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In this paper, we conceive a compressed sensing (CS)-aided multi-dimensional index modulation (IM) scheme, where the benefits of space-time shift keying, orthogonal frequency-division multiplexing relying on the frequency domain IM, and spatial modulation are explored. Explicitly, extra information bits are transmitted through the active indices of both the transmit antennas and subcarriers, while striking a flexible design tradeoff between the throughput and the diversity order. Furthermore, CS is invoked in both the transmitter and the receiver of our multi-dimensional system for the sake of improving the system's design flexibility, while reducing the detector's complexity. We first present the maximum likelihood (ML) detector of the proposed CS-aided multi-dimensional IM system for characterizing the best-case bound of the proposed system's performance. Specifically, an upper bound is derived for the average bit …