  We investigate the one-bit MIMO (1b-MIMO) radar that performs one-bit
sampling with a time-varying threshold in the temporal domain and employs
compressive sensing in the spatial and Doppler domains. The goals are to
significantly reduce the hardware cost, energy consumption, and amount of
stored data. The joint angle and Doppler frequency estimations from noisy
one-bit data are studied. By showing that the effect of noise on one-bit
sampling is equivalent to that of sparse impulsive perturbations, we formulate
the one-bit $\ell_1$-regularized atomic-norm minimization (1b-ANM-L1) problem
to achieve gridless parameter estimation with high accuracy. We also develop an
iterative method for solving the 1b-ANM-L1 problem via the alternating
direction method of multipliers. The Cram$\acute{\text{e}}$r-Rao bound (CRB) of
the 1b-MIMO radar is analyzed, and the analytical performance of one-bit
sampling with two different threshold strategies is discussed. Numerical
experiments are presented to show that the 1b-MIMO radar can achieve
high-resolution parameter estimation with a largely reduced amount of data.
