  This paper focuses on the joint design of transmit waveforms and receive
filters for airborne multiple-input-multiple-output (MIMO) radar systems in
spectrally crowded environments. The purpose is to maximize the output
signal-to-interference-plus-noise-ratio (SINR) in the presence of
signal-dependent clutter. To improve the practicability of the radar waveforms,
both a multi-spectral constraint and a peak-to-average-power ratio (PAPR)
constraint are imposed. A cyclic method is derived to iteratively optimize the
transmit waveforms and receive filters. In particular, to tackle the
encountered non-convex constrained fractional programming in designing the
waveforms (for fixed filters), we resort to the Dinkelbach's transform,
minorization-maximization (MM), and leverage the alternating direction method
of multipliers (ADMM). We highlight that the proposed algorithm can iterate
from an infeasible initial point and the waveforms at convergence not only
satisfy the stringent constraints, but also attain superior performance.
