Blind Channel Estimation and Equalization for Multiple FIR Channels
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Blind Channel Estimation and Equalization for Multiple FIR Channels Shiann-Jeng Yu National Center for High Performance Computing, Hsin-Shi Tainan Country 744, Taiwan Email: [email protected]
Fang-Biau Ueng Department of Electrical Engineering, National Chung Hsing University, 250 Kuo-Kuang Road, Taichung 402, Taiwan Email: [email protected] Received 15 February 2004; Revised 1 June 2004; Recommended for Publication by Xiaodong Wang This paper deals with the problem of blind equalizations based on effective channel order determination for multiple FIR channels. Most popular order determination methods use the eigenvalue decomposition (EVD) technique with an overmodeled data correlation matrix. However, performing the EVD consumes huge computation resources. In this paper, we consider the channel with infinite small leading and tailing terms which is natural for measured microwave radio channels, and develop a computationally simple method for effective channel order determination. Based on multiple-shift property of a data correlation matrix, a new performance index is analyzed. The channel order is determined if the performance index is greater than a threshold. To select the threshold, we model the performance index as an F-distributed random variable. For a specified confidence level, the threshold can be found from the table. This proposed method does not require EVD, the computation load is much lower than that of the EVD-based methods. Keywords and phrases: second-order statistics, channel equalization, channel order estimation, F-distribution.
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INTRODUCTION
Blind adaptive equalization of multiple FIR channels without training data available was studied intensively in the literature. Several algorithms have been developed by using the second-order statistics (SOS) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. For the SOS-based algorithms, channel order is a crucial parameter for computing the equalization parameters. However, methods for estimating the channel order are quite limited. The most popular methods for order determination, for example, AIC and MDL, are developed based on the information theoretical criteria [11]. However, researches show the AIC and MDL in the measured microwave radio channels are very sensitive to variations in the signal to noise ratio (SNR) and the number of data samples [12]. This prohibits their application for channel order estimation. Due to the nature of practical microwave radio channels having long small leading and tailing channel terms, it has been shown that blind channel equalization algorithms should attempt to model only the significant part of the channel composed of the large impulse response terms [13]. Small leading and tailing terms being modeled in the
blind equalization algorithms in general lead to poor performance and should be avoided [13]. The number of significant part of the channel is referred to the “effective” channel order. Using numerical analysis arguments and concept of angles of analysis between subspaces and invariant subspace perturbation results, a d
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