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Philosophiae Doctor - PhD / The faint radio population consisting of star forming galaxies (SFG) and radio-quiet active galactic nuclei (AGN) is important in the study of galaxy evolution. However, the bulk of the faint population is below the detection threshold of the current radio surveys. I study this population through a Bayesian-stacking technique that I have adapted to probe the radio luminosity function (RLF) below the typical 5σ detection threshold. The technique works by fitting RLF models to radio flux densities extracted at the position of galaxies selected from an auxiliary catalogue. I test the technique by adding Gaussian noise (σ) to simulated data and the RLF models are in agreement with the simulated data for up to three orders of magnitude (3 dex) below the detection threshold (5σ). The source of radio emission from radio quiet quasars (subset of AGN) is widely debated. I apply the technique to 1.4-GHz flux densities from the Faint Images of the Radio Sky at Twenty-cm survey (FIRST) at the positions of the optical quasars from the Sloan Digital Sky Survey (SDSS). The RLF models are constrained to 2 dex below the FIRST detection threshold. I found that the radio luminosity where radio-quiet quasars emerge coincides with the luminosity where SFGs are expected to start to dominate the RLF. This Implies that the radio emission of radio-quiet quasars and radio-quiet AGN, in general, could have a significant contribution from star formation in the host galaxies.

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Signal detection and modulation classification are becoming increasingly important in a variety of wireless communication systems such as those involving spectrum management and electronic warfare and surveillance, among others. The majority of the signal detection and modulation classification algorithms available in the literature assume that the additive noise has a Gaussian distribution. However, while this is a good model for thermal noise, various studies have shown that the noise experienced in most radio channels, due to a variety of man-made and natural electromagnetic sources, is non-Gaussian and exhibits impulsive characteristics. Unfortunately, conventional signal processing algorithms developed for Gaussian noise conditions are known to perform poorly in the presence of non-Gaussian noise. For this reason, the main goal of this dissertation is to develop statistical signal processing algorithms for the detection and modulation classification of signals in radio channels where the additive noise is non-Gaussian. One of the major challenges involved in the design of these algorithms is that they are expected to operate with limited or no prior knowledge of the signal of interest, the fading experienced by the signal, and the distribution of the noise added in the channel. Therefore, this dissertation develops new techniques for estimating the parameters that characterize the additive non-Gaussian noise process, as well as the fading process, in the presence of unknown signals. These novel estimators are an integral contribution of this dissertation. The signal detection and modulation classification problems considered here are treated as hypothesis testing problems. Using a composite hypothesis testing procedure, the unknown fading and noise process parameters are first estimated and then used in a likelihood ratio test to detect the presence or identify the modulation scheme of a signal of interest. The proposed algorithms, which are developed for different non-Gaussian noise models, are shown to outperform conventional algorithms which assume Gaussian noise conditions and also algorithms based on other impulsive noise mitigation techniques. This dissertation has three major contributions. First, in environments where the noise can be modeled using a Gaussian mixture distribution, a new expectation-maximization algorithm based technique is developed for estimating the unknown fading and noise distribution parameters. Using these estimates, a hybrid likelihood ratio test is used for modulation classification. Second, a five-stage scheme for signal detection in symmetric α stable noise environments, based on a class of robust filters called the matched myriad filters, is presented. New algorithms for estimating the noise distribution parameters are also developed. Third, a modulation classifier is proposed for environments in which the noise can be modeled as a time-correlated non-Gaussian random process. The proposed classifier involves the use of a whitening filter followed by likelihood-based classification. A new H_â filter-based technique for estimating the whitening filter coefficients is presented. / Ph. D.

In recent years, the field of Fractional Brownian motion, Fractional Gaussian noise and long-range dependent processes has gained growing interest. Fractional Brownian motion is of great interest for example in telecommunications, hydrology and the generation of artificial landscapes. In fact, Fractional Brownian motion is a basic continuous process through which we show that it is neither a semimartingale nor a Markov process. In this work, we will focus on the path properties of Fractional Brownian motion and will try to check the absence of the property of a semimartingale. The concept of volatility will be dealt with in this work as a phenomenon in finance. Moreover, some statistical method like R/S analysis will be presented. By using these statistical tools we examine the volatility of shares and we demonstrate empirically that there are in fact shares which exhibit a fractal structure different from that of Brownian motion.

