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In this paper, we study the problem of signal- presence detection, assuming a generic source transmission which can consist of separate pilot and data portions, in the high-power regime. In particular, we derive the optimum non- decision-directed test for the signal-presence hypothesis, which universally applies to all PSK data modulation strategies. For wireless fading channels, the optimum decision test is obtained by computing and thresholding a new proposed decision statistic: the "hybrid" non-coherent accumulation. Hybrid accumulation combines magnitude and power accumulations of the received antenna data, across multiple coherence intervals, or multiple coherence bands. All findings in this paper are derived theoretically, and subsequently verified using computer simulations.