A stopping radius for the sphere decoder and its application to MSDD of DPSK

In this letter we use a lower bound on the packing radius of discrete sets as a stopping radius in the sphere decoder (SD). This enables us to terminate the SD search process as early as possible while preserving the optimality of the final decoder output. As an example we investigate the application of this SD with early termination in multiple-symbol differential detection (MSDD) of differential phase-shift keying (DPSK) transmitted over time-varying fading channels, and provide numerical evidence that the proposed stopping radius achieves a notable complexity reduction.