Linear precoding design for MIMO channels with finite alphabet constraints

Considering that the channel input of a practical communication system is finite-alphabetic, the design and optimization of precoding matrixes were studied under the finite alphabet input, and a scheme for precoding metrix design was proposed by taking the maximized mutual information of a multiple input and multiple output (MIMO) system as an objective function. The scheme translates the problem of precoding matrix design into two sub problems of designing the power allocation matrix and the right unitary matrix. The first problem is a convex optimization problem and it can be solved by the classical steepest descent algorithm. The second problem is a unitary-matrix constrained optimization problem, and it can be translated into a problem without constraints in the Riemannian geometry. Consequently, it can be solved by the steepest descent (SD) algorithms on the Lie group of unitary matrices. The simulation results show that the proposed algorithm has the good performance and the high speed in convergences.