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Cognitive radio (CR) is an unlicensed data transmission technique with two main objectives: a) providing highly reliable communications and b) efficient utilization of the spectrum. We focus in this paper on the interference a CR transmission imposes on the primary (licensed) transmission. The amount of this interference is directly related to the accuracy of the “spectrum sensing” unit in CR which is in charge to detect the presence or absence of the primary user signal. We propose new spectrum sensing methods that lead to the minimal bit-error-rate degradation for the primary transmission as compared to state of the art methods. Our results give some practical insights to the design of CR networks with the key objective of minimizing the interference to the primary transmission system.