Cross-Layer Scheduling for OFDMA-based Cognitive Radio ...

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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.2014.2387879, IEEE Transactions on Vehicular Technology

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Cross-Layer Scheduling for OFDMA-basedCognitive Radio Systems with Delay and Security

ConstraintsXingzheng Zhu, Bo Yang, Cailian Chen, Liang Xue, Xinping Guan, Fan Wu

Abstract—This paper considers the resource allocation prob-lem in an Orthogonal Frequency Division Multiple Access(OFDMA) based cognitive radio (CR) network, where the CRbase station adopts full overlay scheme to transmit both privateand open information to multiple users with average delayand power constraints. A stochastic optimization problem isformulated to develop flow control and radio resource allocationin order to maximize the long-term system throughput of openand private information in CR system and ensure the stabilityof primary system. The corresponding optimal condition foremploying full overlay is derived in the context of concurrenttransmission of open and private information. An online resourceallocation scheme is designed to adapt the transmission of openand private information based on monitoring the status ofprimary system as well as the channel and queue states in theCR network. The scheme is proven to be asymptotically optimalin solving the stochastic optimization problem without knowingany statistical information. Simulations are provided to verifythe analytical results and efficiency of the scheme.

Index Terms—Cognitive radio, physical-layer security, delay-aware network, full overlay, cross-layer scheduling.

I. INTRODUCTION

THE emergency of high-speed wireless applications andincreasing scarcity of available spectrum remind re-

searchers of spectrum utilizing efficiency. The concept ofCR provides the potential technology in increasing spectrumutilizing efficiency [1], [2] because CR allows unlicensedusers (also known as secondary users (SUs)) to access somespectrum which is already allocated to primary user (PU) or

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].

The work was partially supported by National Basic Research Program ofChina under the grant no. 2010CB731803; by NSF of China under 61174127,61221003, 61290322, 61273181, 61374107, 61304131, U1405251; by Min-istry of Education of China under NCET-13-0358; by the Research Found forthe Doctoral Program of Higher Education under Grants 20110073120025and 20110073130005; by the Shanghai Municipal Science and TechnologyCommission, China under 14511107903 and 13QA1401900; by HuaweiInnovation Research Program with no. YB2014030021; by the ScientificResearch Project of Hebei Education Department BJ2014019;

X. Zhu, B. Yang, C. Chen and X. Guan are with Department of Automation,Shanghai Jiao Tong University, and Key Laboratory of System Control andInformation Processing, Ministry of Education of China, Shanghai 200240,China (Emails:{wendyzhu, bo.yang, cailianchen, xpguan}@sjtu.edu.cn). B.Yang, C. Chen and X. Guan are also with the Cyber Joint InnovationCenter, Hangzhou, China. L. Xue is with School of Information and ElectricalEngineering, Hebei University of Engineering, Handan 056038, China (Email:[email protected]). F. Wu is with the Department of Computer Scienceand Engineering, Shanghai Key Laboratory of Scalable Computing andSystems, Shanghai Jiao Tong University, Shanghai 200240, China (E-mail:[email protected]). B. Yang is the corresponding author of this paper.

licensed user who has the authority to access the spectrum byspectrum sensing [3], [4]. As another promising technologyof high speed wireless communication system, OFDMA is acandidate for CR systems [1] due to its flexibility in allocatingspectrum among SUs [5]. Hence, OFDMA-based CR networksare catching great attention [6], [7]. This paper focuses on anOFDMA-based CR network without loss of generality.

In order to exploit the capacity of the whole OFDMA-bsed CR system, this paper aims at maximizing the sec-ondary network capacity in consideration of the whole systemtransmission efficiency. Thus, the following three main issuesshould be considered.

Firstly, an efficient spectrum sharing scheme is essentialfor exploiting the unused spectrum in OFDMA-based CRnetwork. When a SU wants to access some spectrum, it mustensure that the spectrum is not accessed by any PU or adaptits parameter to limit the interference to PU. Both of these twomentioned spectrum utilization manners, known as overlay andunderlay schemes, are conservative in some ways, since theyignore the PU’s ability to tolerate some inference.

Secondly, due to that CR networks as well as many otherkinds of wireless communication systems have a nature ofbroadcast, security issues at physical layer have always beenunavoidable in designing CR systems. Furthermore, to SUs,it is obviously practical that there exist both private and opentransmission requirements. Then, the scheduling among thesetwo different kinds of transmission should be considered.In addtion, delay performance is an indispensable quality ofservice (QoS) index in scheduling different transmissions.

Last but not least, the dynamic nature of OFDMA-basedCR communication system brings another big challenge. Therandom arrival of user requests (from both PU and SU)and time-varying channel states renders dynamic resourceallocation instead of fixed ones in exploiting the OFDMAsecondary network capacity.

