本篇論文提出多蜂巢多使用者的多輸入多輸出波束成形系統下的多目標能量最小化設計。首先，我們考慮的環境是一個多蜂巢多使用者的多輸入多輸出系統，其中一個基地台同時下傳資料到多個手機端的使用者。其次，我們規劃出一個多目標最佳化問題同時最小化不同組的蜂巢傳送能量並且透過訊號對干擾雜訊比的能量限制來保持使用者的服務品質。透過間接的方法我們可以有效的找出這個多輸入多輸出波束成形系統的多目標能量最小化問題的解。接著我們透過修改後的線性矩陣不等式限制的多目標最佳化演算法以較低的複雜度來解該多目標最佳化問題。多目標基因演算法可以用來解本篇論文的多目標最佳化問題並且保證能找到一個有全域收斂性質的怕累托最佳化解集合。模擬的結果在最後呈現出來，驗證我們提出的同時最小化不同區域能量的多目標波束成形設計的效能。

In this study, we propose a multi-objective power optimization design in a multicell multiuser multiple-input multiple-output (MIMO) beamforming system. First, we consider a multicell multiuser MIMO system with multiple base station (BS), each BS serve multiple downlink mobile stations (MS) simultaneously. Second, we formulate a multi-objective optimization problem (MOP) to simultaneously minimize the downlink powers of different groups of cells with an QoS subject to a limited signal to interference plus noise ratio (SINR). An indirect method is proposed to efficiently solve the MOP of Multicell Multiuser MIMO beamforming System. Then, a LMIs-constrained multi-objective optimization algorithm is proposed to the multi-objective power minimization problem with a low computational complexity efficiently. Moreover, a novel multi-objective evolutionary algorithm (MOEA) with modification is employed for solving the MOP to guarantee the global convergence of Pareto optimal solutions. Finally, simulation results are provided to validate the performance and show the superiority of the proposed multi-objective beamforming design to minimize the downlink power of different groups of cells simultaneously.

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