In this paper, we propose a novel time of arrival (TOA) estimator for multiple-input-multiple-output (MIMO) backscatter channels in closed form. The proposed estimator refines the estimation precision from the topological structure of the MIMO backscatter channels, and can considerably enhance the estimation accuracy. Particularly, we show that for the general $M \times N$ bistatic topology, the mean square error (MSE) is $\frac{M+N-1}{MN}\sigma^2_0$, and for the general $M \times M$ monostatic topology, it is $\frac{2M-1}{M^2}\sigma^2_0$ for the diagonal subchannels, and $\frac{M-1}{M^2}\sigma^2_0$ for the off-diagonal subchannels, where $\sigma^2_0$ is the MSE of the conventional least square estimator. In addition, we derive the Cramer-Rao lower bound (CRLB) for MIMO backscatter TOA estimation which indicates that the proposed estimator is optimal. Simulation results verify that the proposed TOA estimator can considerably improve both estimation and positioning accuracy, especially when the MIMO scale is large.

翻译：本文提出了一种用于多输入多输出（MIMO）背向散射信道的闭式到达时间（TOA）估计器。该估计器通过利用MIMO背向散射信道的拓扑结构提升了估计精度，能够显著增强定位准确性。特别地，我们证明：对于一般$M \times N$双基地拓扑结构，均方误差（MSE）为$\frac{M+N-1}{MN}\sigma^2_0$；对于一般$M \times M$单基地拓扑结构，对角子信道的MSE为$\frac{2M-1}{M^2}\sigma^2_0$，非对角子信道则为$\frac{M-1}{M^2}\sigma^2_0$，其中$\sigma^2_0$是传统最小二乘估计器的MSE。此外，我们推导了MIMO背向散射TOA估计的克拉美-罗下界（CRLB），表明所提估计器具有最优性。仿真结果验证了该TOA估计器能显著提升估计与定位精度，尤其在MIMO规模较大时效果更为显著。