1564 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 3, MARCH 2016 Spectrum Sensing Performance in Cognitive Radio Networks With Multiple Primary Users António Furtado, Luís Irio, Rodolfo Oliveira, Member, IEEE, Luís Bernardo, Member, IEEE, and Rui Dinis, Senior Member, IEEE Abstract—Radio spectrum sensing (SS) has been an active topic of research over the past years due to its importance to cogni- tive radio (CR) systems. However, in CR networks (CRNs) with multiple primary users (PUs), the secondary users (SUs) can often detect PUs that are located outside the sensing range, due to the level of the aggregated interference caused by the PUs. This effect, known as spatial false alarm (SFA), degrades the performance of CRNs because it decreases the SUs’ medium access probability. This paper characterizes the SFA effect in a CRN, identifying possible actions to attenuate it. Adopting energy-based sensing (EBS) in each SU, this paper starts to characterize the interference caused by multiple PUs located outside a desired sensing region. The interference formulation is then used to write the probabilities of detection and false alarm, and closed-form expressions are pre- sented and validated through simulation. The first remark to be made is that the SFA can be neglected, depending on the path-loss factor and the number of samples collected by the energy detector to decide the spectrum’s occupancy state. However, it is shown that by increasing the number of samples needed to increase the sensing accuracy, the SUs may degrade their throughput, namely, if SUs are equipped with a single radio that is sequentially used for sensing and transmission (split-phase operation). Assuming this scenario, this paper ends by providing a bound for the maximum throughput achieved in a CRN with multiple active PUs and for a given level of PUs’ detection inside the SUs’ sensing region. The results presented in this paper show the impact of path loss and EBS parameterization on SUs’ throughput and are particu- larly useful to guide the design and parameterization of multihop CRNs, including future ad hoc CRNs considering multiple PUs. Index Terms—Aggregate interference, cognitive radio (CR), energy detector. Manuscript received July 18, 2014; revised November 13, 2014; accepted January 24, 2015. Date of publication February 20, 2015; date of current ver- sion March 10, 2016. This work was supported by the Foundation for Science and Technology of the Portuguese Ministry of Education and Science under Project MANY2COMWIN (EXPL/EEI-TEL/0969/2013), Project ADIN (PTDC/EEI- TEL/2990/2012), Project COPWIN (PTDC/EEI-TEL/1417/2012), and Project IT (UID/EEA/50008/2013), and under Fellowship SFRH/BD/88140/2012. The review of this paper was coordinated by Dr. J.-C. Chen. A. Furtado, R. Oliveira, L. Bernardo, and R. Dinis are with the Centre of Technology and Systems, Instituto de Desenvolvimento de Novas Tecnologias, Departamento de Engenharia Electrotécnica, Faculdade de Ciências e Tecnolo- gia, Universidade Nova de Lisboa, 2829-516 Lisbon, Portugal, and are also with Instituto de Telecomunicações (IT), 1049-001 Lisboa, Portugal (e-mail: a.furtado@campus.fct.unl.pt; rado@fct.unl.pt; lflb@fct.unl.pt; rdinis@fct. unl.pt). L. Irio is with the Centre of Technology and Systems, Instituto de Desen- volvimento de Novas Tecnologias, Departamento de Engenharia Electrotéc- nica, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Lisbon, Portugal (e-mail: l.irio@campus.fct.unl.pt). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2015.2406254 I. I NTRODUCTION C OGNITIVE RADIO (CR) has been proposed as a solution to alleviate the increasing demand for radio spectrum [1]. The nodes equipped with CRs, which are usually denominated secondary users (SUs), must be aware of the activity of the licensed users, which are denominated primary users (PUs), to dynamically access the spectrum without causing them harmful interference. SUs ensure a level of protection to PUs by using spectrum sensing (SS) techniques. SS plays a central role in CRNs. The sensing aims at detecting the availability of vacant portions (holes) of spectrum and has been a topic of considerable re- search over the last years [2]. The traditional SS techniques in- clude waveform-based sensing (WBS) [3], which is a coherent technique that consists of correlating the received signal with a priori known set of different waveform patterns; matched- filter-based sensing (MFBS) [4], which is an optimal sensing scheme where the received signal is also correlated with a copy of the transmitted one; and cyclostationarity-based sens- ing (CBS) [5], which is a technique that exploits the periodic characteristics of the received signals, i.e., carrier tones, pilot sequences, etc. Additionally, several sensing techniques have been recently proposed and briefly summarized in [6] and [7]. MFBS assumes prior knowledge of the primary’s signal, whereas WBS assumes that the received signal matches with one of the patterns previously known. This means that these sensing techniques are not feasible in some bands, where sev- eral communication technologies may operate without a priori knowledge. On other hand, CBS is impracticable for signals that do not exhibit cyclostationarity properties. Energy-based sensing (EBS) is the simplest SS technique, and its main advantage is related to the fact that it needs no a priori knowledge of PU’s signal. This paper considers that SUs adopt EBS. It is well known that EBS can exhibit low per- formance in specific comparative scenarios [8] or when noise’s variance is unknown or very large. EBS has been studied in several CR scenarios, namely on local and cooperative sensing schemes [2]. More recently, several EBS schemes adopting sub- Nyquist sampling have been proposed, which are advantageous in terms of the sensing duration [7]. The energy-based detection principle employed in EBS was first studied by Urkowitz, who formulated the problem as a binary hypothesis testing for the detection of deterministic signals considering white [9] and colored [10] Gaussian noise. The analysis of energy- based detection was extended by Kostylev [11] to signals with random amplitude caused by fading effects. Similar analysis of 0018-9545 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.