Performance Analysis of Receive Diversity RIS and RPM Assisted Index Modulated Communication System

In reconfigurable intelligent surface (RIS) aided communication implementing space-shift keying at the transmitter for index modulation, the RIS is proposed to perform the dual function of selecting the phases of the reflecting elements optimally according to the phases of the channel gains, and acting as a modulator by transmitting
$M$
-ary phase-shift keying (PSK) modulated symbols via reflection phase modulation. The target antenna at the receiver is chosen by utilizing the optimal maximum likelihood (ML) detection rule and a hardware- and energy-efficient greedy detector, which performs detection based on the maximum received energy. For these detection scenarios, closed-form expressions for the probability of erroneous detection (PED) of the target antenna are derived, considering Nakagami-
$m$
channel fading. Numerical results supporting the analytical framework show the role of the rotation of the
$M$
-PSKconstellation to improve the reliability of the system. In particular,
$\pi/M{-}$
rotated
$M$
-PSK constellation is optimal for the greedy detector, whereas the ML detector is not dependent on such rotation to yield minimum PED.