Robust Semi-Blind Packing Ratio Estimation for Faster-Than-Nyquist Signaling

Accurate packing ratios are indispensable for the faster-than-Nyquist (FTN) signaling; therefore, we propose two robust semi-blind packing ratio estimation algorithms in this letter. Concretely, we construct a pilot-based FTN transmission scheme over the channel with frequency offset and phase noise. We conduct correlation operations on downsampled pilots, assuming a predetermined downsampling factor. To mitigate the impacts of frequency offset and phase noise, we employ differential post-detection integration (DPDI) and differential-generalized post-detection integration (DGPDI) for correlation operations. The packing ratio is estimated by selecting the downsampling factor corresponding to the maximum decision value. Simulation results demonstrate that the coherent correlation yields optimal estimation accuracy in the absence of frequency offset and phase noise. Otherwise, the estimation algorithms using DPDI and DGPDI, i.e., PRE-DPDI and PRE-DGPDI, realize higher estimation accuracy than that using the coherent correlation. When the packing ratio and the normalized frequency offset are 0.8 and 0.2, signal-to-noise ratios required for PRE-DPDI and PRE-DGPDI to achieve a probability of false alarm of
$10^{-4}$
are about 7 and 3 dB, respectively.