廣義分頻多工系統之矩陣式參數化與其低複雜度收發機與最佳原型濾波器設計之應用

Matrix Characterization for Generalized Frequency Division Multiplexing Systems and its Applications in Low-Complexity Transceivers and Optimal Prototype Filter Designs

陳柏志(Po-Chih Chen)

指導教授 ： 蘇柏青

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201701053

摘要

廣義分頻多工為一極富可能性之調變方式，藉由使用原型濾波器，其具有低頻帶外輻射之特性。然而，當使用文獻中常見的一些原型濾波器時，廣義分頻多工系統通常是非正交的，因而招致相較於正交分頻多工，在接收機均方誤差與符元錯誤率上的頻帶內效能退化。

本論文提出一種新的基於矩陣來將廣義分頻多工傳送機矩陣參數化之方式，而非如傳統上利用原型濾波器之基於向量的參數化方式。此新的參數化方式使我們很容易推導廣義分頻多工（傳送機）矩陣的性質，包括使廣義分頻多工矩陣為非奇異與么正各自的條件。

藉由使用此新的參數化方式，我們推導出使最小均方誤差接收機之一種低複雜度實現方式存在的充分且必要條件。若選用么正的廣義分頻多工傳送機矩陣，此實現方式在多路徑通道的情況下存在。在此實現方式不存在的情況下，我們提出一種低複雜度次最佳最小均方誤差接收機，其效能近似最小均方誤差接收機之效能。

此新的參數化方式也使我們能推導出可最小化接收機均方誤差的最佳原型濾波器。在許多情況下，這些最佳原型濾波器對應於使用么正的廣義分頻多工矩陣。在廣義分頻多工系統使用這些最佳原型濾波器不會導致雜訊增強的問題，使得系統展現與正交分頻多工相同的均方誤差效能。

此外，基於提出的矩陣式參數化方式，我們為廣義分頻多工發展出一個能最小化頻帶外輻射並保持優良頻帶內效能的原型濾波器最佳化演算法。透過將特徵矩陣作為最佳化變數，該濾波器設計問題被表示為一個非凸問題。在一些轉換之後，我們提出一個迭代解決兩個凸問題的演算法來處理原問題。模擬結果顯示在相同頻譜效率的情況下，相較於正交分頻多工與文獻中的原型濾波器，最佳化所得的濾波器在頻帶外輻射與符元錯誤率上皆表現最好。

關鍵字

廣義分頻多工 ； 特徵矩陣 ； 么正矩陣 ； 低複雜度實現方式 ； 最佳原型濾波器 ； 頻帶外輻射 ； 符元錯誤率效能

並列摘要

Generalized frequency division multiplexing (GFDM) is a promising modulation scheme featuring low out-of-band (OOB) radiation, which is achieved through the use of prototype filters. However, GFDM systems are usually non-orthogonal with prototype filters commonly used in the literature, incurring in-band performance degradation in receiver mean square error (MSE) and symbol error rate (SER) compared to that achieved through orthogonal frequency division multiplexing (OFDM).

In this thesis, a new matrix-based characterization of GFDM transmitter matrices is proposed, as opposed to traditional vector-based characterization with prototype filters. The new characterization facilitates deriving properties of GFDM (transmitter) matrices, including conditions for GFDM matrices being nonsingular and unitary, respectively.

Using the new characterization, the necessary and sufficient conditions for the existence of a form of low-complexity implementation for a minimum mean square error (MMSE) receiver are derived. Such an implementation exists under multipath channels if the GFDM transmitter matrix is selected to be unitary. For cases where this implementation does not exist, a low-complexity suboptimal MMSE receiver is proposed, with its performance approximating that of an MMSE receiver.

The new characterization also enables derivations of optimal prototype filters in terms of minimizing receiver MSE. They are found to correspond to the use of unitary GFDM matrices under many scenarios. The use of such optimal filters in GFDM systems does not cause the problem of noise enhancement, thereby demonstrating the same MSE performance as OFDM.

In addition, based on the proposed matrix characterization, a filter optimization algorithm that minimizes OOB radiation while maintaining good in-band performance is developed for GFDM. Through the characteristic matrix as the optimizing variable, the filter design problem is formulated as a nonconvex problem. After some transformations, an algorithm in which two convex problems are solved iteratively is proposed to tackle the original problem. Simulation results show that under the same spectral efficiency, optimized filters perform the best in terms of both OOB radiation and SER performance, compared to OFDM and prototype filters existing in the literature.

並列關鍵字

Generalized frequency division multiplexing (GFDM) ； characteristic matrix ； unitary matrix ； low-complexity implementation ； optimal prototype filters ； out-of-band (OOB) radiation ； symbol-error-rate (SER) performance

參考文獻

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