Optimization of mutual information of AF-DSTBCs over the random set relay channel

We consider cooperative relaying systems employing amplify-and-forward (AF) distributed space-time block codes (DSTBCs) in which only backward channel-state-information (CSI) is known at relays and destination. For such systems, we study the particular case where, in order to minimize overhead, each of N relays decide independently whether to join the cooperation with basis on the received signal as compared to a certain threshold. Since in such a scheme the number of active relays K at a given realization is random, the channel becomes a random set relay channel (RSRC). The mutual information (MI) of AF-DSTBC in the RSRC are analyzed, addressing the ergodic delay-tolerant case. Results on MI are given in the form of three different upper bounds, each offering a different trade-offs of complexity and closeness. It is found that the maximal MI is not achieved under full-time-all-relay cooperation (K = N), even if the total power at the receiver increases with K. It is also shown that the optimum power allocation depends on the threshold, such that the MI is maximized not under equal power allocation, but rather when more power is allocated to the second stage (relaying).