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As radio-frequency (RF) antenna, component and processing capabilities increase, the ability to perform multiple RF system functions from a common aperture is being realized. Conducting both radar and communications from the same system is potentially useful in vehicular, health monitoring, and surveillance settings. This paper considers multiple-input-multiple-output (MIMO) dual-function radar-communication (DFRC) systems in which the radar and communication modes use distinct baseband waveforms. A transmit precoder provides spatial multiplexing and power allocation among the radar and communication modes. Multiple precoder design approaches are introduced for a radar detection mode in which a total search volume is divided into dwells to be searched sequentially. The approaches are designed to enforce a reliance on radar waveforms for sensing purposes, yielding improved approximation of desired ambiguity functions over prior methods found in the literature. The methods are also shown via simulation to enable design flexibility, allowing for prioritization of either subsystem and specification of a desired level of radar or communication performance.