Performance Analysis Of Post Detection Integration Techniques In The Presence Of Model Uncertainties
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In this thesis, we analyze the performance of the Post Detection Integration (PDI) techniques used for detection of weak DS/CDMA signals in the presence of uncertainty in the frequency, noise variance and data bits. Such weak signal detection problems arise, for example, in the first step of code acquisition for applications such as the Global Navigation Satellite Systems (GNSS) based position localization. Typically, in such applications, a combination of coherent and post-coherent integration stages are used to improve the reliability of signal detection. We show that the feasibility of using fully coherent processing is limited due to the presence of unknown data-bits and/or frequency uncertainty. We analyze the performance of the two conventional PDI techniques, namely, the Non-coherent PDI (NC-PDI) and the Differential-PDI (D-PDI), in the presence of noise and data bit uncertainty, to establish their robustness for weak signal detection. We show that the NC-PDI technique is robust to uncertainty in the data bits, but a fundamental detection limit exists due to uncertainty in the noise variance. The D-PDI technique, on the other hand, is robust to uncertainty in the noise variance, but its performance degrades in the presence of unknown data bits. We also analyze the following different variants of the NC-PDI and D-PDI techniques: Quadratic NC-PDI technique, Non-quadratic NC-PDI, D-PDI with real component (D-PDI (Real)) and D-PDI with absolute component (D-PDI (Abs)). We show that the likelihood ratio based test statistic derived in the presence of data bits is non-robust in the presence of noise uncertainty. We propose two novel PDI techniques as a solution to the above mentioned shortcomings in the conventional PDI methods. The first is a cyclostationarity based sub-optimal PDI technique, that exploits the periodicity introduced due to the data bits. We establish the exact mathematical relationship between the D-PDI and cyclostationarity-based signal detection methods. The second method we propose is a modified PDI technique, which is robust against both noise and data bit uncertainties. We derive two variants of the modified technique, which are tailored for data and pilot channels, respectively. We characterize the performance of the conventional and proposed PDI techniques in terms of their false alarm and detection probabilities and compare them through the receiver operating characteristic (ROC) curves. We derive the sample complexity of the test-statistic in order to achieve a given performance in terms of detection and false alarm probabilities in the presence of model uncertainties. We validate the theoretical results and illustrate the improved performance that can be obtained using our proposed PDI protocols through Monte-Carlo simulations.