# Robust Low-Sidelobe Transmit Beamforming under Peak-to-Average-Power Ratio Constraint
## 1 Introduction
Meanwhile, we address the array steering vector mismatch and norm constraint on the weight vector, combined with the sidelobe-level constraint, to further improve the robustness of the array beamformer and then better meet the requirements of actual radar systems. To enhance the target detection performance, the PAPR constraint on transmit weights is introduced to maximize the transmit power efficiency. To resolve the proposed nonconvex problem, we translate it into a series of convex subproblems via convex relaxation. Numerical results show that the proposed TBF method can effectively reduce the sidelobe level on the ground side and satisfy the PAPR constraint, which markedly improves the transmit power efficiency. The main contributions of this paper are summarized as follows:  
1. Based on the detection requirements of LSS radar, we aim to minimize the PSL of the transmit beampattern in a preset region while maintaining the mainlobe gain at the same time to preserve the target detection performance. Specifically, to sufficiently suppress the high-power clutter and rapidly changing interference from the ground, we require the sidelobe levels on the ground side to be sufficiently low but place no limitations on the sidelobe levels on the other side. 2. It is pointed out in [39] that TBF with better performance can be obtained by properly relaxing the CM constraint. Therefore, a PAPR constraint on transmit weights is introduced to ensure that the weight amplitude fluctuates within a certain range to improve the efficiency of transmit power. 3. The steering vector mismatch is considered to further strengthen the sidelobe-level constraint, and a norm upper bound of transmit weights is set to limit the fluctuation degree of the weight vector to a certain extent, thus improving the robustness of TBF. 4. Under the PAPR and norm constraints on transmit weights, we translate the proposed TBF problem into an SOCP problem through a series of convex relaxation processing and then solve it effectively. Numerical results verify that the proposed method can offer a lower PAPR than existing deterministic and adaptive TBF methods. The rest of this paper is organized as follows. In Section 2, linear-array-based array radar is taken as an example to develop the signal model and problem formulation of the proposed robust TBF with PAPR and norm constraints. Section 3 solves the proposed TBF problem by translating it into an SOCP problem with a series of convex relaxations. Numerical results and a performance analysis are provided in Section 4. Finally, Section 5 summarizes the paper. Notations: Throughout this paper, boldfaced upper-case and lower-case characters represent matrices and vectors, respectively. The superscripts \((\cdot)^{*},(\cdot)^{T}\), and \((\cdot)^{H}\) denote conjugate, transpose, and Hermitian transpose operators. The phase and modulus operators are written as \(\angle(\cdot)\) and \(|\cdot|\). The operator \(\mathbb{E}\{\cdot\}\) denotes the mathematical expectation, and \(\left\|{}_{\bullet}\right\|_{2}\) stands for the Euclidean norm of a vector.