Is broadcast plus multiaccess optimal for Gaussian wireless networks?

In this paper we show that "separation"-based approaches in wireless networks do not necessarily give good performance in terms of the capacity of the network. Therefore in optimal design of a wireless network, its total structure should be considered. In other words, achieving capacity on the subnetworks of a wireless network does not guarantee globally achieving capacity. We will illustrate this fact by considering some examples of multistage Gaussian wireless relay networks. We will consider a wireless Gaussian relay network with one stage in both fading and nonfading environment. We show that as the number of relay nodes, n, grows large, the capacity of this network scales like log n. We then show that with the "separation"-based scheme, in which the network is viewed as the concatenation of a broadcast and a multiaccess network, the achievable rate scales as log log n and as a constant for fading and nonfading environment, respectively, which is clearly suboptimal