Waveform design of UNB modulation and performance analysis

To improve the spectrum efficiency and alleviate scarcity, ultra-narrow band (UNB) technique is proposed with high bandwidth efficiency and low bit error rate (BER). In this paper, the waveform design schemes, which are sine amplitude modulation (AM-sine), dual-frequency amplitude modulation (DFAM) and constant modulus dual-frequency (CMDF) modulation for wireless communication networks employing UNB technique, are proposed. We investigate the Euclidean distance of binary modulated signals for UNB communication under the bandwidth restriction compared to very-minimum waveform difference keying (VWDK). We derive the simplicity to optimize our proposed schemes by introducing sine-like signal. By applying the concavity optimization theory, we get more smooth phase waveform than VWDK. We formulate the optimization problem to minimize the average BER subject to these conditions, one is the Euclidean distance between modulated signals and carrier signal, the other one is the signal energy. Simulation results are provided to show the superiority of our proposed schemes as compared to VWDK.