Digital block transmission and time-of-flight estimation : receiver design and performance analysis
Abstract: This thesis is concerned with signal processing aspects of digital block transmission and time-of-flight estimation. Receivers are derived and analysed based on the assumption that the received signals have been corrupted with additive Gaussian noise and linear distortion. A general framework is presented for lower bounding the performance of receivers for digital transmission through linear channels with additive Gaussian noise and intersymbol interference. Building on Forney's concept of the genie, a genie-aided detector based on a stochastic description of the side information is introduced. This statistical description makes the lower bounding a transparent application of Bayesian detection theory. A representation for the minimum bit-error probability receiver is derived using a geometric theory of digital transmission of finite sequences of binary, antipodally, modulated symbols. Assuming that all data sequences are equally probable and transmitted through a linear channel with additive Gaussian noise and intersymbol interference, two properties of the minimum bit-error probability receiver are shown: (1) Asymptotically, as the signal-to-noise ratio (SNR) goes to infinity, the decision regions of the minimum bit-error probability receiver become identical to the decision regions of the maximum likelihood sequence detector; (2) Asymptotically, as the SNR goes to zero, the decision regions of the minimum bit-error probability receiver become identical to the decision regions of the whitened matched filter detector. This confirms the well-known result that the maximum likelihood sequence detector attains minimum bit-error probability for asymptotically high SNR and equally probable sequences. A fast detector of binary, antipodally modulated data that has been corrupted by additive Gaussian noise and intersymbol interference is presented. This detector will make the same decisions as a maximum likelihood sequence detector on scattered bits in a transmitted sequence. It is simple in structure, consisting of a whitened matched filter, two variable thresholds for each bit to be detected and an algorithm to calculate the thresholds. The thresholds are dependent on the received signal and are calculated using an iterative method. Simulation results demonstrate that the probability of bit-error for a decision-feedback equalizer is decreased if this detector is used as a pre-processor. It is also demonstrated that the performance of linear equalizers can be improved substantially. A method for modelling linear distortion of narrowband pulses for the purpose of timeof-flight (TOF) estimation is introduced. This modelling method is based on a known narrowband reference signal being transmitted through an unknown linear and time-invariant system with additive Gaussian noise. The system is modelled in the frequency domain with an M - 1th order complex polynomial around the centre frequency of the reference signal. This enables the output of the system to be modelled as a linear combination of 2M orthonormal base signals. A TOF estimator for this model, based on the criterion of maximum likelihood, is derived. The resulting receiver can be seen as an extension, or generalization, of the cross-correlation, or "matched filter", estimator. The receiver is found to be more robust against unknown linear pulse shape distortion than the crosscorrelation receiver, giving less biased TOF estimates. Also, bias versus noise sensitivity can be controlled by model order selection.
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