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This paper addresses the problem of frame detection in orthogonal frequency-division multiplexing (OFDM) systems. Using fourth-order statistics, a novel approach is presented for detection of a preamble composed of two identical parts in the time domain. First, it is demonstrated that sufficient statistics for detection of a periodic preamble do not exist, and conventional methods are not optimal. Next, looking at the detection of a preamble from the viewpoints of hypothesis testing and classification, a new method is presented based on the idea that fourth-order statistics can increase class separability (between-class distance) and consequently improve detection performance. It is proven that the proposed method has a considerably lower probability of false alarm. Along with the missed-detection performance comparisons, it will be presented that the new scheme offers a superior detection performance and makes threshold selection significantly easier.