A Group-Theoretic Approach to the WSSUS Pulse Design Problem

We consider the pulse design problem in multicarrier transmission where the pulse shapes are adapted to the second order statistics of the WSSUS channel. Even though the problem has been addressed by many authors analytical insights are rather limited. First we show that the problem is equivalent to the pure state channel fidelity in quantum information theory. Next we present a new approach where the original optimization functional is related to an eigenvalue problem for a pseudo differential operator by utilizing unitary representations of the Weyl--Heisenberg group.A local approximation of the operator for underspread channels is derived which implicitly covers the concepts of pulse scaling and optimal phase space displacement. The problem is reformulated as a differential equation and the optimal pulses occur as eigenstates of the harmonic oscillator Hamiltonian. Furthermore this operator--algebraic approach is extended to provide exact solutions for different classes of scattering environments.Comment: 5 pages, final version for 2005 IEEE International Symposium on Information Theory; added references for section 2; corrected some typos; added more detailed discussion on the relations to quantum information theory; added some more references; added additional calculations as an appendix; corrected typo in III.

Gas Dynamics and Large-Scale Morphology of the Milky Way Galaxy

We present a new model for the gas dynamics in the galactic disk inside the Sun's orbit. Quasi-equilibrium flow solutions are determined in the gravitational potential of the deprojected COBE NIR bar and disk, complemented by a central cusp and, in some models, an outer halo. These models generically lead to four-armed spiral structure between corotation of the bar and the solar circle; their large-scale morphology is not sensitive to the precise value of the bar's pattern speed, to the orientation of the bar with respect to the observer, and to whether or not the spiral arms carry mass. Our best model provides a coherent interpretation of many observed gas dynamical features. Its four-armed spiral structure outside corotation reproduces quantitatively the directions to the five main spiral arm tangents at |l|<=60deg observed in a variety of tracers. The 3-kpc-arm is identified with one of the model arms emanating from the ends of the bar, extending into the corotation region. The model features an inner gas disk with a cusped orbit shock transition to an x_2 orbit disk of radius R~150pc. The bar's corotation radius is fairly well--constrained at R_c=3.5 +/- 0.5 kpc. The best value for the orientation angle of the bar is probably 20-25deg, but the uncertainty is large since no detailed quantitative fit to all features in the observed lv-diagrams is yet possible. The Galactic terminal velocity curve from HI and CO observations out to l=+/-45deg (=5 kpc) is approximately described by a maximal disk model with constant mass-to-light ratio for the NIR bulge and disk.Comment: 24 pages, 16 figures, Latex, to appear in MNRAS. Available with full resolution figures at http://www.astro.unibas.ch/galaxies/papers.htm

Two modes of gas flow in a single barred galaxy

We investigate stationary gas flows in a fixed, rotating barred potential. The gas is assumed to be isothermal with an effective sound speed c_s, and the equations of motion are solved with smoothed particle hydrodynamics (SPH). Since the thermal energy in cloud random motions is negligible compared to the orbital kinetic energy, no dependence of the flow on c_s is expected. However, this is not the case when shocks are involved. For low values of c_s an open, off-axis shock flow forms that is characteristic for potentials with an inner Lindblad resonance (ILR). Through this shock the gas streams inwards from x_1 to x_2-orbits. At high sound speeds the gas arranges itself in a different, on-axis shock flow pattern. In this case, there is no gas on x_2-orbits, demonstrating that the gas can behave as if there were no ILR. The critical effective sound speed dividing the two regimes is in the range of values observed in the Milky Way. We give a heuristic explanation for this effect. A possible consequence is that star formation may change the structure of the flow by which it was initiated. Low-mass galaxies should predominantly be in the on-axis regime. A brief comparison of our SPH results with those from a grid-based hydrodynamic code is also given.Comment: 12 pages, Latex. 9 figures (gif). Submitted to MNRAS. Also available with figures as ps-file at http://www.astro.unibas.ch/dynamics/papers.htm

On Time-Variant Distortions in Multicarrier Transmission with Application to Frequency Offsets and Phase Noise

Phase noise and frequency offsets are due to their time-variant behavior one of the most limiting disturbances in practical OFDM designs and therefore intensively studied by many authors. In this paper we present a generalized framework for the prediction of uncoded system performance in the presence of time-variant distortions including the transmitter and receiver pulse shapes as well as the channel. Therefore, unlike existing studies, our approach can be employed for more general multicarrier schemes. To show the usefulness of our approach, we apply the results to OFDM in the context of frequency offset and Wiener phase noise, yielding improved bounds on the uncoded performance. In particular, we obtain exact formulas for the averaged performance in AWGN and time-invariant multipath channels.Comment: 10 pages (twocolumn), 5 figure

In-phase and anti-phase synchronization in noisy Hodgkin-Huxley neurons

We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation time of an action potential along the neuronal axon. We quantify this delay-coupling of the Pyragas-type in terms of the difference between corresponding presynaptic and postsynaptic membrane potentials. For an elementary neuronal network consisting of two coupled neurons we detect characteristic stochastic synchronization patterns which exhibit multiple phase-flip bifurcations: The phase-flip bifurcations occur in form of alternate transitions from an in-phase spiking activity towards an anti-phase spiking activity. Interestingly, these phase-flips remain robust in strong channel noise and in turn cause a striking stabilization of the spiking frequency

Noisy saltatory spike propagation: The breakdown of signal transmission due to channel noise

Noisy saltatory spike propagation along myelinated axons is studied within a stochastic Hodgkin-Huxley model. The intrinsic noise (whose strength is inverse proportional to the nodal membrane size) arising from fluctuations of the number of open ion channels influences the dynamics of the membrane potential in a node of Ranvier where the sodium ion channels are predominantly localized. The nodes of Ranvier are linearly coupled. As the measure for the signal propagation reliability we focus on the ratio between the number of initiated spikes and the transmitted spikes. This work supplements our earlier study [A. Ochab-Marcinek, G. Schmid, I. Goychuk and P. H\"anggi, Phys. Rev E 79, 011904 (2009)] towards stronger channel noise intensity and supra-threshold coupling. For strong supra-threshold coupling the transmission reliability decreases with increasing channel noise level until the causal relationship is completely lost and a breakdown of the spike propagation due to the intrinsic noise is observed.Comment: To appear in EPJS