Millimeter wave (mmWave) full-duplex (FD) is a promising technique for improving capacity by maximizing the utilization of both time and the rich mmWave frequency resources. Still, it has restrictions due to FD self-interference (SI) and mmWave's limited coverage. Therefore, this study dives into FD mmWave MIMO with the assistance of reconfigurable intelligent surfaces (RIS) for capacity improvement. First, we demonstrate the angular-domain reciprocity of FD antenna arrays under the far-field planar wavefront assumption. Accordingly, a strategy for joint downlink-uplink (DL-UL) channel estimation is presented. For estimating the SI channel, the direct channel, and the cascaded channel, the Khatri-Rao product-based compressive sensing (KR-CS), distributed CS (D-CS), and two-stage multiple measurement vector-based D-CS (M-D-CS) frameworks are proposed, respectively. Additionally, we propose a passive beamforming optimization solution based on the angulardomain cascaded channel. With hybrid beamforming architectures, a novel hybrid weighted minimum mean squared error method for SI cancellation (H-WMMSE-SIC) is proposed. Simulations have revealed that joint DL-UL processing significantly improves estimation performance in comparison to separate DL/UL channel estimation. Particularly, when the interference-to-noise ratio is less than 35 dB, our proposed H-WMMSE-SIC offers spectral efficiency performance comparable to fully-digital WMMSE-SIC. Finally, the computational complexity is analyzed for our proposed methods.
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