Localization of packet based radio transmitters in space, time, and frequency

Abstract

We consider the scenario where one or more sensors observe a frequency band potentially used by multiple radio transmitters forming packet based networks. Our goal is to develop algorithms for estimation of spectrum usage in space, time, and frequency. This estimation is obtained by performing some form of analysis of the received signals at the sensors. The proposed algorithms can be used for achieving efficient spectrum utilization by identifying unused portions of spectrum in space, time and frequency as well as for other applications requiring spectrum monitoring.The received signals consist of packets from multiple transmitters with possible timefrequency collisions. Each received signal consists of multiple statistically homogeneous segments where each combination of active transmitted signals creates one or more of such segments. In order to perform any form of statistical analysis using conventional methods for stationary or cyclostationary signals these segments must be first localized in time. In the first part of the thesis we propose a nonparametric algorithm for solving this problem. Initial segmentation is computed using a variant of mean shift algorithm, which is a clustering tool based on nonparametric estimate of the underlying probability distribution. We show that this type of mean shift algorithm is based on the modified Newton's method and provide a convergence analysis which explains how and why ii the algorithm works. Final segmentation results are obtained after applying a cluster validation procedure and impulse noise filtering on the initial segmentation results.In the second part of the thesis we propose a method for analysis of the segments localized in the first step. This method is useful if transmitted signals are linearly modulated or can be approximated as sums of linearly modulated signals. For each set of segments generated by the same combination of the transmitted signals we compute a certain two dimensional slice of the fourth order spectrum. These slices are arranged in a three way array. We show that under certain conditions it is possible to recover contributions of individual signals to the observed three way array by decomposing the array into low rank terms. Thus, for each received signal we can estimate its spectrum and the associated activity sequence in time. We discuss the uniqueness conditions, treat the nontrivial problem of fourth order spectrum estimation and propose a numerical algorithm for estimation of the spectra and the associated activity sequences of individual signals from the observed three way array.The algorithms for segmentation and fourth order spectrum based analysis require only one sensor. In the third part of the thesis we assume that multiple sensors are available. Using the algorithms mentioned above for each transmitter we can estimate its received spectrum at different sensors. From the received spectra of the same transmitted signal at different sensors it is possible to estimate the source signal spectrum and transfer functions of the ch...