In cognitive radio networks, the signal-to-noise ratio (SNR) of the primary receiver (PR), called primary-link SNR, is critical for underlay spectrum sharing. However, it is very difficult for the cognitive user (CU) to obtain the primary-link SNR. In this letter, we propose a new method to let the CU autonomously estimate the primary-link SNR, where the full-duplex relay technique is used. Then, the CU can conduct the underlay spectrum sharing more efficiently. Simulation results indicate the effectiveness of the proposed method.