  Multiple-input multiple-output (MIMO) radars transmit a set of sequences that
exhibit small cross-correlation sidelobes, to enhance sensing performance by
separating them at the matched filter outputs. The waveforms also require small
auto-correlation sidelobes to avoid masking of weak targets by the range
sidelobes of strong targets and to mitigate deleterious effects of distributed
clutter. In light of these requirements, in this paper, we design a set of
phase-only (constant modulus) sequences that exhibit near-optimal properties in
terms of Peak Sidelobe Level (PSL) and Integrated Sidelobe Level (ISL). At the
design stage, we adopt weighted lp-norm of auto- and cross-correlation
sidelobes as the objective function and minimize it for a general p value,
using block successive upper bound minimization (BSUM). Considering the
limitation of radar amplifiers, we design unimodular sequences which make the
design problem non-convex and NP-hard. To tackle the problem, in every
iteration of the BSUM algorithm, we introduce different local approximation
functions and optimize them concerning a block, containing a code entry or a
code vector. The numerical results show that the performance of the optimized
set of sequences outperforms the state-of-the-art counterparts, in both terms
of PSL values and computational time.
