Cognitive radio today is considered to be the solution to solving the problem of spectrum scarcity. One of the most important features of cognitive radio is spectrum sensing. In spectrum sensing it is sometimes necessary to operate in a low SNR regime, in which the performance of most of the classical detectors decreases, especially when they have to deal with imprecise knowledge of the noise characteristics. In fact, in practical applications, the underlying noise often can not be assumed to be Gaussian. In this paper, we design a locally optimum detector, assuming that the underlying noise follows a Student's t-distribution, which is very suitable for modeling heavy-tailed noise. We also assume that BPSK signals are used by primary users and that we have a flat fading channel. Simulation results show that our proposed detector outperforms energy detector in all pre-determined scenarios. It is also more robust in dealing with outliers than both the energy detector and the locally optimum detector based on the assumption of complex Gaussian noise.