recently the indexed modulation
(IM) technique in conjunction with the
multi-carrier modulation gains an increasing
attention. It conveys additional information
on the subcarrier indices by activating specific
subcarriers in the frequency domain besides
the conventional amplitude-phase modulation
of the activated subcarriers. Orthogonal frequency
division multiplexing (OFDM) with
IM (OFDM-IM) is deeply compared with
the classical OFDM. It leads to an attractive
trade-off between the spectral efficiency (SE)
and the energy efficiency (EE). In this paper,
the concept of the combinatorial modulation
is introduced from a new point of view. The
sparsity mapping is suggested intentionally to
enable the compressive sensing (CS) concept
in the data recovery process to provide further
performance and EE enhancement without
SE loss. Generating artificial data sparsity in
the frequency domain along with naturally
embedded channel sparsity in the time domain
allows joint data recovery and channel estimation
in a double sparsity framework. Based
on simulation results, the performance of the
proposed approach agrees with the predicted
CS superiority even under low signal-to-noise
ratio without channel coding. Moreover, the
proposed sparsely indexed modulation system
outperforms the conventional OFDM system
and the OFDM-IM system in terms of error
performance, peak-to-average power ratio
(PAPR) and energy efficiency under the same
spectral efficiency.