spectrum-map-empowered opportunistic routing for cognitive radio ad hoc networks

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TVT.2013.2296597, IEEE Transactions on Vehicular Technology

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Spectrum Map Empowered Opportunistic Routingfor Cognitive Radio Ad Hoc Networks

Shih-Chun Lin Student Member, IEEE, and Kwang-Cheng Chen, Fellow, IEEE

Abstract—Cognitive radio emerges as a key technology to en-hance spectrum efficiency by creating opportunistic transmissionlinks. Supporting the routing function on top of opportunisticlinks is a must to transport packets in a cognitive radio ad hocnetwork (CRAHN) consisting of cooperative relay multi-radiosystems. However, there lacks thorough understanding of thesehighly dynamic opportunistic links and a reliable end-to-endtransportation mechanism over the network. Aspiring to meetthis need, with innovative establishment of the spectrum mapfrom local sensing information, we first provide mathematicalanalysis to deal with transmission delay over such opportunisticlinks. Benefited from the theoretical derivations, we then proposespectrum map empowered opportunistic routing protocols forregular and large-scaled CRAHNs with wireless fading channels,employing a cooperative networking scheme to enable multi-path transmissions. Simulations confirm that our solutions enjoysignificant reduction on end-to-end delay and achieve dependablecommunications for CRAHNs, without commonly needed feed-back information from nodes in CRAHN to significantly save thecommunication overhead at the same time.

Index Terms—Ad hoc networks, spectrum map, dynamicspectrum access, cooperative relay, opportunistic routing, multi-hop networks, and cognitive radio networks.

I. INTRODUCTION

AS FCC [1] promotes the spectrum usage of data bases toregulate the use of licensed bands for unlicensed users,

cognitive radio (CR) [2], which equips short-range communi-cation and sensing capability, is widely considered for efficientspectrum utilization. Dynamic spectrum access (DSA) allowsmultiple CRs to access the transmission opportunity after de-tecting the spectrum hole from utilization of primary system(s)(PS) [3]. Once successful DSA is achieved, the packets dueto successful leverage of transmission opportunities could betransported to the destination node, which results in a demandfor multi-hop networking of cognitive radio ad hoc network(CRAHN) consisting of CRs and PSs via cooperative relaytechnology [4]–[6]. However, CRAHN routing still remain atechnology challenge now.

To dynamically access the pre-assigned spectrum bands,CR must collect and process information about coexisting

Copyright (c) 2013 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

This research was supported by the Intel, National Taiwan University, andNational Science Council under the contract of NSC 101-I-002-001, NTU102R7501, and NSC 102-2221-E-002-016-MY2.

S. C. Lin was with the INTEL-NTU Connected Context Comput-ing Center and is with the School of Electrical and Computer En-gineering, Purdue University, West Lafayette, IN 47907-2035, e-mail:[email protected]. K. C. Chen is with the Graduate Institute of Communi-cation Engineering, National Taiwan University, Taipei 106, Taiwan, e-mail:[email protected].

users within the spectrum of interests, which requires ad-vanced sensing and signal-processing capabilities [3], [7].Inspired by general spectrum sensing [8], sensing informationof both CR’s transmitter (CR-Tx) and CR’s receiver (CR-Rx) is critical. This suggests to construct the spectrum mapover possible routing paths. The spectrum map exhibits theavailable spectrum with geographic area, through sensing,locationing, and various inference techniques can be applied toconstruct such spectrum map [9]–[14]. Thus, for the dynamicand the opportunistic nature of CRAHN, the spectrum mapserves as an information aggregation to maintain cumulativeinformation in a reliable way and in a resource-efficientway. As the sporadically available link and heterogeneousnature of CRAHN [15] induces another critical challengein the routing algorithm design, cooperative communicationemerges to support transmissions in such highly dynamicwireless ad hoc network. [16] provides the complete surveythat advocates cooperative spectrum-aware communicationprotocols, which considers spectrum management for its cross-layer design. Characterizing the behavior and constraints formulti-hop cognitive radio network from multiple layers, [17]develops a mathematical formulation to minimize the requiredspectrum resource for a set of user sessions. For mobileCRAHNs, [18] proposes SEARCH protocol that jointly under-takes path and channel selection to avoid PSs’ activity regionsduring route formation. [19] further incorporates spectrumawareness in a transport control protocol for CRAHNs. [20]provides Gymkhana scheme as a connectivity-based routingprotocol that routes the information to avid network zoneswithout guarantee stable and high connectivity. [6] presentsan extensive overview for routing in cognitive radio networkswith respect to available spectrum knowledge. Examining ajoint problem of relay node assignment and multi-hop flowrouting, [21] delineates the benefits of exploiting cooperativecommunication in multi-hop wireless networks. [22] analyzesthe throughput of secondary networks and provides the in-formation on how cognitive radio channel can be utilized atthe network level. [23] focuses on three-node chain topologyand provides end-to-end throughput analysis for multi-hopwireless network. To leverage multiple input multiple output incooperative cognitive radio network, [24] studies cooperativeforwarding with two phases transmissions among primary andsecondary systems. To establish spectrum map via coopera-tive sensors, [25] facilitates quality-of-service guarantees incyber-physical systems by proposing cognitive radio resourcemanagement. Novel opportunistic routing [26]–[29] allowsassistance by intermediate nodes in a probabilistic mannerto explore the cooperative diversity efficiently and practi-




cally with significant throughput gain. Aiming at dynamicad hoc networks, [26] deals with the mobility issue throughcontinuously modifying the packet header. Via network cod-ing approach, MORE [27] provides opportunistic routing formulti-casting scenario. Under Rayleigh fading channels, [28]provides analytical models to characterize the performance ofroutings. [29] indicates that the proper time for opportunisticforwarding in cognitive radio networks depends on the propor-tional timescale of the primary bands’ idle time with cognitivecommunication duration. It is noted that opportunistic routingconcept in [29] are close to the ideas of this paper. However,there still lacks a realistic routing algorithm for CRAHNs withrealistic network size, based on theoretically mathematicalanalysis of data transportation with opportunistic communi-cation links due to wireless fading, access, and operations.Furthermore, relying on feedback communication overheadsfrom nodes can significantly reduce the spectrum efficiency,and thus CRAHN nodes shall simply rely on sensing andinference to execute networking functions like routing.

In this paper, aiming at networking in multi-hop CRAHNs,rather than only focusing on theoretical derivations or routingalgorithm designs, we provide the mathematical analysis oftransmission delay and propose spectrum map empoweredopportunistic routing (SMOR) algorithms based on theoret-ical results. We first tackle the general CRAHNs into reg-ular CRAHNs and large-scaled CRAHNs regarding networksize. [30] only deals with multi-hop networking in a meshstructure. [31] and [19] try to embed location informationbut rely heavily on feedback from nodes to imply tremen-dous communication overhead. Here, without relying on thefeedback information from nodes to avoid tremendous com-plexity, regular networks account for the networks with fewnodes and well-known network topologies, while large-scalednetworks account for the one with a great number of nodesand its topology is characterized by spatial distribution ofnodes. CR’s data transportation is thoroughly studied withspectrum map idea [9], [11]–[13], [32] for both types ofCRAHNs and the transmission delay over opportunistic linksis obtained by queueing network theory. This delay attributedominates the transmission capability of forwarders for multi-hop networking and thus it plays a crucial role for reliableand effective networking. Employing such analytic resultswith cooperative communications, two SMOR algorithms arerespectively proposed for regular and large-scaled CRAHNswith wireless fading channels. These algorithms, based onboth delay and possible connections to neighboring nodes,employ cooperative networking scheme to enable multi-pathtransmissions and facilitate reliable end-to-end transportation.We summarize our methodology as follows:

1) Being aware the only feasible sensing informationof available transmission is around the neighborhoodof each node, we examine network topology andopportunistic links with spectrum map under fadingchannels.

2) For regular CRAHNs, the mathematical analysis fortransmission delay of multi-hop communications isexamined via Markov chain modeling and queueing

network theory, and SMOR-1 algorithm is proposedto exploits opportunistic selections for cooperativerelay regarding link transmission qualities.

