Statistics of the received power for free space optical channels

Free space optical (FSO) communication links can experience extreme signal degradation due to atmospheric turbulence induced spatial and temporal irradiance fuctuations (scintillation) in the laser wavefront. In addition, turbulence can cause the laser beam centroid to wander resulting in power fading, and sometimes complete loss of the signal. Spreading of the laser beam and jitter are also artifacts of atmospheric turbulence. To accurately predict the signal fading that occurs in a laser communication system and to get a true picture of how this affects crucial performance parameters like bit error rate (BER) it is important to analyze the probability density function (PDF) of the integrated irradiance fuctuations at the receiver. In addition, it is desirable to find a theoretical distribution that accurately models these ?uctuations under all propagation conditions. The PDF of integrated irradiance fuctuations is calculated from numerical wave-optic simulations of a laser after propagating through atmospheric turbulence to investigate the evolution of the distribution as the aperture diameter is increased. The simulation data distribution is compared to theoretical gamma-gamma and lognormal PDF models under a variety of scintillation regimes from weak to very strong. Our results show that the gamma-gamma PDF provides a good fit to the simulated data distribution for all aperture sizes studied from weak through moderate scintillation. In strong scintillation, the gamma-gamma PDF is a better fit to the distribution for point-like apertures and the lognormal PDF is a better fit for apertures the size of the atmospheric spatial coherence radius ρ0 or larger. In addition, the PDF of received power from a Gaussian laser beam, which has been adaptively compensated at the transmitter before propagation to the receiver of a FSO link in the moderate scintillation regime is investigated. The complexity of the adaptive optics (AO) system is increased in order to investigate the changes in the distribution of the received power and how this affects the BER. For the 10 km link, due to the non-reciprocal nature of the propagation path the optimal beam to transmit is unknown. These results show that a low-order level of complexity in the AO provides a better estimate for the optimal beam to transmit than a higher order for non-reciprocal paths. For the 20 km link distance it was found that, although minimal, all AO complexity levels provided an equivalent improvement in BER and that no AO complexity provided the correction needed for the optimal beam to transmit. Finally, the temporal power spectral density of received power from a FSO communication link is investigated. Simulated and experimental results for the coherence time calculated from the temporal correlation function are presented. Results for both simulation and experimental data show that the coherence time increases as the receiving aperture diameter increases. For finite apertures the coherence time increases as the communication link distance is increased. We conjecture that this is due to the increasing speckle size within the pupil plane of the receiving aperture for an increasing link distance.

Comparison of Computer-Based and Optical Face Recognition Paradigms

The main objectives of this thesis are to validate an improved principal components analysis (IPCA) algorithm on images; designing and simulating a digital model for image compression, face recognition and image detection by using a principal components analysis (PCA) algorithm and the IPCA algorithm; designing and simulating an optical model for face recognition and object detection by using the joint transform correlator (JTC); establishing detection and recognition thresholds for each model; comparing between the performance of the PCA algorithm and the performance of the IPCA algorithm in compression, recognition and, detection; and comparing between the performance of the digital model and the performance of the optical model in recognition and detection. The MATLAB © software was used for simulating the models. PCA is a technique used for identifying patterns in data and representing the data in order to highlight any similarities or differences. The identification of patterns in data of high dimensions (more than three dimensions) is too difficult because the graphical representation of data is impossible. Therefore, PCA is a powerful method for analyzing data. IPCA is another statistical tool for identifying patterns in data. It uses information theory for improving PCA. The joint transform correlator (JTC) is an optical correlator used for synthesizing a frequency plane filter for coherent optical systems. The IPCA algorithm, in general, behaves better than the PCA algorithm in the most of the applications. It is better than the PCA algorithm in image compression because it obtains higher compression, more accurate reconstruction, and faster processing speed with acceptable errors; in addition, it is better than the PCA algorithm in real-time image detection due to the fact that it achieves the smallest error rate as well as remarkable speed. On the other hand, the PCA algorithm performs better than the IPCA algorithm in face recognition because it offers an acceptable error rate, easy calculation, and a reasonable speed. Finally, in detection and recognition, the performance of the digital model is better than the performance of the optical model.

