在本篇論文中，考慮了多輸入單輸出多播系統中的無線能量蜂巢式網路(WPCN)。假設在基地台中不存在通道的完美通道狀態資訊(CSI)，且通道狀態資訊訊息的不確定性由歐幾里德球形不確定性集合建構。為了最佳化下行鏈路的發射功率，下行時透過三角不等式來求得所能獲取的最小能量，而在上行時提出的方法透過統計共變數矩陣的不確定性的分佈，在中斷概率不超過設定的閾值，且滿足使用者所要求的最小服務品質(QoS)，使總下行鏈路發射功率最小化。由於最佳化問題並非凸函數，因此利用半正定放寬技術(SDR)來解決問題。接著會進一步證明，透過半正定放寬技術所求得的解秩為一，這代表透過半正定放寬技術所得到的解和原始的最佳化問題的解是相同的。再來討論在大規模天線系統下，由於通道向量會隨著天線數增加而彼此趨近正交，透過這個特性吾人可以求得趨近最佳化的封閉解。最後由數據證明可顯示出，我們提出的封閉解性能接近於不完美通道狀態資訊的解。;This paper considers wireless powered communication networks in multiple-input single-output multicasting system. Assuming that perfect channel state information (CSI) for all channels is not available at Base Station, the uncertainty of the CSI is modeled by an Euclidean ball-shaped uncertainty set. To optimize the downlink transmit power, we proposed method uses the knowledge of the statistical distribution of such a covariance uncertainty to minimize the total downlink transmit power under the constraint that the outage probability does not exceed a certain threshold. Due to non-convexity of the problems, we use semidefinite relaxation technique to solve problem. We further show that the solution of the relaxed SDP is always rank one. This indicates that the relaxation is tight and we can get the optimal solution for original problem. Due to the asymptotic orthogonality of the channel vectors when the number of transmit antennas is large, we are able to obtain the closed-form asymptotically optimal solutions. Numerical results show that the asymptotic performance of the proposed scheme is close to ideal case with Imperfect CSI.
