2,999 research outputs found
Kinematic Diffraction from a Mathematical Viewpoint
Mathematical diffraction theory is concerned with the analysis of the
diffraction image of a given structure and the corresponding inverse problem of
structure determination. In recent years, the understanding of systems with
continuous and mixed spectra has improved considerably. Simultaneously, their
relevance has grown in practice as well. In this context, the phenomenon of
homometry shows various unexpected new facets. This is particularly so for
systems with stochastic components. After the introduction to the mathematical
tools, we briefly discuss pure point spectra, based on the Poisson summation
formula for lattice Dirac combs. This provides an elegant approach to the
diffraction formulas of infinite crystals and quasicrystals. We continue by
considering classic deterministic examples with singular or absolutely
continuous diffraction spectra. In particular, we recall an isospectral family
of structures with continuously varying entropy. We close with a summary of
more recent results on the diffraction of dynamical systems of algebraic or
stochastic origin.Comment: 30 pages, invited revie
System performance criteria in CDMA networks using gold codes
First, we have presented the autocorrelation and crosscorrelation properties for periodic and aperiodic binary sequences. The generation of binary sequences using shift registers with feedback was reviewed. We have also included correlation properties for the Gold codes.
Next, we discussed Gold code generation for the balanced and unbalanced Gold codes.
Thirdly, we investigated the number of simultaneous users in a CDMA system using Gold codes for the worst case and the average case of mutual interference.
Finally, we simulated the probability of interference exceeding a threshold value, and the average crosscorrelation value caused by interference in a CDMA network which is using a Gold code. We compared probability and average crosscorrelation values simulated with theoretical bounds calculated. Here the simulation programs are done in C computer language
Close-packed dimers on the line: diffraction versus dynamical spectrum
The translation action of \RR^{d} on a translation bounded measure
leads to an interesting class of dynamical systems, with a rather rich spectral
theory. In general, the diffraction spectrum of , which is the carrier
of the diffraction measure, live on a subset of the dynamical spectrum. It is
known that, under some mild assumptions, a pure point diffraction spectrum
implies a pure point dynamical spectrum (the opposite implication always being
true). For other systems, the diffraction spectrum can be a proper subset of
the dynamical spectrum, as was pointed out for the Thue-Morse sequence (with
singular continuous diffraction) in \cite{EM}. Here, we construct a random
system of close-packed dimers on the line that have some underlying long-range
periodic order as well, and display the same type of phenomenon for a system
with absolutely continuous spectrum. An interpretation in terms of `atomic'
versus `molecular' spectrum suggests a way to come to a more general
correspondence between these two types of spectra.Comment: 14 pages, with some additions and improvement
SPS pilot signal design and power transponder analysis, volume 2, phase 3
The problem of pilot signal parameter optimization and the related problem of power transponder performance analysis for the Solar Power Satellite reference phase control system are addressed. Signal and interference models were established to enable specifications of the front end filters including both the notch filter and the antenna frequency response. A simulation program package was developed to be included in SOLARSIM to perform tradeoffs of system parameters based on minimizing the phase error for the pilot phase extraction. An analytical model that characterizes the overall power transponder operation was developed. From this model, the effects of different phase noise disturbance sources that contribute to phase variations at the output of the power transponders were studied and quantified. Results indicate that it is feasible to hold the antenna array phase error to less than one degree per power module for the type of disturbances modeled
- …