Performance Analysis of Active RIS-aided Systems in the Face of Imperfect CSI and Phase Shift Noise

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.