A Unified Analysis of Spectral Efficiency for Two-Hop Relay Systems With Different Resource Configurations

In this paper, we analyze in a unified way the achievable rate and spectral efficiency of multicarrier and multiantenna two-hop relay systems with an interference-free linear transceiver. We consider two kinds of decode-and-forward (DF) relay systems with three nodes. In the first kind of relay systems where only the relay node employs the full channel state information (CSI) of both the source-relay (S-R) link (first hop) and the relay-destination (R-D) link (second hop), the relay eliminates the interference of these links. In the second kind of systems, where the source node employs the CSI of the first hop, the destination node employs the CSI of the second hop, whereas the relay node employs the full CSI of both the hops; these nodes can jointly eliminate the interference. For the multicarrier relay or multiantenna relay systems supporting different diversity and multiplexing gains and under the aforementioned assumptions for the CSI, we find that the achievable rate of each hop or its lower bound can be unified in the generalized mean of the eigenvalues of an equivalent channel correlation matrix. Furthermore, by using the properties of generalized mean and by resorting to the random matrix theory, we derive the asymptotic spectral efficiency of the multicarrier or multiantenna systems with different CSI assumptions. Finally, we provide simulation results to validate our analytical results. Our studies show that the multicarrier systems using code-division multiplexing (CDM) or the multiantenna systems can benefit more from exploiting the CSI at all the three nodes than the multicarrier systems using frequency-division multiplexing (FDM), particularly, in the case of a high load factor.