Small carrier frequency difference detection based on the relative phase entropy

Carrier frequency difference (CFD) detection plays a special role in signal classification and selection. Unfortunately, the CFD between co-channel signals transmitted by different transmitters at the so-called "same frequency" is often too small to detect. This paper applies the phase entropy theory to small CFD detection and we achieve superior results. We proved that the phase entropy algorithm can also be applied to carrier frequency estimation of MPSK signals shaped with limited-bandwidth pulse as well as rectangular pulse. And the sharp trough of entropy spectrum is expanded using the relative phase entropy, thus nonlinear search algorithms are applicable. The proposed algorithm is computationally efficient at the expense of a performance degradation which is acceptable for practical application. For SNR greater than 10 dB and QPSK modulation, the normalized mean square error (NMSE) is below 1e-11, i.e., a CFD of 4 Hz can be detected.