Concrete MAP Detection: A Machine Learning Inspired Relaxation

Motivated by large linear inverse problems where the complexity of the Maximum A-Posteriori (MAP) detector grows exponentially with system dimensions, e.g., large MIMO, we introduce a method to relax a discrete MAP problem into a continuous one. The relaxation is inspired by recent ML research and offers many favorable properties reflecting its quality. Hereby, we derive an iterative detection algorithm based on gradient descent optimization: Concrete MAP Detection (CMD). We show numerical results of application in large MIMO systems that demonstrate superior performance w.r.t. all considered State of the Art approaches.