  This paper aims to answer a fundamental question in the area of Integrated
Sensing and Communications (ISAC): What is the optimal communication-centric
ISAC waveform for ranging? Towards that end, we first established a generic
framework to analyze the sensing performance of communication-centric ISAC
waveforms built upon orthonormal signaling bases and random data symbols. Then,
we evaluated their ranging performance by adopting both the periodic and
aperiodic auto-correlation functions (P-ACF and A-ACF), and defined the
expectation of the integrated sidelobe level (EISL) as a sensing performance
metric. On top of that, we proved that among all communication waveforms with
cyclic prefix (CP), the orthogonal frequency division multiplexing (OFDM)
modulation is the only globally optimal waveform that achieves the lowest
ranging sidelobe for quadrature amplitude modulation (QAM) and phase shift
keying (PSK) constellations, in terms of both the EISL and the sidelobe level
at each individual lag of the P-ACF. As a step forward, we proved that among
all communication waveforms without CP, OFDM is a locally optimal waveform for
QAM/PSK in the sense that it achieves a local minimum of the EISL of the A-ACF.
Finally, we demonstrated by numerical results that under QAM/PSK
constellations, there is no other orthogonal communication-centric waveform
that achieves a lower ranging sidelobe level than that of the OFDM, in terms of
both P-ACF and A-ACF cases.
