Elsevier

Computer Networks

Volume 54, Issue 14, 6 October 2010, Pages 2519-2536
Computer Networks

Spectrum sharing in cognitive radio networks with imperfect sensing: A discrete-time Markov model

https://doi.org/10.1016/j.comnet.2010.04.005Get rights and content

Abstract

An efficient and utmost utilization of currently scarce and underutilized radio spectrum resources has stimulated the introduction of what has been coined Cognitive Radio (CR) access methodologies and implementations. While the long-established approach has been based on licensed (or primary) spectrum access, this new communication paradigm enables an opportunistic secondary access to shared spectrum resources provided mutual interference is kept below acceptable levels. In this paper we address the problem of primary-secondary spectrum sharing in cognitive radio access networks using a framework based on a Discrete Time Markov Chain (DTMC) model. Its applicability and advantages with respect to other approaches is explained and further justified. Spectrum awareness of primary activity by the secondary users is based on spectrum sensing techniques, which are modeled in order to capture sensing errors in the form of false-alarm and missed-detection. Model validation is successfully achieved by means of a system-level simulator which is able to capture the system behavior with high degree of accuracy. Parameter dependencies and potential tradeoffs are identified enabling an enhanced operation for both primary and secondary users. The suitability of the specified model is justified while allowing a wide range of extended implementations and enhanced capabilities to be considered.

Introduction

The key purpose of dynamic spectrum management is to maximize spectrum reuse amongst users while ensuring that mutual interference between them remains at acceptable levels [1]. This notion has been motivated by the sporadic use of particular spectrum bands while others are profusely used. In this sense, the traditional fixed spectrum assignment to a licensee which has exclusive exploitation rights for a particular spectrum range may not be satisfactory to respond to the new radio use context that requires enhancement in spectrum efficiency and can lead to spectrum underutilization [2]. Consequently, new technical advances are focused on the development of strategies and policies aiming to the utmost and efficient access to shared spectrum resources. Such new developments are usually coined under the global term of cognitive radio networks, which includes a set of different approaches and implementation alternatives [3].

In this paper we tackle the problem of dynamic spectrum access considering the Hierarchical Access Model [3], where the licensed (or primary) spectrum is opened to secondary users (SUs) provided the interference over the primary users (PUs, or licensees) is kept under acceptable limits. In addition, two approaches for spectrum sharing have been devised: Spectrum Underlay and Spectrum Overlay. Spectrum underlay aims at operating below the floor noise of primary users by using ultra-wideband (UWB) techniques which, on the other hand, limits the transmitted power by secondary users. As for spectrum overlay, it targets at spatio-temporal spectrum holes by allowing secondary users to identify and exploit them in a non-intrusive manner. In the remainder of the paper, it will be assumed that spectrum overlay is used as a basis of our model.

From a regulatory perspective, the Federal Communications Commission (FCC) in the U.S. and Ofcom in the U.K. are currently considering the use of cognitive radio technologies [4]. Accordingly, the unlicensed use of VHF and UHF TV bands, provided no harmful interference is caused, was targeted by the FCC in [5]. This was a first milestone in the development of the IEEE 802.22 standard, proposing a cognitive radio-based physical and medium access control (MAC) layer for use of TV spectrum bands by license-exempt devices on a non-interfering basis [6]. Furthermore, the IEEE activities in developing architectural concepts and specifications for network management interoperability, including CR and dynamic spectrum access, are addressed by SCC41/P1900 standardization groups [7]. Finally, many operative standards such as WiFi (IEEE 802.11), Zigbee (IEEE 802.15.4), and WiMAX (IEEE 802.16) already include some degree of CR technology today [4], in the form of coexistence among radios, Dynamic Frequency Selection (DFS) and Power Control (PC).

The primary-secondary (P-S) spectrum sharing operation can take the form of cooperation or coexistence. Cooperation means there is explicit communication and coordination between primary and secondary systems, and coexistence means there is none [8]. When sharing is based on coexistence, secondary devices are essentially invisible to the primary. Thus, all of the complexity of sharing is handled by the secondary and no changes to the primary system are needed. Among the different forms of coexistence, we adopt the opportunistic exploitation of white spaces in spatial–temporal domain sustained on spectrum sensing, coordination with peers and fast spectrum handover, i.e. the spectrum overlay case. As for cooperation, again different forms of P-S interactions are possible. For example, spatial–temporal white spaces can be signaled through a common control channel from the primary network side, such as the Cognitive Pilot Channel (CPC) or the CSCC (Common Spectrum Coordination Channel) [9], [10], [11], [12], [13], [14], which would provide primary spectrum usage information to SUs. In addition, the interaction between PUs and SUs provides an opportunity for the license-holder to demand payment according to the different quality-of-service grades offered to SUs.