<p>In recent years, the field of Fractional Brownian motion, Fractional Gaussian noise and long-range dependent processes has gained growing interest. Fractional Brownian motion is of great interest for example in telecommunications, hydrology and the generation of artificial landscapes. In fact, Fractional Brownian motion is a basic continuous process through which we show that it is neither a semimartingale nor a Markov process. In this work, we will focus on the path properties of Fractional Brownian motion and will try to check the absence of the property of a semimartingale. The concept of volatility will be dealt with in this work as a phenomenon in finance. Moreover, some statistical method like R/S analysis will be presented. By using these statistical tools we examine the volatility of shares and we demonstrate empirically that there are in fact shares which exhibit a fractal structure different from that of Brownian motion.</p>

The Nyquist WDM system realizes a terabit high spectral efficiency transmission system by allocating several subcarriers close to or equal to the baud rate. This system achieves optimal performance by maintaining both temporal and spectral orthogonality. However, ISI and ICI effects are inevitable in practical Nyquist WDM implementations due to the imperfect channel response and tight channel spacing and may cause significant performance degradations. Our primary research goals are to combat the ISI effects via the transmitter digital pre-shaping and to remove the ICI impairments at the receiver using MIMO signal processing. First we propose two novel blind channel estimation techniques that enable the transmitter pre-shaping design for the ISI effects mitigation. Both numerical and experimental results demonstrate that the two methods are very effective in compensating the narrow band filtering and are very robust to channel estimation noise. Besides pre-shaping, the DAC-enabled transmitter chromatic dispersion compensation is also demonstrated in a system with high LO laser linewidth. Next a novel “super-receiver” structure is proposed, where different subchannels are synchronously sampled, and the baseband signals from three adjacent subchannels are processed jointly to remove ICI penalty. Three different ICI compensation methods are introduced and their performances compared. The important pre-processes that enable a successful ICI compensation are also elaborated. Despite ICI compensation, the joint carrier phase recovery based on the Viterbi-Viterbi algorithm is also studied in the carrier phase locked systems. In-band crosstalk arises from the imperfect switch elements in the add-drop process of ROADM-enabled DWDM systems and may cause significant performance degradation. Our third research topic is to demonstrate a systematic way to analyze and predict the in-band crosstalk-induced penalty. In this work, we propose a novel crosstalk-to-ASE noise weighting factor that can be combined with the weighted crosstalk weighting metric to incorporate the in-band crosstalk noise into the Gaussian noise model for performance prediction and analysis. With the aid of the Gaussian noise model, the in-band crosstalk-induced nonlinear noise is also studied. Both simulations and experiments are used to validate the proposed methods.

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We address the problem of image denoising for additive white Gaussian noise (AWGN), Poisson noise, and Chi-squared noise scenarios. Thermal noise in electronic circuitry in camera hardware can be modeled as AWGN. Poisson noise is used to model the randomness associated with photon counting during image acquisition. Chi-squared noise statistics are appropriate in imaging modalities such as Magnetic Resonance Imaging (MRI). AWGN is additive, while Poisson noise is neither additive nor multiplicative. Although Chi-squared noise is derived from AWGN statistics, it is non-additive. Mean-square error (MSE) is the most widely used metric to quantify denoising performance. In parametric denoising approaches, the optimal parameters of the denoising function are chosen by employing a minimum mean-square-error (MMSE) criterion. However, the dependence of MSE on the noise-free signal makes MSE computation infeasible in practical scenarios. We circumvent the problem by adopting an MSE estimation approach. The ground-truth-independent estimates of MSE are Stein’s unbiased risk estimate (SURE), Poisson unbiased risk estimate (PURE) and Chi-square unbiased risk estimate (CURE) for AWGN, Poison and Chi-square noise models, respectively. The denoising function is optimized to achieve maximum noise suppression by minimizing the MSE estimates. We have chosen the bilateral filter as the denoising function. Bilateral filter is a nonlinear edge-preserving smoother. The performance of the bilateral filter is governed by the choice of its parameters, which can be optimized to minimize the MSE or its estimate. However, in practical scenarios, MSE cannot be computed due to inaccessibility of the noise-free image. We derive SURE, PURE, and CURE in the context of bilateral filtering and compute the parameters of the bilateral filter that yield the minimum cost (SURE/PURE/CURE). On processing the noisy input with bilateral filter whose optimal parameters are chosen by minimizing MSE estimates (SURE/PURE/CURE), we obtain the estimate closest to the ground truth. We denote the bilateral filter with optimal parameters as SURE-optimal bilateral filter (SOBF), PURE-optimal bilateral filter (POBF) and CURE-optimal bilateral filter (COBF) for AWGN, Poisson and Chi-Squared noise scenarios, respectively. In addition to the globally optimal bilateral filters (SOBF and POBF), we propose spatially adaptive bilateral filter variants, namely, SURE-optimal patch-based bilateral filter (SPBF) and PURE-optimal patch-based bilateral filter (PPBF). SPBF and PPBF yield significant improvements in performance and preserve edges better when compared with their globally-optimal counterparts, SOBF and POBF, respectively. We also propose the SURE-optimal multiresolution bilateral filter (SMBF) where we couple SOBF with wavelet thresholding. For Poisson noise suppression, we propose PURE-optimal multiresolution bilateral filter (PMBF), which is the Poisson counterpart of SMBF. We com-pare the performance of SMBF and PMBF with the state-of-the-art denoising algorithms for AWGN and Poisson noise, respectively. The proposed multiresolution-based bilateral filtering techniques yield denoising performance that is competent with that of the state-of-the-art techniques.