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This letter exploits the cyclic prefix to create a blind adaptive globally convergent channel-shortening algorithm, with a complexity like least mean squares. The cost function is related to that of the shortening signal-to-noise solution of Melsa et al. (see IEEE Trans. Commun., vol.44, p.1662-72, Dec. 1996), and simulations are provided to demonstrate the performance of the algorithm.

We characterize the nonlinear distortion of frequency-shift keying (FSK) signals due to a multipath channel as a linear time varying channel. The dynamic range of time variation of this time-varying channel model is small for a mild multipath channel and large for a severe multipath channel. This characterization justifies the use of a decision directed adaptive linear equalizer for FSK signals after frequency demodulation in order to mitigate the distortion due to a multipath channel.

This paper provides a stability analysis of a class of acoustic noise control algorithms by showing that the adapted models have more in common with nonlinear, finite impulse response (FIR) equation error models than with the infinite impulse response (IIR) output error models they superficially resemble. Stability results from the adaptive control literature are applied to show global stability in the noise free case, and to show exponential stability when the input is persistently excited. The latter demonstrates a robustness to mismodeling errors, disturbances such as noises, and allows results to be applied to the tracking of time-varying systems.

The vector-constant modulus (VCM) criterion is an extension of the constant modulus (CM) criterion introduced recently for equalization of channels involving Gaussian sources. In this letter, we analyze the behavior of VCM for arbitrary source distributions and combined channel-receiver impulse responses of finite dimension. We begin by pointing out the difference between the VCM and CM cost functions and showing that the VCM criterion can be expressed as a composite criterion combining the CM cost function and a penalty term involving cross-correlations of the equalizer output. We continue by providing conditions for noise-free channels, under which VCM admits stable minima corresponding to zero-forcing (ZF) channel receivers. We find that for sub-Gaussian sources, the VCM and CM criteria share the same global minima. For Gaussian and super-Gaussian sources, however, it appears that only ZF receivers corresponding to input/output transmission delays at the extremes of the range of possible delays are truly stable equilibria of VCM.

In this letter, we extend results regarding the behavior of a symbol-spaced tapped-delay-line LMS-adapted equalizer in frequency domain terms to a fractionally spaced implementation. These results rely on an eigendecomposition of the autocorrelation matrix of the received signal. In fractionally spaced equalization systems, the output of the analog channel is oversampled, resulting in a cyclostationary signal. We derive its autocorrelation matrix. A symbol-spaced representation of the combined channel, equalizer and downsampling device is formed in the frequency domain, and the convergence rate of the time-domain LMS algorithm is described in the frequency domain.

A number of papers have studied blind channel identification/equalization algorithms relying purely on second-order statistics of the fractionally sampled received signal. A class of cyclic allpass channels is shown to be the only class of IIR channels whose cascade with a core channel results in no change in the second-order-statistics indicators used by several of these algorithms. FIR approximations to the poles of these allpass channels result in robustness concerns for the second-order-statistics algorithms, even when FIR identifiability conditions are well satisfied. This sensitivity suggests that excluding only those channels with common subchannel roots is insufficient when applying these second-order-statistics algorithms.

An approximate gradient descent algorithm is proposed for adaptive calibration of the composite error system associated with the transmitter-receiver of a recently proposed scheme for secure communication based on synchronized chaos. >