本文提出一個基於多輸入單輸出正交多工系統的隱藏式感知無線系統，並且是考慮到通道估測不確定性的模型。在此系統中，為了達到次使用者的通訊服務品質以及主使用者的干擾減免的多目標問題，波束成形被利用來同時解決次使用者的最佳通訊服務品質和主使用者的最佳干擾減免的多目標問題。首先，一個基於二次約束的多目標最佳化問題被提出來描述感知無線電系統的多個目標和約束。接著，根據極大極小代換式將一個同時極大化次使用者通訊服務品質和極小化主使用者干擾的多目標波束成形設計問題，轉換成同時極小化最糟情形下的次使用者負的訊號對干擾加雜訊比值（signal-to-interference-plus-noise-ratio）以及極小化最糟情形下的主使用者干擾溫度（interference temperature）的多目標問題。然而，本文所考慮的多目標問題仍然不容易解決，因此我們提出的一個間接方法是透過不斷壓低各個目標的上界值來解決主使用者干擾減免和次使用者通訊品質改善的多目標波束成形設計問題。為了方便加速計算，再將問題轉換成線性矩陣不等式約束的多目標問題。再接著，我們提出一個基於線性矩陣不等式的多目標基因演化搜尋方法來獲取Pareto最佳解，並且為系統設計者提供一個選取最佳改進的程序來取得偏好的唯一波束成形設計。最後，一系列的數值模擬和設計流程說明用來證明這個波束成形設計方法對於我們提出的次使用者通訊服務品質和主使用者干擾溫度的多目標問題在多輸出多輸入正交多工系統的隱藏式感知無線系統上的表現。

In this study, we consider a multi-input-single-output (MISO) orthogonal frequency division multiplexing (OFDM) underlay cognitive radio system with channel uncertainty. In order to solve the multi-objective secondary user’s QoS enhancement and primary user’s interference mitigation problem in this system, a multi-objective beamforming design method is introduced for cognitive radio systems to guarantee optimal secondary user’s QoS performance and primary user’s interference power simultaneously. First, a quadratic constrained optimization problem is derived to represent the cognitive radio system. Then, based on the mini-max formulation, the beamforming design for both secondary user’s QoS enhancement and primary user’s interference mitigation are formulated as a multi-objective optimization problem (MOP) to minimize the worst case of the negative signal-to-interference-plus-noise ratio (SINR) of secondary users and the interference temperature (IT) of primary users for the cognitive radio system at the same time. Since it is not easy to solve the MOP directly, an indirect method is proposed to solve this MOP for multi-objective beamforming design, by minimizing the corresponding upper bounds of two objectives. For the convenience of design, the multi-objective beamforming design problem is transformed to a linear matrix inequalities (LMIs)-constrained multi-objective optimization problem. Further, a LMIs-constrained multi-objective evolutionary algorithm (LMIs-constrained MOEA) is developed to efficiently solve the set of Pareto optimal solutions for the MOP, and an improvement optimization process is provided for designer to select one unique design according to his own preference. Finally, a numeric simulation is given to illustrate the design procedure and to demonstrate the performance of the proposed multi-objective beamforming design for cognitive radio system.

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