Aiming at the above issues, the contributions of this paperare threehold:• First, this paper adopts a novel full overlay spectrum

accessing scheme by exploiting PU’s tolerance to inter-ference. Besides, the theoretic proof of full overlay’soptimality is given in the presence of both open andprivate transmissions.

• Second, a joint encoding model is introduced to allowboth private and open transmissions towards SUs withthe full overlay spectrum sharing scheme. A dynamicresource allocation scheme consisting of flow control



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and radio resource allocation is developed by solvinga formulated stochastic optimization problem under thedelay and power constraints.

• Third, the proposed dynamic resource allocation schemeis proven to be close to optimality although its imple-mentation only depending on instantaneous information.

This paper is organized as follows. Section II presentsthe related work. In Section III, we introduce the systemmodel and relevant constraints in detail. Section IV formulatesthe problem. In Section V, we introduce our cross-layeroptimization algorithm. We give the performance bound andstability results in Section VI. Two different implementationsare proposed in Section VII. In Section VIII, some simulationresults are shown. Finally, we conclude this paper in SectionIX.

II. RELATED WORK

There have been many works on spectrum sharing inOFDMA-based CR networks [8]–[10]. According to [11],[12], the access technology of the SUs can be divided in twocategories: spectrum underlay and spectrum overlay. The firstcategory means that SUs can access licensed spectrum duringPUs’ transmission, while as is mentioned in [12], this approachimposes severe constraints on the transmission power of SUssuch that they can operate below the noise floor of PUs, e.g, in[8], [13], [14]. The second category means that SUs can onlyaccess licensed spectrum when the PU is idle, e.g, in [9], [10],[15]–[17]. Considering both these two strategies suffer fromsome drawbacks, the authors in [18] propose a new cognitiveoverlay scheme requiring SUs to assess and control theirinterference impacts on PUs. In general, the cognitive basestation (CBS) controls the aggregate interference to primarytransmission by allowing SUs to monitor channel qualityindicators (CQIs), power-control notifications and ACK/NAKof primary transmission. In this paper, this novel thought isextended into an OFDMA-based CR system.

On the other hand, dynamic resource allocation plays a crit-ical role in exploiting OFDMA network capacity. The overallperformance as well as the multiuser diversity of the systemcan be improved by proper dynamic resource allocation [17],[19]–[25]. Thus, dynamic resource allocation in OFDMA-based CR system has been attracting more attention recently.The corresponding spectrum sharing schemes in [8]–[10] areall realized by dynamic resource allocation.

Besides the interference constraints, the works of delayaware transmission are also quite relative to this paper. Huangand Fang in [26] investigate both reliability and delay con-straints in routing design for wireless sensor network. Cui etal. in [27] summarize three approaches to deal with delay-aware resource allocation in wireless networks. A constrainedpredictive control strategy is proposed in [28] to compensatefor network-induced delays with stability guarantee. Thosethree methods are based on large deviation theory, Markovdecision theory and Lyapunov optimization techniques. Asto the first two methods, they have to know some statisticalinformation on channel state and random arrival data rate todesign algorithm, while these prior knowledge is expensive

to get, even unavailable. To overcome this problem, manyauthors pay attention to Lyapunov optimization techniques.References [29] and [30] investigate scheduling in multi-hop wireless networks and resource allocation in cooperativecommunications, respectively as two typical applications ofLyapunov optimization in delay-limited system. In this paper,we utilize this tool to dispose the resource allocation problemin OFDMA-based CR networks.

As for secure transmission, Shannon’s information theorylaid the foundation for information-theoretic security [31] andthe concept of wire-tap channel was proposed in [32]. Therehas been some research on exploiting security capacity inOFDMA network by dynamic resource allocation, such as in[33] and [34]. In CR area, the study of secure transmissionfrom information-theoretic aspect is very limited. Pei et al. in[35] first investigate secrecy capacity of the secure multiple-input single-output (MISO) CR channel. Kwon et al. in [36]utilize the concept of security capacity to explore MISO CRsystems where the secondary system secures the primary com-munication in return for permission to use the spectrum. Boththese two works focus on only private message transmission.The security and common capacity of cognitive interferencechannels is analyzed in [37]. The entire capacity of a MIMObroadcast channel with common and confidential messages isobtained in [38]. The paper [39] considers the problem ofoptimizing the security and common capacity of an OFDMAdownlink system by dynamic resource allocation. This paperfurther considers the transmissions of private and open flowsin CR networks with delay constraints.

