Iterative Constrained Least Squares for Robust Constant Modulus Beamforming

This paper addresses robust beamforming in the presence of model uncertainty for constant modulus (CM) signals that are frequently encountered in radar and communication systems. Instead of employing the commonly used minimum variance approach, we utilize a CM criterion that is different from the conventional techniques for blind equalization. The proposed robust beamformer minimizes the CM objective function while constraining the magnitude response of any steering vector within a spherical uncertainty region to exceed unity. We develop two algorithms to solve the resultant nonconvex and nonsmooth optimization problem. The first is subgradient projection method, which is simple but converges slowly and is sensitive to initialization. By introducing auxiliary phase variables, our second scheme reformulates the original nonsmooth problem into a differentiable one, that can be solved by an iterative constrained least squares (ICLS) procedure. At each iteration of the ICLS, a least squares (LS) problem with a second-order cone constraint is solved. More important, a closed-form solution for this constrained LS problem, which has a low computational complexity, is derived. The ICLS has fast convergence and is not sensitive to the initial value. Simulation results demonstrate that the proposed CM beamformer achieves a substantial performance gain compared with several representative robust beamformers.