This paper presents a new method to synthesize high-performance beampatterns, with the aid of linear fractional semidefinite relaxation (LFSDR) technique and quasiconvex optimization approach. We consider two beampattern synthesis problems. The first one is how to determine the weight vector to maximize the array gain (or equivalently, to minimize the gain loss in mainlobe), under the condition that the amplitude response satisfies specific requirements. The second one is how to minimize the notch level at a given region, on the premise of a permissible gain loss in mainlobe. To these ends, two non-convex optimization problems are first formulated and then relaxed to their quasiconvex forms, by using the LFSDR technique. To further solve the resultant problems, the bisection method, which is commonly used in quasiconvex optimization, is adopted. Suboptimal solutions to the original non-convex problems are finally obtained through eigenvalue decomposition (EVD) or randomization manipulations. The proposed method performs well in both cases described above. Moreover, our method is not limited to the array configurations and/or noise environments. Representative simulations are presented to demonstrate the effectiveness of the proposed method in high-performance beampattern synthesis.

This paper presents a novel robust quasi-adaptive beamforming (RQAB) scheme against direction-of-arrival (DOA) mismatch. Unlike existing robust adaptive beamforming (RAB) methods, the proposed approach obtains the ultimate beamformer weight vector in a quiescent manner, nevertheless, it possesses the remarkable ability of interference rejection and desired signal reception. In this method, a two-step procedure is devised to design the quasi-adaptive weight vector. More specifically, the conventional sample matrix inversion (SMI) beamformer is first applied to find out all notch angles outside the region of interest (ROI) where the desired signal comes with a high probability. It is shown that these notch angles contain the DOAs of interferences. Then, a multi-point accurate array response control (MA$^2$RC) algorithm is utilized to synthesize a beampattern with the same sidelobe notch levels as the SMI, and nearly constant response over the ROI. Contrary to conventional approaches which are vulnerable to the contamination of the training data by the desired signal, our proposed approach exhibits outstanding performance under this common scenario. Moreover, besides the DOA mismatch, the proposed approach is also insensitive to the SNR, number of snapshots and mismatch angle. Additionally, different from many optimization-based RAB methods, the proposed RQAB approach offers an analytical expression of the beamformer weight vector and, hence, is computationally attractive. Typical simulation examples are provided to demonstrate the superiority of the RQAB scheme.

This letter deals with the co-design of transmit and receive beamforming weights for the multiple-input multiple-output (MIMO) array with a low probability of interception (LPI) in the presence of multiple targets. Based on that, we formulate an optimization model with constraints on the transmit power, aiming to maximize minimum output signal-to-interference-plus-noise-ratio (SINR). To solve the formed optimization problem, we propose the one-step iterative scheme, which generates the transmit weight vector by iteratively solving a series of convex approximate problems. The receive weight of each target is finally formed with the minimum variance distortionless response (MVDR) algorithm. Numerical experiments are completed to show the effectiveness of the proposed method.

The finite resolution phase shifters pose significant challenges for the beampattern synthesis. In this letter, we propose a novel joint multi-point control and iterative gradient descent (MIGD) algorithm, which aims to minimize the performance losses caused by phase quantization and can be solved efficiently. The deviation caused by quantization is firstly minimized as objective function in optimization problem. Then, an explicit solution of weight vector is obtained by utilizing the iterative gradient descent method. To make sure that the beampattern can be synthesized to the desired one by the weight vector, a multi-point control method is combined during the iteration. Representative examples are presented to illustrate the effectiveness and superiority of the proposed algorithm.