III. SYSTEM MODEL

The system model consists of multiple primary links andmultiple secondary links as Fig. 1 shows. The total bandwidthB is divided into M subcarriers equally using Orthogonal Fre-quency Division Multiplexing (OFDM). Assume that M = Bholds for simplicity of expression. The subcarrier set of thenetwork is denoted as M = {1, 2, · · · ,M} and m ∈ Mdenotes subcarrier index. The downlink case is considered.The primary link is from a single primary base station (PBS)to K PUs. Secondary links are from a common CBS to NSUs. We denote k ∈ {1, 2, · · · ,K} and n ∈ {1, 2, · · · , N} asthe indexes of PU and SU respectively. The system operatesin slotted time, and T is the length of a time slot. Hereafter,[tT, (t+ 1)T ) is just denoted by t for brevity.

The set of subcarriers occupied by PU k on timeslot tis denoted as ΓPUk (t) = {τk1 (t), τk2 (t), · · · , τkmk(t)(t)} wheremk(t) is the number of subcarriers occupied by PU kand ΓPUk (t) ⊆ {1, 2, · · · ,M}. The power set PPU

k (t) ={Pmk (t)|m ∈M} is the set of transmission power from PBSto PU k, where for m ∈ ΓPUk (t), Pmk (t) > 0, else Pmk (t) = 0.For brevity, we will omit the time index (t) somewherein further discussion. P SU = {pmn |∀n, ∀m} denotes theoverall SUs power allocation policy set and pmn represents thepower allocated by CBS to user n in subcarrier m. DenoteΓSUn = {$m

n |∀m} as the subcarrier assignment policy of SUn, where $m

n is either 1 representing subcarrier m is assignedto SU n, or 0 otherwise. Then let ΓSU = {ΓSUn (t),∀n} be theoverall subcarrier assignment policy of secondary network.



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Due to the orthogonal properties of OFDMA technology,there exists no mutual influence between every two SUs.However, there exists mutual interference between the primaryand secondary networks when PU and SU access in the samesubcarrier.

The channel gains include the one of secondary usern on subcarrier m, hmn and the one of primary user kon subcarrier m, Hm

k . The additive white gaussian noise(AWGN) is σ2. The corresponding subcarrier gain-to-noise-ratio1 (C/I) in slot t are thus defined as amn (t) =

hmn (t)2

σ2

and Amk =Hmk (t)2

σ2 respectively as illustrated in Fig.1. Theset a(t) = {Amk (t), amn (t),∀n, ∀m, ∀k} represents the systemchannel state information (CSI). All channels are assumed tobe slow fading, and thus a(t) remains fixed during one slotand changes between two [40]. In this work, there exists anreasonable assumption that the system CSI is known to BS.As in [41], BS can get full-CSI by utilizing pilot symbolsand CSI feedback process. Besides, at the beginning of everyslot, PU reports Pmk A

mk to PBS. For example, the PU reports a

received-signal-strength index to PBS in packets such as RSSIreports. We assume the CBS will listen to the information toderive Pmk A

mk before accessing subcarrier m [18], [41].

Denote hmkS as the cross-link interference channel gain fromCBS to PU k on subcarrier m and let amkS =

hmkS2

σ2 . Similarly,denote hmnP as the cross-link interference channel gain fromPBS to SU n on subcarrier m and let amnP =

hmnP2

σ2 . It isassumed that amkS and amnP can be got by the CBS. amkS canbe estimated by CBS from the PU feedback signal based onreciprocity. amnP can be estimated by SUs through trainingand sensing and the estimation results are sent to CBS [41].Beyond that, information about cross-link channel state couldalso be measured periodically by a band manager either [8],[42].

Compared to pervious work, this paper considers a morecomplicated and practical situation of SU transmission. TheCBS transmits both private and open data to each SU as Fig.2shows. The private data has security requirement and open datahas long-term time-average delay constraint. Instead of thatboth open and private data have delay constraint, only delayconstraints on open transmissions are considered in this paperfor simplifying the mathematic expressions, since the handlingof delay constraint in secure transmission is totally the same asopen transmission. Actually, in real wireless communicationsystems, there exists some private transmission having no strictdelay constraint, e,g. updating contact information in mobiledevices. At the beginning of every time slot, random datapackets arrive at CBS. CBS decides whether to admit it intothe system or not. Besides, CBS is also in charge of resourceallocation to assign power and subcarriers among SUs. CBSutilizes the information of data queue and CSI to allocateresources. The system performance can be optimized and thequeuing delay of open data can be ensured to fulfill by flowcontrol and resource allocation.

In the side of CBS, the amount of open data packet of SUn, Do

n(t), and private data, Dpn(t) that arrive at CBS during

1Also called gain-to-noise-plus-interference-ratio when SU and PU accessin the same subcarrier.

Primary Network

Secondary Network

Mutual Interference

SU 1SU N

SU n

Subcarrier 1

...

Subcarrier m

...

