Outage Performance of Uplink Two-tier Networks Under Backhaul   Constraints
  Multi-tier cellular communication networks constitute a promising approach to expand the coverage of cellular networks and enable them to offer higher data rates. In this paper, an uplink two-tier communication network is studied, in which macro users, femto users and femto access points are geometrically located inside the coverage area of a macro base station according to Poisson point processes. Each femtocell is assumed to have a fixed backhaul constraint that puts a limit on the maximum number of femto and macro users it can service. Under this backhaul constraint, the network adopts a special open access policy, in which each macro user is either assigned to its closest femto access point or to the macro base station, depending on the ratio between its distances from those two. Under this model, upper and lower bounds on the outage probabilities experienced by users serviced by femto access points are derived as functions of the distance between the macro base station and the femto access point serving them. Similarly, upper and lower bounds on the outage probabilities of the users serviced by the macro base station are obtained. The bounds in both cases are confirmed via simulation results. 
Shirin Jalali, Zolfa Zeinalpour-Yazdi, and H. Vincent Poor
cs.IT math.IT