使用訊號空間分割技術之適應性貝氏等化

Abstract

貝氏等化器是符元型等化器中最佳的等化器。然而貝氏等化器的複雜度通常都非常高。最近訊號空間分割的技術已經被應用來降低貝氏等化器的複雜度。這個方法所形成的決策邊界是由一組平面組成，這些平面是由一個系統化的狀態搜尋程序所找到的。然而此方法的缺點有二，第一是，這些平面的個數是由通道特性所決定，而不能由我們控制，另一個缺點是他的搜尋程序不是很有效率。在本論文中，我們提出兩種演算法來解決這些缺點並且探討他的可能應用。對於第一種演算法，我們提出一個近似之貝氏成本函數，使得這些平面的個數是可以自由給定的。這樣所設計出來的等化器可以在複雜度和效能間取得一個平衡。在很多情況下，所提出來的等化器可以犧牲一點效能卻可以大大的降低複雜度。而這些平面的決定是由一個適應性的演算法所決定。這個適應性的方法非常的強健且複雜度低。

對於第二種演算法，我們將等化器的問題視為一個傳統分類問題。類似的看法最近也有人提出，現存之方法是使用非線性鑑別函數當作分類器。由於使用非線性鑑別器的緣故，往往很難同時達到很好的效能並且享有較低的複雜度。我們提出了一個新的方法來克服這樣的問題。我們的想法是利用比較多組的線性鑑別器來取代比較少組的非線性鑑別器。這樣的想法可以使鑑別器上的參數容易決定而且複雜度較低。而決定這些線性鑑別器的方法也跟第一個演算法類似。由於適應性的做法，所以我們所設計的等化器可以應用於時變的通道中。模擬顯示出我們所提出的方法可以很有效率的逼近貝氏等化器。

我們也同時將我們所提出的等化器應用於陣列天線的通訊系統中。這樣可以形成一個新的非線性空時等化器。這個等化器可以很有效率的逼近空時貝氏等化器。最後，我們針對非線性的最大似然序列估計等化器作了一些探討。眾所週知，在使用最大似然序列估計等化器必須知道通道的響應，然而非線性通道的響應並無一個通用的通道模型。我們提出了一個新的方法來克服這問題，使用這種方法我們完全無需通道模型，而且計算複雜度還可能較低。

The Bayesian equalizer, with or without decision feedback, is known to be optimal for the symbol-by-symbol type of equalizer. However, the computational complexity for the Bayesian equalizer is usually very high. Recently, the signal space partitioning technique has been proposed to solve the problem. It was shown that the decision boundary for the Bayesian equalizer consists of a set of hyperplanes and a systematic state-search process was proposed to find these planes. The main problem of the existing approach is that the number of hyperplanes cannot be controlled. Also, the state-search process is not always efficient. In this dissertation, we propose two new algorithms to remedy these problems and explore their potential applications. For the first algorithm, we propose an approximate Bayesian criterion that allows the number of hyperplanes to be arbitrarily set. As a consequence, a tradeoff can be made between performance and computational complexity. In many cases, the resulting performance loss is small while the computational complexity reduction can be large. An adaptive method using stochastic gradient descent is also developed to identify the functions. The adaptive method is robust and has very low computational complexity.

For the second algorithm, we treat equalization as a classical pattern classification problem. This type of equalization approach has been proposed recently also. Existing algorithms employed nonlinear discriminant functions in the classifier. Due to nonlinear characteristics of the discriminant functions, it is found that the classifier is difficult to save significant computations and at the same time achieve satisfactory results. We propose a new discriminant function approach to overcome this problem. Our idea is to employ a large set of linear discriminant functions instead of a small set of nonlinear functions. By this manner, parameter identification becomes much easier and the computational complexity becomes lower. Similar to the first approach, the number of discriminant functions can be arbitrarily set and an easy trade-off between performance and computational complexity can be made. An adaptive method is developed such that the proposed algorithm is applicable in time-varying environments. Simulations show that our approaches can efficiently approximate the Bayesian equalizer. Also, the low complexity property makes the proposed equalizers suitable for real-world implementation.

We also apply the proposed algorithms to antenna array communication systems. This results in new nonlinear spatio-temporal equalizers. While these algorithms efficiently approximate the spatio-temporal Bayesian equalizers, they inherent other good properties of the temporal counterparts. Finally, we consider the maximum likelihood sequence estimation (MLSE) equalizer for nonlinear channels. It is known that the channel response is required in the MLSE equalizer. However, there does not exist a general model for nonlinear channels. We propose a new MLSE equalizer that does not require any channel modeling and the computational complexity can be much lower than the MLSE equalizer with channel modeling.