This paper introduces a novel multi-objective integrated sensing and communications (ISAC) framework to enable collaborative wireless sensing in conjunction with over-the-air federated-edge learning (OTA-FEEL). The framework enables multi-task OTA aggregation to handle sensing and learning simultaneously, while benefiting from dual-purpose uplink signals for both communications and target sensing. Starting from characterizing the local sufficient statistics at each edge device and establishing its stationary, we develop a tractable analytical expression for the local sufficient statistics. To suppress the interference from uplink transmissions of other devices through matched filtering, we then propose a novel orthogonal pulse shaping method. Then, we derive the optimal unbiased estimate of the target's coordinates by casting the centralized problem of joint likelihood function maximization of all devices as the distributed likelihood maximization of each device (which requires only local sufficient statistics). A lower bound on the sensing error variance is then characterized using the Cramer-Rao bound (CRB). We then formulate a multi-objective optimization (MOOP) problem to minimize the mean square error (MSE) and sensing error bound simultaneously. The considered problem is then solved using the epsilon-constrained method. Numerical results demonstrate that the proposed dual-purpose OTA-FEEL-enabled collaborative ISAC framework enhances sensing accuracy without adversely affecting the performance of the primary OTA-FEEL task. While conventional single-shot collaborative sensing schemes are limited by the average error of local estimators, the proposed algorithm achieves the CRB of the considered problem.

翻译：本文提出了一种新颖的多目标集成感知与通信框架，旨在结合空中联邦边缘学习实现协同无线感知。该框架支持多任务空中聚合，能够同时处理感知与学习任务，并受益于兼具通信与目标感知功能的双用途上行链路信号。首先通过刻画各边缘设备的局部充分统计量并建立其平稳性，我们推导出局部充分统计量的可处理解析表达式。为通过匹配滤波抑制其他设备上行传输产生的干扰，我们进而提出一种新颖的正交脉冲成形方法。随后，我们将所有设备联合似然函数最大化的集中式问题转化为各设备的分布式似然最大化问题（仅需局部充分统计量），从而推导出目标坐标的最优无偏估计。继而利用克拉美-罗界刻画了感知误差方差的下界。我们随后构建了一个多目标优化问题，以同时最小化均方误差与感知误差界。该问题通过ε约束法求解。数值结果表明，所提出的双用途空中联邦边缘学习协同集成感知与通信框架在提升感知精度的同时，不会对主要空中联邦边缘学习任务的性能产生负面影响。传统单次协同感知方案受限于局部估计器的平均误差，而所提算法能够达到所研究问题的克拉美-罗界。