Multi-Hop Cooperative G-SFIM System With Low-Complexity Detection Under Imperfect CSI

This paper proposes a multi-hop cooperative grouping space-frequency index modulation (G-SFIM) system with decode-and-forward (DF) protocol. By using group mapping and 3D constellation, the minimum Euclidean distance of the G-SFIM signals is increased. Meanwhile, the signals are conveyed through the multi-hop architecture to improve the communication reliability. Under the imperfect and perfect channel state information (CSI), the closed-form expressions of the average bit error probability (ABEP) are derived. To reduce the complexity of the optimal maximum-likelihood (ML) detection, the minimum mean-squared error (MMSE) based grouping ML (MMSE-GML), the MMSE based grouping greedy detection (MMSE-GGD), and the grouping ordered block based ML (GOB-ML) detection algorithms are proposed. Numerical results validate the correctness of the theoretical ABEP of the multi-hop cooperative G-SFIM system under different CSI conditions. Meanwhile, the proposed system achieves better ABEP performance and is less sensitive to the imperfect CSI. Additionally, the three presented low-complexity detection algorithms offer the flexible compromise between the ABEP performance and the complexity.