abstract: Signal compressed using classical compression methods can be acquired using brute force (i.e. searching for non-zero entries in component-wise). However, sparse solutions require combinatorial searches of high computations. In this thesis, instead, two Bayesian approaches are considered to recover a sparse vector from underdetermined noisy measurements. The first is constructed using a Bernoulli-Gaussian (BG) prior distribution and is assumed to be the true generative model. The second is constructed using a Gamma-Normal (GN) prior distribution and is, therefore, a different (i.e. misspecified) model. To estimate the posterior distribution for the correctly specified scenario, an algorithm based on generalized approximated message passing (GAMP) is constructed, while an algorithm based on sparse Bayesian learning (SBL) is used for the misspecified scenario. Recovering sparse signal using Bayesian framework is one class of algorithms to solve the sparse problem. All classes of algorithms aim to get around the high computations associated with the combinatorial searches. Compressive sensing (CS) is a widely-used terminology attributed to optimize the sparse problem and its applications. Applications such as magnetic resonance imaging (MRI), image acquisition in radar imaging, and facial recognition. In CS literature, the target vector can be recovered either by optimizing an objective function using point estimation, or recovering a distribution of the sparse vector using Bayesian estimation. Although Bayesian framework provides an extra degree of freedom to assume a distribution that is directly applicable to the problem of interest, it is hard to find a theoretical guarantee of convergence. This limitation has shifted some of researches to use a non-Bayesian framework. This thesis tries to close this gab by proposing a Bayesian framework with a suggested theoretical bound for the assumed, not necessarily correct, distribution. In the simulation study, a general lower Bayesian Cram\'er-Rao bound (BCRB) bound is extracted along with misspecified Bayesian Cram\'er-Rao bound (MBCRB) for GN model. Both bounds are validated using mean square error (MSE) performances of the aforementioned algorithms. Also, a quantification of the performance in terms of gains versus losses is introduced as one main finding of this report. / Dissertation/Thesis / Masters Thesis Computer Engineering 2019

The purpose of this thesis is to derive and analyze the theoretical limits for estimatingthe symboltiming delayof Multiple-Input Multiple-Output (MIMO)systems. Two main N X M system models are considered, where N represents the number of transmit antennas and M denotes the number of receive antennas, the 2 X 2 system used by S.-A. Yangand J. Wu and the 4 X 4system used by Y.-C. Wu and E. Serpedin. The second model has been extended to take into account the symbol time-varying fading. The theoretical estimation limits are shown by several bounds: modified Cramer-Rao bound (MCRB), Cramer-Rao bound (CRB) and Barankin bound (BB). BB will be exploited to obtain accurate information regarding the necessary length of data to obtain good estimation. Two scenarios for synchronization are presented: data-aided (DA) and non-data-aided (NDA). Two models for the fading process are considered: block fading and symbol time-varying fading, respectively, the second case being assumed to be Rayleigh distributed. The asymptotic Cramer-Rao bounds for low signal-to-noise ratio (low-SNR) and for high-SNR are derived and the performance of several estimators is presented. The performance variation of bounds and estimators is studied byvarying different parameters, such as the number of antennas, the length of data taken into consideration during the estimation process, the SNR, the oversampling factor, the power and the Doppler frequency shift of the fading.

In certain applications involving direction of arrival (DOA) estimation the operator may have a-priori information on some of the DOAs. This information could refer to a target known to be present at a certain position or to a reflection. In this study, the authors investigate a methodology for array processing that exploits the information on the known DOAs for estimating the unknown DOAs as accurately as possible. Algorithms are presented that can efficiently handle the case of both correlated and uncorrelated sources when the receiver is a uniform linear array. The authors find a major improvement in estimator accuracy in feasible scenarios, and they compare the estimator performance to the corresponding theoretical stochastic Cramer-Rao bounds as well as to the performance of other methods capable of exploiting such prior knowledge. In addition, real data from an ultra-sound array is applied to the investigated estimators. / <p>QC 20130107</p>

