On the MIMO Channel Capacity of Multi-Dimensional Signal Sets

In this contribution we evaluate the capacity of Multi-Input Multi-Output (MIMO) systems using multi-dimensional PSK/QAM signal sets. It was shown that transmit diversity is capable of narrowing the gap between the capacity of the Rayleigh-fading channel and the AWGN channel. However, since this gap becomes narrower when the receiver diversity order is increased, for higher-order receiver diversity the performance advantage of transmit diversity diminishes. A MIMO system having full multiplexing gain has a higher achievable throughput than the corresponding MIMO system designed for full diversity gain, although this is attained at the cost of a higher complexity and a higher SNR. The tradeoffs between diversity gain, multiplexing gain, complexity and bandwidth are studied

On the MIMO Channel Capacity of Multi-Dimensional Signal Sets

In this contribution two general formulae were derived for the capacity evaluation of Multi-Input Multi-Output (MIMO) systems using multi-dimensional signal sets, different modulation schemes and an arbitrary number of transmit as well as receive antennas. It was shown that transmit diversity is capable of narrowing the gap between the capacity of the Rayleigh-fading channel and the AWGN channel. However, since this gap becomes narrower when the receiver diversity order is increased, for higher-order receiver diversity the performance advantage of transmit diversity diminishes. A MIMO system having full multiplexing gain has a higher achievable capacity, than the corresponding MIMO system designed for achieving full diversity gain, provided that the channel SNR is sufficiently high

A Call-by-Need Strategy for Higher-Order Functional-Logic Programming

We present an approach to truely higher-order functional-logic programming based on higher-order narrowing. Roughly speaking, we model a higherorder functional core language by higher-order rewriting and extend it by logic variables. For the integration of logic programs, conditional rules are supported. For solving goals in this framework, we present a complete calculus for higher-order conditional narrowing. We develop several refinements that utilize the determinism of functional programs. These refinements can be combined to a narrowing strategy which generalizes call-by-need as in functional programming, where the dedicated higher-order methods are only used for full higher-order goals. Furthermore, we propose an implementational model for this narrowing strategy which delays computations until needed

Theorem Proving Modulo Revised Version

Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of general interest because it permits to separate computations and deductions in a clean way. The first contribution of this paper is to define a sequent calculus modulo that gives a proof theoretic account of the combination of computations and deductions. The congruence on propositions is handled via rewrite rules and equational axioms. Rewrite rules apply to terms but also directly to atomic propositions. The second contribution is to give a complete proof search method, called Extended Narrowing and Resolution (ENAR), for theorem proving modulo such congruences. The completeness of this method is proved with respect to provability in sequent calculus modulo. An important application is that higher-order logic can be presented as a theory in deduction modulo. Applying the Extended Narrowing and Resolution method to this presentation of higher-order logic subsumes full higher-order resolution

Nonlinear spectroscopic studies using sum- and difference-frequency generation

A detailed study is presented of resonant sum- and difference-frequency generation for the mixed-crystal system azulene in naphthalene. The S0 -> S1, S0 -> S2 and S1 -> S2 transitions of azulene provide the 3 needed dipoles for the existence of c(2), and a relatively small static elec. field was used to break the interference between the waves generated in the 2 crystal sublattices. Second-order nonlinear processes can occur sep. in each sublattice. All the theor. predicted resonances, except the DICE effect, were obsd. The generated field intensity satd. at higher fields, and in certain circumstances exhibited hysteresis as a function of the d.c. field strength. The line-narrowing capabilities of these new forms of spectroscopy were explored

