  Optimization of slow-time transmit sequence endows cognitive radar with the
ability to suppress strong clutter in the range-Doppler domain. However, in
practice, inaccurate target velocity information or random phase error would
induce uncertainty about the actual target steering vector, which would in turn
severely deteriorate the the performance of the slow-time matched filter. In
order to solve this problem, we propose a new optimization method for slow-time
transmit sequence design. The proposed method transforms the original
non-convex optimization with an uncertain target steering vector into a
two-step worst-case optimization problem. For each sub-problem, we develop a
corresponding trust-region Riemannian optimization algorithm. By iteratively
solving the two sub-problems, a sub-optimal solution can be reached without
accurate information about the target steering vector. Furthermore, the
convergence property of the proposed algorithms has been analyzed and detailed
proof of the convergence is given. Unlike the traditional waveform optimization
method, the proposed method is designed to work with an uncertain target
steering vector and therefore, is more robust in practical radar systems.
Numerical simulation results in different scenarios verify the effectiveness of
the proposed method in suppressing the clutter and show its advantages in terms
of the output signal-to-clutter plus noise ratio (SCNR) over traditional
methods.
