Compressed Sensing-Aided Multi-Dimensional Index Modulation

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 error probability, and it is observed that the derived theoretical upper bound becomes very tight with the ML detector simulation curves as the signal-to-noise ratio increases. Then, we propose a reduced complexity detector imposing only a modest bit-error-ratio degradation, where we analyze the computational complexities of both the ML detector and the reduced complexity detector. Furthermore, a soft-input soft-output decoder is proposed for attaining a near-capacity performance, which is analyzed with the aid of extrinsic information transfer (EXIT) charts. The maximum achievable rate of the proposed CS-aided multidimensional IM system relying both on the ML detection and on our reduced-complexity-based detector is also evaluated using EXIT charts. In addition, the discrete-input continuous-output memoryless channel capacity of the proposed CS-aided multidimensional IM scheme is formulated.