On the maximum achievable rates in the decode-forward diamond channel

This paper studies the problem of two-hop transmission from a single-antenna source to a single-antenna destination via two single-antenna relays. The relays operate in a full-duplex mode and they are not capable of buffering data. The links from the source to the relays and from the relays to the destination are considered to be Rayleigh block fading and there is no direct link between the source and the destination. There is also no link between the relays. Consequently, the half-duplex mode is a direct result of the full-duplex mode with frequency or time division. All nodes are assumed to be oblivious to their forward-channel gains, however, they have perfect information about their backward-channel gains. We also assume a stringent decoding delay constraint of one fading block that makes the definition of ergodic (Shannon) capacity meaningless. Hence, we adopt the broadcast approach (multi-layer coding) to maximize the expected-rate received at the destination. For this purpose, the decode-forward (DF) relaying adopting the broadcast approach is proposed. The main feature of the proposed scheme is that the layers being decoded at both relays are added coherently at the destination although each relay has no information about the number of layers being successfully decoded by the other relay. It is proved that the optimum strategy maximizing the throughput and expected-rate is to send uncorrelated signals over the relays. The maximum throughput is analytically formulated. An achievable rate as well as upper-bounds are presented for the maximum expected-rate of the channel.