An Explanation of Deep MIMO Detection From a Perspective of Homotopy Optimization

Since the work of detection network (DetNet) by Samuel, Diskin and Wiesel in 2017, deep unfolding for MIMO detection has become a popular topic. We have witnessed significant growth of this topic, wherein various forms of deep unfolding were attempted in the empirical way. DetNet takes insight from the proximal gradient method in terms of the use of the network structure. In this paper, we endeavor to give an explanation of DetNet—in a fundamental way—by drawing connection to a homotopy optimization approach. The intuitive idea of homotopy optimization is to gradually change the optimization landscape, from an easy convex problem to the difficult MIMO detection problem, such that we may follow the solution path to find the optimal MIMO detection solution. We illustrate that DetNet can be interpreted as a homotopy method realized by the proximal gradient method. We also illustrate how this interpretation can be extended to the Frank-Wolfe and ADMM variants of realizing the homotopy optimization approach, which result in new DetNet structures. Numerical results are provided to give insights into how these homotopy-inspired DetNets and their respective non-deep homotopy methods perform.