In this paper, multiple-input multiple-output (MIMO) integrated radar and communications (IRC) system is studied, where the radar and communications parts work cooperatively, leading to a hybrid active-passive (HAP) MIMO radar and a radar-aided (RA) MIMO communications subsystems. To unify the performance metric for both subsystems, the diversity gain and multiplexing gain are derived for the RA MIMO communications and the HAP MIMO radar subsystems, based on which the tradeoff between the diversity and multiplexing gains is analyzed theoretically for each of the subsystems. The obtained diversity gain and multiplexing gain can facilitate the design and optimization of the IRC system. Employing these two unified performance metrics, the IRC system antenna number assignment is formulated as a multi-objective optimization problem, and the Pareto solutions are provided. The correctness of theoretical analysis is verified by simulations. Our results can provide useful guidance for system designers.
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