Random DS/CDMA for the amplify and forward relay channel

This paper presents a communication system where point-to-point transmissions are aided by L half-duplex, amplify and forward relays which access a common channel by means of random spreading matrices. During the relaying phase, the source can either remain silent or send new symbols. The two cases are compared in terms of spectral efficiency, showing that the latter is always preferable. Next, a sufficient condition for the superiority of the presented relaying scheme over the simple direct-link channel is derived. Particularizing to the one relay case, this condition turns out to be also necessary and allows to identify which is the best time-sharing strategy between relay receiving and transmitting phases. We conclude the paper by discussing the suboptimal linear-minimum-mean-square-error receiver, which is known to be the linear filter that guarantees the maximum signal to noise and interference ratio at its output. To avoid dealing with the randomness introduced by the spreading matrices, the analysis is carried out in the asymptotic regime, i.e. when letting the number of transmitted symbols and the signature length grow without bound but with constant ratio. Under these hypotheses, indeed, random matrix theory results show that it is possible to derive deterministic almost sure equivalents which are excellent approximations of the finite reality.