A new stopping criterion for the Sphere Decoder in UWB impulse-radio multiple-symbol differential detection

Multiple-symbol differential detection (MSDD) is a powerful technique for power-efficient low-complexity autocorrelation receivers in ultra-wideband impulse-radio (UWBIR) systems. Since MSDD can be represented as a tree search problem, it is efficiently implemented by the sphere decoder (SD) algorithm. In this paper, we introduce a novel stopping criterion for the SD, which is based on a lower bound on the packing radius of lattices and enables early termination of the search process. As a result, the application of this stopping criterion reduces the number of search steps and thus lowers the complexity of MSDD for UWB-IR. Numerical results show that the proposed stopping criterion achieves optimal MSDD performance at reduced SD complexity.