  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.
