基于GAMP-MAP估计器的非对齐空中计算

Misaligned over-the-air computation based on GAMP-MAP estimator

现有的空中计算依赖融合中心的最大似然(maximum likelihood,ML)估计恢复来自不同设备传输信号的算术和,但在实践中,实现准确的信道增益预编码和设备之间的严格同步很困难,ML估计在非对齐空中计算场景中会遭受严重的错误传播,而且计算复杂度高。针对非对齐空中计算问题,设计了一个基于广义近似消息传递(generalized approximate message passing,GAMP)计算框架的最大后验估计器,即GAMP-MAP。该估计器使用传输符号数据的均值和方差作为先验以提高估计准确性,利用GAMP算法标量估计特性降低计算复杂度。在不同信道相位偏移和时间偏移下进行仿真实验,实验结果表明GAMP-MAP估计器的准确性明显优于ML估计器,其运行时间相对ML估计器和LMMSE估计器有显著下降。

Existing over-the-air computation relies on maximum likelihood(ML)estimation of fusion centers to recover the arithmetic sum of transmitted signals from different devices.But it is difficult to achieve accurate channel gain precoding and strict synchronization between devices in practice.ML estimation suffers from severe error propagation in misaligned over-the-air computation scenarios,and its computational complexity is high.To solve the problem of misaligned over-the-air computation,this paper designed a maximum a posteriori estimator based on generalized approximate messaging passing(GAMP)calculation framework:GAMP-MAP.It used the mean and variance of the transmitted symbol data as a priori to improve the estimation accuracy,and utilized the scalar estimation feature of the GAMP algorithm to reduce the computational complexity.Simulation experiments were carried out under different channel phase offsets and time offsets.The experimental results show that the accuracy of the GAMP-MAP estimator is significantly better than that of the ML estimator,and its running time is significantly lower than that of the ML estimator and the LMMSE estimator.