An alpha-stable approach to the study of the P(D) distribution of unresolved point sources in CMB sky maps

We present a new approach to the statistical study and modelling of number counts of faint point sources in astronomical images, i.e. counts of sources whose flux falls below the detection limit of a survey. The approach is based on the theory of alpha-stable distributions. We show that the non-Gaussian distribution of the intensity fluctuations produced by a generic point source population -- whose number counts follow a simple power law -- belongs to the alpha-stable family of distributions. Even if source counts do not follow a simple power law, we show that the alpha-stable model is still useful in many astrophysical scenarios. With the alpha-stable model it is possible to totally describe the non-Gaussian distribution with a few parameters which are closely related to the parameters describing the source counts, instead of an infinite number of moments. Using statistical tools available in the signal processing literature, we show how to estimate these parameters in an easy and fast way. We demonstrate that the model proves valid when applied to realistic point source number counts at microwave frequencies. In the case of point extragalactic sources observed at CMB frecuencies, our technique is able to successfully fitting the P(D) distribution of deflections and to precisely determining the main parameters which describe the number counts. In the case of the Planck mission, the relative errors on these parameters are small either at low and at high frequencies. We provide a way to deal with the presence of Gaussian noise in the data using the empirical characteristic function of the P(D). The formalism and methods here presented can be very useful also for experiments in other frequency ranges, e.g. X-ray or radio Astronomy.Comment: 16 pages, 6 figures, final version to appear in A&A (in press

Analysis of low-density parity-check codes on impulsive noise channels

PhD ThesisCommunication channels can severely degrade a signal, not only due to fading effects but also interference in the form of impulsive noise. In conventional communication systems, the additive noise at the receiver is usually assumed to be Gaussian distributed. However, this assumption is not always valid and examples of non-Gaussian distributed noise include power line channels, underwater acoustic channels and manmade interference. When designing a communication system it is useful to know the theoretical performance in terms of bit-error probability (BEP) on these types of channels. However, the effect of impulses on the BEP performance has not been well studied, particularly when error correcting codes are employed. Today, advanced error-correcting codes with very long block lengths and iterative decoding algorithms, such as Low-Density Parity-Check (LDPC) codes and turbo codes, are popular due to their capacity-approaching performance. However, very long codes are not always desirable, particularly in communications systems where latency is a serious issue, such as in voice and video communication between multiple users. This thesis focuses on the analysis of short LDPC codes. Finite length analyses of LDPC codes have already been presented for the additive white Gaussian noise channel in the literature, but the analysis of short LDPC codes for channels that exhibit impulsive noise has not been investigated. The novel contributions in this thesis are presented in three sections. First, uncoded and LDPC-coded BEP performance on channels exhibiting impulsive noise modelled by symmetric -stable (S S) distributions are examined. Different sub-optimal receivers are compared and a new low-complexity receiver is proposed that achieves near-optimal performance. Density evolution is then used to derive the threshold signal-tonoise ratio (SNR) of LDPC codes that employ these receivers. In order to accurately predict the waterfall performance of short LDPC codes, a nite length analysis is proposed with the aid of the threshold SNRs of LDPC codes and the derived uncoded BEPs for impulsive noise channels. Second, to investigate the e ect of impulsive noise on wireless channels, the analytic BEP on generalized fading channels with S S noise is derived. However, it requires the evaluation of a double integral to obtain the analytic BEP, so to reduce the computational cost, the Cauchy- Gaussian mixture model and the asymptotic property of S S process are used to derive upper bounds of the exact BEP. Two closed-form expressions are derived to approximate the exact BEP on a Rayleigh fading channel with S S noise. Then density evolution of different receivers is derived for these channels to nd the asymptotic performance of LDPC codes. Finally, the waterfall performance of LDPC codes is again estimated for generalized fading channels with S S noise by utilizing the derived uncoded BEP and threshold SNRs. Finally, the addition of spatial diversity at the receiver is investigated. Spatial diversity is an effective method to mitigate the effects of fading and when used in conjunction with LDPC codes and can achieve excellent error-correcting performance. Hence, the performance of conventional linear diversity combining techniques are derived. Then the SNRs of these linear combiners are compared and the relationship of the noise power between different linear combiners is obtained. Nonlinear detectors have been shown to achieve better performance than linear combiners hence, optimal and sub-optimal detectors are also presented and compared. A non-linear detector based on the bi-parameter Cauchy-Gaussian mixture model is used and shows near-optimal performance with a significant reduction in complexity when compared with the optimal detector. Furthermore, we show how to apply density evolution of LDPC codes for different combining techniques on these channels and an estimation of the waterfall performance of LDPC codes is derived that reduces the gap between simulated and asymptotic performance. In conclusion, the work presented in this thesis provides a framework to evaluate the performance of communication systems in the presence of additive impulsive noise, with and without spatial diversity at the receiver. For the first time, bounds on the BEP performance of LDPC codes on channels with impulsive noise have been derived for optimal and sub-optimal receivers, allowing other researchers to predict the performance of LDPC codes in these type of environments without needing to run lengthy computer simulations

