In this paper we consider a non-coherent and coherent spectrum sensing scheme for OFDM signals. In addition to perfect symbol timing information we also assume full channel knowledge in the coherent case. For the non-coherent and the coherent scheme we derive analytical expressions for the detection error probability. In a comparison of these analytical and additional numerical results we find that the increased complexity of the coherent scheme does not necessarily result in a better performance. We thus provide an important insight in the complexity performance trade-off of spectrum sensing schemes.