In the abovementioned context, the use of Markov models becomes an important aid in modeling problems dealing with the dynamic access to shared spectrum resources. In this sense, a significant number of papers in the literature have been devoted to the characterization of such scenarios using Markov models as, e.g., in [15], [16], [17], [18], [19], [20], [21]1.

Work in [15], [16], [17], which employ similar CTMC-based models considering infinite, [15], and finite, [16], [17], population models, assume perfect spectrum sensing conditions, i.e. free from sensing errors. In this respect, our contribution goes further in considering the effect of erroneous sensing given by false-alarm and missed-detection probabilities.

In turn, work in [18], [19] also assume CTMC-based models. Therefore, as the transition rates of the CTMC indicate, these works consider that sensing information is instantly available upon user arrival. In this paper, the DTMC allows to capture the sensing instants and the effect of sensing information ageing into the model. This is because in a DTMC we observe the system at discrete time instants which, in our proposed model, correspond to the periodic sensing instants. In addition, work in [18], [19] considers false-alarm and missed-detection probabilities as numerical inputs with no explicit reference to any particular sensing mechanism (e.g. energy detection, pilot detection, etc. [23]). Conversely, our work adopts an energy-based detector for sensing implementation in Rayleigh fading, [24], [25] from which false-alarm and missed-detection probabilities are extracted, thus offering a wider applicability range and a higher degree of practicality.

Finally, although not strictly related to our work, in [20], [21], CTMC models are used to characterize the interactions between primary and secondary users where random spectrum access protocols, as opposed to channelization schemes considered herein, are proposed and evaluated. In this sense, sensing errors along with sensing periodicity and ageing issues are not considered.

In this work, a Markovian framework based on Discrete Time Markov Chains (DTMC) to evaluate the opportunistic spectrum access in a P-S spectrum sharing scenario is proposed. The rationale behind using DTMCs instead of CTMCs is based on the fact that sensing mechanisms operate on a periodic time basis, and where the sensing periodicity is an important design parameter. Therefore, the DTMC models, which observe the state of the system at discrete-time instants, can accurately model the proposed scenarios by considering the observation instants of the DTMC as the sensing instants.

Model validation and evaluation studies considering several parameter dependency issues and tradeoffs are addressed in this paper revealing the usefulness of the proposed model for cognitive radio networks system design, realization and operation. In particular, relevant parameters are identified that influence the performance of the spectrum sharing model. Among these, sensing periodicity (how often do we sense?) and sensing accuracy (how well do we sense?) are shown to be key parameters that greatly affect the behavior of the system. In addition, this work reflects the importance of time-sharing between spectrum sensing (for how long do we sense?) and data transmission (for how long do we transmit?), which tradeoffs the sensing accuracy with the obtained throughput, thus leading to possible parameter optimization which will be also addressed in this work. Finally, the awareness of both primary and secondary traffic load distributions also enables to identify optimized parameter values for an overall enhanced network operation as will be shown in the following.

The remainder of the paper is organized as follows. In Section 2 the system model is described along with the considered procedures and the implementation approach. Subsequently, in Section 3, the DTMC model is formulated along with the main hypothesis and considerations. A number of relevant performance metrics are derived in Section 4 which will be evaluated numerically in Section 5. Finally, Section 6 concludes the paper with some final remarks and future considerations. For the sake of readability, in Appendix A, Table A.2 contains the notation used in this paper.

Section snippets

System model

The considered system involves a Primary Network (PN), serving PUs, and a Secondary Network (SN), serving SUs. Both the PN and the SN operate autonomously and each network implements efficient protocols for the correct and coordinated operation among their own users (i.e. PUs and SUs respectively). Thus, the PN is aware of the spectrum occupancy by PUs and, correspondingly, the SN is aware of the spectrum occupancy of SUs. The PN has been assigned a total number of C channels, partitioning a

DTMC model formulation

The proposed DTMC model is devoted to determine the statistical occupancy of the shared spectrum by PUs and SUs. It is mainly fed by traffic-related input parameters, such as arrival and departure rates (λp and λs along with μp and μs for PUs and SUs correspondingly), and also the number of channels to be shared, C.

It is assumed that arrival processes follow a Poisson distribution and that service times are exponentially distributed. While adopting general distributions for arrival and

Performance metrics

From the resulting transition probability matrix P defined through (23), we obtain the true steady-state probabilities, P(i,j) = limn→∞Pr[Xn = S(i,j)], for each true state S(i,j) in the state space S. The knowledge of such statistical distribution enables the definition of several performance metrics which are addressed in the following.