Subcarrier M

Primary & Secondary

Channel to Noise Ratio

Cross-link Channel to

Noise Ratio

…

…

Fig. 1. General network model

slot t are independent identically distributed (i.i.d) stochasticprocesses, e,g. Bernoulli processes, with the long-term averagearrival rates λon and λpn, and their upper bounds are µmax andDmax, respectively. These packets can not be transmitted totarget users instantaneously due to the time-varying channelconditions and they are enqueued at the CBS. However, onlyparts of these packets are admitted into each queue towardseach user for stability reason to be specified later. The amountsof open and private data admitted by respect queues areT on(t) and T pn(t) and CBS is in charge of determining T on(t)and T pn(t) according to a certain principle which would bespecified in Section V.

A. Capacity model

In OFDMA-based CR networks, SU and PU can access inthe same subcarrier with mutual interference. However, due tothe characteristic of OFDMA networks, each subcarrier cannot be assigned to more than solitary user in any secondaryor primary network. Thus the following formulation is set toensure the limitation in CBS:

0 ≤N∑n=1

$mn ≤ 1, ∀m (1)

CBS will realize the occupied subcarrier set ΓPUk ={m|Pmk > 0,∀m}, and we denote ΓSU = {1, 2, · · · ,M} −⋃Kk=1 ΓPUk . Thus the transmission rates of PU and SUs can

be analysed by dividing M subcarriers into two parts: oneis m ∈

⋃Kk=1 ΓPUk where there exists interference between

PU and SUs; another is m ∈ ΓSU which means SUs canaccess these subcarriers without influencing primary link. Thusaccording to information theory the transmission rate of PU kon subcarrier m is:

Rmk =

{log2(1 +

Pmk Amk

1+amkSpmn′) m ∈ ΓPUk , n′ ∈ Γm

0 m ∈ ΓSU



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where Γm is the set of SUs accessing subcarrier m. Further-more, since in secondary network, only one SU can accessone subcarrier, n′ is the only one element in set Γm.

It should be noticed that the total transmission rate in anOFDMA network equals to the sum rates on all subcarriers.So the transmission rate of PU is:

RPUk =∑

m∈ΓPUk

Rmk (2)

The channel capacities of SU n on subcarrier m can beexpressed as:

Cmn =

{log2(1 +

pmn amn

1+Pmk′ a

mnP

) m ∈⋃Kk=1 ΓPUk , k′ ∈ Γm

log2(1 + pmn amn ) m ∈ ΓSU

where Γm is the set of PUs accessing subcarrier m. Fur-thermore, since only one PU can access one subcarrier, k′

is the only one element in set Γm. Denote RSUn =∑m C

mn

as the sum transmission rate of SU n without considerationof security.

By introducing the joint transmission model, open and pri-vate data of one SU can be transmitted simultaneously. Openmessage is jointly encoded with security message as randomcodes. In this way, although open message may be decodedby eavesdroppers, security message would be perfectly secureif the channel fading is properly utilized [43]. According tothe theory of physical-layer security [34], if the transmissionrate of private data is less than security capacity, the pro-posed joint-encoding model can at least realize physical-layersecurity in theory. [44], [45] propose physical-layer securityrealization applications using error correcting codes and pre-processor, which lays the foundation of realizing physical-layer security of the joint encoding model. For each SU, CBSmakes decision if his secure data could be transmitted in thisslot and this decision is expressed as the secure transmissioncontrol vector ζ = (ζ1, ζ2, · · · , ζN ). The indicator variableζn = 1 implies that private and open messages are encoded atrate Rpn and RSUn − Rpn respectively in timeslot t and ζn = 0means that only open messages can be transmitted at rate RSUn .

When CBS is transmitting private messages to SU n, all theother SUs except SU n are treated as potential eavesdroppers[34]. According to [46], subject to perfect private of SU n,the instantaneous private rate of SU n on subcarrier m is theachievable channel capacity minus the highest eavesdroppercapacity if there is no cooperation among eavesdroppers. Foreach SU n, we define the most potential eavesdropper onsubcarrier m as SU n and n = argmax

n′,n′ 6=namn′ . So the security

capacity of SU n on subcarrier m is:

Rmpn =

{[Cmn − log2(1 +

pmn bmn

1+Pmk′ b

mnP

)]+ m ∈ ΓPUk , k′ ∈ Γm

[Cmn − log2(1 + pmn bmn )]+ m ∈ ΓSU

(3)where [·]+ = max{·, 0}, bmn = amn and bmnP is the cross-linkCSI from PBS to SU n on subcarrier m. Obviously, Rpn =∑m∈M

Rmpn . Thus the achievable private rate of user n is:

Rpn = ζnRpn

Primary Network

Private data flow

Open data flow

Secondary Network SU 1

SU N

SU n

...

...

Cognitive Base station

Valve

Flow controlResource

allocation

Private

& O

pen transm

ission

rp1

and

ro1

Private & Open transmission

Private & Open transmission

Delay

rpn and ro

n

r pN and r o

N

Interference

CSI

Queuing Delay

Open data queue

Private data queue

Delivery Delay

PBS

…

Fig. 2. Transmission model of secondary network

and the open rate of user n is: Ron = RSUn −Rpn.

