Automatic modulation recognition (AMR) critically contributes to spectrum sensing, dynamic spectrum access, and intelligent communications in cognitive radio systems. The introduction of deep learning has greatly improved the accuracy of AMR. However, current automatic identification methods require the input of key parameters such as the carrier frequency, which is necessary to convert the radio frequency (RF) to a base-band signal before it can be used for identification. In addition, the high complexity of deep learning models leads to high computational effort and long recognition times of existing methods, which are difficult to implement in demodulation system deployments. To address the above issues, in this paper, we first use power spectrum analysis to estimate the carrier frequency and signal bandwidth, which realizes the effective conversion from RF signals to base-band signals. This paper chooses the long short-term memory (LSTM) network as the model for automatic identification, which has low implementation complexity while maintaining high accuracy. Finally, by training the LSTM with actual sampling data combined with parameter estimation (PE), the method proposed in this paper can guarantee more than 90% format recognition accuracy.