  In this paper, reconfigurable intelligent surface (RIS)-assisted generalized
receive quadrature spatial modulation (RIS-GRQSM) is proposed to improve the
spectral efficiency of RIS-aided quadrature spatial modulation (QSM) systems by
utilizing the concept of generalized spatial modulation (GSM). That is,
multiple antennas are activated at the receiver independently for both the real
and imaginary parts. We propose a max-min optimization problem to adjust the
phase shifts of all RIS elements to maximize the relevant signal-to-noise
ratios (SNRs) at all activated receive antennas. Using Lagrange duality, the
non-convex optimization problem involving the phase shifts of all RIS elements
reduces to a convex optimization involving a number of variables equal to the
number of activated receive antennas. A successive greedy detector (GD) can be
used at the receiver to detect the active antennas, which simplifies the
detection process. The numerical results show that the proposed scheme
outperforms the benchmark schemes in terms of error rate performance,
especially in systems with a larger number of receive antennas. In the special
case where each receive antenna corresponds to a user and is activated, the
RIS-GRQSM system becomes a multicast communication system. In this context, in
contrast to existing phase shift optimization algorithms which exhibit an
impractical level of complexity, our proposed solution offers the advantage of
low complexity and practical feasibility of implementation.
