Jointly enhancing both energy efficiency (EE) and spectrum efficiency (SE) of modulation schemes becomes one of the main issues for 5G mobile communications. Recently, an indexed modulation (IM) technique provides an interesting tradeoff between EE and SE. Data can be conveyed through the combination of subcarriers pattern that can be divided between activated/non-activated subcarriers in the frequency domain. Maximum SE can be attained at half subcarrier activation, hence producing symbols with half energy of the conventional orthogonal frequency-division multiplexing (OFDM) system. In this paper, alternatively, the new concept of sparsely indexing modulation (SIM) on overall subcarrier space is clarified. Sparse (few) subcarrier activations provide much higher EE, while the combinatorial indexing of the sparse subcarriers on the overall subcarriers as a single group spans huge combinatorial …