Signal parameters estimation and its applications in communication systems

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NO FULL TEXT AVAILABLE. Access is restricted indefinitely. ----- Parameter estimation of frequency tones is one of the oldest problems in signal processing. It involves estimating the frequency, phase and amplitude of a single or multiple complex exponential signal(s). Embedded in the frequencies, phases and amplitudes is information which can be extracted for tracking movement of a moving object or alternatively be translated by digital decoders into meaningful data for the intended recipient. In fact, signal parameter estimation can be applied in many different fields ranging from biomedical technology such as ultrasound [29] [37] [8], sophisticated military applications like radar and sonar [27] [38] [105], to carrier synchronisation for communication systems. Over the years, researchers have proposed numerous solutions to the problem of estimating the parameters of frequency tones. They all in general, however, suffer from either one or the other of the following impairments: high computational complexity or very poor error performance in noisy environments. The former may prohibit the algorithm being applied in real time applications such as carrier synchronisation and the latter compromises on accuracy of the estimates when operating in noisy environments. This thesis is aimed at developing state of the art carrier acquisition and tracking algorithms for the next generation of software radio modems. The work is divided into two parts. The first part of the thesis is devoted to the investigation into and development of parameter estimation algorithms for complex frequency tones and general bandpass signals, that are computationally efficient and yet effective in very noisy environments. It begins by identifying an existing highly accurate DFT based single tone frequency estimation algorithm that holds the key to the answer. It will be shown by combining this DFT based frequency estimator with ML phase and amplitude estimators yields a highly accurate parameter estimation algorithm for a single complex tone. By exploiting a key property of the aforementioned DFT based frequency estimation algorithm, it is possible to derive a computationally efficient parameter estimation algorithm for complex bandpass signals. The performance of these estimation algorithms are comparable and, in some circumstances, exceed existing state of the art techniques. The second part of the thesis begins by revisiting the theory of digital phase locked loop (DPLL), in particular the four quadrant arctangent phase detector based DPLL, which is suited for digital signal processor (DSP) implementation [49]. A by product of digitally implementing a feedback loop is the inherent delay between the input and output of the loop. If the ratio between speed of the digital signal processor and sampling rate of the analog to digital converter (ADC) is relatively low, this delay can be significant, up to several sample periods. This inherent delay affects the characteristics of the DPLL such as loop stability [128] [10] [11] and frequency pull-in and hold in range [21] [76]. This thesis revisits the analysis of the effective noise bandwidth of the DPLL, taking into account of the aforementioned loop delay at low sampling rate relative to the continuous time noise bandwidth of the PLL. This study of the effective noise bandwidth leads to a better understanding of how loop delay affects the steady noise variance performance of the DPLL. Traditionally, the acquisition process of the DPLL is described with the aid of a phase plane which provides a graphical illustration of the frequency vs phase trajectory over time [34] [17] [50]. In this thesis, a new way of describing the noiseless acquisition behaviour of the DPLL is presented, based on time series analysis of the individual loop components. It will be shown that the number of expected cycle slips and acquisition time for a given frequency and phase can be precisely calculated from the time series equations using numerical methods. Finally, a new discriminator aided DPLL (DA-DPLL) is presented. This discriminator aided DPLL is formed by integrating the proposed DFT based parameter estimation algorithm with the DPLL. Feeding the frequency and phase estimates into the DPLL helps accelerate the acquisition process. Using the error distribution analysis of the DFT based parameter estimator, it is possible predict the worst case error transient of the DA-DPLL in noisy conditions.
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