在多天線系統下使用Kalman濾波器之Tomlinson-Harashima 前置編碼設計

Abstract

在本篇論文中， 我們研究了如何在多天線(MIMO)系統下運用Kalman 濾 波器來對通道做追蹤估計，並且結合Tomlinson-Harashima 前置編碼器來做通道等化的設計。在隨時間和距離變化而持續變動的多天線系統底下， 多天線的 Tomlinson-Harashima 前置編碼器是一項可以用來消除不同訊號流之間的干擾的技術，這項技術是髒紙編碼(Dirty paper coding)的延伸應用，和其他等化技術不同的地方是，它可以在保持通道容量不變的前提下完成等化。而Kalman 濾波器是一個運用了隨機過程觀念所延伸出來的估計方法，和其他估計技術不同的是，它是將以前到現在對要估計的變數所做的所有觀察集合起來當作估計的參考，而非只用要估計的當時所觀察到的資訊來做估計，因此可以獲得較為準確的結果。在假設當中，Tomlinson-Harashima 前置編碼器必頇在傳輸端和接收端都完整的知道通道資訊的前提下才會是完美的，而這個前提卻是不實際的假設。因此，為了更貼近現實的情況，我們研究了在只有部分通道資訊的前提下，運用Kalman 濾波器來估計通道並且在把通道估計誤差也考慮進去的狀況下來做Tomlinson-Harashima 前置編碼器的最佳化系統設計。在模擬結果的部分，我們比較了在TDD 的系統下本篇論文所提出的方法和用線性最小均方差(LMMSE)估計法來結合Tomlinson-Harashima 前置編碼器的結果，發現使用Kalman 濾波器的BER 會表現得比使用線性最小均方差(LMMSE) 估計法還要好， 並且當都卜勒速度改變時使用THP-Kalman 會比THP-LMMSE 還來得不易受影響。最後，我們也比較了在不同的模擬假設情形下THP-Kalman 和THP-LMMSE 的計算複雜度差異。

In this thesis, we study the problem of combining Kalman filter for channel tracking and Tomlinson-Harashima precoding for channel equalization in MIMO systems. The multiple-input multiple-output (MIMO) Tomlinson-Harashima precoder (THP) is a well known equalization structure for mitigating inter-stream interference in fading MIMO systems, which is the application of “dirty paper coding“ and can reserve the channel capacity. Kalman filter is an estimator based on the conception of random process, compare to other estimators, Kalman filter collects all previous channel information for estimating, yet the other estimators estimate the variables by considering the present observation. THP is optimal by assuming perfect channel state information (CSI) at both transmitter and receiver. However, this assumption is not achievable in real world. In this work, under the assumption of partial channel state information (P-CSI), we use Kalman estimation for channel tracking and combine the estimation into THP optimization which considers the channel estimation error. In simulation results, we compare the proposed approach with earlier works and can show that the performance (BER) of THP system with Kalman estimation (THP-Kalman) for channel tracking is superior to THP with linear-minimum-mean-square-error (LMMSE) estimator (THP-LMMSE) in time-division-duplex (TDD) system. Besides, we also compare the computation complexity of THP-Kalman and THP-LMMSE. By changing the Doppler rate (the parameter of mobility), THP-Kalman performs more flexible, while THP-LMMSE is sensitive to the varying rate of channel.