B. Queuing model

There exist data queues in both PBS and CBS. Althoughwe want to maximize the weighted throughput of SUs, PUqueue stability is a constraint in ensuring that PU’s long-term throughput is not affected by SU’s transmission. It isassumed that the transmission rate of PBS without interferenceis sufficient to serve PU’s demand. However, the primarynetwork and the secondary network will be influenced by eachother if they work on the same channel. The transmissionrate decrease of PU is due to the interference brought bySU transmission, while the CBS can adjust its schedule tolimit interference in order to ensure that PU’s time-varyingrate demands can be satisfied. Later, the notation of queuestability will be used to measure whether PU’s demand can befulfilled. In [18], the interference is limited by that PU queueis kept stable under the influence caused by the only one SUaccess. We continue to utilize this technique in scheduling ourmulti-SU access system.

First, it is necessary to introduce the concept of strongstability. As a discrete time process, Q(t + 1) = [Q(t) −S(t)]+ +D(t) is strongly stable if:

lim supt→∞

1

t

t−1∑τ=0

E{Q(τ)} <∞ (4)

In particular, a multi-queue network is stable when all queuesof the network are strongly stable. According to Strong Stabil-ity Theorem in [47], for finite variable S(t) and D(t), strongstability implies rate stability of Q(t). The definition of ratestability can be found in [47] and omitted here.

Furthermore, according to Rate Stability Theorem in [47],Q(t) is rate stable if and only if d ≤ s holds where d =limt→∞

1t

∑t−1τ=0D(τ) and s = lim

t→∞1t

∑t−1τ=0 S(τ).

Since the data can not be delivered instantly to PUs orSUs, there are data backlogs in the PBS and CBS waitingfor transmitting to respective users.



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1) PU queue: In PBS, the data queue of PU k is updatedas following:

Qk(t+ 1) = [Qk(t)−RPUk (t)]+ +DPUk (t) (5)

where DPUk (t) is the amount of data packets randomly arriving

at PBS during slot t with the destination of PU k. Weassume DPU

k (t) is an i.i.d stochastic process with its upperbound of DPU

max and its long-term average arrival rates λk =limt→∞

1t

∑t−1τ=0D

PUk (τ). As it has been mentioned before, Qk

should be kept stable by limiting SUs’ interference to primarylink. As Rate Stability Theorem shows, Qk is rate stable ifand only if rPUk ≥ λk where rPUk , lim

t→∞1t

∑t−1τ=0R

PUk (τ).

Therefore, if PU system is strongly stable, its long-termtransmission is not affected by SUs.

2) SU data queues: In CBS, there exist actual data queuesof open and private data which are represented by Qon and Qpnrespectively for all n ∈ {1, · · · , N}. These queues are updatedas follows:

Qon(t+ 1) = [Qon(t)−Ron(t)]+ + T on(t) (6)

Qpn(t+ 1) = [Qpn(t)−Rpn(t)]+ + T pn(t) (7)

All Qk, Qon and Qpn have initial values of zero. Wedefine ton , lim

t→∞1t

∑t−1τ=0 T

on(τ), t

pn , lim

t→∞1t

∑t−1τ=0 T

pn(τ)

as the long-term time-average admission rates of open dataand private data respectively. The long-term time-averageservice rates of Qon and Qpn are also defined as: ron ,limt→∞

1t

∑t−1τ=0R

on(τ) and rpn , lim

t→∞1t

∑t−1τ=0R

pn(τ). Q

on and

Qpn should be kept strongly stable in order to ensure the raterequirements of open and private date can be supported by theCR system, which means ton ≤ ron and tpn ≤ rpn hold.

Virtual queues of open data, Xon(t), and private data Xp

n(t)are introduced in (8) and (9) to assist in developing ouralgorithms, which would guarantee that the actual queues Qonand Qpn are bounded deterministically in the worst case.

Xon(t+ 1) = [Xo

n(t)− T on(t)]+ + µon(t) (8)

Xpn(t+ 1) = [Xp

n(t)− T on(t)]+ + µpn(t) (9)

Denote µon and µpn as the virtual admission rates of open dataand private data, which are upper bounded by Do

n and Dpn

respectively. Notice that Xon, Xp

n, µon and µpn do not stand forany actual queue and data. They are only generated by theproposed algorithms. According to queuing theory, when Xo

n

and Xpn are stable, the long-term time-average value of µon and

µpn would satisfy:

νon = limt→∞

1

t

t−1∑τ=0

µon(τ) ≤ ton (10)

νpn = limt→∞

1

t

t−1∑τ=0

µpn(τ) ≤ tpn (11)

To summarise, as shown in Fig. 2 the control space χof the system can be expressed as χ = {PSU ,ΓSU , ζ,T},which includes admission control T = {T on , T pn |∀n}, powercontrol decision PSU , subcarrier assignment ΓSU and securitytransmission control ζ.