On the other hand, it is also relevant to determine the steady-state probabilities of the detected states (i.e. including possible sensing errors): P(i,j)=limnPr[

Performance evaluation

In the following, the considered parameter setup for the numerical evaluation and also some implementation aspects for the uncoordinated spectrum awareness case are introduced. Subsequently, numerical results address, in the first place, the model validation by means of a system-level simulator. Secondly, numerical results will be given so as to capture the tradeoff between the time devoted to sensing and the throughput, the impact on the number of considered channels (C) and, finally, the

Concluding remarks and future work

In this work a generalized and flexible framework for the definition and evaluation of opportunistic shared spectrum scenarios has been presented. This framework is capable of supporting a wide range of implementation possibilities and functionalities. In this sense, the suitability of a DTMC model as the core of the framework has been suggested and further justified. The DTMC model has been formulated with a high degree of generality and some performance metrics extracted. An uncoordinated

Acknowledgment

This work has been supported by the Spanish Research Council under COGNOS Grant (ref. TEC2007-60985.

Xavier Gelabert (Alaior, 1978) received the Telecommunications Engineering degree (equivalent to B.S. plus M.S.) from the Universitat Politécnica de Catalunya (UPC), Barcelona, in 2004. He also holds an M.S. degree in electrical engineering, with a major in wireless communications, from the Royal Institute of Technology (KTH), Stockholm, 2003. In 2004, he joined the Radio Communication Research Group in the Department of Signal Theory and Communications, UPC, where he is pursuing his PhD. From

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    Xavier Gelabert (Alaior, 1978) received the Telecommunications Engineering degree (equivalent to B.S. plus M.S.) from the Universitat Politécnica de Catalunya (UPC), Barcelona, in 2004. He also holds an M.S. degree in electrical engineering, with a major in wireless communications, from the Royal Institute of Technology (KTH), Stockholm, 2003. In 2004, he joined the Radio Communication Research Group in the Department of Signal Theory and Communications, UPC, where he is pursuing his PhD. From August to December 2008 he was a visiting researcher at the Broadband Wireless Networking Laboratory (BWN-Lab) at Georgia Institute of Technology. From January to August 2009, he was a visiting researcher at the Instituto de Telecomunicaciones y Aplicaciones Multimedia (iTEAM), Universidad Politécnica de Valencia (UPV). His current research interests are in the field of mobile radio communication systems, with a special emphasis on Common Radio Resource Management (CRRM) strategies in multi-access networks, quality-of-service provisioning, and opportunistic/cognitive spectrum management. He has been actively involved in European-funded projects EVEREST, AROMA, and E3 along with Spanish projects COSMOS and COGNOS. He is a member of the IEEE.

    Oriol Sallent is Associate Professor at the Universitat Politécnica de Catalunya (UPC). His research interests are in the field of radio resource and spectrum management for heterogeneous cognitive wireless networks, where he has published 100 + papers in IEEE journals and conferences. He has participated in many research projects and consultancies funded by either public organizations or private companies.

    Jordi Pérez-Romero received the Telecommunications Engineering and Ph.D. degrees from the Universitat Politécnica de Catalunya (UPC), Barcelona, Spain, in 1997 and 2001, respectively. He is currently an Associate Professor with the Department of Signal Theory and Communications, UPC. He has been involved in several different European projects as well as projects for private companies. He has authored papers in international journals and conference proceedings and has coauthored one book on mobile communications. His research interests are mobile communication systems, particularly packet radio techniques, radio resource and quality-of-service management, heterogeneous wireless networks, and cognitive networks.

    Ramon Agustí received the Engineer of Telecommunications degree from the Universidad Politécnica de Madrid, Spain, in 1973, and the Ph.D. degree from the Universitat Politécnica de Catalunya (UPC), Spain, 1978. In 1973 he joined the Escola Técnica Superior d’Enginyers de Telecomunicació de Barcelona, Spain, where he became Full Professor in 1987. After graduation he was working in the field of digital communications with particular emphasis on transmission and development aspects in fixed digital radio, both radio relay and mobile communications. For the last 15 years he has been mainly concerned with the performance analysis, development of planning tools and equipment for mobile communication systems and he has published about 200 papers in that areas. He participated in the European program COST 231 and in the COST 259 as Spanish representative delegate. He has also participated in the RACE, ACTS, IST European research programs as well as in many private and public funded projects. He received the Catalonia Engineer of the year prize in 1998 and the Narcís Monturiol Medal issued by the Government of Catalonia in 2002 for his research contributions to the mobile communications field. He is part of the editorial board of several Scientific International Journals and since 1995 is conducting a post graduate annual course on mobile communications. He co-authored two books on Mobile communications.

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