Worst-Case Riemannian Optimization with Uncertain Target Steering Vector for Slow-Time Transmit Sequence of Cognitive Radar

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.