  Reconfigurable intelligent surface (RIS) has emerged as a cost- and
energy-efficient solution to enhance the wireless communication capacity.
However, recent studies show that a very large surface is required for a
RIS-assisted communication system; otherwise, they may be outperformed by the
conventional relay. Furthermore, the performance gain of a RIS can be
considerably degraded by hardware impairments such as limited-resolution phase
shifters. To overcome those challenges, we propose a novel concept of hybrid
relay-reflecting intelligent surface (HR-RIS), in which a single or few
elements are deployed with power amplifiers (PAs) to serve as active relays,
while the remaining elements only reflect the incident signals. Two
architectures are proposed, including the fixed and dynamic HR-RIS. Their
coefficient matrices are obtained based on alternating optimization (AO) and
power allocation strategies, which enable understanding the fundamental
performances of RIS and relaying-based systems with a trade-off between the
two. The simulation results show that a significant improvement in both the
spectral efficiency (SE) and energy efficiency (EE) with respect to the
conventional RIS-aided system can be attained by the proposed schemes,
especially, by the dynamic HR-RIS. In particular, the favorable design and
deployment of the HR-RIS are analytically derived and numerically justified.