3) On the other hand, for large-scaled CRAHNs, thecorresponding delay of opportunistic links is derivedvia stochastic geometry and queueing network anal-ysis, and SMOR-2 algorithm is proposed to fulfillgeographic opportunistic routing, exhibiting cooper-ative diversity in such large-scaled networks.

Simulation results confirm that our solutions enjoy less end-to-end delay due to theoretical analysis and yield dependablecommunications for regular and large-scaled CRAHNs. Con-sidering spectrum map together with opportunistic routing forcross-layer designs, our proposed methodology resorts to fun-damental routing algorithms via analytical analysis and createsgreat application potential in spectrum sharing networks, suchas machine-to-machine communications and wireless sensornetworks.

The rest of this paper is organized as follows. The systemmodel is presented in Section II. Mathematical analysis fordata transportation in regular CRAHNs is proposed in Sec-tion III and the corresponding one in large-scaled CRAHNs isexamined in Section IV. Two routing protocols (i.e. SMOR-1and SMOR-2 algorithms) are proposed in Section V to bringthe theoretical results into practice. Performance evaluation isprovided in Section VI and the paper concludes in Section VII.

II. SYSTEM MODEL

To exploit the merit of spectrum map for routing algorithmdesigns, we adopted the underlay CRAHN paradigm [7] thatmandates concurrent PSs’ and CRs’ transmissions only ifthe interference generated by CR-Txs at the PS’s receivers(PS-Rxs) is below some acceptable threshold. That is, CR-Tx’s transmit power should be limited by the interferenceconstraint. In the following, we first present the network modelregarding network topology and spectrum map usages. Then,we give four types of traffic models for both regular andlarge-scaled CRAHNs. Important notations in this paper aresummarized in Table I.

A. Network Model

According to [16], an entire CRAHN topology consistsof a CR source (CRS), a CR destination (CRD), severalCRs as the cooperative relay nodes (CRRs) that can forwardthe packet(s) from CRS to CRD, and primary mobile sta-tions (PSs) with its infrastructure. CRs forward the trafficthrough relay nodes without PSs’ help and shall prevent PSs’transmission from interruption. We assume there are n CRnodes, exclusive CRD in CRAHN. The ith CR node has Tipossible opportunistic paths to CRD and the jth opportunisticpath (denoted by Pij) consisting of Lij links. Therefore, theopportunistic paths for the ith CR node to CRD are labeledby Pi=Pi1,Pi2,...,PiTi.

As mentioned, spectrum map indicates available spectrumwith the geographic area, acting as an information aggregationplatform of all kinds of sensing and inference results toserve CRAHN functions. For regular CRAHNs, we consider




(b) Spectrum map for large-scaled CRAHN.(a) Quantized spectrum map for regular CRAHN.

X-axis(102m)

Y-axis(102m)

dBmSpectrum block used by PSsCRDCRS CRR

Spectrum block unused by PSs

Fig. 1. Spectrum map for spectrum-aware communication in regular and large-scaled CRAHNs.

PS-Rx

PS-Tx

CR-Tx

RTS signaling

CTS signaling

Data

Overheard

transmission

Fig. 2. Wireless overhearing phenomenon between heterogeneous CR andPS devices.

a quantized spectrum map as in Figure 1 (a) and query linkqualities down paths for CR-Txs in Section III. On the otherhand, to seek more opportunities for CRs’ transmissions inlarge-scaled CRAHNs, we study a general spectrum map as inFigure 1 (b) that reveals the actual sensing results (i.e. powerdetection) instead of just two states for quantized maps. Inaddition to the available spectrum map, CR-Tx could exercisethe power level, which prevents the interference to the PS-Rxvia the reciprocal inference as in Figure 2. Specifically, dueto the broadcast nature for every transmission via the samemedium in wireless communication, CR-Tx might overhearthe transmission from a PS-Rx’s location, while PS devicesare in RTS-CTS or other control signaling period. CR-Tx thenpredicts the distance to the PS-Rx from the channel model forPS-Rx to CR-Tx and deploys the distance into the converselychannel model (i.e. from CR-Tx to PS-Rx) to obtain itsinterference to PS-Rx. Such reciprocal inference accompaniedwith spectrum map is examined in in Section IV. In sum,aiming at highly dynamic communication links in CRAHNs,we utilize the cross-layer design to employ the broadcastingnature of wireless communication with cooperative multi-pathtransmission.

B. Traffic Model

Four patterns of data packet transmissions are consideredfor both regular and large-scale CRAHNs:

• Deterministic packet size in slotted system (DS),• Variable packet size in slotted system (VS),• Deterministic packet size in unslotted system (DU),• Variable packet size in unslotted system (VU).

The system perspective (i.e. slotted and unslotted) comes fromCRs’ observation, which characterizes the interaction betweenPSs’ and CRs’ traffic. For slotted perspective in Figure 3 (a)

and (b), it is supposed that CRS and CRD are synchronouswith time slot and the sth time slot [ts,ts+1) equals to ∆tswhere s ∈ I. PS’s transmission activity can be modeled asan embedded two-state discrete-time Markov chain (DTMC),with state “1” represented for spectrum available and state“0” represented for spectrum unavailable when consideringopportunistic link [4], [15]. In each slot (i.e. ∆ts), if PS isactive/idle for transmission(s), the entire time slot is unavail-able/available for CR transmission. On the other hand, forunslotted perspective in Figure 3 (c) and (d), we adopt trafficflow concept that CR’s link utilization can be interrupted byPS’s traffic. Therefore, there is one system perspective foreach studied CRAHN. We further consider two types of packetsizes that are transmitted by PSs’ and CRs’ transmitter-receiverpairs. The deterministic packet size suggests that ∆ts equalsto ∆t for all time slots. It means in each time slot, a singlepacket can be transmitted for PS’s or CR’s traffic, assumingPS and CR have the same packet size. The variable packet sizedeals with the exponential distributed packet size to generalizeour study. Hence, all possibly traffic patterns are thoroughlyincluded by our four traffic patterns.

III. REGULAR COGNITIVE RADIO AD HOC NETWORKS

Regular CRAHN aims at the network with regular sizeas the required information for transmissions is likely awarefor each CR. In the following, under four kinds of trafficpatterns (i.e. DS, VS, DU, and VU), we examine essentialcharacteristics (i.e. spectrum availability, wireless fading, andlink service rate) for networking in regular CRAHN andthen provide the end-to-end delay for data transportation viaqueueing network analysis.

A. Problem Formulation for Regular CRAHN

To mitigate inter-system interference for networking inCRAHN, CRs’ link transmissions should notice PSs’ spec-trum usage and we model spectrum available probability forCRs by formulating Markov chains with spectrum map inSection III-A1. Furthermore, to accommodate the effects fromwireless communication channel, the successful transmissionrate is examined in Section III-A2. The link service rate ofCR’s packet for underlay paradigm is further proposed inSection III-A3.




TABLE IUSEFUL NOTATIONS IN THIS PAPER.

Notation Description Notation Description

TiAmounts of opportunistic paths from Pij The jth path to CRD

ith CR node to CRD from ith CR node

LijAmounts of links for jth path of ∆ts The period of the sth

ith CR node to CRD time slotλ CR’s Poisson packet arrival rate µ CR’s packet service rate

Regular CRAHN

NAmounts of spectrum blocks for

NPSAmounts of spectrum blocks used

quantized spectrum map by PS

l The length of spectrum block MkAmounts of blocks need for CR’s

the kth opportunistic link

σijSpectrum available probability

νijSuccessful transmission rate

of CRi-CRj of CRi-CRj

Large-scaled CRAHNψ PS-Rx’s required power level WT Total spectrum band under concern

|hiT−jR|2The exponential distributed channel gain with parameter Hij

where i (j) is P for PS and S for secondary CRNiT−jR The noise power between node i and j where i (j) is P for PS and S for secondary CR

τPR and τr The SINR requirement for successful PSs’ and CRs’ link transmissions.λPT and λST PS’s and CR’s densitiesPPT and PST PSs’ and CRs’ transmitted powers

(Observation by CRs) time

∆t

(a) Deterministic packet size for slotted system. (DS)

∆t ∆t ∆t

(b) Variable packet size for slotted system. (VS)

Available

Exponential distributed size

Unavailable

(Observation by CRs) time

PSs occupation

(d) Variable packet size for unslotted system. (VU)

Available

Exponential distributed size

Unavailable

(c) Deterministic packet size for unslotted system. (DU)

Available

∆t

Unavailable

∆t ∆t ∆t

(Observation by CRs) time (Observation by CRs) time

Fig. 3. Time diagrams for CRs’ spectrum usages in slotted and unslotted systems.