Robust adaptive filtering algorithms for α-stable random processes

A new class of algorithms based on the fractional lower order statistics is proposed for finite-impulse response adaptive filtering in the presence of α-stable processes. It is shown that the normalized least mean p-norm (NLMP) and Douglas' family of normalized least mean square algorithms are special cases of the proposed class of algorithms. A convergence proof for the new algorithm is given by showing that it performs a descent-type update of the NLMP cost function. Simulation studies indicate that the proposed algorithms provide superior performance in impulsive noise environments compared to the existing approaches

Underwater acoustic communications in warm shallow water channels

Ph.DDOCTOR OF PHILOSOPH

Adaptive Equalisation for Impulsive Noise Environments

This thesis addresses the problem of adaptive channel equalisation in environments where the interfering noise exhibits non–Gaussian behaviour due to impulsive phenomena. The family of alpha-stable distributions has proved to be a suitable and flexible tool for the modelling of signals with impulsive nature. However,non–Gaussian alpha–stable signals have infinite variance, and signal processing techniques based on second order moments are meaningless in such environments. In order to exploit the flexibility of the stable family and still take advantage of the existing signal processing tools, a novel framework for the integration of the stable model in a communications context is proposed, based on a finite dynamic range receiver. The performance of traditional signal processing algorithms designed under the Gaussian assumption may degrade seriously in impulsive environments. When this degradation cannot be tolerated, the traditional signal processing methods must be revisited and redesigned taking into account the non–Gaussian noise statistics. In this direction, the optimum feed–forward and decision feedback Bayesian symbol–by–symbol equalisers for stable noise environments are derived. Then, new analytical tools for the evaluation of systems in infinite variance environments are presented. For the centers estimation of the proposed Bayesian equaliser, a unified framework for a family of robust recursive linear estimation techniques is presented and the underlying relationships between them are identified. Furthermore, the direct clustering technique is studied and robust variants of the existing algorithms are proposed. A novel clustering algorithm is also derived based on robust location estimation. The problem of estimating the stable parameters has been addressed in the literature and a variety of algorithms can be found. Some of these algorithms are assessed in terms of efficiency, simplicity and performance and the most suitable is chosen for the equalisation problem. All the building components of an adaptive Bayesian equaliser are then put together and the performance of the equaliser is evaluated experimentally. The simulation results suggest that the proposed adaptive equaliser offers a significant performance benefit compared with a traditional equaliser, designed under the Gaussian assumption. The implementation of the proposed Bayesian equaliser is simple but the computational complexity can be unaffordable. However, this thesis proposes certain approximations which enable the computationally efficient implementation of the optimum equaliser with negligible loss in performance

NASA patent abstracts bibliography: A continuing bibliography. Section 1: Abstracts (supplement 40)

Abstracts are provided for 181 patents and patent applications entered into the NASA scientific and technical information system during the period July 1991 through December 1991. Each entry consists of a citation, an abstract, and in most cases, a key illustration selected from the patent or patent application