The purpose of this thesis is to derive and analyze the theoretical limits for estimatingthe symboltiming delayof Multiple-Input Multiple-Output (MIMO)systems. Two main N X M system models are considered, where N represents the number of transmit antennas and M denotes the number of receive antennas, the 2 X 2 system used by S.-A. Yangand J. Wu and the 4 X 4system used by Y.-C. Wu and E. Serpedin. The second model has been extended to take into account the symbol time-varying fading. The theoretical estimation limits are shown by several bounds: modified Cramer-Rao bound (MCRB), Cramer-Rao bound (CRB) and Barankin bound (BB). BB will be exploited to obtain accurate information regarding the necessary length of data to obtain good estimation. Two scenarios for synchronization are presented: data-aided (DA) and non-data-aided (NDA). Two models for the fading process are considered: block fading and symbol time-varying fading, respectively, the second case being assumed to be Rayleigh distributed. The asymptotic Cramer-Rao bounds for low signal-to-noise ratio (low-SNR) and for high-SNR are derived and the performance of several estimators is presented. The performance variation of bounds and estimators is studied byvarying different parameters, such as the number of antennas, the length of data taken into consideration during the estimation process, the SNR, the oversampling factor, the power and the Doppler frequency shift of the fading.

This thesis presents an analysis of the Modified Cramer Rao Bound (MCRB) for synchroniser performance in burst mode communication applications. This is accomplished by introducing the topic of burst mode communications and its practical applications, discussing the importance of synchronisation, presenting a model through which the mathematical analysis of this thesis is based upon, deriving a set of equations which can be used to calculate the MCRB and finally by performing various calculations of the MCRB with different parameters to examine their effects on the MCRB. The methods presented in this thesis are different from those presented in existing literature, which generally do not address the issue of burst mode synchronisation directly. The differences between the methods presented in this thesis and those of existing literature is also discussed.

No description available.

Field-wise wind estimation (also known as model-based wind estimation) is a sophisticated technique to derive wind estimates from radar backscatter measurements. In contrast to the more traditional method known as point-wise wind retrieval, field-wise techniques estimate wind field model parameters. In this way, neighboring wind vectors are jointly estimated, ensuring consistency. This work presents and implementation for field-wise wind retrieval for the SeaWinds scatterometer on the QuikSCAT satellite. Due to its sophistication, field-wise wind retrieval adds computational complexity and intensity. The tradeoffs necessary for practical implementations are examined and quantified. The Levenberg-Marquardt algorithm for minimizing the field-wise objective function is presented. As the objective function has several near-global local minima, several wind fields represent ambiguous wind field estimates. A deterministic method is proposed to ensure sufficient ambiguities are obtained. An improved method for selecting between ambiguous wind field estimates is also proposed. With a large set of Sea-Winds measurements and estimates available, the σ° measurement statistics are examined. The traditional noise model is evaluated for accuracy. A data-driven parameterization is proposed and shown to effectively estimate measurement bias and variance. The parameterized measurement model is used to generate Cramer-Rao bounds on estimator performance. Using the Cramer-Rao bound, field-wise and point-wise performances are compared.

Maximum likelihood symbol timing estimation for communication over a frequency non-selective MIMO fading channel is developed. The cases of known data (data-aided estimation) and unknown data (non-data-aided estimation) together with known channel and unknown channel are considered. The analysis shows that the log-likelihood functions and their approximations can be interpreted as SISO log-likelihood functions operating on each of the receive antennas. Previously published symbol timing estimators are shown to be special cases of the more general framework presented. Architectures based on both block processing and sequential processing using a discrete-time phase-locked loop are summarized. Performance examples over a MIMO channel based on measured data and on a simple stochastic MIMO channel model are given. These examples show that the mean-squared error performance of these techniques is not strongly dependent on the MIMO channel and is able to reach the Cramer Rao bound when sufficient complexity is applied.

