  Hybrid digital/analog architecture and low-resolution
analog-to-digital/digital-to-analog converters (ADCs /DACs) are two low-cost
implementations for large-scale millimeter wave (mmWave) systems. In this
paper, we investigate the problem of constant-envelope transmit beamforming for
large-scale multiple-input multiple-output (MIMO) radar system, where the
transmit array adopts a hybrid digital/analog architecture with a small number
of RF chains and the receive array adopts a fully digital architecture with
low-resolution ADCs. We derive the relative entropy between the probability
density functions associated with the two test hypotheses under low-resolution
ADCs. We formulate our optimization problem by maximizing the relative entropy,
subject to the constant envelope and orthogonality constraints. To suboptimally
solve the resultant problem, a two-stage framework is developed. In the first
stage, we optimize the transmit power at the directions of the target and
clutter. In the second stage, an efficient iterative algorithm based on
majorization-minimization is presented to obtain the constant-envelope
beamformer according to the attained transmit power. Specifically, we apply a
quadratic function as the minorizer, leading to a low-complexity solution at
each iteration. In addition, to further facilitate low-cost implementation of
the constant-envelope beamformer, we consider the problem of one-bit
beamforming design and propose an efficient iterative method based on the
Nesterov-like gradient method to solve it. Numerical simulations are provided
to demonstrate the effectiveness of the proposed schemes.
