Minimax Design of Constant Modulus MIMO Waveforms for Active Sensing

Waveform optimization is a crucial step in the design of a multiple-input multiple-output system. This letter considers the joint optimization of constant modulus waveforms and mismatched (or matched) receive filters to suppress the auto- and cross correlations using the minimax (<inline-formula><tex-math notation="LaTeX">$\ell _{\infty }$</tex-math></inline-formula>-norm) design criterion. For practical waveform length and system size, the waveform design problem becomes quite challenging due to the large problem size (more than <inline-formula><tex-math notation="LaTeX">$10^5$</tex-math></inline-formula> unimodular complex variables and <inline-formula><tex-math notation="LaTeX">$10^7$</tex-math></inline-formula> nonlinear constraints). In addition to the large size, this problem is nonconvex, nonsmooth, and as such, cannot be handled effectively by the existing waveform design algorithms or off-the-shelve optimization tools. This letter develops an efficient primal–dual type algorithm with low per-iteration complexity to solve this problem. Numerical comparison shows that the waveforms based on the minimax design outperform those obtained from the existing <inline-formula><tex-math notation="LaTeX">$\ell _2$</tex-math></inline-formula>-norm design by 4–5 dBs in terms of peak sidelobe levels.