1) Spectrum availability via Markov chain modeling: Withquantized spectrum map shown in Figure 1 (a), we assume thatthere are N spectrum blocks with NPS used by PS. For a suc-cessful transmission over opportunistic link, the transmissionshould not interrupt other’s traffic from CR-Tx aspect and itshould not be disturbed by other’s traffic from CR-Rx aspect.Specifically, CR-Tx’s transmitted power must not affect PSs’used spectrum blocks along the route to CR-Rx. And CR-Rx’s occupied block must be unused by PSs for successfullyreception from CR-Tx. The length of spectrum block (i.e. l)is suggested by the area that CR-Rx can conduct successfulsignal reception, even under interference. Thus, the numberof blocks Mk needed to be unoccupied for CR’s transmitter-receiver pair of the kth link follows d/l ≤ Mk ≤ ⌈πd2/l2⌉,

where d is the distance between CR’s transmitter and receiver.It provides the orthogonal property between PSs’ and CRs’spectrum usages in spatial domain for the considered underlayparadigm.

As for slotted perspective (i.e. DS and VS cases), thespectrum availability for single spectrum block implies theprobability of the block being available at sample time. Fora single spectrum block, three statistics of spectrum measure-ment are obtained from the map:

• traffic load φ,• correlated spectrum block for PS η,• and usage dependence for PS ξ.

φ specifies the unavailable ratio of the spectrum block and canbe given according to the direct decision from the location




in the map (i.e. φ is either 0 or 1) or φ = NPS/N withthe assumption that single spectrum block is picked by auniform manner. η and ξ specify the dependence of spectrumblock usage for PS. With transition probability matrix of thespectrum block given from the above statistics and the initialstate probability (denoted by ω), the state probability ω(s) inthe sth time slot [ts,ts+1) is obtained by[1− ω(s) ω(s)

]=[φ 1− φ

] [ ξ 1− ξ1− η + ξ η − ξ

]s.(1)

Furthermore, without the knowledge of initial state probability,limiting state probability of a single spectrum block is adoptedfor an irreducible ergodic Markov chains as ω∗ = 1−ξ/2−η.Therefore, the available probability of the kth opportunisticlink in the sth time slot [ts,ts+1) under slotted perspective(i.e. the probability that Mk spectrum blocks being unusedby PSs) follows a Bernoulli process with σS

sk =

∏Mk

(ω(s))or∏

Mk(ω∗), which depends on the knowledge of initial

state probability. Practically, σSsk is accessible for CRs by the

information collection referred to as cognitive radio networktomography [33]. Alternatively, for unslotted perspective (i.e.DU and VU), the spectrum availability for single spectrumblock accounts for the probability of the block being availableat sample time (i.e. ωDU and ωV U ) and the probability ofthe residual available time being larger than the transmissiontime (i.e. ζDU and ζV U ). Thus, the available probability ofthe kth opportunistic link under unslotted perspective followsa Bernoulli process with σDUk =

∏Mk

(ωDUζDU ) for de-terministic packet size or with σV Uk =

∏Mk

(ωV UζV U ) forvariable size.

2) Wireless channel fading: Each attempt to transmit apacket of the kth link of Pij path for the ith CR’s trans-mission is modeled as a Bernoulli process with a successfultransmission rate νk (i.e. the opposite of outage probability forthe received Signal to Noise Ratio (SNR) SNRr lower thanthe threshold κ). For path-loss and shadowing environment,the received power at given distance from transmitter is log-normally distributed [34] and νk = 1 − Q([Pmin − Ps −10 log10K+10α log10(d/d0)]/σβdB

) where Ps is transmittedsignal power and Pmin is a target minimum received powerlevel. d0 is a reference distance for antenna far field and d isthe distance between transmitter and receiver. K is an unitlessconstant that depends on the antenna characteristics and the av-erage channel attenuation. α is the path-loss exponent and β isthe shadowing effect parameter and is modeled as log-normaldistribution with mean 0 dB and standard derivation σβ dB.In addition, as for multi-path case, received signal may sufferfrom Rayleigh fading and νk = 1− exp(−κN0d

α/ΩPsdα0 ).

3) Link service rate for underlay paradigm: In Figure 3,CRs’ transmission should be developed regarding traffic pat-terns, which involve the service time (or rate) of opportunisticlinks. With regard to deterministic packet size, the servicetime is fixed and equals to ∆t for each CRs’ packet trans-mission. On the other hand, for variable packet size, differentfundamental wireless fading channels [35] (e.g. log-normallydistributed model for large scale fading, Rayleigh fading forsmall scale fading, and the fast fading model) are considered toobtain the service rate as follows. Given link’s capacity C, total

concerned band WT , and PS’s activity τ (0 ≤ η ≤ τ ≤ 1),the service rate of opportunistic link under fading channel isgiven by

µ=BηWTE[log2(1 +|h|2(d/d0)−αPs

N0)]

=

BηWT log2(1 +K(d/d0)

−α10β/10Ps

N0)

in large scale fadingBηWT log2(1 +

|h|2(d/d0)−αPs

N0)

in Rayleigh fading

BηWT(d/d0)

−αPs

√πΩ

2N0log2(e)

in fast fading with low SNR

BηWT

[ln( (d/d0)

−αPs

N0) + E[ln(|h|2)]

]log2(e)

in fast fading with high SNR

(2)

where B denotes packet per bit. With these essential elementsof CRs’ opportunistic links, we are in place for the end-to-enddelay in regular CRAHN as follows.

B. Queueing Network Analysis

While CRs’ traffic might be interrupted by PSs’ traffic,end-to-end delay regarding CR’s link access delay accountsfor reliable communications. In the following, via queueingnetwork analysis [36], we first model an opportunistic linkas a queue with additional access delay. Then, we studyopportunistic link delay and opportunistic path delay underspecific traffic pattern for regular CRAHN.

1) Queue models for various traffic patterns: According toSection II-B, we model the kth opportunistic link of the Pij

path for the ith CR node within four cases. Poisson distributionis chosen as the traffic arrival rate (i.e. packets arrive accordingto a Poisson process), since it is generally considered asa good model for the aggregate traffic of a large numberof similar and independent packet transmissions [37]. Fordeterministic packet size (i.e. all packets have equal length),every transmitted packet is periodic served. Alternatively,exponential distribution is chosen for variable packet size dueto its memoryless character [37]. In the sth time slot [ts,ts+1)of slotted system, λsk denotes for CR’s Poisson packet arrivalrate and E[Ss

k] denotes for packet service rate with servicetime Ss

k. For unslotted system, λkCR denotes for CR’s Poissonpacket arrival rate and µk

CR denotes for packet service ratewith service time Sk

CR. λkPS denotes for PS’s Poisson packetarrival rate and µk

PS denotes for packet service rate withservice time Sk

PS . To simplify notations, we do not specifythe kth link and the sth time slot and use λCR = λ in thefollowing derivations.