C. Basic constraints

1) Power consumption constraint: Let E ,∑∀n,∀m p

mn

as total power consumption of the whole system in one timeslot. There exists a physical peak power limitation Pmax thatE cannot exceed at any time:

0 ≤ E ≤ Pmax (12)

The long-term time-average power consumption also has anupper bound Pavg , which is proposed for energy conservation:

e ≤ Pavg (13)

where e = limt→∞1t

∑t−1τ=0 E{E(τ)}

2) Delay-limited model: The queuing delay is defined asthe time a packet waits in a queue until it can be transmitted.Each SU has a long-term time-average queuing delay ρon forits open data transmission. To each SU, it proposes a delayconstraint ρn as in (14) for its open transmission.

ρon ≤ ρn (14)

IV. PROBLEM FORMULATION

Considering the simplicity and understandability of math-ematic analysis, a special case of one single primary link isconsidered in the following. In the single PU case, the onlyone PU is indexed with number 0. In part C of Section V, thegeneral results of multi-PU case are listed for completeness.

A. Optimization objective and constraints

Following above descriptions, the objective of this paper isto improve throughput of secondary network while ensuringstability of primary network. So the problem is formulated as:Maximize the sum weighted admission rates of all SUs andstabilize the PU data queue Q0 at the same time. Let θn andϕn for all n be the nonnegative weights for private and opendata throughput. Then the optimal problem can be formulatedas:

MaximizeN∑n=1

{θntpn + ϕnton} (15)

Subject to: 0 ≤ tpn ≤ λpn,∀n0 ≤ ton ≤ λon,∀nt = (tpn, t

on) ∈ Υ

lim supt→∞

1

t

t−1∑τ=0

E{Q0(τ)} <∞

(13), (14)

where Υ is the network capacity region of secondary links.Define the service rate vector as υ = (ron, r

pn). The definition

of network capacity region Υ is the region of all non-negativeservice rate vectors υ for any possible control actions [47].When the CBS takes a kind of control policy under a certainchannel condition, the secondary links will have a decidednetwork capacity and the network capacity region is the setof network capacities under all possible control policies andall channel conditions. In the proposed system, the controlpolicy of CBS should fulfill subcarrier assignment rule (1),



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peak power constraint (12) and stabilize all queues includingactual queues and virtual queues. So actually, the controlpolicy that can achieve the network capacity region shouldsatisfy the following constraints:

(1), (12)

lim supt→∞1t

∑t−1τ=0 E{Qon(τ)} <∞

lim supt→∞1t

∑t−1τ=0 E{Qpn(τ)} <∞

lim supt→∞1t

∑t−1τ=0 E{Xo

n(τ)} <∞lim supt→∞

1t

∑t−1τ=0 E{Xp

n(τ)} <∞

Theoretically, we can get the optimal solution to (15) ifwe get the distribution of the system CSI and external dataarrival rate beforehand. However, this information can not beobtained accurately. In this paper an online algorithm requiringonly current information of queue state and channel state isproposed and will be described in detail then.

B. Optimality of SU overlay

Before detailing the control algorithm, it should be specifiedthe conditions that make SU overlay play a positive role inthis cognitive transmission model other than traditional accessmethods. We focus on presenting a sufficient condition onoverlay for constant channel conditions here, then we willextend it to time-varying situation.

In the case of static network condition, the optimal problemof SUs’ weighted throughput is simplified as

Maximize:∑Nn=1{θnrpn + ϕnr

on} (16)

Subject to rPU0 = λ0

where we only consider the optimal case when rPU0 = λ0.Notice here, the system maximal weighted sum data rate underfull overlay scheme must be greater than or at least no worsethan that when SU can only access the subcarrier which is notoccupied by PU. It is easy to understand that full overlay is amore general access scheme than spectrum overlay which isa special access situation. We can get an intuition that whenall subcarriers are assumed to be accessed by PU, SU datarate would be positive under full overlay scheme instead ofzero under traditional overlay scheme. Thus what we want toprove is the sufficient condition of that SUs perform betterin consideration of PU transmission other than accessing thelicensed subcarrier roughly. Let κ be the fraction of time thatPU is actively transmitting, thus:

rPU0 = κ∑

m∈ΓPU0

log2(1 +Am0 P

m0

1 + am0Spmn

) (17)

rpn = {∑

m∈ΓPU0

{(1− κ)[log2(1 + amn pmn )− log2(1 + bmn p

mn )]+

+ κ[log2(1 +pmn a

mn

1 + Pm0 amnP

)− log2(1 +pmn b

mn

1 + Pm0 bmnP

)]+}

+∑

m∈ΓSU

[log2(1 + amn pmn )− log2(1 + bmn p

mn )]+}ζn (18)

ron =∑

m∈ΓSU

log2(1 + amn pmn ) +

∑m∈ΓPU0

[κ log2(1+

pmn amn

1 + Pm0 amnP

) + (1− κ) log2(1 + amn pmn )]− rpn (19)

