The Impact of Unlicensed Access on Small-Cell Resource Allocation
  Small cells deployed in licensed spectrum and unlicensed access via WiFi provide different ways of expanding wireless services to low mobility users. That reduces the demand for conventional macro-cellular networks, which are better suited for wide-area mobile coverage. The mix of these technologies seen in practice depends in part on the decisions made by wireless service providers that seek to maximize revenue, and allocations of licensed and unlicensed spectrum by regulators. To understand these interactions we present a model in which a service provider allocates available licensed spectrum across two separate bands, one for macro- and one for small-cells, in order to serve two types of users: mobile and fixed. We assume a service model in which the providers can charge a (different) price per unit rate for each type of service (macro- or small-cell); unlicensed access is free. With this setup we study how the addition of unlicensed spectrum affects prices and the optimal allocation of bandwidth across macro-/small-cells. We also characterize the optimal fraction of unlicensed spectrum when new bandwidth becomes available. 
Cheng Chen, Randall A. Berry, Michael L. Honig, Vijay G. Subramanian
cs.IT math.IT