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A novel hypothesis-based preamble detection method for uncoordinated, high-density packet-based communication over an additive white Gaussian noise channel is proposed and analyzed. Received samples are observed over a window of length equal to that of the preamble and a metric is computed for each sample shift of the window. A metric exceeding a noise dependent pre-computed threshold flags the presence of a preamble. The preamble sequence consists of concatenated sections of spreading sequences whose length is at most the coherence time of the channel. These sections are then differentially combined. A differential correlation-based detection is employed to locate the boundaries of the preamble. A theoretical framework is developed to provide exact analytical solutions for missing and falsely detecting a preamble using matrix analysis of quadratic Gaussian statistics. Furthermore, the robustness of the proposed methodology in a two path channel is studied. The effects of frequency and timing offsets on the system performance is evaluated. Simulation results are presented to validate the analytical expressions. Additionally, a performance comparison of the proposed differential detection scheme with that of a noncoherent square-law detector is presented.