  Extremely low-resolution (e.g. one-bit) analog-to-digital converters (ADCs)
and digital-to-analog converters (DACs) can substantially reduce hardware cost
and power consumption for MIMO radar especially with large scale antennas. In
this paper, we focus on the detection performance analysis and joint design for
the MIMO radar with one-bit ADCs and DACs. Specifically, under the assumption
of low signal-to-noise ratio (SNR) and interference-to-noise ratio (INR), we
derive the expressions of probability of detection ($\mathcal{P}_d$) and
probability of false alarm ($\mathcal{P}_f$) for one-bit MIMO radar and also
the theoretical performance gap to infinite-bit MIMO radars for the noise-only
case. We further find that for a fixed $\mathcal{P}_f$, $\mathcal{P}_d$ depends
on the defined quantized signal-to-interference-plus-noise ratio (QSINR), which
is a function of the transmit waveform and receive filter. Thus, an
optimization problem arises naturally to maximize the QSINR by joint designing
the waveform and filter. For the formulated problem, we propose an
alternatin\emph{g} wavefo\emph{r}m and filt\emph{e}r d\emph{e}sign for QSINR
maximiza\emph{t}ion (GREET). At each iteration of GREET, the receive filter is
upadted via the minimum variance distortionless response (MVDR) method, and the
one-bit waveform is optimized based on the alternating direction method of
multipliers (ADMM) algorithm where the closed-form solutions are obtained for
both the primary and slack variables. Numerical simulations are consistent to
the theoretical performance analysis and demonstrate the effectiveness of the
proposed design algorithm.
