  The problem of sparse array design for dual-function radar-communications is
investigated. Our goal is to design a sparse array which can simultaneously
shape desired beam responses and serve multiple downlink users with the
required signal-to-interference-plus-noise ratio levels. Besides, we also take
into account the limitation of the radiated power by each antenna. The problem
is formulated as a quadratically constrained quadratic program with a
joint-sparsity-promoting regularization, which is NP-hard. The resulting
problem is solved by the consensus alternating direction method of multipliers,
which enjoys parallel implementation. Numerical simulations exhibit the
effectiveness and superiority of the proposed method which leads to a more
power-efficient solution.
