  We consider the design of polyphase waveforms for ground moving target
detection with airborne multiple-input-multiple-output (MIMO) radar. Due to the
constant-modulus and finite-alphabet constraint on the waveforms, the
associated design problem is non-convex and in general NP-hard. To tackle this
problem, we develop an efficient algorithm based on relaxation and cyclic
optimization. Moreover, we exploit a reparameterization trick to avoid the
significant computational burden and memory requirement brought about by
relaxation. We prove that the objective values during the iterations are
guaranteed to converge. Finally, we provide an effective randomization approach
to obtain polyphase waveforms from the relaxed solution at convergence.
Numerical examples show the effectiveness of the proposed algorithm for
designing polyphase waveforms.