We have the following lemma:Lemma 1: In high SINR region, a sufficient condition for

full overlay to be optimum in SU n accessing subcarrier m(both security and open transmission) is:

am0S ≤ min{C1nm, C

2nm},∀m (20)

where C1nm = bmn /[(1 + Pm0 b

mnP + bmn Pmax) log2(1 +

bmn Pmax)], C2nm = amn /[(1 + Pm0 a

mnP + amn Pmax) log2(1 +

amn Pmax)].We can have an intuitive explanation on Lemma 1, for SU

n’s accessing subcarrier m. If the cross link (from CBS toprimary link) condition is bad enough (worse than weightedCBS-to-SU channel condition C2

nm and weighted CBS-to-eavesdropper channel condition C1

nm), the full overlay schemewould be the optimal scheme when both security and opentransmission happen. The proof of Lemma 1 can be found inAppendix C of reference [48] and omitted here for simplicity.

It would be obvious to derive the following lemma onsufficient condition of optimality of the whole system overlay.Thus we get:

Lemma 2: In high SINR region, a sufficient condition forfull overlay to be optimum in the whole OFDMA-based CRsystem is:

am0S ≤ minn{C1

nm, C2nm},∀m (21)

Notice that, the sufficient condition does not mean thatsubcarrier m ∈ ΓPU0 would provide a greater data rate thanm′ ∈ ΓSU under the same power allocation scheme. It meansthat for m ∈ ΓPU0 , full overlay would achieve the optimalresult other than any other access policy such as partial overlayor underlay. We assume the sufficient condition of Lemma 2 isfulfilled in this paper and we proceed considering time-varyingchannels then.

V. ONLINE CONTROL ALGORITHM

It is worth noticing that problem (15) has long-term time-average limitations on power consumption and queuing delay.Using the technique similar to [47], we construct power virtualqueue Y and delay virtual queue Zn to track the powerconsumption and queuing delay respectively. These virtualqueues do not exist in practice, and they are just generatedby the iterations of (22) and (23):

Y (t+ 1) = [Y (t)− Pavg]+ + E(t) (22)Zn(t+ 1) = [Zn(t)− ρnµon]+ +Qon(t) (23)

Similar to actual queues, Y and Zn have initial values ofzero. According to Necessary Condition for Rate Stability in[47], if Y is stable, constraint (13) is satisfied. In addition, ifZn is stable, qon = lim

t→∞1t

∑t−1τ=0 E{Qon(τ)} ≤ ρnνn ≤ ρnt

on

holds. According to Little’s Theorem, qon/ton = ρon, when Zn

is stable, the delay constraint (14) would be achieved. It willbe proven that the proposed optimal control algorithm canstabilize these queues in section VI, that is to say the long-term time-average constraints are fulfilled.



7

Using virtual queues Xn, Zn and Y , we decouple problem(15) into two parts: one is flow control algorithm whichdecides the admission of data, and another is resource allo-cation algorithm in charge of subcarrier assignment, powerallocation and secure transmission control in every slot. Allthese control actions aim at secondary links and happen inCBS. The whole algorithm is named CBS-side online controlalgorithm (COCA).

A. Flow control algorithm

When external data arrives at CBS, CBS will decide whetherto admit it according to queue lengthes. Let V be a fixed non-negative control parameter. Let qomax ≥ µmax and qpmax ≥Dmax hold. They are actually the deterministic worst caseupper bounds of relative queue length to be proven later. Theflow control rules of open data and private data are obtainedby solving (24) and (25) respectively:

Minimize T on [Qon − qomax + µmax] (24)

Subject to: 0 ≤ T on ≤ Don

Minimize T pn [Qpn − qpmax +Dmax] (25)

Subject to: 0 ≤ T pn ≤ Dpn

The corresponding solutions to (24) and (25) are easy to get:

T on =

{0 if Qon − qomax + µmax ≥ 0Don otherwise (26)

T pn =

{0 if Qpn − qpmax +Dmax ≥ 0Dpn otherwise (27)

Here we can have an intuitive explanation on flow controlrules. They work like valves. When any actual data queueexceeds some threshold, the corresponding valve would turnoff and no data would be admitted.

