In the context of integrated sensing and communication (ISAC), a full-duplex (FD) transceiver can operate as a monostatic radar while maintaining communication capabilities. This paper investigates the design of precoders and combiners for a joint radar and communication (JRC) system at mmWave frequencies. The primary goals of the design are to minimize self-interference (SI) caused by FD operation, while guaranteeing certain performance in terms of some sensing and communication metrics, as well as taking into account the hardware limitations coming from a hybrid MIMO architecture. Specifically, we introduce a generalized eigenvalue-based precoder that takes into account downlink user rate, radar gain, and SI suppression. Since the hybrid analog/digital architecture degrades the SI suppression capability of the precoder, we further enhance SI suppression with the analog combiner. Our numerical results demonstrate that the proposed architecture achieves the required radar gain and SI mitigation while incurring a small loss in downlink spectral efficiency. Additionally, the numerical experiments also show that the use of orthogonal frequency division multiplexing (OFDM) for radar processing with the proposed beamforming architecture results in highly accurate range and velocity estimates for detected targets.

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