This paper addresses the problem of Minimum Peak Sidelobe Transmit Beampattern (MPSTB) design for colocated MIMO radar systems. Two new methods are proposed to achieve it via designing Constant Modulus (CM) waveforms directly. One is to maximize the ratio of the Minimum Mainlobe Level (MML) to the Peak Sidelobe Level (PSL) without specifying pattern masks. Another is to minimize PSL under the mainlobe ripple and unspecified waveform modulus constraints. The resultant optimization problems are difficult to solve due to the coupled numerator and denominator of the Quadratic Fractional Programming (QFP) problem formulation in the former and double-sided quadratic constraints and unknown waveform modulus in the latter. For the former, we decouple the numerator and denominator by equivalent transform and introduction of boundary-type auxiliary variables in order that feasible methods are derived to tackle them independently and efficiently. For the latter, we simplify the coupled double-sided quadratic constraints on the same waveform vector into those on different single auxiliary variables to tackle the corresponding nonconvex optimization problem. Numerical examples show that the proposed algorithms can attain sufficient low peak sidelobe beampattern levels under the CM constraints.

In this paper, we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers (ADMM). Unlike the usual weighted l1 norm, we utilize the lp norm of the array weight vector, where 0 < p < 1, as the objective function to enhance its sparsity for arbitrary array configurations. To solve the resultant nonconvex and nonlinear optimization problem, we introduce auxiliary variables to decouple the array weight vector in the objective function from the complicated constraints on mainlobes and sidelobes, and then the array weight vector and auxiliary variables are updated alternately via ADMM. To determine the array weight vector with the lp norm, we analyze the convexity or concavity of the subfunction related to each weight element using its derivatives. On the other hand, we divide the objective function of auxiliary variables into multiple nonlinear subfunctions, each of which is only dependent of the magnitude of the corresponding auxiliary variable and is calculated in parallel via analyzing simplified two-sided constraints. Furthermore, we extend our methodology to the symmetric excitation case with symmetric array configurations. Numerical examples show that the proposed methods can obtain satisfactory radiation pattern with fewer antennas than existing techniques, and are applicable for arbitrary or symmetric array configurations.

This paper investigates the problem of wideband multiple-input multiple-output radar transmit beampattern synthesis in a spectrally dense environment, and two optimization problems are formulated according to practical consideration. The first one is beampattern matching design under the scenario of known interference spectral band while the second addresses minimum peak sidelobe beampattern design given both interference spectral band and interference direction. In addition, to improve transmission efficiency, other than the peak-to-average power ratio constraint, a useful modulus constraint, namely, dynamic range ratio, is adopted in our development. The resultant problems are nonconvex and nonsmooth, together with multiple constraints. The advantages of the majorization-minimization and alternating direction method of multipliers (ADMM) are combined to handle them. We first use the majorization technique to handle the nonconvex and nonsmooth issues and then utilize the ADMM to solve the multi-constrained problem. Two variants of the ADMM, called majorization-ADMM and proximal-ADMM, are devised, and their convergence is also studied. Finally, numerical examples are provided to verify the effectiveness of the proposed algorithms.

This paper considers the problem of designing unimodular sequence with low PSL of local ambiguity function. The optimization problem is difficult because of the mixed nonconvex unimodulus and highly nonlinear fourth-order polynomial-like constraints. To solve the problem, we propose a hybrid Lagrange Programming Neural Network-Alternating Direction Method of Multipliers (LPNN-ADMM) approach. To separately deal with the complex nonconvex and nonlinear constraints, we introduce auxiliary variables to transfer the fourth-order polynomials from the nonlinear constraints into the Lagrange function. As a result, the original optimization variables and auxiliary variables are updated alternately in the ADMM framework. Especially, the original optimization variables are updated from the newly formed nonlinear objective function together with the unimodular constraints via the LPNN method, in which an adaptive selection scheme of the penalty parameter is developed to minimize the corresponding Lagrange function while satisfying the constraints. The performance of the proposed method is demonstrated via numerical examples.

In this paper, under the peak-to-average power ratio (PAR) and energy constraints on the transmit waveforms, a new efficient weighted $\ell_p$ -norm metric (with $p\geq2$ ) is introduced for colocated wideband/narrowband multiple-input multiple-output radar transmit beampattern matching design. The proposed metric can achieve quasi-equiripple beampattern, which is desirable to improve the robustness of radar systems for the imprecisely known direction of the targets and reduce the radar clutter. In addition, mainlobe ripple control, peak sidelobe suppression and deep null/notch formation can be obtained. On the other hand, the PAR and energy constraints cause the radar waveform losing the degree of freedom to match arbitrary pattern shape, and the desired pattern usually lies in matching an appropriately scaled version of the shape. Thus, a scaling factor is introduced into the proposed metric to tackle the scaling ambiguity problem. The resultant optimization problems are difficult to solve due to higher-order polynomial objective function with coupled scaling factor and waveform matrix, and also the nonconvex PAR constraint. To develop a fast and efficient algorithm, by utilizing the majorization-minimization technique, we decouple the coupled variables (scaling factor and radar waveform matrix) by a majorization step, derive a new quadratic majorizer to tackle the quadratic function with matrix variable and surrogate the nonsmooth nonconvex functions by convex functions. Numerical examples show that the devised approach can synthesize beampattern with lower peak sidelobe level and more flat mainlobe compared to the existing algorithms.