Abstract
Recently, closed-form approximated expressions were obtained for the residual Inter Symbol Interference (ISI) obtained by blind adaptive equalizers for the biased as well as for the non-biased input case in a noisy environment. But, up to now it is unclear under what condition improved equalization performance is obtained in the residual ISI point of view with the non-biased case compared with the biased version. In this paper, we present for the real and two independent quadrature carrier case a closed-form approximated expression for the difference in the residual ISI obtained by blind adaptive equalizers with biased input signals compared with the non-biased case. Based on this expression, we show under what condition improved equalization performance is obtained from the residual ISI point of view for the non-biased case compared with the biased version.
Highlights
We consider a blind deconvolution problem in which we observe the output of an unknown, possibly nonminimum phase, linear system from which we want to recover its input using an adjustable linear filter [1]-[5]
This expression depends on the step-size parameter, equalizer’s tap length, input signal statistics, channel power and signal to noise ratio (SNR)
This expression is valid for blind adaptive equalizers where the error fed into the adaptive mechanism, which updates the equalizer’s taps, can be expressed as a polynomial function of order three of the equalized output and where the gain between the input and equalized output signal is equal to one as is in the case of Godard’s algorithm [17]. Based on this new derived expression we show under what condition improved equalization performance is obtained from the residual Inter Symbol Interference (ISI) point of view for the non-biased case compared with the biased version
Summary
We consider a blind deconvolution problem in which we observe the output of an unknown, possibly nonminimum phase, linear system from which we want to recover its input using an adjustable linear filter (equalizer) [1]-[5]. We derive for the real and two independent quadrature carrier case a closed-form approximated expression for the difference in the residual ISI obtained by blind adaptive equalizers with biased input signals compared with the non-biased case This expression depends on the step-size parameter, equalizer’s tap length, input signal statistics, channel power and signal to noise ratio (SNR). This expression is valid for blind adaptive equalizers where the error fed into the adaptive mechanism, which updates the equalizer’s taps, can be expressed as a polynomial function of order three of the equalized output and where the gain between the input and equalized output signal is equal to one as is in the case of Godard’s algorithm [17] Based on this new derived expression we show under what condition improved equalization performance is obtained from the residual ISI point of view for the non-biased case compared with the biased version.
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