Control algorithms for large scale adaptive optics

In this dissertation, the problem of creating effective large scale Adaptive Optics (AO) systems control algorithms for the new generation of giant optical telescopes is addressed. The effectiveness of AO control algorithms is evaluated in several respects, such as computational complexity, compensation error rejection and robustness, i.e. reasonable insensitivity to the system imperfections. The results of this research are summarized as follows: 1. Robustness study of Sparse Minimum Variance Pseudo Open Loop Controller (POLC) for multi-conjugate adaptive optics (MCAO). The AO system model that accounts for various system errors has been developed and applied to check the stability and performance of the POLC algorithm, which is one of the most promising approaches for the future AO systems control. It has been shown through numerous simulations that, despite the initial assumption that the exact system knowledge is necessary for the POLC algorithm to work, it is highly robust against various system errors. 2. Predictive Kalman Filter (KF) and Minimum Variance (MV) control algorithms for MCAO. The limiting performance of the non-dynamic Minimum Variance and dynamic KF-based phase estimation algorithms for MCAO has been evaluated by doing Monte-Carlo simulations. The validity of simple near-Markov autoregressive phase dynamics model has been tested and its adequate ability to predict the turbulence phase has been demonstrated both for single- and multiconjugate AO. It has also been shown that there is no performance improvement gained from the use of the more complicated KF approach in comparison to the much simpler MV algorithm in the case of MCAO. 3. Sparse predictive Minimum Variance control algorithm for MCAO. The temporal prediction stage has been added to the non-dynamic MV control algorithm in such a way that no additional computational burden is introduced. It has been confirmed through simulations that the use of phase prediction makes it possible to significantly reduce the system sampling rate and thus overall computational complexity while both maintaining the system stable and effectively compensating for the measurement and control latencies.

Soft-decision equalization techniques for frequency selective MIMO channels

Multi-input multi-output (MIMO) technology is an emerging solution for high data rate wireless communications. We develop soft-decision based equalization techniques for frequency selective MIMO channels in the quest for low-complexity equalizers with BER performance competitive to that of ML sequence detection. We first propose soft decision equalization (SDE), and demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered, and linear in the signal constellation size. Building upon the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Motivated by the need for low-complexity receiver processing, we further present an alternative low-complexity soft-decision equalization approach for frequency selective MIMO communication systems. With the help of iterative processing, two detection and estimation schemes based on second-order statistics are harmoniously put together to yield a two-part receiver structure: local multiuser detection (MUD) using soft-decision Probabilistic Data Association (PDA) detection, and dynamic noise-interference tracking using Kalman filtering. The proposed Kalman-PDA detector performs local MUD within a sub-block of the received data instead of over the entire data set, to reduce the computational load. At the same time, all the inter-ference affecting the local sub-block, including both multiple access and inter-symbol interference, is properly modeled as the state vector of a linear system, and dynamically tracked by Kalman filtering. Two types of Kalman filters are designed, both of which are able to track an finite impulse response (FIR) MIMO channel of any memory length. The overall algorithms enjoy low complexity that is only polynomial in the number of information-bearing bits to be detected, regardless of the data block size. Furthermore, we introduce two optional performance-enhancing techniques: cross- layer automatic repeat request (ARQ) for uncoded systems and code-aided method for coded systems. We take Kalman-PDA as an example, and show via simulations that both techniques can render error performance that is better than Kalman-PDA alone and competitive to sphere decoding. At last, we consider the case that channel state information (CSI) is not perfectly known to the receiver, and present an iterative channel estimation algorithm. Simulations show that the performance of SDE with channel estimation approaches that of SDE with perfect CSI.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Control design and genetic algorithm optimization for electrostatic MEMS

