This paper presents the physical-layer cell identity (PCID) detection probability using the narrowband primary synchronization signal (NPSS) and narrowband secondary synchronization signal (NSSS) based on the narrowband Internet-of-Things (NB-IoT) radio interface considering frequency offset and the maximum Doppler frequency in the 28-GHz band. Simulation results show that the autocorrelation based NPSS detection method is more effective than the cross-correlation based NPSS detection using frequency offset estimation and compensation before the NPSS received timing detection from the viewpoints of PCID detection probability and computational complexity. We also show that when using autocorrelation based NPSS detection, the loss in the PCID detection probability at the carrier frequency of f_c =28GHz compared to that for f_c =3.5GHz is only approximately 5% at the average received signal-to-noise ratio (SNR) of 0dB when the frequency stability of a local oscillator of a user equipment (UE) set is 20ppm. Therefore, we conclude that the multiplexing schemes and sequences of NPSS and NSSS based on the NB-IoT radio interface associated with autocorrelation based NPSS detection will support the 28-GHz frequency spectra.