Novel Sparse Codebook Design for MIMO-SCMA

The combination of multiple-input multiple-output (MIMO) and sparse code multiple access (SCMA), referred to as MIMO-SCMA, can be leveraged to achieve high spectrum efficiency and provide massive connectivity for future machine-type communication networks. This paper aims to design enhanced sparse codebooks for MIMO-SCMA by jointly combining frequency and spatial diversity over Rayleigh fading channels. First, based on the pairwise error probability (PEP), novel codebook design criteria have been presented, namely the hybrid minimum product distance of the Euclidean distance (MPD-ED) and the minimum Euclidean distance of the superimposed constellation at each frequency element (MED-FE). Then, enhanced mother constellations (MC) are proposed by maximizing the MPD-ED of the MC based on the alternating optimization. Subsequently, the multi-dimensional codebooks are obtained by applying user-specific rotation of the proposed MC to maximize the MED-FE, where the unitary rotations are considered to fully leverage the Euclidean space of the transmit antennas while maintaining the MPD-ED value of the codebook. Finally, numerical results demonstrate that the proposed approach significantly outperforms the state-of-the-art codebooks.