Compressive sampling based multiple symbol differential detection for UWB IR signals

In this paper, a compressive sampling (CS) based multiple symbol differential detector is proposed, using the principle of a generalized likelihood ratio test (GLRT). The proposed detector works on the compressed samples directly, thereby avoiding the reconstruction step and thus resulting in a reduced implementation complexity along with a reduced sampling rate (much below the Nyquist rate). We also propose the compressed sphere decoder (CSD) to resolve the detection of multiple symbols. Our proposed detector is valid for scenarios where the measurement matrices are the same as well as where they are different for each received symbol.