• Deterministic Packet Size in Slotted or Unslotted Sys-tem (DS or DU): We model the opportunistic link asM /D/1/∞/FCFS queue. In Section III-A2, wirelessfading channel can be treated as an erasure channel andsuffers packet loss. Therefore, each attempt to transmit apacket is a Bernoulli process with successful transmissionrate ν. For slotted systems, assuming Y ∼ Geo(ν) ac-counts for successful transmission rate and X ∼ Geo(σ)accounts for available probability from opportunistic na-ture (with Geo stands for geometric distribution), X and




Y are uncorrelated from independent events and totalservice time S of queue model becomes the summationfrom X1 to XY . Thus, we model M/Geo/1/∞/FCFSwith Geo(cS) where cS equals to σν. As for unslot-ted systems, the successful transmission rate for PSs’or CRs’ traffic is νPS or ν, respectively. The spec-trum availability is a Bernoulli process with probabilityσDU =

∏Mk

(ωDUζDU ). ωDU is the probability ofchannel available for transmission at the observation time,and ωDU = 1−λPS∆t/νPS . ζDU is the probability of theresidual available time larger than the transmission timeas: ζDU = 1−

∑∞k=1[(1− exp−λPS∆tk)ν(1− ν)k−1] =

ν exp−λPS∆t /(1 − exp−λPS∆t +ν exp−λPS∆t). There-fore, we adopt M/Geo/1/∞/FCFS queue model withGeo(cDU ) where cDU equals to σDUν.

• Variable Packet Size in Slotted or Unslotted System(VS or VU): We model such an opportunistic link asM /M /1/∞/FCFS queue. ν still represents the suc-cessful transmission rate. For exponential service rateµ and Bernoulli process with available probability σ,the equivalent service rate is µσ by the formulation ofgeometrical sum of exponential distribution. We haveM/M/1/∞/FCFS queue with service rate µcS forslotted case. In unslotted systems, spectrum availabilityfollows a Bernoulli process with σV U =

∏Mk

(ωV UζV U )where ωV U = 1 − λPS/µPS and ζV U = µCR/(λPS +µCR). Thus, we have M/M/1/∞/FCFS queue modelwith service rate µcV U where cV U equals to σV Uν.

2) Opportunistic link delay: In unslotted perspective, CR’straffic can be intervened by PS’s traffic even in an availableslot of CR’s transmission. CR’s traffic arrival rate is λ undersuccessful transmission rate ν and PS’s traffic arrival rate isλPS . For deterministic packet size, the available probabilityfor CR’s traffic is σDU and the successful transmission rateof PS’s traffic is νPS . For variable packet size, CR’s trafficservice rate is µ with available probability σV U and PS’s trafficservice rate is µPS . The link delay for various traffic patternsis obtained in the following.

Lemma 1: Given CR’s traffic rate λ no more than theservice rate 1/E[S], the opportunistic link delay for DU orVU case is (3) or (4), respectively. Alternatively, the one forDS or VS case is (5) or (6), respectively.

Proof: To avoid the buffer size becoming infinity, thepacket arrival rate of λ should less than or equal to thepacket service rate 1/E[S] for service time S. With deter-ministic packet size, E[S] = ∆t/cDU and E[S2] = ∆t2(2 −cDU )/c

2DU . By Pollaczek-Khinchin (P-K) formula [36], the

expected waiting time of a packet in queue is shown by Wq =λE[S2]/2(1−λE[S]) = λ∆t2(2− cDU )/2cDU (cDU −λ∆t).The delay for DU case is

∆t(2− λ∆t)

2(cDU − λ∆t). (3)

With variable packet size, the waiting time distribution isw(t) = (µcV U − λ) exp−(µcV U−λ)t for t > 0 and Wq =λ/µcV U (µcV U − λ). The delay for opportunistic link within

VU case is1

µcV U+Wq =

1

µcV U − λ(4)

From above, for DS case,

∆t(2− λ∆t)

2(cS − λ∆t)(5)

or for VS case1

µcS − λ. (6)

3) Opportunistic path delay: Since one-hop opportunisticpaths as direct links are provided in Section III-B2, wederive the multi-hop path delay by first considering two-hopopportunistic paths and then extending to N -hop opportunisticpaths. It is noted that to derive path delay for multi-hopopportunistic path, we consider single path transmission assuch single chain link assumption simplifies the calculationsfor metrics and are well-fitted for highly dynamic CRAHN,without loss of generality.

Lemma 2: Given CR’s traffic arrival rate λ no more thanthe lower service rate (i.e. min1≤j≤2 1/E[Sj ]), the path delayof two-hop opportunistic path for DU or VU case is (7) or (8),respectively. Alternatively, the one for DS or VS case is (9) or(10), respectively.

Proof: To avoid the buffer size becoming infinity, thepacket arrival rate of λ should be less than or equal to the lowerservice rate of two hops. That is λ ≤ min1≤j≤2 1/E[Sj ].The path delay can be derived from tandem queue modelby summation of waiting time random variables for eachsingle hop. With deterministic packet size, from Lemma 1,we have E[S1] + λE[S2

1 ]/2(1 − λE[S1]) as the mean delayof the first hop. Since Poisson arrival with rate λ to the pathcan be approximated as a Bernoulli process with probabilityq. The Bernoulli process is further modeled as two-stateDTMC with transition probabilities a

(0)01 and a

(0)10 and thus

q = a(0)01 /(a

(0)10 +a

(0)01 ). a

(0)01 equals to λ and the sum of a(0)01 and

a(0)10 equals to 1. Then with GI/Geo/1 queue modeling [38],

the output process of the first hop is approximated as an on-off process with transition probabilities a(1)11 and a

(1)01 , both

equal to λ as a(1)11 = 1/E[S1] − a

(0)01 (1 − ρ1)/ρ1 = λ

and a(1)01 = λ(1 − a

(1)11 )/(1 − λ) = λ. We get the mean

delay of 2nd hop with ρ2 for the server utilization: E[w2] =

1+ρ2(1−µ2)/a(1)01 (1−ρ2) = 1+(E[S2]− 1)/(1−λE[S2]).

Therefore, two-hop opportunistic path delay for DU case is(∆t(2− λ∆t)

2(cDU − λ∆t)

)+

(1 +

E[S2]− 1

1− λE[S2]

). (7)

For VU case, w1 is the waiting time of first hop with p.d.f.fw1(t) = (µ1cV U 1 − λ1) exp

−(µ1cV U 1−λ1)t and fw2(t) =(µ2cV U 2−λ2) exp−(µ2cV U 2−λ2)t is for the second hop, havingcV U i equals to σV U iνi. The arrival rate for each link is thesame from the Burke’s Theorem [36] (i.e. λ1 and λ2 equal toλ). Then, the delay is obtained as

E[w1 + w2] =1

µ1cV U 1 − λ+

1

µ2cV U 2 − λ. (8)




Follows from unslotted cases, for DS or VS case, the pathdelay is respectively(

∆t(2− λ∆t)

2(cS − λ∆t)

)+

(1 +

E[S2]− 1

1− λE[S2]

)(9)

or1

µ1cS1 − λ+

1

µ2cS2 − λ. (10)

We then derive path delay of N -hop opportunistic paths forunslotted/slotted systems.

Lemma 3: Given CR’s traffic arrival rate λ no more thanthe lowest service rate (i.e. min1≤j≤N 1/E[Sj ]), the pathdelay of N -hop opportunistic path for DU or VU traffic caseis (11) or (12), respectively. Alternatively, the one for DS orVS case is (13) or (14), respectively.

Proof: To avoid the buffer size becoming infinity, thepacket arrival rate of λ should less than or equal to the lowestservice rate of N hops. That is λ ≤ min1≤j≤N 1/E[Sj ].From Lemma 2, since the departure process of the secondhop is observed as another on-off process with transitionprobability a

(2)01 and a

(2)10 , same procedure can be applied for

the N -hop path by iteratively calculating (a(i+1)01 , a

(i+1)10 ) from

(a(i)01 , a

(i)10 ). Owing to Poisson arrival process of the first hop,

the output process of the (i+1)th hop is approximated as anon-off process with transition probabilities a(i+1)

10 and a(i+1)01

equal to λ. We have the mean delay of the (i+2)th hop asE[wi+2] = 1 + (E[Si+2] − 1)/(1 − λE[Si+2]). Therefore,N -hop opportunistic path delay for DU case is(

∆t(2− λ∆t)

2(cDU − λ∆t)

)+

N−2∑i=0

(1 +

E[Si+2]− 1

1− λE[Si+2]

). (11)

For VU case, N -hop opportunistic path delay is directlyobtained as

E[w1 + · · ·+ wN ] =N∑i=1

1

µicV U i − λ. (12)

For DS or VS case, the path delay is respectively(∆t(2− λ∆t)

2(cS − λ∆t)

)+

N−2∑i=0

(1 +

E[Si+2]− 1

1− λE[Si+2]

)(13)

orN∑i=1

1

µicSi − λ. (14)

The above derivations exhibit the necessary delay for packettransmissions through a single path between CR’s source-destination pair, thus playing the essential role in routingalgorithms as illustrated later in Section V.

