A randomized algorithm for joint power and channel allocation in 5G D2D communication

We formulate the joint power and channel allocation problem (JPCAP) for device to device (D2D) communication as a cost minimization problem, where cost is defined as a linear combination of the number of channels used and total power requirement. We first show that JPCAP is a NP-hard problem and providing n(1/epsilon) approximation for JPCAP for all epsilon > 0 is also NP-hard. Then we propose a mixed integer linear programming (MILP) to solve this problem. As solving MILP is a NP-hard problem we propose a greedy channel and power allocation (GCPA) algorithm to assign channels and powers to the links. We design GCPA in such a fashion that there exists an order of the links for which it produces optimum solution. We show that an order is equivalent to many orders and hence design an incremental algorithm (IA) to efficiently search good orders. Finally using IA we develop a randomized joint channel and power allocation (RJCPA) algorithm. We show that if a certain condition holds we can find the optimum in expected polynomial time else a slowly growing exponential time with very high probability. We then theoretically calculate the expected cost and energy efficiency (EE) produced by RJCPA. Through simulation, we show that RJCPA outperforms two existing approaches with respect to both cost and EE significantly. Finally we validate our theoretical findings through simulation.