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From formula (12), we can conclude that R describes the envelope information of bi-spectrum slice sequence, which directly explains why it can be used for MFSK signal individual identification.
4 shows the envelop parameters R of different MFSK signals under different SNRs.
3.2 The first time wavelet transform of MFSK signals
When the analyzed and wavelet analysis window are at the same symbol period, the first time wavelet transform of MFSK signals is:
When the analyzed and wavelet analysis window are at the adjacent symbol period, the first time wavelet transform of MFSK signals is:
5 shows the instantaneous frequency of different MFSK signals after the first time wavelet transform, and the mutation frequency can be observed clearly.
The instantaneous frequency amplitude of MFSK signals after wavelet transform can be approximated as followed:
3.3 The secondary wavelet transform of MFSK signals
6 that different MFSK signals have different instantaneous frequencies of the secondary wavelet transforms.
7 shows the energy variance of low frequency wavelet coefficients of different MFSK signals under different SNRs.
Therefore, it is urgent to fuse these two features to achieve MFSK signal individual identification under low SNR.
As single feature individual recognition scheme has its instability to a certain extent because of random interruption, this article achieves a two-dimensional feature fusion of bi-spectrum slice envelop parameter and low frequency wavelet coefficients by introducing the idea of information fusion, which ensures the high recognition rate and robustness for MFSK signal individual identification under low SNR.
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