IV. LARGE-SCALE COGNITIVE RADIO AD HOCNETWORKS

Large-scale CRAHN aims at the network with large size(e.g. thousands or millions nodes) and such network can becharacterized by spatial distribution of nodes [39]. Inspired

by [40] with regard to four kinds of node deployment scenarios(i.e. protocol model of primary interference, protocol model ofn interferences, physical model, and per-node based model),we study essential elements (i.e. power control and radioresource allocation) for networking in large-scale CRAHN andthen examine one-hop forwarding capability of CR relay viastochastic geometry analysis as follows.

A. Problem Formulation for Large-scale Networks

To seek more transmission opportunities for spatial reusein a more reliable way for large-scale CRAHNs, we mitigatethe restriction to CRs’ transmissions (i.e allows CRs operatingwhen the interference to PSs is below a given threshold) viapower control procedures with the reciprocal inference and thespectrum map (i.e. shown in Figure 1 (b)) in Section IV-A1.Moveover, the link service rate of CR’s packet for suchlarge networks is proposed by radio resource allocation inSection IV-A2.

1) Power control procedures: To achieve underlayparadigm within large-scale CRAHNs, CRs’ transmissionsare guided by power control procedures with two steps:

1) Examine the maximum power that CR-Tx can apply(without avoiding PS’s transmission) from the recip-rocal inference.

2) Characterize CR-Rx’s SINR by the spectrum map.The wireless overheard transmissions and wireless channelmodeling are utilized for the reciprocal inference as in Fig-ure 2. Specifically, with these transmissions and PS devices’transmitted power (i.e. PPT in the following), CR-Tx pre-dicts the distance between CR-Tx and PS-Rx by the channelmodel, since the receiving strengths now only depend on thedistances. We consider these procedures for four differentdeployment scenarios (i.e. Protocol Model of one primaryor n interference(s), Physical Model, and Per-node BasedModel) to generalize our study. Protocol models at MAC layerseek the interferers (i.e. interference sources) within a fixedregion. Furthermore, physical model deals with receiver SINR,which accumulates the effects from all interferers by physicallayer information (i.e. location). The avoidance region is notfixed anymore and might depend on node density. Per-nodebased model proposes the effective distance extracted from thegiven map and does not need location information anymore. Itprovides each specific transmitter with dedicated power controlin distributed manner, certifying its practicability. It is notedthat to increase readability, we adopt “theoretical modeling”for protocol and physical models considering their theoreticalsettings and “engineering modeling” for per-node based modelconsidering its feasibility in engineering.

For theoretical modeling, the channel gains of wireless fad-ing follow the exponential distributions; engineering modelingadopts the path-loss model for wireless transmissions. Thus,without precise knowledge of PS-Rx’s location, CR-Tx iscapable to determine the interference caused to PS-Rx(s). Onthe other hand, the nice feature of spectrum map is to actas a spectrum information aggregation platform to tackle theheterogeneous nature of CR and PS devices. Enhanced by thespectrum map, CR-Tx can obtain the information about the




receiving capability of CR-Rxs and therefore make successfultransmissions to desired CR-Rxs.

2) Link service rate from radio resource allocation: Re-garding various traffic patterns (i.e. DS, VS, DU, and VU)between CRs’ and PSs’ as shown in Figure 3, we shall considerradio resource allocation for service process of opportunisticlinks after power control procedures. For theoretical modeling,the outage probability is qT and the equivalent service rateof opportunistic link with capacity C for CR’s packet isµT = qTBC where B stands for packet per bit and dependson packet size. For engineering modeling, qP is used forgeometric service rate in deterministic packet size and theequivalent service rate becomes µP = BW log2(1 + SINR)from the Shannon formula. For unslotted systems, differentfrom the cases in regular CRAHNs that adopt availableprobability to characterize the opportunistic nature, actual PS’sarrival traffic is precisely concerned in large-scale CRAHNs.That is, CR’s link transmission can be interrupted by PS’straffic anytime (i.e. CR should avoid transmission wheneverPS has its own traffic to transmit). For such kind of linktransmissions, non-preemptive priority queue [36] is adoptedwhile PS’s traffic is Poisson arrival with rate λPS and itsservice rate is qPS for deterministic packet size and µPS forvariable one. With the crucial elements of CRs’ opportunisticlinks, we are ready for the link transmission delay that exhibitsone-hop forwarding capability of CR relay over large-scaleCRAHN in the following.

B. Stochastic Geometry Analysis

To tackle large-scale CRAHNs with regard to possibleinterrupts from PSs’ traffic, CR’s link access delay is con-sidered via stochastic geometry analysis [39], [41] in thefollowing. Specifically, for theoretical and engineering modelsin slotted/unslotted systems, we first derive outage probability(i.e. qT and qP ) and obtain average service rate (i.e. µT

and µP ). Then, we examine opportunistic link delay for suchCRAHNs.

1) Protocol Model of one primary interference: One pri-mary interferer exists for both PS-Rxs and CR-Rxs. Thechannel gain |hiT−jR|2 of wireless fading is modeled asexponential distribution with parameter Hij where i (j) isP for PS and S for secondary CR. It involves two stepsto decide the qT for a CR’s transmitter-receiver pair. Wefirst decide the optimal transmission power P ∗

ST for CR-Txfrom PS-Rx’s SINR requirement τPR. Given the probabil-ity qo that CR-Tx overhears PS-Rx’s transmission and theSINR requirement τr for successful CRs’ link transmissions,dPR−ST = [HPSτrNPR−ST /PPT ln(1/qo)]

−1/α, where α isthe path-loss exponent. With outage probability requirementfor PS-Rx ε, the successful transmission probability becomes

exp

(−HPP τPRNPT−PR

PPT d−αPT−PR

)×

HSPPPT d−αPT−PR

HSPPPT d−αPT−PR +HPP τPRPST d

−αST−PR

(15)

and

PST =HSPPPT d

−αPT−PR

HPP τPRd−αST−PR(1− ε)

×

exp


PPT d−αPT−PR

− 1 + ε

)(16)

where dST−PR is measured from overheard transmission.Therefore, P ∗

ST = minPR PST and the optimal PR∗ wouldbe the closest one to the CR-Tx. Next, from P ∗

ST and theinterferer of CR-Rx (i.e. PS-Tx), we get qT . The interferer isthe PS-Tx which affects target CR-Rx most and is likely theclosest one (in effective metric) to the CR-Rx. With τCR,

qT=exp

(−HSSτCRNST−SR

PST d−αST−PR

)×

HPSPST d−αST−PR

HPSPST d−αST−PR +HSSτCRPPT d

−αPT−SR

. (17)

2) Protocol Model of n interferences: There are n interfer-ers for PS-Rxs and CR-Rxs, given ε and τPR, the successfultransmission probability is

exp


PPT d−αPT−PR

)×

∏i

HSPiPPT d−αPT−PR

HSPiPPT d−αPT−PR +HPP τPRPSTid

−αSTi−PR

. (18)

We then obtain P ∗ST . And by given τCR,

qT = exp

(−HSSτCRNST−SR

P ∗ST d

−αST−PR

)×

∏j

HPSjP∗ST d

−αST−PR

HPSjP∗ST d

−αST−PR +HSSτCRPPTjd

−αPTj−SR

(19)

where dST−PR is obtained from overheard transmission.

