合作式放大傳遞多輸入多輸出中繼系統之強健性Tomlinson-Harashima來源端與線性中繼端前置編碼設計

Abstract

在現存的合作式放大傳遞多輸入多輸出中繼系統傳收機的設計，通常假設此系統可得到完美的通道狀態資訊(perfect CSI)。但在實際系統應用上，可能無法獲得完美的通道狀態資訊。基於非完美通道狀態資訊的考量下，強健性的傳收機設計在實際應用上是需要被考慮的。在本論文中，我們提出一種強健性的傳收機設計，此傳收機中的來源端使用Tomlinson-Harashima 前置編碼 (THP)、線性中繼端前置編碼與最小均方錯誤(minimum mean-squared error)接收機。當兩個前置編碼的組合及非完美通道狀態資訊被考慮進來時，傳收機的設計變得相當困難。為了克服這個設計上的困難，我們提出一種前置編碼結構與設計方法，使得原本的傳收機設計可轉換為凹曲線最佳化問題，由此導出解析解。我們在TH前置編碼後串接一個單位前置編碼。這個額外的前置編碼的功能不僅可以簡化最佳化的問題而且可改善整個系統的效能表現。由於最佳化的問題是由多個前置編碼組成，我們使用最初分解(primal decomposition)將原本的最佳化問題分解成次要問題(subproblem)與主要問題(master problem)。依序解決次要問題與主要問題，原本由兩個前置編碼構成的問題，可簡化成設計單一中繼端前置編碼的問題。但是要解決主要問題仍然相當困難，因此我們對這個主要問題提出一個最低界線，並經由一些操作將此問題轉換成凹曲線最佳化的形式。透過Karush-Kuhn-Tucker(KKT)條件可以推導出解析解。模擬的結果顯示在完美/非完美的通道狀態資訊環境下，所提出的強健性傳收機設計在效能上的表現比現存的線性傳收機設計好。

The existing transceiver design in amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay systems often assume the perfect channel state information (CSI) is available. In practice, the perfect CSI is not attainable and the robust design with considering imperfect CSI is applied. In this paper, we propose a robust transceiver design for the system with Tomlinson-Harashima (TH) precoder, a linear relay precoder and a minimum-mean-square (MMSE) receiver. Since two precoders and the imperfect CSI are involved, the robust design problem is difficult. To overcome the difficulty, we additionally cascade a unitary precoder after the TH precoder. The unitary precoder can not only simply the optimization problem but improve the performance of the system. With the precoders, we use the primal decomposition to divide the original optimization problem into a subproblem and a master problem. The subproblem can be solved and the two-precoder problem can be reduced to the problem composed of single relay precoder. However, the master problem is still difficult to solve. We then proposed a lower bound for the cost function and transfer the master problem to a convex optimization problem. A closed-form solution can then be obtained by Karush-Kuhn-Tucker (KKT) conditions. Simulations show the that the proposed transceiver design have better performance than existing linear transceiver with either perfect/imperfect CSI.