多載波系統之時域等化

Abstract

在多載波系統中，循環前置(cyclic prefix)是用以避免符元之間的干擾(intersymbol interference)。然而循環前置需額外的頻寬，其長度通常取決於傳輸效率和系統效能之間的一個權衡。假如通道響應長度超過循環前置的範圍，則會產生符元之間的干擾而導致系統效能降低。一個簡單的補救方法是使用一時域等化器，將通道響應縮短至循環前置之範圍以內。本論文針對兩個眾所周知的多載波系統：離散多頻系統和正交分頻多工系統，發展出新的時域等化器之設計方法。時域等化器是一普遍用於離散多頻系統的裝置。許多方法已經被提出用來以設計容量最大化之時域等化器。在這些已提出的方法中都有一共同的假設即循環迴旋(circular convolution)可被用於雜訊信號及時域等化器。然而這個假設是不成立的，因為在一離散多頻系統中雜訊信號並不含有循環前置。對於等化後殘留之符元之間干擾，現存方法亦有類似的假設。由於這些不正確的假設，導致經過時域等化後之子載波雜訊和殘留之符元之間干擾量並未被正確的計算出，因而現存 之最佳解事實上並不是最佳的。在本論文的第一部份，我們嘗試解決此問題。我們首先仔細的分析經時域等化後的雜訊信號和殘留之符元之間干擾信號之統計特性，並推導出計算時域等化後的雜訊和殘留符元之間干擾功率的正確公式。然後我們重新審視通道容量並設計一真正最佳的時域等化器。模擬顯示我們所提出的方法優於現存的方法，且效能非常接近於理論之上限。

一典型的無線通道有多路徑(multipath)響應，這響應通常具有限脈衝響應(finite impulse response)的特性。因此其所對應的時域等化器會有無限脈衝響應(infinite impulse response)，這將導致傳統的時域等化器設計及其應用會有很高的計算複雜度。另在正交分頻多工系統中時域等化器的設計標的是平均位元錯誤率(bit- error-rate)，而平均位元錯誤率是等化器的一複雜函數，因此要求出最佳的時域等化器是一個非常困難的問題。在本論文的第二部份中，我們發展一些新的方法用以克服上述問題。首先我們提出一具無限脈衝響應之時域等化器來縮短通道的響應。在理論上吾人可以證明無線通道之時域等化器具有低階的無限脈衝響應特性，因此其階數可以遠小於有限脈衝響應之時域等化器。模擬顯示我們所提出的方法可以有效的降低計算複雜度，而其效能幾乎與現存之方法相同。我們接者進一步的提出一具有么正前置編碼(unitary precoding)之正交分頻多工系統。經過前置編碼的正交分頻多工系統不只可以提高子載波的多樣性(diversity)，同時也可以方便時域等化器之設計。我們提出一時域等化器的設計方法稱之為最大訊雜干擾比(maximum signal-to-interference-plus-noise ratio)。我們證明最佳的時域等化器可以將所有子載波的訊雜干擾比最大化，並且其解可以很容易的被導出。另一方面，要能完全的得到通道所提供的多樣性，接收端必須使用最大相似(maximum likelihood)偵測器。然而，用於前置編碼之正交分頻多工系統之最大相似偵測器的計算複雜度相當高，我們因此提出一偵測的方法稱之為混合型球型解碼和連續干擾消除(sphere-decoding-and-successive-interference-cancellation)。由模擬得知，此方法可以逼近最佳之效能，但其計算複雜度低。

In multicarrier systems, cyclic prefix (CP) is introduced to avoid intersymbol interference (ISI). The CP is an overhead and its size is chosen as a compromise between the transmission efficiency and system performance. If the length of the channel response exceeds the CP range, the ISI is induced and the system performance will be degraded. A simple remedy for this problem is to apply a time-domain equalizer (TEQ) such that the channel response can be shortened into the CP range. This dissertation is aimed to develop new TEQ design methods for two well known multicarrier systems: discrete multitone (DMT) and orthogonal frequency division multiplexing (OFDM). The TEQ is a commonly used device in DMT systems. Many methods have been proposed to design the TEQ with a capacity maximization criterion. An implicit assumption used by existing methods is that circular convolution can be conducted for the noise signal and the TEQ. This assumption is not valid because the noise vector, observed in a DMT symbol, does not have a CP. A similar assumption is also made for the residual ISI signal. Due to these invalid assumptions, the TEQ-filtered noise and residual ISI powers in each subcarrier were not properly evaluated. As a result, the existing optimum solutions are actually not optimal. In the first part of the dissertation, we attempt to resolve this problem. We first analyze the statistical properties of the TEQ-filtered noise signal and the residual ISI signal in detail, and derive precise formulae for the calculation of the TEQ-filtered noise and residual ISI powers. Then, we re-formulate the capacity maximization criterion to design the true optimum TEQ. Simulations show that the proposed method outperforms the existing ones, and its performance closely approaches the theoretical upper bound.

A wireless channel typically has the multi-path response, exhibiting a finite impulse response (FIR) characteristic. Thus, the corresponding TEQ will have an infinite impulse response (IIR). The direct application of conventional TEQ designs results in a filter with high computational complexity. In OFDM systems, the criterion for the TEQ design is the average bit error rate (BER) which is a complicated function of the TEQ, and the optimum TEQ is difficult to obtain. In the second part of the dissertation, we develop new methods to overcome the problems. We propose using an IIR TEQ to shorten the CIR. It can be shown that the ideal TEQ exhibits low-order IIR characteristics, and the order of the IIR TEQ can be much lower than that of the FIR TEQ. Simulations show that while the proposed method can reduce the computational complexity significantly, its performance is almost as good as existing methods. We then further propose an OFDM system with a unitary precoding. The precoded OFDM system not only enhances the diversity of subcarriers, but also facilitates the TEQ design. We propose a TEQ design method called the maximum signal-to-interference-plus-noise ratio (MSINR). It is shown that the optimum TEQ, maximizing the SINR of all subcarriers, can be easily derived. To full explore the diversity the channel provides, the detector used at the receiver must be the maximum-likelihood (ML). The computational complexity of the ML detector for the precoded OFDM system can be very high. We then propose a detection method, called the sphere-decoding-and-successive-interference-cancelation (SDSIC). The proposed method can have near-optimal performance but the computational complexity is low.