Map based differential detectors for compressed UWB impulse radio signals

We propose maximum a posteriori (MAP) based noncoherent differential detector for ultra-wideband (UWB) impulse radio (IR) signals, received at a sub-Nyquist sampling rate. We build our detector for a Laplacian distributed multipath channel, which models sparsity. Our MAP based detector outperforms differential detectors based on other state-of-the-art approaches from a practical point of view. Our work highlights the critical role of different measurement matrices for the compressed differential detectors in general and the MAP based compressed differential detectors in particular.