濾波器組多載波系統中使用半正定放寬之具深度正交對濾波器設計

Design of Depth-L Biorthogonal Partners Filters in Filter Bank Multicarrier Systems using Semidefinite Relaxation

林奕秀(Yi-Hsiu Lin)

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(2021年)

https://doi.org/10.6342/NTU202102036

摘要

近年來，由於濾波器組多載波（Filter Bank Multicarrier, FBMC）系統具有低帶外發射（Out-of-Band Emission, OoBE），因此被推出來替代正交分頻多工（Orthogonal Frequency Division Multiplexing, OFDM）系統。然而，濾波器組多載波系統在頻率選擇性通道（Frequency-Selective Channel）下會受到符元間干擾（Inter-Symbol Interference, ISI）的影響，使得接收端需使用比較複雜的等化器（Equalizer）。因此，過去很多研究探討利用深度正交對（Depth-L Biorthogonal Partners）濾波器在頻率選擇性通道下的濾波器組多載波系統中透過簡單的一階等化器（One-tap Equalizer）達到無符元間干擾的傳輸，並且提出多種深度正交對濾波器的設計方法。本論文提出了兩個設計深度正交對低通濾波器的方法使得系統的訊號雜訊比（Signal-to-Noise Ratio, SNR）被最大化。再者，我們提出的設計方法1針對濾波器的阻帶能量（Stopband Energy）有功率限制以更好地抑制射頻干擾（Radio Frequency Interference, RFI），而我們提出的設計方法2針對濾波器的阻帶（Stopband）中的峰值能量有功率限制以減少對濾波器的通帶（Passband）的干擾。此外，我們利用半正定放寬（Semidefinite Relaxation, SDR），結合Dattorro等人所提出的一個迭代演算法，來解決我們設計濾波器的問題。模擬結果顯示，我們提出的設計方法1是在濾波器的阻帶能量及系統的位元錯誤率（Bit Error Rate, BER）間進行權衡取捨，而我們提出的設計方法2是在濾波器的阻帶中的峰值能量及系統的位元錯誤率間進行權衡取捨

關鍵字

深度正交對濾波器 ； 濾波器組多載波系統 ； 阻帶衰減 ； 凸函數最佳化 ； 半正定放寬

並列摘要

In recent year, filter bank multicarrier (FBMC) systems have been promoted as an alternative to orthogonal frequency division multiplexing (OFDM) systems due to having low out-of-band emission (OoBE). However, FBMC systems suffer from inter-symbol interference (ISI) when the channels are frequency-selective and additional equalizers are needed at the receivers. Therefore, the connection between depth-L biorthogonal partners and ISI-free transmission in FBMC systems under frequency-selective channels with simple one-tap equalizers has been studied in the past, and various design methods for the depth-L biorthogonal partner filters have been proposed. In this thesis, two methods are proposed to design the depth-L biorthogonal partner low-pass filters such that the signal-to-noise ratio (SNR) is maximized, while our proposed method 1 has a power constraint on the stopband energy of the designed filters to have better suppression of radio frequency interference (RFI) and our proposed method 2 has a power constraint on the peak power in the stopband region of the designed filters to reduce the main interference to the passband region. In addition, the semidefinite relaxation (SDR) together with an iterative algorithm proposed by Dattorro et al. are applied to solve the problem. Simulation results show that our proposed method 1 has a trade-off between the stopband energy of the designed filters and the BER performance, while our proposed method 2 has a trade-off between the peak power in the stopband region of the designed filters and the BER performance.

並列關鍵字

depth-L biorthogonal partners ； filter bank multicarrier (FBMC) ； stopband attenuation ； convex optimization ； semidefinite relaxation (SDR)

參考文獻

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