  Wireless channel sensing is one of the key enablers for integrated sensing
and communication (ISAC) which helps communication networks understand the
surrounding environment. In this work, we consider MIMO-OFDM systems and aim to
design optimal and robust waveforms for accurate channel parameter estimation
given allocated OFDM resources. The Fisher information matrix (FIM) is derived
first, and the waveform design problem is formulated by maximizing the log
determinant of the FIM. We then consider the uncertainty in the parameters and
state the stochastic optimization problem for a robust design. We propose the
Riemannian Exact Penalty Method via Smoothing (REPMS) and its stochastic
version SREPMS to solve the constrained non-convex problems. In simulations, we
show that the REPMS yields comparable results to the semidefinite relaxation
(SDR) but with a much shorter running time. Finally, the designed robust
waveforms using SREMPS are investigated, and are shown to have a good
performance under channel perturbations.
