A Study of Universal Formulas for Nonlinear Channel Identification in Orthogonal Frequency-Division Multiplexing Systems

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Project title

Code/計畫編號

NSC101-2221-E019-046

Translated Name/計畫中文名

正交分頻多工系統非線性通道鑑定之通用公式的研究

Project Coordinator/計畫主持人

Ching-Hsiang Tseng

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Electrical Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=2643544

Year

2012

Start date/計畫起

01-08-2012

Expected Completion/計畫迄

31-07-2013

Bugetid/研究經費

636千元

ResearchField/研究領域

電信工程

在本計畫中，我們將推導鑑定正交分頻多工系統中任意階非線性通道之通用公式。正交分頻多工是一種使用於寬頻通訊應用上已發展成熟之調變架構。它已經被許多有線及無線的通訊標準所採用以達到高速之資料傳輸。正交分頻多工訊號可能會對通訊鏈中之功率放大器相當敏感已是廣為所知的事實。因此，非線性通訊通道的估測對於設計一個正交分頻多工系統而言是不可或缺的。伏特拉級數是描述非線性通道常用的一種模型。一個非線性帶通通道通常可以用一個基頻等效伏特拉級數將其模式化。在此一模式中我們可將通道之輸入及輸出訊號的複數波封寫成數學關係式。在將非線性通道模式化的過程中我們需要鑑定通道之時域或頻域伏特拉核心。由於即使是在相對低階的伏特拉模型中，所需的核心係數通常都相當龐大，因此伏特拉核心之鑑定是一個非常具有挑戰性的困難任務，尤其是在非線性階數較高的場合。在文獻中我們可以找到許多鑑定非線性通道之伏特拉核心的方法。這些方法雖然適用於某些非線性階數較低的特定場合，但是他們都無法輕易地被直接推廣而應用在較高階之非線性通道。我們最近剛推導出一個鑑定正交分頻多工系統中三次非線性通道之頻域基頻等效伏特拉核心的創新方法。這個方法是透過探索正交分頻多工訊號之高階自動差頻譜來得到頻域基頻等效伏特拉核心之封閉解。這個方法可適用於上至三階之非線性通道以及正交分頻多工系統之子通道是使用QAM或PSK調變技術的場合。此方法所得到的解是在最小均方誤差下的最佳解，但此方法只限使用於三階非線性通道。本計畫為上述方法之進階研究，其目標為進行系統化的數學推導以得到適用於任意階非線性正交分頻多工系統的簡易鑑定方法。具體而言，我們將推導出任意階非線性正交分頻多工系統之頻域伏特拉核心的通用閉合表示式。這個封閉表示式所呈現的伏特拉核心值將是在最小均方誤差準則下的理論最佳解。此外，我們也將探索能保證實際獲得最小均方誤差下最佳估測值的新技術。我們將透過電腦模擬及實際實驗來驗證所推導出之通用公式的正確性及其效能。本計畫之完成有助於更加鞏固伏特拉級數在鑑定正交分頻多工系統中非線性通道上之理論及應用。In this project, we propose to derive universal formulas for identifying arbitrary-order nonlinear channels in orthogonal frequency-division multiplexing (OFDM) systems. The OFDM is a well-developed modulation scheme for wideband communication applications. It has been adopted by many wireline and wireless communication standards to achieve high-speed data transmissions. It is well known that the OFDM signal could be very sensitive to nonlinearities of power amplifiers in a communication link. Therefore, estimation of the nonlinear communication channel is essential to the design of an OFDM system. One com-monly used model for characterizing nonlinear channels is the Volterra series. A nonlinear bandpass channel is commonly modeled by a baseband equivalent Volterra series which re-lates the complex envelopes of the channel input and output. Modeling the nonlinear channel requires the identification of the time-domain or the frequency-domain Volterra kernels of the channel. The number of the required kernel coefficients is often very large even for a rela-tively low-order Volterra model. This makes the identification of the Volterra kernels a very challenging task, especially when the order of the nonlinearities is large. Various methods for identifying the Volterra kernels of nonlinear channels have been proposed in the literature. These methods, although are suitable for certain occasions with relatively low order nonli-nearities, might not be easily extendable to be applied to cases with higher-order nonlineari-ties in a straightforward manner. We have recently derived a novel method to estimate the frequency-domain baseband equivalent Volterra kernels of cubically nonlinear bandpass channels in OFDM systems. By exploring the higher-order auto-moment spectral properties of the OFDM signal, this method gives the closed-form solution for the frequency-domain baseband equivalent Volterra kernels of the nonlinear channel up to the third order. It can be used to identify cubically nonlinear channels in OFDM systems which employ QAM or PSK modulations in their subchannels. The obtained kernel estimates by this method are optimal in the minimum mean square error (MMSE) sense. A limitation of this method is that it is appli-cable only up to third-order nonlinear OFDM systems. The goal of this project is to perform an advanced and systematic study on generalizing the method we have derived for cubically nonlinear OFDM systems, so that it can be applicable to nonlinear OFDM systems of any or-der. Specifically, we will derive universal formulas of closed-form expressions for the fre-quency-domain Volterra kernels of nonlinear OFDM systems with an arbitrary order. The de-rived universal formulas will theoretically give the optimal MMSE solution of the Volterra kernels. Moreover, techniques for guaranteeing the estimated Volterra kernels to attain their optimal the MMSE solution will also be investigated. The correctness of the derived universal formulas and the effectiveness of the proposed method will be justified by computer simula-tion and real experiment. The completion of this project can consolidate the theory and appli-cation of the Volterra series for nonlinear channel identification in OFDM systems.

Keyword(s)

正交分頻多工
非線性通道
通道估測
伏特拉核心
系統鑑定
高階自動差頻譜
OFDM
nonlinear channel
channel estimation
Volterra kernel
system identification
higher-order auto-moment spectrum

DSpace CRIS

A Study of Universal Formulas for Nonlinear Channel Identification in Orthogonal Frequency-Division Multiplexing Systems

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