Achievable Rates for the AWGN Channel with Multiple Parallel Relays

Relaying is a key technology to increase capacity in wireless networks. In this paper, the point-to-point AWGN channel with N parallel relays and time-invariant,frequency-flat fading is studied. For it, we derive achievable rates with four coding techniques, namely: decode-and-forward, partial decode-and-forward, compress-and-forward and linear relaying. The first two are based on signal regeneration at the relay nodes and aim at mimicking a transmit antenna array. We study their scaling law for N -> infinity and Rayleigh fading, and show that is lower than log(2) log (N) due to the source-relays broadcast limitation. In turn, compress-and-forward aims at mimicking a receive antenna array and consists of relay nodes distributedly compressing their signals and transmitting them to destination. We provide its achievable rate considering distributed Wyner-Ziv compression at the relays, and show that it also scales as log(2) log (N); in this case, due to the relays-destination MAC limitation. Finally, linear relaying is the extension of amplify-and-forward to full-duplex operation. For it we derive the optimum transmitted signal at the source and propose suboptimum linear relaying functions at the relays. All techniques are compared with the max-flow-min-cut upper bound, evaluated for AWGN channels.