Asymptotic behavior of ultra-dense cellular networks and its economic impact

Abstract

Abstract—This paper investigates the relationship between base station (BS) density and average rate in downlink cellular networks. This relationship has been well known for sparse de-ployment, i.e. when the number of base stations is low compared to the number of users, showing average rate is independent of BS density. As BS density grows, on the other hand, several preceding works proved BS increases average rate, but no tractable form for the rate-density relationship has yet been derived. In this paper we derive such a closed-form result that reveals the rate is asymptotically a logarithmic function of BS density as the density grows. Further, we study the impact of this result on the network operator’s profit when user demand varies, and derive the profit maximizing BS density and the optimal amount of spectrum to be utilized in closed forms. Consequently, we provide deployment planning guidelines that will aid the operator in his decision if he should invest more in BS densification or in acquiring more spectrum for his ultra-dense cellular network. Index Terms—Ultra-dense cellular network, base station den-sity, average rate, spectrum amount, profit maximization. I.