Wireless Networks of Bounded Capacity

The channel capacity of wireless networks is often studied under the assumption that the communicating nodes have perfect channel-state information (CSI) in the sense that they have access to the fading coefficients in the network. To the best of our knowledge, one of the few works that studies wireless networks without this assumption is by Lozano, Heath, and Andrews. Inter alia, Lozano et al. show that in the absence of perfect CSI, and if the channel inputs are given by the square-root of the transmit power times a power-independent random variable, then the achievable information rate is bounded in the signal-to-noise ratio (SNR). However, such inputs do not necessarily achieve capacity, so one may argue that the information rate is bounded in the SNR because of the suboptimal input distribution. In this paper, it is demonstrated that if the nodes do not cooperate and they all use the same codebook, then the achievable information rate remains bounded in the SNR even if the input distribution is allowed to change arbitrarily with the transmit power.