The invention discloses a manifold optimization transmitting directional diagram synthesis method for an analog digital
hybrid array. According to the manifold optimization transmitting directional diagram synthesis method for the analog digital
hybrid array, the HAD array transmitting directional diagram synthesis problem with the criterion of minimizing the matching error between an expected beam directional diagram and an actual beam directional diagram is researched. According to the method, the solution is carried out by utilizing block
coordinate descent (BCD) and Riemannian manifold optimization. Firstly, a constant modulus auxiliary variable is introduced to equivalently represent that an objective function is a smooth biquadratic function; then, alternately optimizing a scaling factor, a digital weight, a
simulation weight and a constant modulus auxiliary variable under a BCD framework, reexpressing the
simulation weight and the auxiliary variable as a quadratic
programming problem under constant modulus constraint, and solving through a Riemannian
gradient descent method; the globally optimal solution of the digital weight is obtained through a
Lagrange multiplier method. A numerical result shows that compared with other representative algorithms, the
algorithm provided by the invention has better
beam matching performance.