3) Physical Model: It is assumed that the spatial dis-tributions of interferers follow homogeneous Poisson pointprocesses [41] with density λST for PS-Rx and with den-sity λPT for CR-Rx, ΦST and ΦPT denote the locations.The interference for PS-Rx is IS = IST † + IST =PST † |hST †−PR|2 (dST †−PR)

−α+∑

i∈ΦSTPST |hSTi−PR|2

(dSTi−PR)−α where ST † is the CR-Tx of interests. For given

ε and τPR, successful transmission probability changes into

exp


PPT d−αPT−PR

)×

exp

(−λSTH

2/αPP τ

2/αPR P

2/αST d2PT−PRKα

P2/αPT

)×

HST †PPPT d−αPT−PR

HST †PPPT d−αPT−PR +HPP τPRPST †d−α

ST †−PR

(20)

where Kα = 2π2/α sin(2π/α). Then, P ∗ST is obtained. The

interference of CR-Rx is IP =∑

j∈ΦPTPPTj |hPTi−SR|2




(dPTi−SR)−α. With τCR,

qT = exp

(−HSSτCRNST−SR

P ∗ST d

−αST−PR

)×

exp

(−λPTH

2/αSS τ

2/αCR P

2/αPT d

2ST−PRKα

P∗2/αST

)(21)

and dST−PR is from overheard transmission.

4) Per-node Based Model: Due to signal propagation infading channels, the observed spectrum map is reconstructedbased on the “effective distance” for the geographic areainstead of Euclidean distance. With the power level of trans-mitter PTx, the power at receiver PRx, and the interferencesfrom other transmitters be neglected (i.e. far away from thetarget receiver) in spectrum map, the effective distance isdeff = (PRx/PTx)

−1/α. Transfer the original map intoeffective distance between transmitter-receiver pair, we easilyget the essential location information and exploit the powercontrol in the per-node based model.

For the power level ψr of overheard transmission from thePS-Rx, dPR−ST = (ψr/PPT )

−1/α. We also assume PS-Rx’srequired power level is ψ, its permissible interference level isχ, and CR-Tx’s maximum power is Pmax

CT . For the successfulreceiving of PS-Rx from PS-Tx, the prohibited transmissionregion for CR-Tx under the effective distance is a disk centeredat PS-Rx with radius r1 = (ψ/PPT )

−1/α. The full powerregion (i.e. Pmax

CT ) for CR-Tx is also a disk centered at PS-Rxwith radius r2 = (χ/Pmax

CT )−1/α. Hence, CR-Tx’s maximum

power function is

Q(r) =

0 0 ≤ r ≤ r1χ (r − r1)

αr1 ≤ r ≤ r2

PmaxCT r2 ≤ r ≤ ∞

(22)

where r is the distance from the PS-Rx. With dST−PR fromoverheard transmission, CR-Rx’s SINR is

SINRCR−Rx =d−αST−SRQ(dST−PR)

N + γ(23)

with the interference level at CR-Rx γ read directly from mapand µP is further obtained through radio resource allocation.With τCR,

qP =

0 0 ≤ SINRCR−Rx ≤ τCR

1 τCR ≤ SINRCR−Rx. (24)

CR-Rx’s avoidance region with interference level χ1 is a diskcentered at PS-Tx with radius ra = (χ1/PPT )

−1/α.

5) Opportunistic link delay for various deployment scenar-ios: For theoretical modeling (i.e. including Section IV-B1,Section IV-B2, and Section IV-B3) and engineering modeling(i.e. Section IV-B4), opportunistic link delay for slotted systemis in Lemma 4 and for unslotted system is in Lemma 5 asfollows.

Lemma 4: Given CR’s traffic arrival rate λ no more thanthe service rate 1/E[S], for DS traffic case, the opportunisticlink delay for theoretical or engineering modeling is respec-

tively

∆t(2− λ∆t)

2(qT − λ∆t)or

∆t(2− λ∆t)

2(qP − λ∆t); (25)

for VS traffic case, the one for theoretical or engineeringmodeling is respectively

1

(µT − λ)or

1

(µP − λ). (26)

Proof: Follows from Lemma 1.Lemma 5: Given CR’s traffic arrival rate λ no more than

the service rates 1/E[SCR] and 1/E[SPS ], for DU case,the opportunistic link delay for theoretical or engineeringmodeling is respectively (27) or (28); for VU case, the onefor theoretical or engineering modeling is respectively (29) or(30).

Proof: To avoid the buffer size of non-preemptive pri-ority queue [36] becoming infinity for unslotted systems,the packet arrival rate of λ should be less than or equalto the lower service rate of CR and PS. That is λ ≤min(1/E[SCR], 1/E[SPS ]). With deterministic packet size,E[SPS ] = ∆t/qPS , E[SCR] = ∆t/qT for theoretical model-ing, and E[SCR] = ∆t/qP for engineering modeling. There-fore, the opportunistic link delay for theoretical or engineeringmodeling is respectively

E[SCR] +λPS(E[SPS ])

2(2− qPS) + λ(E[SCR])2(2− qT )

2(1− λPSE[SPS ])(1− λPSE[SPS ]− λE[SCR])(27)

or

E[SCR] +λPS(E[SPS ])

2(2− qPS) + λ(E[SCR])2(2− qP )

2(1− λPSE[SPS ])(1− λPSE[SPS ]− λE[SCR]).

(28)

Alternatively, with variable packet size, the opportunistic linkdelay for theoretical or engineering modeling is respectively

1

µT+

λPS(µT )2 + λ(µPS)

2

µT (µPS − λPS)(µPSµT − λPSµT − λµPS)(29)

or1

µP+

λPS(µP )2 + λ(µPS)

2

µP (µPS − λPS)(µPSµP − λPSµP − λµPS). (30)

With regard to different node deployments, above investiga-tions provide the one-hop forwarding capability of CR relayin terms of required forwarding time (i.e. delay), facilitatingthe relay section for networking in large-scaled CRAHNs asshown in Section V.

V. PROTOCOL DESCRIPTION FOR CRAHNS

To bring analytical derivations for regular and large-scaledCRAHNs into practice, we develop two routing algorithmssuitable for our previous considerations. Specifically, thesealgorithms need to be aware of PSs’ spectrum usages toavoid interference. Furthermore, inspiring from cooperativediversity of CR relay, it is beneficial to exploit cooperativecommunications in CRAHN’s multi-hop transportation. In the




following, SMOR-1 (i.e. for regular networks) and SMOR-2(i.e. for large-scaled networks) are proposed to incorporatespectrum sharing and opportunistic routing [27], [42] intorouting protocol design for CRAHNs.

A. Spectrum Map Empowered Opportunistic Routing-1

Algorithm 1 (SMOR-1:)1) Source partitions its traffic into batches of packets for

transmissions.2) At each Sources available time slot, Source collects link

information (i.e. δi,j and νi,j , i, j ∈ CRS , n, CRD)from the map to prioritize forwarders into the candidatelist regarding node metric mi, i ∈ n, randomly mixespackets in a batch via random network coding [43], andbroadcasts coded packet with the list.

3) While the ACK message is not heard from Destination,a) Source repeats Step 2 until it hears ACK.b) For each relay node z, if z receives a packet

from node y, it decodes the packet, saves unheardinformation in its buffer, and check the list.i) If z lines before y in the list, z advances its

counter by its triggering ratio Φz .c) At each z’s available time slot, z examines whether

its counter is positive.i) If so, z randomly mixes its buffered pack-

ets, broadcasts coded packet with the list, anddecrements its counter by one.

4) Destination continuously decodes the collection ofcoded packets to verify whether it gets all packets ofthe batch. If so, Destination broadcasts ACK back toSource, eliminating the packets buffered in relay nodesand enabling the next transmission batch.

The scheme exploits opportunistic relay selection regardingtransmission qualities of cooperative links into packet delay.Specifically, it designs triggering ratios with counters andproposes node metrics and candidate lists in delay perspective.To establish the candidate list for Source, the node metric isprovided in Proposition 1.

Proposition 1 [Node metric mi for node i]. For nodei ∈ n, it has Ti possible opportunistic paths to CRD andcan be distinguished into a direct link, T (2)

i two-hop paths,up to T

(N)i N -hop paths where N is the largest amount of

opportunistic links constitute opportunistic paths). Then, thenode metric mi is obtained as the minimum path delay ofthese Ti paths.

It is noted that the required path delay is stated in Lemmas1-3. Furthermore, we formulate CR node metric as the smallestpath metric among every possible path to destination. Themetrics specify the delay status of each node’s forwardingpath to destination and therefore indicate “good” forwarders.Considering node metric given in Proposition 1, the candidatelist is consequently proposed as follows.

