说明：  The papers are special sections about the applications of convex optimization in signal processing, and they are especially related to physical layer security and beamforming. As a mathmatical tool, convex optimization can help resolve weight design issues subject to certain constraints in beamforming. The semidefinite relaxation technique is of great importance to convert a non-convex problem to a convex one. The papers included are: 1.Convex optimization based beamforming 2.Convex optimization in signal processing from the guest editors 3.Dynamic resource allocation in cognitive radio networks 4.Real-time convex optimization in signal processing 5.Semidifinite relaxation of quadratic optimization problems