Engineering a Low-Cost Remote Sensing Capability for Deep-Space Applications

Systems engineering (SE) has been a useful tool for providing objective processes to breaking down complex technical problems to simpler tasks, while concurrently generating metrics to provide assurance that the solution is fit-for-purpose. Tailored forms of SE have also been used by cubesat mission designers to assist in reducing risk by providing iterative feedback and key artifacts to provide managers with the evidence to adjust resources and tasking for success. Cubesat-sized spacecraft are being planned, built and in some cases, flown to provide a lower-cost entry point for deep-space exploration. This is particularly important for agencies and countries with lower space exploration budgets, where specific mission objectives can be used to develop tailored payloads within tighter constraints, while also returning useful scientific results or engineering data. In this work, a tailored SE tradespace approach was used to help determine how a 6 unit (6U) cubesat could be built from commercial-off-the-shelf (COTS)-based components and undertake remote sensing missions near Mars or near-Earth Asteroids. The primary purpose of these missions is to carry a hyperspectral sensor sensitive to 600-800nm wavelengths (hereafter defined as “red-edge”), that will investigate mineralogy characteristics commonly associated with oxidizing and hydrating environments in red-edge. Minerals of this type remain of high interest for indicators of present or past habitability for life, or active geologic processes. Implications of operating in a deep-space environment were considered as part of engineering constraints of the design, including potential reduction of available solar energy, changes in thermal environment and background radiation, and vastly increased communications distances. The engineering tradespace analysis identified realistic COTS options that could satisfy mission objectives for the 6U cubesat bus while also accommodating a reasonable degree of risk. The exception was the communication subsystem, in which case suitable capability was restricted to one particular option. This analysis was used to support an additional trade investigation into the type of sensors that would be most suitable for building the red-edge hyperspectral payload. This was in part constrained by ensuring not only that readily available COTS sensors were used, but that affordability, particularly during a geopolitical environment that was affecting component supply surety and access to manufacturing facilities, was optimized. It was found that a number of sensor options were available for designing a useful instrument, although the rapid development and life-of-type issues with COTS sensors restricted the ability to obtain useful metrics on their performance in the space environment. Additional engineering testing was conducted by constructing hyperspectral sensors using sensors popular in science, technology, engineering and mathematics (STEM) contexts. Engineering and performance metrics of the payload containing the sensors was conducted; and performance of these sensors in relevant analogous environments. A selection of materials exhibiting spectral phenomenology in the red-edge portion of the spectrum was used to produce metrics on the performance of the sensors. It was found that low-cost cameras were able to distinguish between most minerals, although they required a wider spectral range to do so. Additionally, while Raspberry Pi cameras have been popular with scientific applications, a low-cost camera without a Bayer filter markedly improved spectral sensitivity. Consideration for space-environment testing was also trialed in additional experiments using high-altitude balloons to reach the near-space environment. The sensor payloads experienced conditions approximating the surface of Mars, and results were compared with Landsat 7, a heritage Earth sensing satellite, using a popular vegetation index. The selected Raspberry Pi cameras were able to provide useful results from near-space that could be compared with space imagery. Further testing incorporated comparative analysis of custom-built sensors using readily available Raspberry Pi and astronomy cameras, and results from Mastcam and Mastcam/z instruments currently on the surface of Mars. Two sensor designs were trialed in field settings possessing Mars-analogue materials, and a subset of these materials were analysed using a laboratory-grade spectro-radiometer. Results showed the Raspberry Pi multispectral camera would be best suited for broad-scale indications of mineralogy that could be targeted by the pushbroom sensor. This sensor was found to possess a narrower spectral range than the Mastcam and Mastcam/z but was sensitive to a greater number of bands within this range. The pushbroom sensor returned data on spectral phenomenology associated with attributes of Minerals of the type found on Mars. The actual performance of the payload in appropriate conditions was important to provide critical information used to risk reduce future designs. Additionally, the successful outcomes of the trials reduced risk for their application in a deep space environment. The SE and practical performance testing conducted in this thesis could be developed further to design, build and fly a hyperspectral sensor, sensitive to red-edge wavelengths, on a deep-space cubesat mission. Such a mission could be flown at reasonable cost yet return useful scientific and engineering data

Timing and Time Perception: Procedures, Measures, and Applications

Timing and Time Perception: Procedures, Measures, and Applications is a one-of-a-kind, collective effort to present the most utilized and known methods on timing and time perception. Specifically, it covers methods and analysis on circadian timing, synchrony perception, reaction/response time, time estimation, and alternative methods for clinical/developmental research. The book includes experimental protocols, programming code, and sample results and the content ranges from very introductory to more advanced so as to cover the needs of both junior and senior researchers. We hope that this will be the first step in future efforts to document experimental methods and analysis both in a theoretical and in a practical manner