Proposition 2 [For Step 2 of SMOR-1]. For Source CRS ,the jth node in the candidate list is node i if j = |Vi| wherethe set

Vx = k|k ∈ n and mk ≤ mx. (31)

The candidate list prioritizes CR forwarders with respect tonode metric (i.e. mi, i ∈ n). Triggering ratio and counter ofrelay enable opportunistic forwarding for SMOR-1. Specifi-cally, the relay uses packet reception as a signal to transmitby advancing its counter with ratio. We propose the ratio Φz

for relay z as follows.Proposition 3 [Triggering ratio Φi for node i]. Let j<i

denotes node j has a smaller node metric than i. For relaynode i, its triggering ratio is set as

Φi =Λi∑

j>i Λjϑji(32)

where ϑji equals to cSji in slotted system and equals to cDUji

or cV Uji in unslotted system. Λi, the expected number oftransmissions that i must make to route one packet from sourceto destination, is obtained as

Λi =

∑j>i[Λjϑji

∏k<i(1− ϑik)]

1−∏

k<i(1− ϑik). (33)

Proof: ϑji denotes the workable probability of oppor-tunistic link ji. Considering one packet transmits from sourceto destination, the number of packets that node i must forwardis∑

j>i[Λjϑji∏

k<i(1 − ϑjk)] in expectation. Furthermore,for each forwarded packet, the number of transmissions that imakes is a geometric random variable with success probability1−

∏k<i(1−ϑik). Thus, we obtain Λi and end the proof.

Via multi-hop transmissions of SMOR-1, Source’s datapackets traverse the whole network to Destination, avoidinginterference to PSs by cooperative relay and thus fulfillingreliable communications in regular CRAHNs.

B. Spectrum Map Empowered Opportunistic Routing-2

To deal with networking in large-scaled CRAHNs, weinvolve the concept of opportunistic routing with geographicrouting and propose SMOR-2. Specifically, such scenarioshappen when the network grows larger (million nodes withspatial distribution) and local information alone is not suitablefor reliable end-to-end routing anymore. Then, SMOR-2 ex-ploits the global information (i.e. the direction from the sourceto the destination) for networking in such large network.In the following, we assume Source knows the direction ofDestination in large-scaled CRAHN.

Algorithm 2 (SMOR-2:)1) The Source firstly partitions its traffic into batches of

packets for transmissions.2) At each Source’s available time slot, Source makes its

forwarder set (i.e. i ∈ R(CRS)) by the Destination’sdirection, requests workable probabilities from its for-warders (i.e. ϑCRSi, i ∈ R(CRS)), and prioritizesforwarders in the forwarding candidate list with respectto link metric mCRS ,i. Source then randomly mixespackets in a batch via random network coding [43] andbroadcasts coded packet with the list and the availabilityinformation (i.e. ϑCRSi, i ∈ R(CRS)).

3) While the ACK message is not heard from Destination,a) Source repeats Step 2 until it hears ACK.




b) For each relay node z, if z receives a packetfrom others, it decodes the packet and recodespacket’s incoming direction in θz , saves unheardinformation in its buffer, and check the list.i) If z is in the list, z calculates its triggering

ratio Φz according to the list and advances itscounter by the ratio.

c) At each z’s available time slot, z examines whetherits counter is positive.i) If so, z makes its forwarder set (i.e. i ∈ R(z))

from θz , requests ν0z,i, and priorities forwardersin the new list according to mz,i. z then ran-domly mixes its buffered packets, broadcastscoded packet with the new list and ν0z,i (i ∈R(z)), and decrements its counter by one.

4) Destination continuously decodes the collection ofcoded packets to verify whether it gets all packets of thebatch. If so, Destination broadcasts ACK back to Source,eliminating the packets buffered in relay machines andenabling the next transmission batch.

SMOR-2 utilizes link metrics and candidate lists in delayperspective, extends the random concept of networks to geo-graphic opportunistic routing, and thus fulfills the cooperativediversity in large-scaled CRAHNs. To guide link transmissionsalong the direction from Source to Destination, forwarderselections for Source in Step 2 and for relay nodes in Step3c (i) are given in the following proposition.

Proposition 4. Given Destination CRD’s direction, theforwarder set of Source CRS , denoted by R(CRS), is

R(CRS)=j|j ∈ N(CRS) and

|∠−−−−−−−→CRSCRD − ∠−−−→CRSj| ≤ 90 (34)

where N(i) is i’s neighbors and ∠x is the angle of vector x;for relay z, when it receives a packet from i, θz is updated as

θz ∩ [∠−→xz − 90,∠−→xz + 90] ; (35)

if the intersection gives ϕ, θz is set to [0, 360]. Furthermore,z’s forwarder set, denoted by R(z), is given as

R(z) = j|j ∈ N(z) and ∠−→Sj ∈ θz. (36)

With the aid of Proposition 4, all packets are transmittedalong

−−−−−−−→CRSCRD direction in multi-hop forwarding. In addi-

tion, to establish the candidate list for Source and relay nodes,the link metric on the direct transmission of Source and relaynode z (i.e. mCRS ,i and mz,i) are provided in Proposition 5.

Proposition 5 [Link metric mi,j for Li,j]. For the link Li,j

between node i and node j, the link metric mi,j is obtainedas the opportunistic link delay.

It is noted that the required link delay of Proposition 5is given in Lemma 4 and Lemma 5. Then, the forwardingcandidate lists are proposed as follows.

Proposition 6 [For Step 2 and Step 3c (i)]. For SourceCRS , the jth node in CRS’s forwarding candidate list ismachine i if j = |V CRS

i | where the set

V CRSx = k|k ∈ R(CRS) and mCRS ,k ≤ mCRS ,x. (37)

For relay z receiving a packet from node y, the jth node inz’s candidate list is i if j = |V z

i | where the set

V zx = k|k ∈ R(z)/y and mz,k ≤ mz,x. (38)

Proof: The candidate list prioritizes machine’s forwardersregarding link metric (i.e. mCRS ,i and mz,i). For relay z, z’slist should not include the one that transmits packet to z foravoiding invalid transmissions and thus we end the proof.

As similar to SMOR-1, a CR relay uses packet reception toindicate its forwarding by advancing its counter with triggeringratio and we propose the ratio Φz for relay z as follows.

Proposition 7. For relay node z receiving a packet with thecandidate list from node y , if z is the jth candidate of list,z’s triggering ratio is set as

Φz =∏k<z

(1− ϑyk) (39)

where i<j denotes node i is preferred as y’s forwarder thannode j (i.e. my,i < my,z .)

Proof: As a packet receiving from y, relay z shouldforward only when other relay(s), who have better forwardingqualities regarding link metric, fail the reception from y.Φz gives the probability for that event and thus triggers z’sforwarding.

By concatenating multiple opportunistic routings along thesource-destination direction, SMOR-2 successfully providesdependable data transportation in large-scaled CRAHNs.

VI. PERFORMANCE EVALUATION

We list all simulation parameters and values in TABLE IIand evaluate SMOR-1 and SMOR-2 algorithms, respectively.The usages of both algorithms depend on the network size (orprecisely the network models). When the network are small(i.e. only a few nodes or regular CRAHNs), SMOR-1 servesas a great feasible data transportation. However, when thenetwork grows larger (million nodes with spatial distribution)and local information is not enough for reliable end-to-endrouting anymore, SMOR-2 takes charge of packet deliverywith the aid of global information (i.e. the direction fromthe source to the destination). To validate SMOR-1 protocol,we deliberate it over three-node relay network for variablepacket size in slotted system (i.e. VS case). Through thissimple but meaningful network topology, it clearly reveals thepracticability of SMOR-1 over opportunistic fading links inregular CRAHNs and the advantage of opportunistic forward-ing than predetermined routes strategy through further study inwireless relay network. On the other hand, to validate SMOR-2 protocol, we deploy the protocol with per-node based modelover Poisson network topology [41] for VS case. Given thearea and density settings for PS and CR in TABLE II, thePoisson network topology is established. We endorse the favorof SMOR-2 as a geographic opportunistic routing in largeCRAHNs and further evaluate the superiority of SMOR-2 overprominent routing algorithms in a wireless Poisson network.Simulation results verify remarkable delay improvement overbenchmarks in literatures due to SMOR-1 and SMOR-2 with




TABLE IIPARAMETER SETTING FOR PERFORMANCE EVALUATION OVER REGULAR AND LARGE-SCALED CRAHNS.

