Two-slope path-loss design of energy harvesting in random cognitive radio networks

Abstract

There has recently been substantial interest in applying the principles of wireless radio frequency energy harvesting in battery-operated devices to cognitive radio networks. Although implementation of energy harvesting technique increases the complexity of network planning, it reduces battery power usage and enables eco-friendly cognitive radio network. In this paper, we report a comprehensive study of energy harvesting cognitive radio network where locations of users of primary and secondary networks follow a Poisson point process. In the design of random cognitive radio network, we focus on the two-slope path-loss function so as to have a realistic scenario of propagation environments. First, a new expression of outage probability is theoretically derived for secondary receiver in active mode. Second, we obtain an explicit expression of harvested energy for secondary receiver in active and inactive modes. Finally, we investigate the harvested energy maximization problem under a particular outage probability constraint, and also obtain an optimal solution of transmission power and density of secondary transmitters. Numerical results for outage probability, harvested energy, and maximization of harvested energy are presented for evaluation of the performance and characteristics of this network.

Introduction

In recent decades, there has been an explosive growth of battery-operated wireless devices, such as cell phones, tablets, and notebooks. One essential element of wireless devices is the battery, which needs to be charged regularly and replaced occasionally. Wireless designers are trying to improve battery longevity for greater utility of wireless devices. Wireless energy harvesting (WEH) technology, a well-being approach for recharging batteries from various radio frequency (RF) energy sources, was first introduced in 1899 in the pioneering work of Nicola Tesla, who demonstrated wireless energy transfer (WET) experimentally [1]. However, energy harvested from RF energy sources (e.g., small or large base stations (BSs) of cellular networks) is not a good choice because wireless devices can harvest little energy. For that reason, cognitive radio (CR) network with WEH is a potential candidate for harvesting energy from licensed¹ and unlicensed² RF energy sources [2]. Unlicensed users (i.e., secondary users) can harvest energy from both licensed and unlicensed RF energy sources and store the harvested energy in rechargeable batteries.

The motivation for implementing CR network with WEH is based on free space signal loss (known as the Friss transmission equation) provided in the Powercast³ wireless power calculator [3]. According to the Friss transmission equation, the received power is formulated as, $P_r=P_t{g}_t{g}_r{(\lambda /4\pi d)}^2,$ where P_t is the transmission power, g_t and g_r are the transmit and receive antenna gains, λ is the wavelength of the carrier, and d is the distance between the transmitter-receiver pair. Received RF power⁴ is converted into usable DC power by RF harvester circuit. After RF-to-DC conversion, total DC power can be expressed as DC power = ξ · P_r, where ξ is the conversion efficiency of RF-to-DC power. It is clear from Fig. 1 that high transmission power is required for harvesting substantial amounts of DC power. Thus, it is not possible to transmit high power from secondary networks (i.e., cellular networks) as the cellular network transmission power is limited. To solve this problem, we could take two different approaches: (1) set up a hybrid access point in a wireless-powered cellular network to transmit energy and information to/from subscribers [4], [5]; and (2) collect RF power from the primary networks (i.e., licensed networks), where CR devices are required [6]. The results, shown in Fig. 2, indicate that the lower carrier frequency option is better for harvesting energy from the same power source. Thus, the deployment of CR with WEH technology is a suitable approach to harvesting DC power.

Energy harvesting from wireless networks has recently been the focus of substantial research on the provision/supply of power in battery-operated wireless devices. A practical scenario of simultaneous wireless information and power transfer is discussed in [7], which provides an overview of resource allocation and cooperative CR networks. RF energy harvesting in various types of wireless networks, for example, single-hop networks, multi-antenna networks, relay networks, and CR networks has been examined and surveyed comprehensively in [8]. A recent comprehensive survey of energy harvesting communications and networking provides a broad perspective of past, present, and future issues [9]. Liu et al. investigated the underlay cognitive relay network to derive outage probability under three power constraints, and also derived throughput in both delay-sensitive and delay-tolerant transmission modes [10]. In addition, Wang et al. analyzed outage probability, rate-energy trade-off, and also three optimization techniques for improving spectrum and energy efficiency [11]. Liu et al. in [12] presented a device-to-device communication design for energy harvesting in large-scale CR networks, and evaluated its power outage probability, secrecy outage probability, and secrecy throughput.

In [13], Krikidis investigated RF energy harvesting for cooperative and non-cooperative protocols when transmitter-receiver pairs are deployed following a Poisson point process (PPP). Lee et al. in [14] derived transmission probability, outage probability, and maximization of network throughput for a PPP in CR networks by considering a single-slope path-loss analytical model. In [15], Sakr and Hossain developed a multi-tier uplink cellular network using a PPP and investigated its transmission probability, coverage probability, and success probability. In [16], Flint et al. studied a wireless sensor network where sources are distributed as a Ginibre α-determinantal point process (DPP). They derived an expression for the expectation and variance of the energy harvesting rate and investigated the upper bound of power outage probability and transmission outage probability. In a recent study of Ginibre DPP, [17] analyzed the performance of self-sustainable communications with RF energy harvesting.

As discussed in Section 1.2 above, previous literature focused mainly on the performance analysis of the single-slope path-loss model. However, to the best of our knowledge, no previous study has evaluated two-slope path-loss model in CR network using a PPP. In this paper, we apply a PPP to develop a secondary network model considering the two-slope path-loss model, and develop some new analytical formulas. The contributions of this paper are summarized as follows:

• We use stochastic geometry to provide a tractable analytical framework for the analysis of energy harvesting from primary transmitters and secondary transmitters in secondary networks. For the two-slope path-loss model, we derive an analytical expression for outage probability in active mode. We also obtain a closed-form expression of outage probability for active mode. Furthermore, we evaluate the performance of outage probability.

• We analyze harvested DC power for active and inactive modes in the secondary network. In addition, we present the harvested DC power in closed-form. Furthermore, we also compare the performance of active and inactive modes numerically.

• Finally, we formulate the optimization problem for the closed-form expressions and present the optimal design with some numerical solutions for energy harvesting via this network. To develop closed-form expressions of outage probability and harvested DC power, we derive the solution to harvested DC power maximization for active mode.

The rest of the paper is organized as follows. Section 2 presents an overview of the CR network model, channel model, time-slot structure, and receiver design. Section 3 analyzes the performance metrics, e.g., outage probability and harvested power of this network. Section 4 discusses the numerical results of CR networks and Section 5 draws conclusions about the findings of this study.