Second-order statistics for equal gain and maximal ratio diversity-combining reception

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for equal gain combining and maximal ratio combining schemes, assuming an arbitrary number of independent branches in a Rayleigh environment. The analytical results are thoroughly validated by simulation.

Second-order statistics for diversity-combining, techniques in Nakagami-fading channels

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for the M branch pure selection combining (PSC), equal gain combining (EGC), and maximal ratio combining (MRC) techniques, assuming independent branches in a Nakagami environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The model developed here is general and can be easily applied to other fading statistics (e.g., Rice).

Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

Direction Finding Estimators of Cyclostationary Signals in Array Processing for Microwave Power Transmission

A solar power satellite is paid attention to as a clean, inexhaustible large- scale base-load power supply. The following technology related to beam control is used: A pilot signal is sent from the power receiving site and after direction of arrival estimation the beam is directed back to the earth by same direction. A novel direction-finding algorithm based on linear prediction technique for exploiting cyclostationary statistical information (spatial and temporal) is explored. Many modulated communication signals exhibit a cyclostationarity (or periodic correlation) property, corresponding to the underlying periodicity arising from carrier frequencies or baud rates. The problem was solved by using both cyclic second-order statistics and cyclic higher-order statistics. By evaluating the corresponding cyclic statistics of the received data at certain cycle frequencies, we can extract the cyclic correlations of only signals with the same cycle frequency and null out the cyclic correlations of stationary additive noise and all other co-channel interferences with different cycle frequencies. Thus, the signal detection capability can be significantly improved. The proposed algorithms employ cyclic higher-order statistics of the array output and suppress additive Gaussian noise of unknown spectral content, even when the noise shares common cycle frequencies with the non-Gaussian signals of interest. The proposed method completely exploits temporal information (multiple lag ), and also can correctly estimate direction of arrival of desired signals by suppressing undesired signals. Our approach was generalized over direction of arrival estimation of cyclostationary coherent signals. In this paper, we propose a new approach for exploiting cyclostationarity that seems to be more advanced in comparison with the other existing direction finding algorithms.

Synthesis of new Fe(II) and Ru(II) eta(5)-monocyclopentadienyl compounds showing significant second order NLO properties

A series of new ruthenium(II) complexes of the general formula [Ru(eta(5)-C5H5)(PP)(L)][PF6] (PP = DPPE or 2PPh(3), L = 4-butoxybenzonitrile or N-(3-cyanophenyl)formamide) and the binuclear iron(II) complex [Fe(eta(5)-C5H5)(PP)(mu-L)(PP)(eta(5)-C5H5)Fe][PF6](2) (L = (E)-2-(3-(4-nitrophenyl)allylidene)malononitrile, that has been also newly synthesized) have been prepared and studied to evaluate their potential in the second harmonic generation property. All the new compounds were fully characterized by NMR, IR and UV-Vis spectroscopies and their electrochemistry behaviour was studied by cyclic voltammetry. Quadratic hyperpolarizabilities (beta) of three of the complexes have been determined by hyper-Rayleigh scattering (HRS) measurements at fundamental wavelength of 1500 nm and the calculated static beta(0) values are found to fall in the range 65-212 x 10(-30) esu. Compound presenting beta(0) = 212 x 10(-30) esu has revealed to be 1.2 times more efficient than urea standard in the second harmonic generation (SHG) property, measured in the solid state by Kurtz powder technique, using a Nd:YAG laser (1064 nm). (C) 2013 Elsevier B.V. All rights reserved.

GNSS signal detection based on first-order absolute statistics

Aquest projecte es centra principalment en el detector no coherent d’un GPS. Per tal de caracteritzar el procés de detecció d’un receptor, es necessita conèixer l’estadística implicada. Pel cas dels detectors no coherents convencionals, l’estadística de segon ordre intervé plenament. Les prestacions que ens dóna l’estadística de segon ordre, plasmada en la ROC, són prou bons tot i que en diferents situacions poden no ser els millors. Aquest projecte intenta reproduir el procés de detecció mitjançant l’estadística de primer ordre com a alternativa a la ja coneguda i implementada estadística de segon ordre. Per tal d’aconseguir-ho, s’usen expressions basades en el Teorema Central del Límit i de les sèries Edgeworth com a bones aproximacions. Finalment, tant l’estadística convencional com l’estadística proposada són comparades, en termes de la ROC, per tal de determinar quin detector no coherent ofereix millor prestacions en cada situació.

Calibration of stochastic volatility models via second order approximation: the Heston model case

Using a suitable Hull and White type formula we develop a methodology to obtain asecond order approximation to the implied volatility for very short maturities. Using thisapproximation we accurately calibrate the full set of parameters of the Heston model. Oneof the reasons that makes our calibration for short maturities so accurate is that we alsotake into account the term-structure for large maturities. We may say that calibration isnot "memoryless", in the sense that the option's behavior far away from maturity doesinfluence calibration when the option gets close to expiration. Our results provide a wayto perform a quick calibration of a closed-form approximation to vanilla options that canthen be used to price exotic derivatives. The methodology is simple, accurate, fast, andit requires a minimal computational cost.

Multi-sample analysis of moment-structures: Asymptotic validity of inferences based on second-order moments

In moment structure analysis with nonnormal data, asymptotic valid inferences require the computation of a consistent (under general distributional assumptions) estimate of the matrix $\Gamma$ of asymptotic variances of sample second--order moments. Such a consistent estimate involves the fourth--order sample moments of the data. In practice, the use of fourth--order moments leads to computational burden and lack of robustness against small samples. In this paper we show that, under certain assumptions, correct asymptotic inferences can be attained when $\Gamma$ is replaced by a matrix $\Omega$ that involves only the second--order moments of the data. The present paper extends to the context of multi--sample analysis of second--order moment structures, results derived in the context of (simple--sample) covariance structure analysis (Satorra and Bentler, 1990). The results apply to a variety of estimation methods and general type of statistics. An example involving a test of equality of means under covariance restrictions illustrates theoretical aspects of the paper.

Motion estimation using higher-order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimatingmotion even for small regions or blocks. Using higher than second-orderstatistics is appropriate in case the image sequence is severely corruptedby additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

On a Second Order Condition for Max-Semistable Laws

2000 Mathematics Subject Classification: 62G32, 62G20.

Second-order cyclostationarity-based detection and classification of LTE SC-FDMA signals for cognitive radio

Cognitive radio (CR) was developed for utilizing the spectrum bands efficiently. Spectrum sensing and awareness represent main tasks of a CR, providing the possibility of exploiting the unused bands. In this thesis, we investigate the detection and classification of Long Term Evolution (LTE) single carrier-frequency division multiple access (SC-FDMA) signals, which are used in uplink LTE, with applications to cognitive radio. We explore the second-order cyclostationarity of the LTE SC-FDMA signals, and apply results obtained for the cyclic autocorrelation function to signal detection and classification (in other words, to spectrum sensing and awareness). The proposed detection and classification algorithms provide a very good performance under various channel conditions, with a short observation time and at low signal-to-noise ratios, with reduced complexity. The validity of the proposed algorithms is verified using signals generated and acquired by laboratory instrumentation, and the experimental results show a good match with computer simulation results.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.