本論文探討的是在大規模多用戶多輸入單輸出下行鏈路無線通訊系統中，使用
基於動態超表面天線 (DMA) 架構的基地台，為多個單天線用戶提供服務的場景。我們的目標是聯合最佳化預編碼器和 DMA 的電磁超材料元件係數，以最大化系統的加權總速率。由於這些參數互相耦合，且在電磁超材料元件係數的限制條件中具有非凸性，因此這項任務極具挑戰性。現有的解決方法 AO-RMO 是採用基於交替最佳化 (AO) 框架的演算法來克服這個問題。具體而言，使用加權最小均方誤差 (WMMSE) 演算法來設計預編碼器，並使用黎曼流形最佳化 (RMO) 來處理 DMA 的電磁超材料元件係數。雖然 AO-RMO 演算法在效能上表現卓越，但其時間複雜度和計算複雜度相對較高。為了解決這個問題，我們提出了一種計算效率更高的替代方法：基於投影梯度下降法 (PGD) 的演算法，以最佳化 DMA 的電磁超材料元件係數。此外，為了符合實際應用的需求，我們提出了基於交叉熵最佳化法 (CEO) 的演算法來設計具有離散值的電磁超材料元件係數。模擬結果顯示，在考慮連續型電磁超材料元件係數的情況下，我們提出的 AO-PGD 演算法實現了接近 AO-RMO 的效能，同時在時間複雜度和計算複雜度方面都優於 AO-RMO。當考慮離散型的電磁超材料元件係數時，我們提出的 AO-CEO 演算法提供了卓越的效能表現。

The research topic of this paper is the dynamic metasurface antenna (DMA). In our system model, a base station based on the DMA architecture is employed to provide services to users, operating in a millimeter-wave channel environment. To optimize the overall system weighted sum rate, we aim to jointly design the precoder and coefficients of the DMA. The challenge in this task lies in the Lorentzian-constrained model of the DMA coefficients. Existing literature has proposed Riemannian manifold optimization (RMO) to address this issue, but its computational and time complexity is high. To improve this problem, we propose the projection gradient descent (PGD) algorithm to enhance execution speed. Additionally, in practical applications, the DMA coefficients should consider discrete phase shifts, and for this issue, we propose the cross entropy optimization (CEO) to resolve it.

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