On the amplify-and-forward cooperative diversity with time-hopping ultra-wideband communications

In this paper, we extend the Amplify-and-Forward cooperative diversity scheme to the context of impulse radio ultra wideband (IR-UWB). In particular, we present the construction of three families of minimal-delay and totally-real distributed algebraic space-time (ST) codes suitable for IR-UWB. The first family encodes adjacent symbols and is based on totally-real cyclic division algebras. The second family encodes the pulses used to transmit one information symbol and permits to achieve high performance levels with lower complexity. Both families of codes achieve full rate, full diversity with non-vanishing determinants for various number of relays. These schemes can be associated with pulse position modulation (PPM), pulse amplitude modulation (PAM) and hybrid pulse position and amplitude modulation (PPM-PAM). The third family of codes is information-lossless and does not require any pulse repetitions. It is specific to M-PPM-M'-PAM with M >= 3 and for all values of M'. Simulations performed over realistic indoor UWB channels are provided to verify the theoretical results.