A Stepwise Iterative Convex optimization (SI-CVX) algorithm is proposed for directional modulation signal synthesis of time modulated sparse antenna array.By analyzing the switch-on duration time and the switch-on moment of the array element,the upper and non-convex lower bounds of the pattern are converted to convex problems.By optimizing the main band pattern and sideband pattern step by step,only the main band is remained in the desired radiation direction,and the sideband signal is null.The efficiency and stability of the stepwise iterative convex optimization algorithm is verified by the simulation of time modulated sparse linear array and the purpose of directional modulation signal synthesis is achieved.