Invariant detection of orthogonal frequency division multiplexing signals with unknown parameters for cognitive radio applications

The authors propose a computationally efficient spectrum sensing solution for an orthogonal frequency division multiplexing (OFDM) signal in a frequency-selective fading channel with additive white Gaussian noise (AWGN). The authors´ assumption is that the data symbols, channel coefficients and the noise variance are all unknown. The nature of the problem leads them to find an invariant detector. The optimum one is uniformly most powerful invariant (UMPI); their effort shows that this test does not exist, as the final decision statistic depends on some unknown parameters; although, they derive the most powerful invariant (MPI) detector, implanting these parameters, to provide an upper bound for invariant detectors. Instead, the authors develop the generalised likelihood ratio test (GLRT), substituting the unknown parameters by their maximum likelihood (ML) estimates in the Neyman´Pearson likelihood ratio. Furthermore, they propose a computationally efficient implementation of the resulting detector. Simulation results show a slight decrease in efficiency against gaining so much computational complexity (CC) improvement. For more comparisons they also derive the conventional energy detector, namely, generalised energy detector (GED) for a binary phase shift keying (BPSK) signal, to show the adequacy of the GLR detector performance which would be demonstrated by simulation results.