The bispectrum of sampled data. II. Monte-Carlo simulations ofdetection and estimation of the sampling jitter

For pt.I see IEEE Trans. Acoust. Speech, Signal Process., vol.41, no.1, p.296-312 (1993). The effect of jitter in sampling on the spectrum and bispectrum of the sampled data has been considered previously. Methods of detecting the presence of jitter in a uniform sampling process and of estimating its variance based on a test statistic calculated from the bispectrum estimates have been proposed. The present authors demonstrate, by means of Monte-Carlo simulations, how these results can be applied in an actual case. For this purpose, samples taken from a stationary band-limited process in sampling times given by a random jitter process are generated by computer. The authors then apply the jitter detection and estimation methods that have been developed in previous work and study how their performance depends on signal duration and on jitter variance. They examine the actual simulation results concerning detection probability, estimation bias, and estimation variance in comparison with the theoretical results. This comparison indicates that the bispectrum is a domain where jitter detection and estimation with high performance can be achieved, provided that a signal with sufficiently long duration and high skewness is available     

Feasibility study of parameter estimation of random sampling jitter using the bispectrum

An actual sampling process can be modeled as a random process, which consists of the regular (uniform) deterministic sampling process plus an error in the sampling times which constitutes a zero-mean noise (the jitter). In this paper we discuss the problem of estimating the jitter process. By assuming that the jitter process is an i.i.d. one, with standard deviation that is small compared to the regular sampling time, we show that the variance of the jitter process can be estimated from thenth order spectrum of the sampled data,n=2, 3, i.e., the jitter variance can be extracted from the 2nd-order spectrum or the 3rd-order spectrum (the bispectrum) of the sampled data, provided the continuous signal spectrum is known. However when the signal skewness exceeds a certain level, the potential performance of the bispectrum-based estimation is better than that of the spectrum-based estimation. Moreover, the former can also provide jitter variance estimates when the continuous signal spectrum is unknown while the latter cannot. This suggests that the bispectrum of the sampled data is potentially better for estimating any parameter of the sampling jitter process, once the signal skewness is sufficiently large.     

A maximum likelihood digital receiver using coordinate ascent andthe discrete wavelet transform

In this paper, a maximum likelihood (ML) method is presented for joint estimation of amplitude, phase, time delay, and data symbols in a single-user direct-sequence spread-spectrum communication system. Since maximization of the likelihood function is analytically intractable, a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters. The novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter. The multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding. Computer simulations of the single-user system show that the algorithm has fast convergence, and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance