  Reconfigurable intelligent surfaces (RISs) represent a promising candidate
for sixth-generation (6G) wireless networks, as the RIS technology provides a
new solution to control the propagation channel in order to improve the
efficiency of a wireless link through enhancing the received signal power. In
this paper, we propose RIS-assisted receive quadrature space-shift keying
(RIS-RQSSK), which enhances the spectral efficiency of an RIS-based index
modulation (IM) system by using the real and imaginary dimensions independently
for the purpose of IM. Therefore, the error rate performance of the system is
improved as all RIS elements reflect the incident transmit signal toward both
selected receive antennas. At the receiver, a low-complexity but effective
greedy detector (GD) can be employed which determines the maximum energy per
dimension at the receive antennas. A max-min optimization problem is defined to
maximize the received signal-to-noise ratio (SNR) components at both selected
receive antennas; an analytical solution is provided based on Lagrange duality.
In particular, the multi-variable optimization problem is shown to reduce to
the solution of a single-variable equation, which results in a very simple
design procedure. In addition, we investigate the average bit error probability
(ABEP) of the proposed RIS-RQSSK system and derive a closed-form approximate
upper bound on the ABEP. We also provide extensive numerical simulations to
validate our derivations. Numerical results show that the proposed RIS-RQSSK
scheme substantially outperforms recent prominent benchmark schemes. This
enhancement considerably increases with an increasing number of receive
antennas.
