應用於多輸入多輸出系統之最佳收發器設計

Abstract

本論文包含兩個部分，在第一個部分我們考慮應用在多輸入多輸出系統的收發器以及位元分配的設計。在早期的文獻當中，收發器的設計都是針對某一個特定的位元配置而設計出來的。在近期的研究中，位元配置也會被考慮在收發器的設計中。在這個部分中，我們考慮的問題是當總功率以及錯誤率有條件限制時，如何最大化傳輸速率。在這問題之下，我們提出了同時設計收發器和位元配置的方法。一般而言，我們推算出來的最佳位元配置都不會是正整數。可是這並不符合實際情況，所以在本篇論文我們也有考慮當位元配置是限制在整數的時候。首先我們先推導出最大化傳輸速率系統和最小化功率系統之間的關係。然後利用這個關係我們可以找到當位元配置被限制在整數的時候，最大化傳輸速率的最佳解。我們也用了很多模擬結果來驗證我們的推導。 在第二個部分，我們考慮的是應用於多載波系統上的傳送與接收窗框之設計。對於多載波系統而言,在設計傳送端和接收端的時候，傳送端濾波器和接收端濾波器的頻譜響應非常重要。對於傳送端而言，如果頻譜響應表現不理想，會導致功率能量的散溢，並且影響到其他的傳輸系統。對於接收端而言，如果頻譜響應表現不理想，受到外界電台的雜訊干擾將會非常嚴重。為了改善頻譜響應，我們會使用所謂的傳送與接收窗框。在這個部分，我們使用小波理論來設計傳送與接收窗框。我們會引入所謂的子濾波器。我們發現使用小波理論設計的系統在對抗電台雜訊干擾以及抑制功率能量的散溢有較為出色的表現。

This dissertation consists of two parts. In the first part, we consider the joint design of transceiver and bit allocation for multiple-input multiple-output (MIMO) channels. In the literature, there have been many results on designing transceivers for MIMO channels. In these results, the transceivers are designed for a given bit allocation or designed with real bit allocation. In this thesis, first we jointly optimize the transceiver with real-valued bit allocation for maximizing bit rate over MIMO channels. The optimal transceiver and bit allocation are obtained in a closed form. Second we consider the connection between the power-minimizing and rate-maximizing problems with bit allocation. We will show that if a transceiver is optimal for the power-minimizing problem, it is also optimal for the rate maximizing problem and the converse is true. The result holds whether the bit allocation is integer-constrained or not. Based on the duality, we develop algorithms to find the optimal solution for the power-minimizing problem and rate-maximizing problem with integer bit constraint.

In the second part, we consider the design of transmitting and receiving windows for multicarrier systems. For multicarrier systems, frequency characteristics play an important role in the design of the transmitting and receiving filters. To improve frequency separation, windowing techniques are often used. As these are frequency based characteristics, a filterbank representation provides a natural and useful way for formulating the problem. In this thesis, we propose a unified filterbank approach to design the transmitting and receiving windows for multicarrier systems. Using the filterbank approach, the frequency separation among the subchannels can be improved.