Blind Constant Modulus Multiuser Detection based on Riemannian Manifold Optimization

For direct spread spectrum code division multiple access (DS-CDMA) communication systems, blind constant modulus multiuser detection technology shows excellent robustness and anti-interference capability. However, the blind constant modulus multiuser detection model is a non-convex NP-hard optimization problem because of the fourth-order objective function and the nonconvex rank constraint. In order to solve the problem that it is difficult to obtain a closed-form solution directly due to the existence of multiple local points of the cost function, we reformulate the blind constant modulus multiuser detection model as an unconstrained manifold optimization problem on a fixed-rank positive semi-definite matrix manifold space. Further, we strictly derive the expressions of Riemannian gradient and Riemannian Hessian. Finally, the Riemannian trust region optimization method is used to solve the optimization problem. Simulations under different environments show that the blind constant modulus multiuser detector based on Riemannian manifold optimization can obtain higher output performance than other algorithms.