  Reconfigurable intelligent surface (RIS) based reflection modulation has been
considered as a promising information delivery mechanism, and has the potential
to realize passive information transfer of a RIS without consuming any
additional radio frequency chain and time/frequency/energy resources. The
existing on-off reflection modulation (ORM) schemes are based on manipulating
the "on/off" states of RIS elements, which may lead to the degradation of RIS
reflection efficiency. This paper proposes a frequency reflection modulation
(FRM) method for RIS-aided OFDM systems. The FRM-OFDM scheme modulates the
frequency of the incident electromagnetic waves, and the RIS information is
embedded in the frequency-hoping states of RIS elements. Unlike the ORM-OFDM
scheme, the FRM-OFDM scheme can achieve higher reflection efficiency, since the
latter does not turn off any reflection element in reflection modulation. We
propose a block coordinate descent (BCD) algorithm to maximize the user
achievable rate for the FRM-OFDM system by jointly optimizing the phase shift
of the RIS and the power allocation at the transmitter. Further, we design a
bilinear message passing (BMP) algorithm for the bilinear recovery of both the
user symbols and the RIS data. Numerical simulations have verified the
efficiency of the designed BCD algorithm for system optimization and the BMP
algorithm for signal detection, as well as the superiority of the proposed
FRM-OFDM scheme over the ORM-OFDM scheme.