This dissertation discusses structural-electrostatic modeling techniques, genetic algorithm based optimization and control design for electrostatic micro devices. First, an alternative modeling technique, the interpolated force model, for electrostatic micro devices is discussed. The method provides improved computational efficiency relative to a benchmark model, as well as improved accuracy for irregular electrode configurations relative to a common approximate model, the parallel plate approximation model. For the configuration most similar to two parallel plates, expected to be the best case scenario for the approximate model, both the parallel plate approximation model and the interpolated force model maintained less than 2.2% error in static deflection compared to the benchmark model. For the configuration expected to be the worst case scenario for the parallel plate approximation model, the interpolated force model maintained less than 2.9% error in static deflection while the parallel plate approximation model is incapable of handling the configuration. Second, genetic algorithm based optimization is shown to improve the design of an electrostatic micro sensor. The design space is enlarged from published design spaces to include the configuration of both sensing and actuation electrodes, material distribution, actuation voltage and other geometric dimensions. For a small population, the design was improved by approximately a factor of 6 over 15 generations to a fitness value of 3.2 fF. For a larger population seeded with the best configurations of the previous optimization, the design was improved by another 7% in 5 generations to a fitness value of 3.0 fF. Third, a learning control algorithm is presented that reduces the closing time of a radiofrequency microelectromechanical systems switch by minimizing bounce while maintaining robustness to fabrication variability. Electrostatic actuation of the plate causes pull-in with high impact velocities, which are difficult to control due to parameter variations from part to part. A single degree-of-freedom model was utilized to design a learning control algorithm that shapes the actuation voltage based on the open/closed state of the switch. Experiments on 3 test switches show that after 5-10 iterations, the learning algorithm lands the switch with an impact velocity not exceeding 0.2 m/s, eliminating bounce.

MODELING OF TRANSFER PATH FOR DETERMINATION OF COMBUSTION AND NOISE METRICS ON DIESEL ENGINES

Determination of combustion metrics for a diesel engine has the potential of providing feedback for closed-loop combustion phasing control to meet current and upcoming emission and fuel consumption regulations. This thesis focused on the estimation of combustion metrics including start of combustion (SOC), crank angle location of 50% cumulative heat release (CA50), peak pressure crank angle location (PPCL), and peak pressure amplitude (PPA), peak apparent heat release rate crank angle location (PACL), mean absolute pressure error (MAPE), and peak apparent heat release rate amplitude (PAA). In-cylinder pressure has been used in the laboratory as the primary mechanism for characterization of combustion rates and more recently in-cylinder pressure has been used in series production vehicles for feedback control. However, the intrusive measurement with the in-cylinder pressure sensor is expensive and requires special mounting process and engine structure modification. As an alternative method, this work investigated block mounted accelerometers to estimate combustion metrics in a 9L I6 diesel engine. So the transfer path between the accelerometer signal and the in-cylinder pressure signal needs to be modeled. Depending on the transfer path, the in-cylinder pressure signal and the combustion metrics can be accurately estimated - recovered from accelerometer signals. The method and applicability for determining the transfer path is critical in utilizing an accelerometer(s) for feedback. Single-input single-output (SISO) frequency response function (FRF) is the most common transfer path model; however, it is shown here to have low robustness for varying engine operating conditions. This thesis examines mechanisms to improve the robustness of FRF for combustion metrics estimation. First, an adaptation process based on the particle swarm optimization algorithm was developed and added to the single-input single-output model. Second, a multiple-input single-output (MISO) FRF model coupled with principal component analysis and an offset compensation process was investigated and applied. Improvement of the FRF robustness was achieved based on these two approaches. Furthermore a neural network as a nonlinear model of the transfer path between the accelerometer signal and the apparent heat release rate was also investigated. Transfer path between the acoustical emissions and the in-cylinder pressure signal was also investigated in this dissertation on a high pressure common rail (HPCR) 1.9L TDI diesel engine. The acoustical emissions are an important factor in the powertrain development process. In this part of the research a transfer path was developed between the two and then used to predict the engine noise level with the measured in-cylinder pressure as the input. Three methods for transfer path modeling were applied and the method based on the cepstral smoothing technique led to the most accurate results with averaged estimation errors of 2 dBA and a root mean square error of 1.5dBA. Finally, a linear model for engine noise level estimation was proposed with the in-cylinder pressure signal and the engine speed as components.