On capacity bound of opportunistic cooperative diversity

The opportunistic cooperative diversity is promising to improve the capacity of the wireless communications because it yields the same diversity order as using all relay nodes while requires bandwidth for only one relay node. The more number of relay nodes we employ, the higher diversity order we obtain. From the results in the literature, the recently published paper conjectures that there exists the saturation in obtaining the capacity improvement from increasing the number of employing relay nodes. This means the capacity converges to an upper bound as a function of the number of employed relay nodes. In this paper, we prove that the upper bound does not exist, which means the outage capacity diverges as a function of the number of employed relay nodes.