Self-Tuning Blind Identification and Equalization of IIR Channels
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Self-Tuning Blind Identification and Equalization of IIR Channels Miloje Radenkovic Department of Electrical Engineering, College of Engineering and Applied Science, University of Colorado at Denver, Denver, CO 80127-3364, USA Email: [email protected]
Tamal Bose Department of Electrical and Computer Engineering, Center for High-speed Information Processing (CHIP), Utah State University, Logan, UT 84322, USA Email: [email protected]
Zhurun Zhang Department of Electrical and Computer Engineering, Center for High-speed Information Processing (CHIP), Utah State University, Logan, UT 84322, USA Email: [email protected] Received 10 September 2002 and in revised form 18 February 2003 This paper considers self-tuning blind identification and equalization of fractionally spaced IIR channels. One recursive estimator is used to generate parameter estimates of the numerators of IIR systems, while the other estimates denominator of IIR channel. Equalizer parameters are calculated by solving Bezout type equation. It is shown that the numerator parameter estimates converge (a.s.) toward a scalar multiple of the true coefficients, while the second algorithm provides consistent denominator estimates. It is proved that the equalizer output converges (a.s.) to a scalar version of the actual symbol sequence. Keywords and phrases: blind identification, self-tuning equalization, recursive estimation, digital filtering, parameter convergence.
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INTRODUCTION
Intersymbol interference (ISI) imposes limits on data transmission rates in many physical channels. Traditionally, channel equalization is based on initial training period, during which a known data sequence is sent to identify channel coefficients. When the training is completed, the equalizer enters its decision-directed mode, aiming at retrieving the information symbols. Due to severe time variations in channel characteristic, as it is the case in a mobile wireless HF communication system, the training sequence has to be sent periodically to update the estimate, thereby reducing the effective channel rate. In addition, time-varying multipath propagation can cause significant channel fading, leading to system outage and equalizer failure during the training periods. It is desirable that the channel be equalized without using training signal, that is, in a blind manner, by using only the received signal. The first blind channel equalization methods were based on a single-input single-output (SISO) channel models, sam-
pled at the symbol rate. Some of them, such as the constant modulus algorithms (CMAs), involve nonlinear optimization and higher-order statistics (cummulants) of the channel output [1, 2]. An exhaustive list of references of CMA methods is given in [3]. Interesting results regarding steady-state performance analysis of CMA are presented in [4, 5]. Accurate estimation of cummulants requires large sample sizes. Although nonminimum-phase SISO channel is invertible by an infinitely long equalizer, this equalizer is not implementable with a causal IIR filter,
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