The factor graph (FG) based iterative detection is considered an effective and practical method for multiple-input and multiple-out (MIMO), particularly massive MIMO (m-MIMO) systems. However, the convergence analysis for the FG-based iterative MIMO detection is insufficient, which is of great significance to the performance evaluation and algorithm design of detection methods. This paper investigates the mutual information update flow for the FG-based iterative MIMO detection and proposes a precise mutual information computation mechanism with the aid of Gaussian approximation and error functions, i.e., the error functions-aided analysis (EF-AA) mechanism. Numerical results indicate that the theoretical result calculated by the EF-AA mechanism is completely consistent with the bit error rate performance of the FG-based iterative MIMO detection. Furthermore, the proposed EF-AA mechanism can reveal the exact convergent iteration number and convergent signal-to-ratio value of the FG-based iterative MIMO detection, representing the performance bound of the MIMO detection.
The air-ground integrated sensing and communications (AG-ISAC) network, which consists of unmanned aerial vehicles (UAVs) and ground terrestrial networks, offers unique capabilities and demands special design techniques. In this article, we provide a review on AG-ISAC, by introducing UAVs as ``relay'' nodes for both communications and sensing to resolve the power and computation constraints on UAVs. We first introduce an AG-ISAC framework, including the system architecture and protocol. Four potential use cases are then discussed, with the analysis on the characteristics and merits of AG-ISAC networks. The research on several critical techniques for AG-ISAC is then discussed. Finally, we present our vision of the challenges and future research directions for AG-ISAC, to facilitate the advancement of the technology.