Price-based time and energy allocation in cognitive radio multiple access networks with energy harvesting

Cognitive radio (CR), a concept that can solve the conflict between spectrum scarcity and low spectrum utilization, has been researched widely recently [1]. There are mainly three CR models: interweave, overlay and underlay [1]. Among the three CR models, the underlay model is the simplest and the easiest to implement in practice, where the secondary users (SUs) can transmit simultaneously on the same spectrum band with the primary users (PUs) as long as the interference power from the former to the later is under a certain threshold. Meanwhile, energy harvesting is a promising way to support continuous green energy supply to communication systems by continually harvesting energy from nature. There are a lot of works focusing on investigating the energy harvesting CR networks. Specifically, the works in [2,3] studied the harvesting-sensing-throughput tradeoff problems in the energy harvesting interweave CR networks, and the works in [4, 5] studied the energy-data cooperation problems in the energy harvesting overlay CR networks. However, very few work focused on the energy harvesting underlay CR networks. Notably, under the energy causality constraint, ref. [6] used a geometric water-filling power allocation to maximize the SU throughput with the peak transmit power constraint, and ref. [7] proposed a robust power allocation scheme to maximize the SU throughput with the interference power constraint. In this article, we consider an underlay CR multiple access network where N SUs communicate to a cognitive base station (CBS) that shares a narrow spectrum band with the PU. The communications of the SUs are time-slotted with duration T and the inter-SU interference is avoided by allocating each SU a fraction of time in each time slot. The CBS is assumed to harvest energy from nature and then transfer the energy to the SUs through wired power lines. The CBS prices the interference power and allocated energy to regulate the interference and energy consumption of the SUs. The price-based joint time and energy allocation problem subject to the interference power and the energy causality constraints is studied. We formulate the problem as a Stackelberg game to jointly maximize the revenue of the CBS (the leader) and the individual utilities of the SUs (the followers). The Stackelberg equilibrium is then investigated. We derive the optimal interference price, the optimal energy price, the optimal time allocation at the CBS’s side, and the optimal energy allocation at the SUs’ side. It is shown that one SU occupying the entire time slot is optimal. It is also shown that the optimal interference price and energy price are not unique. It is noted that, to