In cognitive radio (CR) networks, spectrum sensing has to be performed in a reliable manner in challenging environments that arise due to propagation channels which undergo multi-path fading and non-Gaussian noise at CRs. Most existing literature on spectrum sensing has focused on impairments introduced by additive white Gaussian noise (AWGN). However, this assumption fails to model the behavior of certain noise types in practice, such as impulsive noise. In this paper, the use of a non-parametric, easily implementable detection device, polarity-coincidence-array (PCA) detector, is proposed for weak primary signal detection with a cognitive radio equipped with multiple antennas. The detector performance in terms of the probabilities of detection and false alarm is derived when the communication channels between the primary user transmitter and the multiple antennas at the cognitive radio undergo Rayleigh fading. From the numerical results, it is observed that a significant performance enhancement is achieved by the PCA detector compared to that of the simple energy detector as the heaviness of the tail of the non-Gaussian noise increases.