SMOR-1 with VS case in regular SMOR-2 with per-node based modelCRAHN and VS case in large-scaled CRAHN

Parameter Value Parameter Valuen+ 1 3 The Area for PPP [41] 36

σSD[0.1, 1] in CRAHN; λST 11 in wireless network

λPT0.3 in CRAHN;

σSR and σRD 1 0 in wireless networkνSD 0.45 ψ 0.01 (dB)

νSR and νRD 0.97 PST and N0 0.42 (dB)λ [0, 9] (pkt/sec) WT 5× 103 (Hz)

µ200 (pkt/sec) in CRAHN; α 3.5

50 (pkt/sec) in wireless network λ in Figure 6 5 (pkt/sec)

0.20.4

0.60.8

1

0

2

4

6

8

0.015

0.02

0.025

0.03

σSD

λ (pkt/sec)

End

to

end d

ela

y (

sec)

SMOR-1

Fig. 4. End-to-end delay of SMOR-1 with respect to λ and σSD in regularCRAHN.

respect to regular and large-scaled CRAHNs, fulfilling reliablecommunications over cognitive radio ad hoc networks.

A. Performance of SMOR-1 Protocol in Regular CRAHNs

SMOR-1 fulfills cooperative networking by opportunisticrouting concept in regular CRAHNs. The spectrum availableprobability (i.e. σxy) represents the opportunistic and dynamicspectrum availability and accounts for the spectrum usage ofPS’s traffic over the geographic area. To include the wirelessfading effects, we further set the successful transmission rate(i.e. νxy) accounting for the distance between node x and y.Finally, CR’s Poisson packet arrival rate (i.e. λ) and packetservice rate of links (i.e. µ) are set for the avoidance ofthe whole network being crashed from traffic overloaded.As verified in Figure 4, SMOR-1 has larger delay in lowavailability of direct link and with heavily traffic flow fromCRS . That is, SMOR-1 identifies good transmission qualityfor CRs through opportunistic nature of links and successfullyprovides a practically workable end-to-end transportation forregular CRAHN.

Moreover, to compare with state-of-the-art algorithms, wedeploy SMOR-1 in wireless networks. σSD, σSR, and σRD

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are all set to 1 for SMOR-1 in wireless relay network. Wecompare our protocol with MORE [27], which utilizes aheuristic-base solution with network coding and serves as thebenchmark for opportunistic routing in wireless networks. InFigure 5, different from other algorithms, SMOR-1 concernsfading channel with successful transmission rate (i.e. νxy) andallows cooperative relay with good transmitted capability toforward Source’s traffic. With increasingly incoming trafficflow, SMOR-1 achieves prominent improvement from its co-operative diversity and elaborates routing mechanism againstdelay performance. It approves that SMOR-1 remarkablyoutperforms other algorithms.

B. Performance of SMOR-2 Protocol in Large-scaledCRAHNs

In order to exhibit the success of SMOR-2 in front of furtherchallenge of large-scaled CRAHNs, we compare SMOR-2with greedy routing algorithm, which aims to route packetswithin the shortest path [44]. Under different opportunisticnatures of the network characterized by activity of PS-Txs,Figure 6 shows the better performance of SMOR-2 fromits cooperative diversity gain with the aid of cooperative




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relays. Due to different available geographical information,Figure 7 demonstrates SMOR-2’s capability for large-scaldednetworks. When source-destination pair is far apart in largearea, the algorithm might not access the destination by justone time. In that case, SMOR-2 could localize forwardingwith concatenation between each time. With λST = 1 andλPT = 0.3, Figure 7 depicts different times of opportunisticrouting needed for the algorithm. It also verifies that moreavailable geographic information implies less operations ofopportunistic routing and yields better performance of SMOR-2. To further evaluate the superiority of SMOR-2 over severalprominent routing algorithms, we deploy SMOR-2 in wirelessPoisson network by setting λPT = 0. Figure 8 depicts thatSMOR-2’s performance approaches the lower bound betterthan others, and suggests preferred cooperative in Poissonnetwork.

VII. CONCLUSION AND FUTURE WORK

This paper provided the complete analysis for transmissiondelay over underlay CRAHNs with wireless fading channels

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and proposed SMOR-1 and SMOR-2 algorithms to establish areliable end-to-end transportation. Cogitating the opportunisticnature, the spectrum map serves as an information aggregationplatform to dynamically update all kinds of sensing and infer-ence results for both algorithms. Aiming at regular CRAHNs,SMOR-1 set orthogonal property between PSs’ and CRs’spectrum usages in spatial domain and perfectly protected PSs’traffic from interruption by CRs’ transmission. On the otherhand, SMOR-2 promoted spatial reuse in given geographicarea by enabling CR concurrent transmissions in large-scaledCRAHNs. Simulations demonstrated remarkable performancedue to network coding inspired cross-layer opportunistic rout-ing with highly dynamic available opportunistic links.

With the feasible transportation over CRAHNs establishedby this paper, the possible future work is classified into threecategories: Upper layer control designs, physical informationretrieval, and realistic implementation. First, while the work-able routing algorithms are designed, there is still a needto guarantee the traffic QoS, such as network throughput.Possible research direction might be to study the relation-ship between end-to-end delay and throughput. Second, aswe extract the physical transmission qualities from spectrummap, such physical information can be further examined frompractical testbed. Practical implementation of spectrum mapmight degrade our benchmark of network delay due to theinaccuracy of map. Last but not least, the realistic imple-mentation serves as the validation of our cross-layer design.Although such issue is often a great challenge, our protocol-oriented design is independent to any practical module andthus enjoy great practicability in implementation. Therefore,this research certifies the feasibility of spectrum maps to servespectrum-aware functions and facilitates a new paradigm formulti-hop transmissions in cognitive radio ad hoc networks.

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Shih-Chun Lin received his B.S. degree in elec-trical engineering and M.S. degree in communica-tion engineering from National Taiwan Universityin 2008 and 2010, respectively. He is currently withthe School of Electrical and Computer Engineering,Purdue University, West Lafayette, United States.His research interests include large-scale sensornetworks, dynamic spectrum access, and statisticalscheduling in wireless systems.




Kwang-Cheng Chen (M’89-SM’93-F’07) receivedthe B.S. from the National Taiwan University in1983, and the M.S. and Ph.D from the Universityof Maryland, College Park, United States, in 1987and 1989, all in electrical engineering. From 1987 to1998, Dr. Chen worked with SSE, COMSAT, IBMThomas J. Watson Research Center, and NationalTsing Hua University, in mobile communicationsand networks. Since 1998, Dr. Chen has been withNational Taiwan University, Taipei, Taiwan, ROC,and is the Distinguished Professor and Associate

Dean in academic affairs for the College of Electrical Engineering andComputer Science, National Taiwan University. Dr. Chen has been activelyinvolved in the organization of various IEEE conferences as General/TPCchair/co-chair. He has served in editorships with a few IEEE journals andmany international journals and has served in various positions within IEEE.Dr. Chen also actively participates in and has contributed essential technologyto various IEEE 802, Bluetooth, and 3GPP wireless standards. He has authoredand co-authored over 250 technical papers and more than 20 granted USpatents. He co-edited (with R. DeMarca) the book Mobile WiMAX publishedby Wiley in 2008, and authored the book Principles of Communicationspublished by River in 2009, and co-authored (with R. Prasad) another bookCognitive Radio Networks published by Wiley in 2009. Dr. Chen is anIEEE Fellow and has received a number of awards including the 2011 IEEECOMSOC WTC Recognition Award and has co-authored a few award-winningpapers published in the IEEE ComSoc journals and conferences. Dr. Chen’sresearch interests include wireless communications and network science.

spectrum-map-empowered opportunistic routing for cognitive radio ad hoc networks

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