Power Allocation for OTFS-based AirComp System with Robust Precoding

In this work, we consider a high-mobility AirComp scenario, where orthogonal time frequency space (OTFS) modulation is employed to eliminate the effects of high-mobility channels. Specifically, firstly, a two-stage transmission scheme is developed for the considered system. The estimated channel in the first stage is used to design the minimum mean square error precoder utilized for data transmission in the second stage for the current frame. To further enhance the computation accuracy, the estimated channel is used for the power allocation between the pilot symbol and data symbols for the next frame. Therein, we derive the normalized mean square error (NMSE) by taking into account the imperfect channel estimation and then find the optimal power allocation which minimizes the computation NMSE under the total power constraint via the interior point method. The simulation results show that, compared to the benchmark schemes (i.e., the non-robust precoder and the robust precoder without power allocation), the proposed scheme can effectively improve the computation accuracy of the AirComp system.