Throughput Analysis for Compressive Spectrum Sensing with Wireless Power Transfer Zhijin Qin * , Yuanwei Liu * , Yue Gao * , Maged Elkashlan * , and Arumugam Nallanathan † * Queen Mary University of London, London, UK † King’s College London, London, UK Abstract—In this paper, we consider a cognitive radio (CR) network in which energy constrained secondary users (SUs) can harvest energy from the randomly deployed power beacons (PBs). A new frame structure which includes four time slots, namely, energy harvesting, spectrum sensing, energy harvesting and data transmission is proposed. In the energy harvesting slot, a new wireless power transfer (WPT) scheme in a bounded power transfer model is proposed to enable power SUs wirelessly. Closed-form expressions for the power outage probability of the proposed WPT scheme are derived. In the spectrum sensing slot, we propose to utilize the compressive sensing (CS) technique which enables sub-Nyquist sampling to further reduce the energy consumption at SUs. Throughput of the secondary network with the proposed frame structure is formulated into a nonlinear constraint problem. Three methods are provided to obtain the maximal throughput of secondary network by optimizing the time slots allocation and the transmit power. I. I NTRODUCTION Energy efficiency and spectrum efficiency are two critical issues in designing wireless networks. Recent developments in energy harvesting provides a promising technique to improve the energy efficiency in wireless networks. Different from harvesting energy from traditional energy sources [1], the emerging wireless power transfer (WPT) further underpins the trend of green communications by harvesting energy from radio frequency (RF) signals [2]. Two practical receiver archi- tectures, namely a time switching (TS) receiver and a power splitting (PS) receiver, were proposed in a multi-input and multi-output (MIMO) system in [3], which laid a foundation in the recent research of WPT. In cellular networks, the authors in [4] proposed a novel design in a more practical scenario which deployed power beacons (PBs) randomly to enable the mobile devices to adopt RF energy harvesting. Along with improving energy efficiency through energy harvesting, cognitive radio (CR) technique can improve the spectrum efficiency and capacity of wireless networks through dynamic spectrum access [5]. Therefore, to achieve both spectrum and energy efficiencies, the secondary users (SUs) in a CR network can be equipped with the energy harvesting capability. Recent work on the CR networks powered by energy harvesting mainly focuses on throughput optimization under various constraints. The authors in [6] considered a RF- powered CR network under an energy causality constraint. The model was formulated as a constrained partially observable Markov decision process and the throughput is maximized by the design of a spectrum sensing policy and a detection threshold. The authors in [7] consider a similar energy con- straint RF-powered CR network by optimizing the pair of the sensing duration and the energy detectors sensing threshold maximize the average throughput of the secondary network. Furthermore, these existing works aim to maximize the throughput by optimizing parameters such as threshold and sensing time which are vary related to spectrum sensing. However, the high sampling rate is difficult to achieve in wideband spectrum sensing. It is noticed that the spectrum exhibits a sparse property in the frequency domain as spectrum utilization is low in practice. Compressive sensing (CS) tech- nique can be implemented to achieve sub-Nyquist sampling and reduce the energy consumption at an SUs by utilizing this sparse property of signals [8]. CS technique was firstly applied to wideband spectrum sensing in [9], where fewer compressed samples would be needed on the basis of Nyquist sampling theory. Subsequently, the CS based wideband spectrum sensing has attracted much attention. In order to improve robustness against noise, a denoised algorithm for CS based wideband spectrum sensing has been proposed in [10]. When considering the energy efficiency and spectrum effi- ciency, it is meaningful to introduce CS to further reduce the energy consumption for spectrum sensing in a CR network. In this paper, we propose a new frame structure which includes four time slots: energy harvesting, spectrum sensing, energy harvesting and data transmission. Based on the proposed frame structure, we introduce a bounded power transfer model and a compressive spectrum sensing model during the energy harvesting slot and spectrum sensing slot, respectively. In the bounded power transfer model, we propose a new WPT scheme where each SU selects a PB nearby with the strongest channel to harvest energy. A stochastic geometry approach is used to model the positions of PBs and evaluate the performance. For the proposed WPT scheme, we derive a new closed-form expression for the power outage probability. In the compressive spectrum sensing model, the CS technique is implemented at each SU to perform sampling at sub-Nyquist rate. As a result, the energy consumption during spectrum sensing period is reduced. In addition, the signal recovery process is performed at a remote powerful fusion center (FC) to allow the continuing energy harvesting in the third time slot. Furthermore, throughput of the proposed frame structure is formulated as a nonlinear constraint problem and is solved by using three different methods to obtain the maximal achievable throughput.