  Beampattern synthesis is a key problem in many wireless applications. With
the increasing scale of MIMO antenna array, it is highly desired to conduct
beampattern synthesis on a sparse array to reduce the power and hardware cost.
In this paper, we consider conducting beampattern synthesis and sparse array
construction jointly. In the formulated problem, the beampattern synthesis is
designed by minimizing the matching error to the beampattern template, and the
Shannon entropy function is first introduced to impose the sparsity of the
array. Then, for this nonconvex problem, an iterative method is proposed by
leveraging on the alternating direction multiplier method (ADMM) and the
majorization minimization (MM). Simulation results demonstrate that, compared
with the benchmark, our approach achieves a good trade-off between array
sparsity and beampattern matching error with less runtime.
