  Orthogonal frequency division multiplexing (OFDM) has been widely recognized
as the representative waveform for 5G wireless networks, which can directly
support sensing/positioning with existing infrastructure. To guarantee superior
sensing/positioning accuracy while supporting high-speed communications
simultaneously, the dual functions tend to be assigned with different resource
elements (REs) due to their diverse design requirements. This motivates
optimization of resource allocation/waveform design across time, frequency,
power and delay-Doppler domains. Therefore, this article proposes two
cross-domain waveform optimization strategies for effective convergence of
OFDM-based communications and sensing/positioning, following communication- and
sensing-centric criteria, respectively. For the communication-centric design,
to maximize the achievable data rate, a fraction of REs are optimally allocated
for communications according to prior knowledge of the communication channel.
The remaining REs are then employed for sensing/positioning, where the sidelobe
level and peak-to-average power ratio are suppressed by optimizing its
power-frequency and phase-frequency characteristics for sensing performance
improvement. For the sensing-centric design, a `locally' perfect
auto-correlation property is ensured for accurate sensing and positioning by
adjusting the unit cells of the ambiguity function within its region of
interest (RoI). Afterwards, the irrelevant cells beyond RoI, which can readily
determine the sensing power allocation, are optimized with the communication
power allocation to enhance the achievable data rate. Numerical results
demonstrate the superiority of the proposed waveform designs.
