具深度正交對濾波器及時變通道估測於多載波通訊系統

Depth-L Biorthogonal Partners and Time-Varying Channel Estimation in Multicarrier Communication Systems

白植帆(Chih-Fan Pai)

指導教授 ： 馮世邁

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202001643

摘要

此篇論文包含兩個部分，探討了兩個在多載波通訊系統中遇到的問題。在第一個部分，我們提出一種新類別的濾波器，並探討如何將之應用於多載波通訊系統，在多重路徑通道干擾下達成零符元干擾的通訊。此種新型提出的濾波器是奈奎斯特濾波器的延伸。在第二個部分，我們聚焦於正交分頻多工系統的時變通道估測問題。
在過去，奈奎斯特濾波器已經被許多研究者探討過。當一組濾波器串聯時成為一個奈奎斯特濾波器，我們稱它們為一組正交對濾波器。傳統正交對濾波器已經被廣泛探討過。在此篇論文的第一個部分，我們將奈奎斯特濾波器及正交對濾波器，分別推廣延伸至具深度奈奎斯特濾波器及具深度正交對濾波器。我們推導出有限脈衝響應具深度正交對濾波器存在的充分必要條件。我們發現這個充分必要條件與最大的一致零點集合的基數有關。藉由特徵濾波器方法，我們也提出了具深度奈奎斯特濾波器及具深度正交對濾波器的設計方法。另外，我們探討了具深度正交對濾波器的兩種應用。第一個應用是在部分間隔等化器，第二個是在濾波器組多載波系統。最後，我們進行了表現比較以展示具深度正交對濾波器的優勢。結果顯示，具深度版本的濾波器在對抗符元干擾及時間同步誤差時，具有比傳統版本濾波器更好的穩健性。
在許多無線通訊系統中，傳送通道除了具有頻率選擇性也具有時間選擇性。在過去，我們採用正交分頻多工系統解決了通道頻率選擇性的問題。然而，當通道同時具有頻率和時間選擇性時，正交分頻多工系統中子載波的正交性會被破壞並造成子載波之間的互相干擾。隨著都卜勒效應及通道的時間選擇性越趨嚴重，大家對於時變通道產生更多研究興趣。在此篇論文的第二個部分，我們聚焦於基於基擴展模型的正交分頻多工系統時變通道估測問題。藉由傳送一組訓練序列，我們展示基擴展模型的通道係數可以被分開估測並推導出它們的解析解。之後，我們將此基於訓練序列的方法推廣至領航符碼配置的方法。在領航符碼配置的方法中，除了傳送幫助通道估測的領航符碼外，還能傳送額外資料。我們提出的方法具有相當低的複雜度，並且對於通道長度有很強的穩健性。模擬結果顯示，相比另一個具領導地位的符碼配置方法，此提出的方法具有更好的表現。

關鍵字

奈奎斯特濾波器 ； 正交對濾波器 ； 濾波器組多載波系統 ； 部分間隔等化器 ； 通道估測 ； 正交分頻多工 ； 基擴展模型

並列摘要

In this thesis, we study two separate problems in multicarrier communication systems. Our works include two parts. In the first part, we propose a new class of filters and study their applications for multicarrier systems that can achieve transmission free of inter-symbol interference (ISI) for multipath channels. The proposed new filters are an extension of the class of Nyquist filters. In the second part, we focus on the time-varying (TV) channel estimation in orthogonal frequency division multiplexing (OFDM) systems.
In the past, Nyquist filters have been studied by many researchers. A pair of filters are said to be biorthogonal partners of each other if their cascade forms a Nyquist filter. The theory and design of traditional biorthogonal partners have been studied extensively. In the first part of this thesis, we extend these results to depth-L Nyquist filters and biorthogonal partners. A necessary and sufficient condition is derived for the existence of an finite impulse response (FIR) depth-L biorthogonal partner. We find out that the existence depends on the cardinality of the largest so-called congruous-zero set. We also propose the design method for these filters by applying the eigenfilter method. Additionally, two potential applications of depth-L biorthogonal partners are discussed in fractionally spaced equalizer (FSE) and filter bank multicarrier (FBMC) systems. Performance comparisons are carried out to demonstrate the advantage of depth-L biorthogonal partners. It is shown that the depth-L version is more robust against ISI and timing synchronization error compared to the traditional biorthogonal partner.
In many wireless communication systems, the transmission channels are not only frequency selective but also time selective. In the past, the issue of frequency selectivity is solved by adopting OFDM. However, when the channels are selective in both time and frequency, the subcarrier orthogonality of an OFDM system is destroyed and this leads to inter-carrier interference (ICI). As the Doppler effect and the resulting time selectivity of transmission channels becomes more severe, there is an increasing interest in the study of TV channels in OFDM systems. In the second part of this thesis, we focus on the study of TV channel estimation in OFDM systems based on basis expansion model (BEM). By transmitting a periodic training sequence, we show that the BEM channel coefficients can be estimated separately and the closed form formula for them is derived. Afterwards, this training sequence method is extended to the pilot-aided method, in which case we are able to transmit some data in addition to pilots for channel estimation. The proposed method enjoys low complexity and robustness against the channel length. Simulation results show that the proposed method compares favorably with a leading work on pilot-based estimation of BEM channels.

並列關鍵字

Nyquist Filter ； Biorthogonal Partner ； Filter Bank Multicarrier (FBMC) ； Fractionally Spaced Equalizer (FSE) ； Channel Estimation ； Orthogonal Frequency Division Multiplexing (OFDM) ； Basis Expansion Model (BEM)

參考文獻

[1] B. Farhang-Boroujeny, “OFDM versus filter bank multicarrier,” IEEE Signal Process. Mag., vol. 28, no. 3, pp. 92–112, 2011.

[2] R. Nissel, S. Schwarz, and M. Rupp, “Filter bank multicarrier modulation schemes for future mobile communications,” IEEE J. Sel. Areas Commun., vol. 35, no. 8, pp. 1768–1782, 2017.

[3] J. Kim, Y. Park, S. Weon, J. Jeong, S. Choi, and D. Hong, “A new filterbank multicarrier system: The linearly processed FBMC system,” IEEE Trans. Wireless Commun., vol. 17, no. 7, pp. 4888–4898, 2018.

[4] J. Nadal, C. A. Nour, and A. Baghdadi, “Design and evaluation of a novel short prototype filter for FBMC/OQAM modulation,” IEEE Access, vol. 6, pp.19 610–19 625, 2018.

[5] P. P. Vaidyanathan, Multirate systems and filter banks. Pearson Education India, 2006.