Small-cell deployment in licensed and unlicensed spectrum is considered to be one of the key approaches to cope with the ongoing wireless data demand explosion. Compared to traditional cellular base stations with large transmission power, small-cells typically have relatively low transmission power, which makes them attractive for some spectrum bands that have strict power regulations, for example, the 3.5GHz band [1]. In this paper we consider a heterogeneous wireless network consisting of one or more service providers (SPs). Each SP operates in both macro-cells and small-cells, and provides service to two types of users: mobile and fixed. Mobile users can only associate with macro-cells whereas fixed users can connect to either macro- or small-cells. The SP charges a price per unit rate for each type of service. Each SP is given a fixed amount of bandwidth and splits it between macro- and small-cells. Motivated by bandwidth regulations, such as those for the 3.5Gz band, we assume a minimum amount of bandwidth has to be set aside for small-cells. We study the optimal pricing and bandwidth allocation strategies in both monopoly and competitive scenarios. In the monopoly scenario the strategy is unique. In the competitive scenario there exists a unique Nash equilibrium, which depends on the regulatory constraints. We also analyze the social welfare achieved, and compare it to that without the small-cell bandwidth constraints. Finally, we discuss implications of our results on the effectiveness of the minimum bandwidth constraint on influencing small-cell deployments.
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