Invariance principles for standard-normalized and self-normalized random fields

We investigate the invariance principle for set-indexed partial sums of a stationary field $(X\_{k})\_{k\in\mathbb{Z}^{d}}$ of martingale-difference or independent random variables under standard-normalization or self-normalization respectively.Comment: Submitted for publicatio

On the Normalization of the QSO's Lyman alpha Forest Power Spectrum

The calculation of the transmission power spectrum of QSO's Lyman alpha absorption requires two parameters for the normalization: the continuum Fc and mean transmission, i.e. average of e^{-tau}. Traditionally, the continuum is obtained by a polynomial fitting truncating it at a lower order, and the mean transmission is calculated over the entire wavelength range considered. The flux F is then normalized by the average of Fc e^{-tau}. However, the fluctuations in the transmitted flux are significantly correlated with the local background flux on scales for which the field is intermittent. In this paper, we develop a self-normalization algorithm of the transmission power spectrum based on a multiresolution analysis. This self-normalized power spectrum estimator needs neither a continuum fitting, nor pre-determining the mean transmission. With simulated samples, we show that the self-normalization algorithm can perfectly recover the transmission power spectrum from the flux regardless of how the continuum varies with wavelength. We also show that the self-normalized power spectrum is also properly normalized by the mean transmission. Moreover, this power spectrum estimator is sensitive to the non-linear behavior of the field. That is, the self-normalized power spectrum estimator can distinguish between fields with or without the fluctuation-background correlation. This cannot be accomplished by the power spectrum with the normalization by an overall mean transmission. Therefore, the self-normalized power spectrum would be useful for the discrimination among models without the uncertainties caused by free (or fitting) parameters.Comment: 24 pages, 8 figures, to appear in ApJ tentatively in the Nov 1 2001 issu

Diversity Combining for Fast Frequency Hopping Multiple Access Systems Subjected to Nakagami-m Fading

The achievable performance of various diversity combining schemes used in fast frequency hopping (FFH) aided M-ary frequency shift keying (MFSK) systems operating in a multiple access scenario subjected to Nakagami-m fading is investigated. Specifically, linear, self-normalization, hard limiting majority vote, soft limiting, product combining and order statistics-normalized envelope detection based diversity combining schemes are considered. The comparison of various diversity combining schemes is based on the achievable bit error rate versus the number of simultaneous users supported. It is shown using simulation results that although some of the combining schemes considered result in an inferior performance compared to the optimum soft limiting combiner, they offer the advantage of achieving an acceptable interference suppression performance without requiring side information