  This paper derives a generalized class of waveforms with an application to
machine-type communication (MTC) while studying its underlying structural
characteristics in relation to conventional modulation waveforms. First, a
canonical waveform of frequency-error tolerance is identified for a unified
preamble and traffic signal design, ideal for MTC use as a composite waveform,
commonly known as a transmission burst. It is shown that the most widely used
modulation schemes for mIoT traffic signals, e.g., FSK and LoRa modulation, are
simply subsets of the canonical waveform. The intrinsic characteristics and
degrees of freedom the waveform offers are then explored. Most significantly, a
new waveform dimension is uncovered and exploited as additional degrees of
freedom for satisfying the MTC requirements, i.e., energy and resource
efficiency and robustness. The corresponding benefits are evaluated
analytically and numerically in AWGN, frequency-flat, and selective channels.
We demonstrate that neither FSK nor LoRa can fully address the mIoT
requirements since neither fully exploits the degrees of freedom from the
perspective of the generalized waveform class. Finally, a solution is devised
to optimize energy and resource efficiency under various deployment
environments and practical constraints while maintaining the low-complexity
property.
