當在考慮一個時變的多出多入通訊系統時，許多的研究者將研究投入了強韌
性的等化器（Robust equalizer），以對抗因為通道的不確定性（Channel uncertainty）
所帶來的問題。設計強韌性等化器的方法中，最受到歡迎的分別是貝氏法
（Bayesian approach）和最小化最大法（Minimax approach）。不過這樣的強韌性
等化器可能有太過於保守的缺陷。這裡所指的意思是這種等化器可能無法反應到
一個時變的通道：貝氏法只是考慮整個系統可能出現的平均不確定性，而最小化
最大法則只能考慮可能出現的最差不確定性。在這個研究當中，我們發展了一個
次佳最小化最大的合併等化器（Suboptimal minimax combining equalizer），以用
來涵蓋各種可能的時變多出多入通道。這個時變通道，我們則是採取馬可夫模型
（Markov model）來描述其轉換機制。根據次佳設計的概念，我們提出的等化器
將會以最小化最大法處理多種通道不確定性的狀態。接下來，這些不同的等化器
則可以以合適的比重（Weighting）來結合。這些比重的選取方式將會牽涉到可
能性函數（Likelihood function），以及狀態之間的轉換機率（Transition
probabitlities）。
我們首先介紹我們的設計概念：將通道不確定狀態切割成M 種可能之
後，針對此M 種狀態設計出不同的次佳線性強韌等化器。最後則要將這些不同
的次佳線性強韌等化器依照合適的比重來合併，成為合併線性強韌等化器。
接下來的重點可分為兩個部份，亦即：1. 如何求出M 種針對不同狀態
設計的等化器，2. 如何找到合適的比重加以合併。在第一個部份中，我們要先
提出一個引理，利用這個引理我們將可以得到次佳化的設計結果。

When considering time-varying MIMO communication systems, there were a
lot of researchers dedicating to the study of the robust equalizer to combat
the problem caused by channel uncertainty. The most popular approaches to
design a robust equalizer are the Bayesian approach and the minimax approach.
However, the conventional robust equalizer is sometimes too conservative, which
means it may not respond to time-varying channel very well, since they would
always consider only the average uncertainty and worst-case uncertainty in the
Bayesian approach and the minimax approach, respectively. In this study, we
develop a suboptimal minimax-combining equalizer to cover all possible timevarying
MIMO channels, which is modeled as a channel uncertain state switching
system in Markov transition. Due to the idea of suboptimal design, the proposed
equalizer extends the conventional MMSE equalizer to the robust combining
equalizer. This proposed equalizer will deal with the multiple uncertainty ranges
via minimax approach, and then the robust equalization results with respect
to distinct uncertainty ranges are combined together by weightings based on
likelihood function and the channel transition probabilities as the output. The
combination equalization involves the switching probability between the multiple
channel uncertain states and the likelihood functions. The advantage of the
switching system modeling is that when the time-varying channel falls into a
certain channel uncertain state, then a more suitable equalizer can be found.
When combining the multiple equalizers, the likelihood function is defined so
that give the more probable equalizers larger weightings.

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