On the Design of Maximal-Rate Shape-Preserving $2\times 2$ and $3\times 3$ Space-Time Codes for Noncoherent Energy-Detection-Based PPM Communications

In this paper, we propose novel 2×2 and 3×3 noncoherent space-time (ST) codes for impulse-radio ultra-wideband communications with pulse position modulation (PPM). The code design is based on existing coherent ST codes, where the associated constellation is confined in order to achieve full diversity with analog energy detectors. A comprehensive performance analysis guides this confinement and highlights the maximum rates that can be achieved by this specific layered code word structure with two and three transmit antennas. The proposed codes attain these maximum rates without introducing any expansion to the unipolar PPM signal set.