An Overview of Scaling Laws in Ad Hoc and Cognitive Radio Networks

Currently, wireless communications are changing along the lines of three main thrusts. The first is the introduction of secondary spectrum licensing (SSL). Regulations on the usage of licensed spectra are being loosened, encouraging unused primary spectrum to be licensed, often in an opportunistic manner, to secondary devices. The second is the introduction of cognitive radios. These wireless devices are able to sense and adapt in a “smart” manner to their wireless environment, making them prime candidates to becoming secondary users in SSL initiatives. Finally, as we approach the communication limits of point-to-point channels, and as wireless devices become cheap and ubiquitous, the focus is shifting from single to multiple communication links, or networks. In this paper, we provide an overview of the recently established theoretical limits, in the form of sum-rates, or throughput, of two main types of networks: ad hoc networks, in which the devices are homogeneous, and cognitive networks, in which a mixture of primary and secondary (or cognitive) devices are present. We summarize and provide intuition on how the throughput of a network scales with its number of nodes n, as n → ∞, under different network and node capability assumptions.