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Transmit beamforming (TBF) provides the capability of focusing illuminating power in the desired directions while reducing the emitting power in undesired directions. It is significantly important in low-altitude and slow-speed small (LSS) radar, which usually suffers from heavy clutter and rapidly changing interference on the near-ground side. Due to nonideal factors such as an inaccurate target direction and array gain-phase error, the robustness of TBF is also necessary to consider in practical applications. In this paper, we provide a robust TBF method that enables sidelobe control in preset regions and possesses high transmit efficiency in virtue of the peak-to-average-power ratio (PAPR) constraint on transmit weights. To achieve robustness, a norm upper bound is introduced to limit the fluctuation of transmit weights, and the steering vector mismatch is also considered by using a spherical uncertainty set surrounding the nominal steering vector. As the proposed robust TBF is nonconvex because of the nonconvexity of both the objective function and constraints, we translate it into a series of convex subproblems via several kinds of convex relaxation schemes. In particular, based on the special structure of the objective function and constraints, the translation of the nonconvex problem into a tractable SOCP problem is realized by using the combination of the triangle inequality and Cauchy-Schwartz inequality. Numerical results demonstrate the improvement in the efficiency and robustness of the proposed TBF method in comparison with traditional TBF methods.

Robust Low-Sidelobe Transmit Beamforming under Peak-to-Average-Power Ratio Constraint