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.

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