In direct-sequence code division multiple access (DS-CDMA) cellular system, tight power control is used to deal with near-far problem. In order to track a desired signal-to-interference-plus-noise-ratio (SINR), a state-space model is developed and a state feedback controller is taken into consideration for the optimal SINR tracking control. Hence, the optimal SINR tracking problem can be regarded as the single-objective (SO) H2 control problem. However, in order to overcome round-trip delay, channel fading and noises, the H-infinity control is used to efficiently attenuate these interferences to achieve robust SINR tracking. Hence, we propose the multiobjective (MO) H2/H-infinity power control for DS-CDMA cellular system in this paper.
In this study, the proposed multiobjective H2/H-infinity tracking control can achieve the optimal SINR tracking and optimal interference rejection simultaneously. However, the considered multiobjective H2/H-infinity tracking control is a difficult design problem, and is not easy to solve directly. Hence, we minimize the upper bounds of both objectives to solve the multiobjective H2/H-infinity tracking problem from the suboptimal viewpoint. This MO H2/H-infinity tracking control problem is transformed to minimizing two upper bounds under three bilinear matrix inequality (BMI) constraints, a BMIs-constrained MO problem (MOP). By applying the linear matrix inequality (LMI) toolbox in matlab and evolutionary algorithm, we can obtain the multiple solutions called Pareto optimal solutions for designer selection. Numerical simulation has been given to illustrate the design procedure to confirm the performance of the proposed MO H2/H-infinity power control for DS-CDMA cellular system.

在直序展頻分碼多重存取系統中，嚴格的功率控制可以用來處理通訊時所造成的遠近效應。為了去追蹤期望的訊號對干擾及雜訊比例，開發一個狀態空間模型並考慮狀態回授控制器用在最佳的訊號對干擾及雜訊比例的追蹤控制上。因此，最佳的訊號對干擾及雜訊比例追蹤問題可以視為單一目標的H2控制問題。然而，為了去克服通訊時會產生的來回通訊延遲、通道衰減與雜訊干擾，H-infinity控制可以有效率來減弱上述的干擾來達到強健的訊號對干擾及雜訊比例追蹤。因此在本篇論文，我們提出多目標H2/H-infinity功率控制用在直序展頻分碼多重存取系統。在本篇論文裡，所提出的多目標H2/H-infinity追蹤控制可以同時的達到最佳訊雜比追蹤與最佳抗干擾。然而，這個多目標H2/H-infinity追蹤控制是一個困難設計問題而且不容易直接去解決。因此，我們從求次優解的觀點去解決多目標H2/H-infinity追蹤問題藉由讓這個兩個目標的上界值達到越小越好。這個多目標H2/H-infinity追蹤問題就轉換成滿足一些雙線性矩陣不等式約束條件來使得這兩個目標所對應的上界值達到越小越好，我們稱這個問題為雙線性矩陣不等式約束條件的多目標問題。藉由使用matlab裡的線性矩陣不等式toolbox和演化運算法，我們可以在一次模擬中獲得許多不同的解，這些解稱作Pareto最佳解來供設計者做選擇。一些數值模擬可以用來闡述設計流程去證明這個設計問題在所提出多目標H2/H-infinity功率控制問題在直序展頻分碼多重存取系統的表現。

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