We derive a closed-form joint distribution of the first arrival time (FAT) and first arrival position (FAP) in drift-diffusion molecular communication (MC) channels. In contrast to prior studies that analyze FAT or FAP in isolation, our framework explicitly captures the spatiotemporal coupling inherent in multidimensional transport. Building on this derivation, we compute the Fisher information matrix (FIM) and demonstrate that estimation accuracy for diffusivity scales proportionally with the spatial dimension, enabling increased sensitivity in higher-dimensional environments. Furthermore, we show that lateral drift -- which is unobservable from timing data alone -- can be recovered via a closed-form Maximum Likelihood Estimator (MLE) with a simple physical interpretation. Leveraging this spatial degree of freedom, we propose Drift Shift Keying (DSK), proving that joint receivers can reliably detect signals that are undetectable to timing-only receivers due to identical marginal FAT distributions. These results highlight the significant potential of spatiotemporal processing for future nanoscale communication and sensing.

翻译：我们推导了漂移-扩散分子通信信道中首次到达时间与首次到达位置的闭式联合分布。与先前孤立分析首次到达时间或首次到达位置的研究不同，我们的框架明确捕捉了多维传输中固有的时空耦合特性。基于此推导，我们计算了费希尔信息矩阵，并证明扩散系数的估计精度与空间维度成比例缩放，从而在更高维环境中实现更高的灵敏度。此外，我们证明仅凭时序数据不可观测的横向漂移，可通过具有简明物理解释的闭式最大似然估计器进行恢复。利用这一空间自由度，我们提出了漂移移位键控技术，并证明联合接收机能够可靠检测因边缘首次到达时间分布相同而无法被纯时序接收机识别的信号。这些结果凸显了时空处理在未来纳米尺度通信与传感领域的巨大潜力。