  Reconfigurable Intelligent Surface (RIS) is a promising solution to
reconfigure the wireless environment in a controllable way. To compensate for
the double-fading attenuation in the RIS-aided link, a large number of passive
reflecting elements (REs) are conventionally deployed at the RIS, resulting in
large surface size and considerable circuit power consumption. In this paper,
we propose a new type of RIS, called active RIS, where each RE is assisted by
active loads (negative resistance), that reflect and amplify the incident
signal instead of only reflecting it with the adjustable phase shift as in the
case of a passive RIS. Therefore, for a given power budget at the RIS, a
strengthened RIS-aided link can be achieved by increasing the number of active
REs as well as amplifying the incident signal. We consider the use of an active
RIS to a single input multiple output (SIMO) system. {However, it would
unintentionally amplify the RIS-correlated noise, and thus the proposed system
has to balance the conflict between the received signal power maximization and
the RIS-correlated noise minimization at the receiver. To achieve this goal, it
has to optimize the reflecting coefficient matrix at the RIS and the receive
beamforming at the receiver.} An alternating optimization algorithm is proposed
to solve the problem. Specifically, the receive beamforming is obtained with a
closed-form solution based on linear minimum-mean-square-error (MMSE)
criterion, while the reflecting coefficient matrix is obtained by solving a
series of sequential convex approximation (SCA) problems. Simulation results
show that the proposed active RIS-aided system could achieve better performance
over the conventional passive RIS-aided system with the same power budget.
