A framework of spectrum sensing with a multi-class hypothesis is proposed to maximize the achievable throughput in cognitive radio networks. The energy range of a sensing signal under the hypothesis that the primary user is absent (in a conventional two-class hypothesis) is further divided into quantized regions, whereas the hypothesis that the primary user is present is conserved. The non-radio frequency energy harvesting-equiped secondary user transmits, when the primary user is absent, with transmission power based on the hypothesis result (the energy level of the sensed signal) and the residual energy in the battery: the lower the energy of the received signal, the higher the transmission power, and vice versa. Conversely, the lower is the residual energy in the node, the lower is the transmission power. This technique increases the throughput of a secondary link by providing a higher number of transmission events, compared to the conventional two-class hypothesis. Furthermore, transmission with low power for higher energy levels in the sensed signal reduces the probability of interference with primary users if, for instance, detection was missed. The familiar machine learning algorithm known as a support vector machine (SVM) is used in a one-versus-rest approach to classify the input signal into predefined classes. The input signal to the SVM is composed of three statistical features extracted from the sensed signal and a number ranging from 0 to 100 representing the percentage of residual energy in the node’s battery. To increase the generalization of the classifier, k-fold cross-validation is utilized in the training phase. The experimental results show that an SVM with the given features performs satisfactorily for all kernels, but an SVM with a polynomial kernel outperforms linear and radial-basis function kernels in terms of accuracy. Furthermore, the proposed multi-class hypothesis achieves higher throughput compared to the conventional two-class hypothesis for spectrum sensing in cognitive radio networks.