**1.1.4 Weight norm constraint approaches for general mismatch**

Jian Li et al propose a Capon beamforming approach with the norm inequality constraint (NIC) to improve the robustness against array steering vector errors and noise [22], although the exact solution is given, and optimal loading level can be computed via the proposed method, but by analysis and simulation, its efficiency is not as good as expectation. Since the constraint parameter determines its robustness, but how to select the constraint parameter is not discussed.

Quadratic inequality constraints (QIC) on the weight vector of LCMP beamformer can improve robustness to pointing errors and random perturbations in sensor parameter [27]. The weights that minimize the output power subject to linear constraints and an inequality constraint on the norm of the weight vector have the same form as that of the optimum LCMP beamformer with diagonal loading of the data covariance matrix. But the optimal loading level cannot be directly expressed as a function of the constraint in a closed form, and cannot be solved exactly. Hence, its application is restricted by the optimal weight vector finding. So that some numerically algorithms are proposed to implement the QICLCMP, such as Least Mean Squares (LMS) or Recursive Least Squares (RLS) [27], but the application effect isn't good as the expectation.

This chapter is organized as follows [38]. First, the norm inequality constraint Capon beamformer (NICCB) is introduced and analyzed particularly. Second, the choice of the norm constraint parameter and the selecting bound is discussed. Third, the norm equality constraint Capon beamformer (NECCB) is proposed and is solved effectively. Finally, the simulation analyses and the conclusion are given.
