Unitary Space-Time Pulse Position Modulation for Differential Unipolar MIMO IR-UWB Communications

In this paper, we present a general technique for constructing minimal-delay unitary differential Space-Time (ST) block codes for Pulse Position Modulation (PPM) with an arbitrary number of transmit antennas and signal set cardinality. A typical application corresponds to Multiple Input Multiple Output (MIMO) Impulse-Radio Ultra-Wideband (IR-UWB) systems where neither the transmitter nor the receiver knows the channel. The proposed scheme is a pulse-based solution where the information is encoded differentially through the relative shifts of the pulses in one block with respect to the pulse positions in the previous block where each block extends over P symbol durations with P standing for the number of transmit antennas. This technique of time-domain encoding avoids all types of amplitude constellation expansions and achieves a full transmit diversity order while maintaining a single unipolar pulse transmission per symbol in a way that is completely equivalent to single-antenna PPM communications. We also propose a simplified decoder that can be associated with the proposed ST code and we perform a detailed complexity analysis that allows to quantify the reduction in the number of operations offered by this simplified decoding strategy. Finally, the results are validated numerically and through a semi-analytical evaluation of the conditional symbol error rate.