The demand for sophisticated wireless applications capable of conveying information content represented in various forms such as voice, data, audio and video is ever increasing. In order to support such applications, either additional wireless spectrum is needed or advanced signal processing techniques must be employed by the next-generation wireless communication systems. An immediate observation that can be made regarding the first option is that radio frequency spectrum is a limited natural resource. Moreover, since existing spectrum allocation policies of several national regulatory agencies such as the Federal Communications Commission (FCC) restrict spectrum access to licensed entities only, it has been identified that most of the licensed spectrum across time and frequency is inefficiently utilized. To facilitate greater spectral efficiency, many national regulatory agencies are considering a paradigm shift towards spectrum allocation by allowing unlicensed users to temporarily borrow unused spectral resources. This concept is referred to a dynamic spectrum access (DSA). Although, several spectrum measurement campaigns have been reported in the published literature for quantitatively assessing the available vacant spectrum, there are certain aspects of spectrum utilization that need a deeper understanding. First, we examine two complementary approaches to the problem of characterizing the usage of licensed bands. In the first approach, a linear mixed-effects based regression model is proposed, where the variations in percentage spectrum occupancy and activity period of the licensed user are described as a function of certain independent regressor variables. The second approach is based on the creation of a geo-location database consisting of the licensed transmitters in a specific geographical region and identifying the coverage areas that affect the available secondary channels. Both of these approaches are based on the energy spectral density data-samples collected across numerous frequency bands in several locations in the United States. We then study the mutual interference effects in a coexistence scenario consisting of licensed and unclicensed users. We numerically evaluate the impact of interference as a function of certain receiver characteristics. Specifically, we consider the unlicensed user to utilize OFDM or NOFDM symbols since the appropriate subcarriers can be turned off to facilitate non- contiguous spectrum utilization. Finally, it has been demonstrated that multiple-input and multiple-output (MIMO) antennas yield significant throughput while requiring no increase in transmit power or required bandwidth. However, the separation of spectrally overlapping signals is a challenging task that involves the estimation of the channel. We provide results concerning channel and symbol estimation in the scenario described above. In particular, we focus on the MIMO-OFDM transmission scheme and derive capacity lower bounds due to imperfect channel estimation.

Digital communication systems invariably employ an underlying analog communication channel. At the transmitter, data is modulated to obtain an analog waveform which is input to the channel. At the receiver, the output of the channel needs to be mapped back into the discrete domain. To this effect, the continuous-time received waveform is sampled at instants chosen by the timing recovery block. Therefore, timing recovery is an essential component of digital communication systems. A widely used timing recovery method is based on a phase-locked loop (PLL), which updates its timing estimates based on a decision-directed device. Timing recovery performance is a strong function of the reliability of decisions, and hence, of the channel signal-to-noise ratio (SNR). Iteratively decodable error-control codes (ECCs) like turbo codes and LDPC codes allow operation at SNRs lower than ever before, thus exacerbating timing recovery. We propose iterative timing recovery, where the timing recovery block, the equalizer and the ECC decoder exchange information, giving the timing recovery block access to decisions that are much more reliable than the instantaneous ones. This provides significant SNR gains at a marginal complexity penalty over a conventional turbo equalizer where the equalizer and the ECC decoder exchange information. We also derive the Cramer-Rao bound, which is a lower bound on the estimation error variance of any timing estimator, and propose timing recovery methods that outperform the conventional PLL and achieve the Cramer-Rao bound in some cases. At low SNR, timing recovery suffers from cycle slips, where the receiver drops or adds one or more symbols, and consequently, almost always the ECC decoder fails to decode. Iterative timing recovery has the ability to corrects cycle slips. To reduce the number of iterations, we propose cycle slip detection and correction methods. With iterative timing recovery, the PLL with cycle slip detection and correction recovers most of the SNR loss of the conventional receiver that separates timing recovery and turbo equalization.