  Heterogeneity in wireless network architectures (i.e., the coexistence of 3G,
LTE, 5G, WiFi, etc.) has become a key component of current and future
generation cellular networks. Simultaneous aggregation of each client's traffic
across multiple such radio access technologies (RATs) / base stations (BSs) can
significantly increase the system throughput, and has become an important
feature of cellular standards on multi-RAT integration. Distributed algorithms
that can realize the full potential of this aggregation are thus of great
importance to operators. In this paper, we study the problem of resource
allocation for multi-RAT traffic aggregation in HetNets (heterogeneous
networks). Our goal is to ensure that the resources at each BS are allocated so
that the aggregate throughput achieved by each client across its RATs satisfies
a proportional fairness (PF) criterion. In particular, we provide a simple
distributed algorithm for resource allocation at each BS that extends the PF
allocation algorithm for a single BS. Despite its simplicity and lack of
coordination across the BSs, we show that our algorithm converges to the
desired PF solution and provide (tight) bounds on its convergence speed. We
also study the characteristics of the optimal solution and use its properties
to prove the optimality of our algorithm's outcomes.
