Optimal and Sub-Optimal Spectrum Sensing of OFDM Signals in Known and Unknown Noise Variance

We consider spectrum sensing of OFDM signals in an AWGN channel. For the case of completely known noise and signal powers, we set up a vector-matrix model for an OFDM signal with a cyclic prefix and derive the optimal Neyman-Pearson detector from first principles. The optimal detector exploits the inherent correlation of the OFDM signal incurred by the repetition of data in the cyclic prefix, using knowledge of the length of the cyclic prefix and the length of the OFDM symbol. We compare the optimal detector to the energy detector numerically. We show that the energy detector is near-optimal (within 1 dB SNR) when the noise variance is known. Thus, when the noise power is known, no substantial gain can be achieved by using any other detector than the energy detector. For the case of completely unknown noise and signal powers, we derive a generalized likelihood ratio test (GLRT) based on empirical second-order statistics of the received data. The proposed GLRT detector exploits the non-stationary correlation structure of the OFDM signal and does not require any knowledge of the noise power or the signal power. The GLRT detector is compared to state-of-the-art OFDM signal detectors, and shown to improve the detection performance with 5 dB SNR in relevant cases.