  The paper studies the multi-user precoding problem as a non-convex
optimization problem for wireless multiple input and multiple output (MIMO)
systems. In our work, we approximate the target Spectral Efficiency function
with a novel computationally simpler function. Then, we reduce the precoding
problem to an unconstrained optimization task using a special differential
projection method and solve it by the Quasi-Newton L-BFGS iterative procedure
to achieve gains in capacity. We are testing the proposed approach in several
scenarios generated using Quadriga - open-source software for generating
realistic radio channel impulse response. Our method shows monotonic
improvement over heuristic methods with reasonable computation time. The
proposed L-BFGS optimization scheme is novel in this area and shows a
significant advantage over the standard approaches. The proposed method has a
simple implementation and can be a good reference for other heuristic
algorithms in this field.
