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

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 Adaptive Transmit Beamforming under the Constraint of Low Peak-to-Average Ratio.

In radar detection, in order to make the beam have variable directivity, a Capon beamformer is usually used. Although this traditional beamformer enjoys both high resolution and good interference suppression, it usually leads to high sidelobe and is sensitive to array steering vector (ASV) mismatch. To overcome such problems, this study devises a novel, robust adaptive beamformer that is robust to ASV mismatch under the constraint where the sidelobe is oriented to the ground. Moreover, to make full use of the transmit power, the constraint of a low peak-to-average power ratio (PAPR) is also taken into consideration. Accordingly, this robust adaptive beamformer is developed by optimizing a transmitting beamformer constrained by ASV mismatch and low PAPR. This optimization problem is transformed into a second-order cone programming (SOCP) problem which can be efficiently and exactly solved. The proposed transmit beamformer possesses not only adaptive interference rejection ability and robustness against ASV mismatch, but also direct sidelobe control and a low PAPR. Simulation results are presented to demonstrate the superiority of the proposed approach. The proposed method can make the peak sidelobe level (PSL) level on the ground side below -30 dB.