No abstract

We consider the uplink of firefly ultra dense networks which combine the promising features of ultra dense deployment and centralized processing. In these networks, a large number of remote radio units which we denote as firefly nodes (FNs) are spatially distributed over an area. The mobile devices (MDs) in the coverage area are simultaneously connected via sub-6 GHz radio frequency links to all FNs. Unlike the cloud radio access network (C-RAN) architecture, in firefly ultra dense networks, the FNs forward the MDs' data through multi-hop millimeter-wave (mmWave) links to one or multiple root nodes since the coverage radius of each mmWave link is limited. These root nodes then forward the data via optical fiber links further to a central unit (CU), where the MDs' signals are decoded. The amount of data that is received at each FN is potentially huge, and hence, efficient signal processing is needed at each FN before the received signals can be forwarded to other FNs. Therefore, we propose a nonlinear processing strategy, which quantizes the received signals at each FN. In particular, we formulate an optimization problem for a local design strategy for the nonlinear forwarding at the FNs, and present an optimal solution by exploiting strong duality and using the Lagrangian method to convert the optimization problem into an unconstrained problem via its dual formulation. A closed-form solution for the primal variables and a bisection algorithm for finding the optimal dual variables are presented. Moreover, based on the cut-set bound, we develop an upper bound on the achievable sum rate of the considered firefly network. The proposed nonlinear forwarding strategy is shown to outperform a benchmark linear forwarding strategy and to approach the performance upper bound in relevant transmit power regimes at the expense of a higher computational complexity. Our results reveal that having more root nodes in the topology improves the performance of linear and nonlinear forwarding but requires additional optical fiber links to the CU.INDEX TERMS Cloud radio access network (C-RAN), millimeter wave (mmWave), multi-hop system, nonlinear forwarding, ultra dense network (UDN).