About asymptotic spectral efficiency in the DS/CDMA amplify and forward relay channel

This paper considers a simple CDMA-based amplify and forward half-duplex relay transmission scheme. The spectral efficiency of the system is computed for both the optimal and the linear minimum mean square error receivers. These expressions are then approximated with their asymptotic equivalents, assuming that the number of source symbols K and signature length N are infinitely large but with constant ratio alpha = K/N. Asymptotics are then compared with the spectral efficiency of the direct link to identify conditions that guarantee the superiority of relaying. We show that, for one relay and optimal receiver, the sufficient condition is also necessary. Finally, in the low-power regime, we compute the value of alpha that maximizes the information transfer: this coincides with the best time-sharing strategy between source and relay transmission.