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.

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.

Biometric template security using higher order spectra

A method of improving the security of biometric templates which satisfies desirable properties such as (a) irreversibility of the template, (b) revocability and assignment of a new template to the same biometric input, (c) matching in the secure transformed domain is presented. It makes use of an iterative procedure based on the bispectrum that serves as an irreversible transformation for biometric features because signal phase is discarded each iteration. Unlike the usual hash function, this transformation preserves closeness in the transformed domain for similar biometric inputs. A number of such templates can be generated from the same input. These properties are illustrated using synthetic data and applied to images from the FRGC 3D database with Gabor features. Verification can be successfully performed using these secure templates with an EER of 5.85%

A framework for a dense matching algorithm : Results using matching metrics and order statistic filters

An algorithm for computing dense correspondences between images of a stereo pair or image sequence is presented. The algorithm can make use of both standard matching metrics and the rank and census filters, two filters based on order statistics which have been applied to the image matching problem. Their advantages include robustness to radiometric distortion and amenability to hardware implementation. Results obtained using both real stereo pairs and a synthetic stereo pair with ground truth were compared. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.

Order statistic filters for image matching

The rank and census are two filters based on order statistics which have been applied to the image matching problem for stereo pairs. Advantages of these filters include their robustness to radiometric distortion and small amounts of random noise, and their amenability to hardware implementation. In this paper, a new matching algorithm is presented, which provides an overall framework for matching, and is used to compare the rank and census techniques with standard matching metrics. The algorithm was tested using both real stereo pairs and a synthetic pair with ground truth. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.

Statistics and kinetics of single-molecule electron transfer dynamics in complex environments: A simulation model study

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

On a Second Order Condition for Max-Semistable Laws

2000 Mathematics Subject Classification: 62G32, 62G20.

On the computation and interpretation of auto- and cross-trispectra

This paper discusses the principal domains of auto- and cross-trispectra. It is shown that the cumulant and moment based trispectra are identical except on certain planes in trifrequency space. If these planes are avoided, their principal domains can be derived by considering the regions of symmetry of the fourth order spectral moment. The fourth order averaged periodogram will then serve as an estimate for both cumulant and moment trispectra. Statistics of estimates of normalised trispectra or tricoherence are also discussed.

Statistical modelling of wind effects on signal propagation for wireless sensor networks

A wireless sensor network system must have the ability to tolerate harsh environmental conditions and reduce communication failures. In a typical outdoor situation, the presence of wind can introduce movement in the foliage. This motion of vegetation structures causes large and rapid signal fading in the communication link and must be accounted for when deploying a wireless sensor network system in such conditions. This thesis examines the fading characteristics experienced by wireless sensor nodes due to the effect of varying wind speed in a foliage obstructed transmission path. It presents extensive measurement campaigns at two locations with the approach of a typical wireless sensor networks configuration. The significance of this research lies in the varied approaches of its different experiments, involving a variety of vegetation types, scenarios and the use of different polarisations (vertical and horizontal). Non–line of sight (NLoS) scenario conditions investigate the wind effect based on different vegetation densities including that of the Acacia tree, Dogbane tree and tall grass. Whereas the line of sight (LoS) scenario investigates the effect of wind when the grass is swaying and affecting the ground-reflected component of the signal. Vegetation type and scenarios are envisaged to simulate real life working conditions of wireless sensor network systems in outdoor foliated environments. The results from the measurements are presented in statistical models involving first and second order statistics. We found that in most of the cases, the fading amplitude could be approximated by both Lognormal and Nakagami distribution, whose m parameter was found to depend on received power fluctuations. Lognormal distribution is known as the result of slow fading characteristics due to shadowing. This study concludes that fading caused by variations in received power due to wind in wireless sensor networks systems are found to be insignificant. There is no notable difference in Nakagami m values for low, calm, and windy wind speed categories. It is also shown in the second order analysis, the duration of the deep fades are very short, 0.1 second for 10 dB attenuation below RMS level for vertical polarization and 0.01 second for 10 dB attenuation below RMS level for horizontal polarization. Another key finding is that the received signal strength for horizontal polarisation demonstrates more than 3 dB better performances than the vertical polarisation for LoS and near LoS (thin vegetation) conditions and up to 10 dB better for denser vegetation conditions.