Spin-exchange relaxation free magnetometry with Cs vapor

We describe a Cs atomic magnetometer operating in the spin-exchange relaxation-free (SERF) regime. With a vapor cell temperature of $103^\circ\rm{C}$ we achieve intrinsic magnetic resonance widths $\Delta B=17 {\rm \mu G}$ corresponding to an electron spin-relaxation rate of $300 {\rm s^{-1}}$ when the spin-exchange rate is $\Gamma_{SE}=14000 {\rm s^{-1}}$. We also observe an interesting narrowing effect due to diffusion. Signal-to-noise measurements yield a sensitivity of about $400\thinspace{\rm pG/\sqrt{Hz}}$. Based on photon shot noise, we project a sensitivity of $40 {\rm pG/\sqrt{Hz}}$. A theoretical optimization of the magnetometer indicates sensitivities on the order of $2 {\rm pG/\sqrt{Hz}}$ should be achievable in a $1 {\rm cm^3}$ volume. Because Cs has a higher saturated vapor pressure than other alkali metals, SERF magnetometers using Cs atoms are particularly attractive in applications requiring lower temperatures.Comment: 8 pages, 6 figures. submitted to PR

Fourth-order spin correlation function in the extended central spin model

Spin noise spectroscopy has developed into a very powerful tool to access the electron spin dynamics. While the spin-noise power spectrum in an ensemble of quantum dots in a magnetic field is essentially understood, we argue that the investigation of the higher order cumulants promises to provide additional information not accessible by the conventional power noise spectrum. We present a quantum mechanical approach to the correlation function of the spin-noise power operators at two different frequencies for small spin bath sizes and compare the results with a simulation obtained from the classical spin dynamics for large number of nuclear spins. This bispectrum is defined as a two-dimensional frequency cut in the parameter space of the fourth-order spin correlation function. It reveals information on the influence of the nuclear-electric quadrupolar interactions on the long-time electron spin dynamics dominated by a magnetic field. For large bath sizes and spin lengths the quantum mechanical spectra converge to those of the classical simulations. The broadening of the bispectrum across the diagonal in the frequency space is a direct measure of the quadrupolar interaction strength. A narrowing is found with increasing magnetic field indicating a suppression of the influence of quadrupolar interactions in favor of the nuclear Zeeman effect.Comment: 15 pages, 14 figure

Closing the gap between spatial and spin dynamics of electrons at the metal-to-insulator transition

We combine extensive precision measurements of the optically detected spin dynamics and magneto-transport measurements in a contiguous set of n-doped bulk GaAs structures in order to unambiguously unravel the intriguing but complex contributions to the spin relaxation at the metal-to-insulator transition (MIT). Just below the MIT, the interplay between hopping induced loss of spin coherence and hyperfine interaction yields a maximum spin lifetime exceeding 800~ns. At slightly higher doping concentrations, however, the spin relaxation deviates from the expected Dyakonov-Perel mechanism which is consistently explained by a reduction of the effective motional narrowing with increasing doping concentration. The reduction is attributed to the change of the dominant momentum scattering mechanism in the metallic impurity band where scattering by local conductivity domain boundaries due to the intrinsic random distribution of donors becomes significant. Here, we fully identify and model all intricate contributions of the relevant microscopic scattering mechanisms which allows the complete quantitative modeling of the electron spin relaxation in the entire regime from weakly interacting up to fully delocalized electrons

Phonon anomalies in pure and underdoped R{1-x}K{x}Fe{2}As{2} (R = Ba, Sr) investigated by Raman light scattering

We present a detailed temperature dependent Raman light scattering study of optical phonons in Ba{1-x}K{x}Fe{2}As{2} (x ~ 0.28, superconducting Tc ~ 29 K), Sr{1-x}K{x}Fe{2}As{2} (x ~ 0.15, Tc ~ 29 K) and non-superconducting BaFe{2}As{2} single crystals. In all samples we observe a strong continuous narrowing of the Raman-active Fe and As vibrations upon cooling below the spin-density-wave transition Ts. We attribute this effect to the opening of the spin-density-wave gap. The electron-phonon linewidths inferred from these data greatly exceed the predictions of ab-initio density functional calculations without spin polarization, which may imply that local magnetic moments survive well above Ts. A first-order structural transition accompanying the spin-density-wave transition induces discontinuous jumps in the phonon frequencies. These anomalies are increasingly suppressed for higher potassium concentrations. We also observe subtle phonon anomalies at the superconducting transition temperature Tc, with a behavior qualitatively similar to that in the cuprate superconductors.Comment: 5 pages, 6 figures, accepted versio