Fig. 1. (a) Symmetric vs. (b) asymmetric networks. In symmetric networks, the average channel fading (or path loss, respectively) is equal for all links from the cooperating source terminals to the destination. In asymmetric networks, the path loss reduction comes at the cost of loss of symmetry, i.e., the roles of relay and source can no longer be exchanged for the mutual benefit of both stations.

Fig. 2. Example multi-hop network with resource reuse (RRU). Node 1 transmits at resource b, thereby interfering with reception at node k. Likewise, the transmission of node k − 2 at resource a interferers with reception at node 1.

Fig. 3. Reuse of resources in various k = 4 RRU relaying schemes. In conventional relaying (top), the third hop can reuse the resource of the first hop, eventually requiring just two different resources to obey the hard orthogonality constraint. By contrast, full cooperative relaying (middle) calls for the use of four resources. Cooperative cascaded two-hop cooperative relaying (bottom) represents a tradeoff: it requires three resources. (a) Conventional relaying: no combining, here k = 4, k′ = 2. (b) Full cooperative relaying, here combining of max. Four transmissions, k = 4, k′ = 4. (c) Cascaded two-hop cooperative relaying, combining of max. Two transmissions, k = 4, k′ = 3.

Fig. 4. Operation of the cascaded cooperative two-hop relaying scheme. It requires three phases (k′ = 3). In this example, the first phase is reused. Relay nodes combine the transmissions from two phases before retransmission.

Fig. 5. Mean path losses modelled by the distances d_i,j and the path loss exponent α. The reference distance is d_s,d = 1.

Fig. 6. Outage probability vs. SNR for a relay located halfway between source and destination. Parameters: path loss exponent α = 3.0, spectral efficiency R = 2 bit/s/Hz.

Fig. 7. SNR gain over direct transmission as a function of the end-to-end spectral efficiency R. For the considered bandwidth limited scenarios, the relay protocols suffer from the required doubled spectral efficiency. Parameters: outage probability p^(out) = 10⁻², path loss exponent α = 3.0, relay position d_s,r/d_s,d = 1/2.

Fig. 8. SNR gain induced by a reduction of the required SNR, as a function of the position d_s,r/d_s,d of a relay that is located on the straight line between source and destination, for conventional and cooperative relaying. Thick lines: path loss exponent α = 3.0; thin, grey lines: α = 5.0. Parameters: outage probability p^(out) = 10⁻², R = 2 bit/s/Hz.

Fig. 9. SNR gain vs. number of hops in the example scenario for the interference-free NRRU scheme. Parameters: α = 4.0, R = 1 bit/s/Hz, target outage probability p^(out) = 10⁻² (fading case).

Fig. 10. SNR gain vs. interference cancellation capability in the example scenario. Parameters: Rayleigh fading, k = 6 hops, reuse k′ = 3, R = 1 bit/s/Hz, target outage probability p^(out) = 10⁻².

Fig. 11. Optimum number of hops in the example scenario vs. targeted end-to-end spectral efficiency. Using two hops is beneficial for the cooperative protocol for a wide range of end-to-end rates, while conventional relaying falls back to direct transmission already at lower rates (≈2.3 bit/s/Hz). Parameters: NRRU scheme, target outage probability p^(out) = 10⁻², α = 4.0, k = k′.