  Integrated sensing and communication (ISAC) is regarded as the enabling
technology in the future 5th-Generation-Advanced (5G-A) and 6th-Generation (6G)
mobile communication system. ISAC waveform design is critical in ISAC system.
However, the difference of the performance metrics between sensing and
communication brings challenges for the ISAC waveform design. This paper
applies the unified performance metrics in information theory, namely mutual
information (MI), to measure the communication and sensing performance in
multicarrier ISAC system. In multi-input multi-output orthogonal frequency
division multiplexing (MIMO-OFDM) ISAC system, we first derive the sensing and
communication MI with subcarrier correlation and spatial correlation. Then, we
propose optimal waveform designs for maximizing the sensing MI, communication
MI and the weighted sum of sensing and communication MI, respectively. The
optimization results are validated by Monte Carlo simulations. Our work
provides effective closed-form expressions for waveform design, enabling the
realization of MIMO-OFDM ISAC system with balanced performance in communication
and sensing.
