Compressed Sensing-Aided Index Modulation Improves Space-Time Shift Keying Assisted Millimeter-Wave Communications

Abstract

In this treatise, we present the concept of compressed-sensing (CS)-aided space-time shift keying index modulation (STSK-IM), where a virtual domain orthogonal frequency division multiplexing (OFDM) symbol is divided into $N_{a}$ -sized blocks, which carry $K$ STSK codewords over a specific combination of virtual-domain sub-carriers and then converted to the frequency domain with the aid of a CS matrix. We design the system for operation in the milli-meter wave (mmWave) frequency band. Furthermore, we amalgamate our soft-decision-aided scheme both with the concept of coordinate-interleaving as well as a discrete Fourier transform-aided codebook design conceived for analogue beamforming, which is vitally important for mmWave systems. In the proposed system, the number of implicit bits conveyed by the activated sub-carrier frequency index (FI) is determined by the number of the available $K$ to $N_{a}$ sub-carrier permutations. Hence, we propose two FI allocation techniques, namely the distinct FI and the shared FI-based schemes, which strike a tradeoff between the attainable sparsity level and the achievable capacity limit. We then introduce a reduced-complexity detection technique in order to mitigate the detection complexity order of the optimum detector from $\mathcal {O}(N_{c}\cdot (Q\cdot \mathcal {L})^{K})$ to $\mathcal {O}(\hat {N}_{c}\cdot (Q\cdot \mathcal {L})^{K})$ , where $\hat {N}_{c}\le N_{c}$ . We also formulate the discrete-input continuous-output memoryless channel capacity and invoke EXtrinsic Information Transfer charts for characterizing the achievable performance limit of the reduced-complexity aided detector. Finally, we analyze the bit error rate performance of both the uncoded and of our coded CS-aided STSK-IM systems associated with both the optimum and the reduced-complexity detectors.