Why to Use the Phase in Time-Encoding Modulation and Its Effect on the Spectral Efficiency

Modulation schemes that encode information in the time domain play an important role for energy-efficient communications at high and low spectral efficiencies. Verdú showed that a spectrally efficient operation of pulse-based modulation schemes with independent identically distributed symbols at low signal-to-noise ratios is only possible when the phase is used as an additional degree of freedom. In the present work, four maxentropic symbol sequences are considered that encode information in the time domain and make use of the phase to varying degrees. The spectral efficiency is evaluated for the transmission over a bandlimited additive white Gaussian noise channel where the output is quantized with the lowest resolution that allows the reconstruction of the input symbols in the noiseless case. Moreover, faster-than-Nyquist (FTN) signaling is considered. Our results show that using the phase only to provide redundancy already leads to a significantly increased spectral efficiency, a lower required energy per communicated bit, and allows to benefit from FTN signaling. This makes the previously proposed zero-crossing modulation and time-derived zero-crossing modulation, a specific kind of impulse radio, to energy-efficient contenders for wideband millimeter-wave communications and for the operation of lowpower wireless sensor nodes in the Internet of things, respectively.