This paper investigates over-the-air computation (AirComp) over multiple-access time-varying channels, where devices with high mobility transmit their sensing data to a fusion center (FC) for averaging. To combat the Doppler shift induced by time-varying channels, each device adopts orthogonal time frequency space (OTFS) modulation. Our objective is minimizing the mean squared error (MSE) for the target function estimation. Due to the multipath time-varying channels, the OTFS-based AirComp not only suffers from noise but also interference. Specifically, we propose three schemes, namely S1, S2, and S3, for the target function estimation. S1 directly estimates the target function under the impacts of noise and interference. S2 mitigates the interference by introducing a zero padding-assisted OTFS. In S3, we propose an iterative algorithm to estimate the function in a matrix form. In the numerical results, we evaluate the performance of S1, S2, and S3 from the perspectives of MSE and computational complexity, and compare them with benchmarks. Specifically, compared to benchmarks, S3 outperforms them with a significantly lower MSE but incurs a higher computational complexity. In contrast, S2 demonstrates a reduction in both MSE and computational complexity. Lastly, S1 shows superior error performance at small SNR and reduced computational complexity.

翻译：本文研究了多址时变信道上的空中计算（AirComp），其中高移动性设备将感知数据传输至融合中心（FC）进行求平均。为对抗时变信道引起的多普勒频移，各设备采用正交时频空间（OTFS）调制。我们的目标是最小化目标函数估计的均方误差（MSE）。由于多径时变信道，基于OTFS的AirComp不仅受噪声影响，还受干扰影响。具体而言，我们提出了三种方案（S1、S2、S3）用于目标函数估计：S1直接在噪声和干扰影响下估计目标函数；S2通过引入补零辅助OTFS减轻干扰；S3提出一种迭代算法以矩阵形式估计函数。在数值结果中，我们从MSE和计算复杂度角度评估了S1、S2、S3的性能，并将其与基准方案对比。具体而言，与基准方案相比，S3以显著更低的MSE表现更优，但计算复杂度更高；而S2在MSE和计算复杂度上均有降低；最后，S1在低信噪比下展现出更优的误差性能且计算复杂度更低。