Applications of nonuniform sampling in wideband multichannel communication systems

This research is an investigation into utilising randomised sampling in communication systems to ease the sampling rate requirements of digitally processing narrowband signals residing within a wide range of overseen frequencies. By harnessing the aliasing suppression capabilities of such sampling schemes, it is shown that certain processing tasks, namely spectrum sensing, can be performed at significantly low sampling rates compared to those demanded by uniform-sampling-based digital signal processing. The latter imposes sampling frequencies of at least twice the monitored bandwidth regardless of the spectral activity within. Aliasing can otherwise result in irresolvable processing problems, as the spectral support of the present signal is a priori unknown. Lower sampling rates exploit the processing module(s) resources (such as power) more efficiently and avoid the possible need for premium specialised high-cost DSP, especially if the handled bandwidth is considerably wide. A number of randomised sampling schemes are examined and appropriate spectral analysis tools are used to furnish their salient features. The adopted periodogram-type estimators are tailored to each of the schemes and their statistical characteristics are assessed for stationary, and cyclostationary signals. Their ability to alleviate the bandwidth limitation of uniform sampling is demonstrated and the smeared-aliasing defect that accompanies randomised sampling is also quantified. In employing the aforementioned analysis tools a novel wideband spectrum sensing approach is introduced. It permits the simultaneous sensing of a number of nonoverlapping spectral subbands constituting a wide range of monitored frequencies. The operational sampling rates of the sensing procedure are not limited or dictated by the overseen bandwidth antithetical to uniform-sampling-based techniques. Prescriptive guidelines are developed to ensure that the proposed technique satisfies certain detection probabilities predefined by the user. These recommendations address the trade-off between the required sampling rate and the length of the signal observation window (sensing time) in a given scenario. Various aspects of the introduced multiband spectrum sensing approach are investigated and its applicability highlighted

Compressive Sensing Using Random Demodulation

The new theory of Compressive Sensing allows wideband signals to be sampled at a rate much closer to the information contained within. This rate is much lower than the Nyquist rate required by Shannon’s sampling theory. This “Analog to Information Conversion” has allowed an outlet for already overloaded Analog to Digital converters [15]. Although the locations of frequencies can’t be known a priori, the expected sparseness of a signal can be. This is the circumstance that allows this method to be possible. In order to accomplish this very low rate, there is some trade off in sampling rate reduction to computing load. In contrast to the uniform sampling in common acquisition processes, nonlinear methods must be used resulting in convex programming algorithms becoming a necessity to recover the signal. This thesis tests this new theory using a Random Demodulation data acquisition scheme set forth in [1]. The scheme involves a demodulation step that spreads the information content across the spectrum before an anti-aliasing filter prepares for an Analog to Digital converter to sample it at a very slow rate. The acquisition process is simulated using a computer, the data is run through an optimization algorithm and the recovery results are analyzed. Finally, the paper then compares the results to the Compressive Sensing theoretical and empirical results of others

Improving the Performance of the Space Surveillance Telescope as a Function of Seeing Parameter

This research paper investigates ways to improve the detection capability and predict the performance of the Space Surveillance Telescope (SST) system when it\u27s relocated to Exmouth, Australia. The dataset collected by the SST observing the Geosynchronous Earth Orbit (GEO) satellite, ANIK-F1, entering the earth\u27s eclipse is used to test the performance of the three existing and one new detection algorithm. The three existing algorithms are the point detection (Binary Hypothesis Test (BHT)), correlation detection (CD-BHT), and Multi-hypothesis Test using ten hypotheses (MHT10), and the new detection algorithm is the Multi-hypothesis Test using six hypotheses (MHT6). To improve the accuracy and validness of the comparison, a new method of obtaining the true atmospheric seeing parameter, terminator (point before the object entering the eclipse), and parameters used for the comparison are also investigated. It is found that the MHTs vastly outperform the BHTs, and the MHT6 offers a similar or improved performance over the MHT10, but requiring only half of the computing power

Novel Digital Alias-Free Signal Processing Approaches to FIR Filtering Estimation

