。具體而言，我們考慮基地台存在有界的通道估測誤差並且設計能最大化系統最差頻譜效益與最差能量效益的強健式波束成形設計。這個問題已知是NP-hard 的，因此我們尋找有效率且高精準性的次佳解。我們提出的低複雜度演算法是將原本困難非凸的最佳化問題，以一連串的凸近似問題取代，逐步尋找高效能近似解。不論是頻譜效益或能量效益，模擬結果皆顯示本論文提出的方法比目前現有的方法亦或是提供更好的性能或是具有較低的計算複雜度。

This work considers multiuser downlink beamforming design problems for maximizing the system spectrum efficiency and energy efficiency, respectively. Specifically, we assume that the base station has only imperfect, but bounded channel state information (CSI) error, and aim to design beamforming strategies for maximizing the worst-case spectrum efficiency and energy efficiency, respectively. The considered problems have been known to be NP-hard in general. Therefore, we seek computationally efficient and high-quality approximate solutions to the considered problems. The proposed methods are based on the successive convex approximation techniques, in which the difficult problem is approximated by a sequence of convex problems. The presented simulation results demonstrate that the proposed methods either outperform the existing methods or are computationally more efficient.

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