Introduction to Random Signals and Noise

Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals.\ud \ud Key features:\ud • Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains.\ud • Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver.\ud • Examines optimal filtering methods and their consequences.\ud • Presents a detailed discussion of the topic of Poisson processed and shot noise.\u

Species distribution models

Species distribution models are a group of methods often used to estimate consequences of global change, to assess ecological status and for other ecological applications. The main idea behind species distribution models is that the geographical distributions of species can, to a large part, be explained by environmental factors and that species distributions therefore can be predicted in time or space. For robust and reliable applications, models need to be based on sound ecological principles, predictions need to be as accurate as possible, and model uncertainties need to be understood. Two approaches are available for modelling entire species communities: (1) each species can be modelled individually and independently of other species or (2) community information can be incorporated into the models. The first study in this thesis compares these two modelling approaches for predicting phytoplankton assemblages in lakes. The results showed that predictive accuracy was higher when species were modelled individually. The results also showed that phytoplankton can be used for model-based assessment of ecological status. This finding is important because phytoplankton is required for assessing the ecological status of European water bodies according to the European Water Framework Directive. Dispersal barriers in the landscape or limited dispersal ability of species might be a reason for species being absent from suitable habitats, and these factors might therefore affect model accuracy. The second study in this thesis examines the influence of dispersal and the spatial configuration of ecosystems on prediction accuracy of benthic invertebrate and phytoplankton distribution and assemblage composition. The results showed only a minor influence of spatial configuration and no effect of flight ability of invertebrates on model accuracy. However, the models used may partly account for dispersal constraints, since dispersal-related factors, such as lake surface area, are included as predictor variables. The result also showed that composition of littoral invertebrate assemblages was easier to predict at sites located in well-connected lake systems, possibly because the relatively unstable littoral zone necessitates a need for species to re-colonize disturbed habitats from source populations

Linear MMSE-Optimal Turbo Equalization Using Context Trees

Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.Comment: Submitted to the IEEE Transactions on Signal Processin

Adaptive Quantizers for Estimation

In this paper, adaptive estimation based on noisy quantized observations is studied. A low complexity adaptive algorithm using a quantizer with adjustable input gain and offset is presented. Three possible scalar models for the parameter to be estimated are considered: constant, Wiener process and Wiener process with deterministic drift. After showing that the algorithm is asymptotically unbiased for estimating a constant, it is shown, in the three cases, that the asymptotic mean squared error depends on the Fisher information for the quantized measurements. It is also shown that the loss of performance due to quantization depends approximately on the ratio of the Fisher information for quantized and continuous measurements. At the end of the paper the theoretical results are validated through simulation under two different classes of noise, generalized Gaussian noise and Student's-t noise