This thesis aims at developing a new methodology of filtering continuous-time bandlimited signals and piecewise-continuous signals from their discrete-time samples. Unlike the existing state-of-the-art filters, my filters are not adversely affected by aliasing, allowing the designers to flexibly select the sampling rates of the processed signal to reach the required accuracy of signal filtering rather than meeting stiff and often demanding constraints imposed by the classical theory of digital signal processing (DSP). The impact of this thesis is cost reduction of alias-free sampling, filtering and other digital processing blocks, particularly when the processed signals have sparse and unknown spectral support. Novel approaches are proposed which can mitigate the negative effects of aliasing, thanks to the use of nonuniform random/pseudorandom sampling and processing algorithms. As such, the proposed approaches belong to the family of digital alias-free signal processing (DASP). Namely, three main approaches are considered: total random (ToRa), stratified (StSa) and antithetical stratified (AnSt) random sampling techniques. First, I introduce a finite impulse response (FIR) filter estimator for each of the three considered techniques. In addition, a generalised estimator that encompasses the three filter estimators is also proposed. Then, statistical properties of all estimators are investigated to assess their quality. Properties such as expected value, bias, variance, convergence rate, and consistency are all inspected and unveiled. Moreover, closed-form mathematical expression is devised for the variance of each single estimator. Furthermore, quality assessment of the proposed estimators is examined in two main cases related to the smoothness status of the filter convolution’s integrand function, \u1d454(\u1d461,\u1d70f)∶=\u1d465(\u1d70f)ℎ(\u1d461−\u1d70f), and its first two derivatives. The first main case is continuous and differentiable functions \u1d454(\u1d461,\u1d70f), \u1d454′(\u1d461,\u1d70f), and \u1d454′′(\u1d461,\u1d70f). Whereas in the second main case, I cover all possible instances where some/all of such functions are piecewise-continuous and involving a finite number of bounded discontinuities. Primarily obtained results prove that all considered filter estimators are unbiassed and consistent. Hence, variances of the estimators converge to zero after certain number of sample points. However, the convergence rate depends on the selected estimator and which case of smoothness is being considered. In the first case (i.e. continuous \u1d454(\u1d461,\u1d70f) and its derivatives), ToRa, StSa and AnSt filter estimators converge uniformly at rates of \u1d441−1, \u1d441−3, and \u1d441−5 respectively, where 2\u1d441 is the total number of sample points. More interestingly, in the second main case, the convergence rates of StSa and AnSt estimators are maintained even if there are some discontinuities in the first-order derivative (FOD) with respect to \u1d70f of \u1d454(\u1d461,\u1d70f) (for StSa estimator) or in the second-order derivative (SOD) with respect to \u1d70f of \u1d454(\u1d461,\u1d70f) (for AnSt). Whereas these rates drop to \u1d441−2 and \u1d441−4 (for StSa and AnSt, respectively) if the zero-order derivative (ZOD) (for StSa) and FOD (for AnSt) are piecewise-continuous. Finally, if the ZOD of \u1d454(\u1d461,\u1d70f) is piecewise-continuous, then the uniform convergence rate of the AnSt estimator further drops to \u1d441−2. For practical reasons, I also introduce the utilisation of the three estimators in a special situation where the input signal is pseudorandomly sampled from otherwise uniform and dense grid. An FIR filter model with an oversampled finite-duration impulse response, timely aligned with the grid, is proposed and meant to be stored in a lookup table of the implemented filter’s memory to save processing time. Then, a synchronised convolution sum operation is conducted to estimate the filter output. Finally, a new unequally spaced Lagrange interpolation-based rule is proposed. The so-called composite 3-nonuniform-sample (C3NS) rule is employed to estimate area under the curve (AUC) of an integrand function rather than the simple Rectangular rule. I then carry out comparisons for the convergence rates of different estimators based on the two interpolation rules. The proposed C3NS estimator outperforms other Rectangular rule estimators on the expense of higher computational complexity. Of course, this extra cost could only be justifiable for some specific applications where more accurate estimation is required

Methods for Focal Plane Array Resolution Estimation Using Random Laser Speckle in Non-paraxial Geometries

The infrared (IR) imaging community has a need for direct IR detector evaluation due to the continued demand for small pixel pitch detectors, the emergence of strained-layer-super-lattice devices, and the associated lateral carrier diffusion issues. Conventional laser speckle-based modulation transfer function (MTF) estimation is dependent on Fresnel propagation and a wide-sense-stationary input random process, limiting the use of this approach for lambda (wavelength)-scale IR devices. This dissertation develops two alternative methodologies for speckle-based resolution evaluation of IR focal plane arrays (FPAs). Both techniques are formulated using Rayleigh-Sommerfield electric field propagation, making them valid in the non-paraxial geometries dictated for resolution estimation of lambda-scale devices. The generalized FPA MTF estimation approach numerically evaluates Rayleigh-Sommerfeld speckle irradiance autocorrelation functions (ACFs) to indirectly compute the power spectral density (PSD) of a non-wide-sense-stationary (WSS) speckle irradiance random process. The experimental error incurred by making WSS assumptions regarding the associated laser speckle random process is quantified utilizing the Wigner distribution function. This method is experimentally demonstrated on a lambda-scale longwave IR FPA, showing a 27% spatial frequency range improvement over established estimation methodology. Additionally, a resolution estimation approach, which utilizes an iterative maximum likelihood estimation approach and speckle irradiance ACFs to solve for a system impulse response, is developed and demonstrated with simulated speckle imagery

Background Calibration of a 6-Bit 1Gsps Split-Flash ADC

In this MS thesis, a redundant flash analog-to-digital converter (ADC) using a ``Split-ADC\u27 calibration structure and lookup-table-based correction is presented. ADC input capacitance is minimized through use of small, power efficient comparators; redundancy is used to tolerate the resulting large offset voltages. Correction of errors and estimation of calibration parameters are performed continuously in the background in the digital domain. The proposed flash ADC has an effective-number-of-bits (ENOB) of 6-bits and is designed for a target sampling rate of 1Gs/s in 180nm CMOS. The calibration algorithm described has been simulated in MATLAB and an FPGA implementation has been investigated