The linear minimal mean square error (LMMSE) estimator for active reconfigurable intelligent surface (RIS)-aided wireless systems is formulated. Furthermore, based on the moment-matching method, we employ the Gamma distribution to approximate the distribution of the instantaneous received signal-to-interference-plus-noise ratio (SINR), and then derive the closed-form outage probability and ergodic channel capacity in the presence of realistic channel estimation errors, the thermal noise of RIS amplifiers and the RIS phase shift noise. Our theoretical analysis and simulation results show that the introduction of RIS amplifiers is equivalent to increasing of the transmit power, and also present the performance degradation resulting from the channel estimation error and the RIS phase noise.

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Millimeter-wave (mmWave) communication is a promising technology for future wireless systems due to the availability of huge unlicensed bandwidth. However, the need for large number of radio frequency (RF) chains associated with the antenna array and the corresponding increase in hardware complexity and power consumption are major stumbling blocks to its implementability. In this paper, we propose a low-complexity in-band full-duplex relay-assisted mmWave communication system design. We obtain the proposed multiple-input multiple-output analog-digital hybrid transceivers and relay filters by minimizing the overall sum-mean-square-error while mitigating the effect of residual loopback self-interference (LSI) in the system. The number of RF chains required in the proposed design is less than the number of antennas. We first present a design assuming the availability of perfect channel state information (CSI) at all the nodes. Later, we extend it to a robust design assuming a more realistic scenario, where the available CSI is imperfect. Furthermore, the LSI channel knowledge is assumed to be imperfect for both the designs rendering them robust to errors in loopback CSI. We employ sparse approximation technique to reduce the hardware complexity in the proposed system designs. The proposed algorithms are shown to converge to a limit even though the global convergence is hard to prove since the overall problem is nonconvex. The hardware complexity-performance tradeoff of the proposed design is analyzed. Furthermore, the resilience of the robust design in the presence of CSI errors and the performance of both the proposed designs over various parameters are illustrated via numerical simulations. INDEX TERMSFull-duplex, hybrid beamforming, millimeter-wave communication, residual self-interference, robust design.