A Generalized Algorithm for Blind Channel Identification with Linear Redundant Precoders
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Research Article A Generalized Algorithm for Blind Channel Identification with Linear Redundant Precoders Borching Su and P. P. Vaidyanathan Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Received 25 December 2005; Revised 19 April 2006; Accepted 11 June 2006 Recommended by See-May Phoong It is well known that redundant filter bank precoders can be used for blind identification as well as equalization of FIR channels. Several algorithms have been proposed in the literature exploiting trailing zeros in the transmitter. In this paper we propose a generalized algorithm of which the previous algorithms are special cases. By carefully choosing system parameters, we can jointly optimize the system performance and computational complexity. Both time domain and frequency domain approaches of channel identification algorithms are proposed. Simulation results show that the proposed algorithm outperforms the previous ones when the parameters are optimally chosen, especially in time-varying channel environments. A new concept of generalized signal richness for vector signals is introduced of which several properties are studied. Copyright © 2007 B. Su and P. P. Vaidyanathan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Wireless communication systems often suffer from a problem due to multipath fading which makes the channels frequency-selective. Channel coefficients are often unknown to the receiver so that channel identification needs to be done before equalization can be performed. Among techniques for identifying unknown channel coefficients, blind methods have long been of great interest. In the literature many blind methods have been proposed based on the knowledge of second-order statistics (SOS) or higher-order statistics of the transmitted symbols [1, 2]. These methods often need to accumulate a large number of received symbols until channel coefficients can be estimated accurately. This requirement leads to a disadvantage when the system is working over a fast-varying channel. A deterministic blind method using redundant filterbank precoders was proposed by Scaglione et al. [3] by exploiting trailing zeros introduced at the transmitter. Figure 1 shows a typical linear redundant precoded system. Source symbols are divided into blocks with size M and linearly precoded into P-symbol blocks which are then transmitted on the channel. It is well known that when P ≥ M + L, where L is the maximum order of the FIR channel, interblock interference (IBI) can be completely eliminated in absence of
noise. When the block size M increases, the bandwidth efficiency η = (M + L)/M approaches unity asymptotically. The deterministic method proposed in [3] (which we will call the SGB method) exploits trailing zeros with length L introduced in each transmitted block and assumes the input sequence is rich. That i
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