Combining orthogonalized partial metrics: Efficient enumeration for soft-input sphere decoder

Using the Schnorr-Euchner (SE) order for soft-input sphere decoders is inefficient for implementation, because it requires exhaustive calculation and sorting of partial metrics of all constellation points. Instead, low-complexity methods can be applied by separating the partial metric into channel information and a priori information and solely enumerating based on one of them. With such an orthogonalization, this paper presents an algorithm that effectively combines these two enumerations to deliver an order close to the SE one. Mathematical analyses and simulation results demonstrate that this is the first algorithm allowing for a low-complexity implementation with optimal error rate performance for any number of iterations.