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This paper proposes a simple multi-cycle cyclostationary based signal detection (spectrum sensing) algorithm for Orthogonal Frequency Division Multiplexed (OFDM) signals in cognitive radio networks. We assume that the noise samples are independent and identically distributed (i.i.d) random variables all with unknown (imperfect) variance. Our detection algorithm employ the following three steps. First, we formulate the test statistics as a ratio of two quadratic cyclic autocorrelation functions. Second, we derive a closed form expression for the false alarm probability. Third, we evaluate the detection probability of our algorithm for a given false alarm probability. The derived probability of false alarm expression fits to that of the simulation result. Moreover, we demonstrate that the proposed multi-cycle algorithm yields significantly superior probability of detection compared to the existing low complexity cyclostationary based and the well known energy detection algorithms.