As to virtual variable µon and µpn, there are also theirrespective virtual flow control algorithms (28) and (29) soas to update virtual queues Xo

n and Xpn which will play an

important role in resource allocation:

Minimize µon[qomax − µmax

qomaxXon − ρnZn − V ϕn](28)

Subject to: 0 ≤ µon ≤ Don

Minimize µpn[qpmax −Dmax

qpmaxXpn − V θn] (29)

Subject to: 0 ≤ µpn ≤ Dpn

Solutions to (28) and (29) are (30) and (31) respectively:

µon =

{0 if (

qomax−µmaxqomax

Xon − ρnZn − V ϕn) ≥ 0

Don otherwise

(30)

µpn =

{0 if (

qpmax−Dmaxqpmax

Xpn − V θn) ≥ 0

Dpn otherwise

(31)

B. Resource allocation algorithm

The resource allocation policy can be found in solving thefollowing optimization problem.

Maximize U(P SU , ζ) (32)Subject to: (1), (12)

where U(P SU , ζ) =∑Nn=1(

XonQon

qomaxRon +

XpnQpn

qpmaxRpn) +

Q0RPU0 − Y E.

At the beginning of every slot, all Xon, X

pn, Q

on, Q

pn and

Y can be regarded as constants because they all have beendecided in the previous slot. Q0 can be estimated by CBSby overhearing PBS feedback. In section VII we propose animperfect estimation scheme of Q0 and compare the perfor-mances of perfect and imperfect estimations in simulations.Notice that, the resource allocation is determined at thebeginning of every slot and all queues are updated at the endof every slot.

Firstly, we can easily decide the vector ζ maximizing Uby assuming that all elements of ζ are continuous variablesbetween 0 and 1 and in further discussion, we can get adiscrete implementation of ζn.

We take partial derivative in U(P SU , ζ) with respect to ζn:

∂U(P SU , ζ)

∂ζn= (

XpnQ

pn

qpmax− Xo

nQon

qomax)

M∑m=1

Rmpn (33)

Observing (33),∑Mm=1 R

mpn is no-negative and U is mono-

tonic in ζn, and thus the optimality condition of securetransmission control is:

ζ∗n =

{1 if (

XpnQpn

qpmax− XonQ

on

qomax) ≥ 0

0 otherwise(34)

Then we use ζ∗ to assign subcarrier and power which isthe solution to the following optimization problem PS,

PS: Maximize U(P SU )

Subject to: (1), (12)

where U(P SU ) = U(P SU , ζ∗). PS is a typical Weighted SumRate (WSR) maximization problem, and it is difficult to find aglobal optimum since U(P SU ) is neither convex nor concaveof P SU . Obviously, PS has a typical D.C. structure whichcan be optimally solved by D.C. programming [49]. In [50]there lists a dual decomposition iterative suboptimal algorithmsolving this kind of constrained nonconvex problem instead ofD.C. programming. In addition, because of the characteristicsof OFDMA networks, the duality gap is equal to zero evenif PS is nonconvex when the number of subcarriers is closeto infinity [51]. So we take a more computationally effectivedual method to solve PS and due to space limitation, we givethe key steps here only.

We define Rmpn = ζ∗nRmpn and Rmon = Cmn − Rmpn . Then

the Lagrange function of PS is expressed as:

J(δ,P SU ) =

M∑m=1

{N∑n=1

[XonQ

on

qomaxRmon +

XpnQ

pn

qpmaxRmpn − Y pmn ]



8

+Q0Rm0 }+ δ(Pmax − E) (35)

where δ is the non-negative Lagrange multiplier for the peakpower constraint in problem PS. The dual problem of PS is:minδ≥0

H(δ), where H(δ) = maxPSU≥0

{J(δ,P SU )}.

When δ is fixed, we can decide the parameters P SU

maximizing the objective of H(δ). Observing H(δ), we findthat it can be decoupled into M subproblem as:

H(δ) =

M∑m=1

maxPmSU

Jm(δ,PmSU ) + δPmax

=

M∑m=1

maxPmSU

N∑n=1

Jmn (δ, pmn ) + δPmax (36)

where PmSU = {pmn |1 ≤ n ≤ N}, Jm(δ,Pm

SU ) =∑Mm=1 J

mn (δ, pmn ), Jmn (δ, pmn ) =

XonQon

qomaxRmon +

XpnQpn

qpmaxRmpn −

(Y + δ)pmn +Q0Rm0 (n) and

Rm0 (n) =

{0 m ∈ ΓSURm0 m ∈ ΓPU0 , $m

n = 1(37)

For m ∈ ΓSU , we can get pm∗n by taking partial derivativeof J(δ,P SU ) with respect to pmn and making (38) equal tozero:

for m ∈ ΓSU :

∂(J(δ,P SU ))

∂pmn=XonQ

on

qomax

1

ln 2{ amn1 + pmn a

mn

− ζn[amn

1 + pmn amn

− bmn1 + pmn b

mn

]}+ XpnQ

pn

qpmax

1

ln 2ζn[

amn1 + pmn a

mn

− bmn1 + pmn b

mn

]

− (Y + δ) (38)

However, for m ∈ ΓPU0 , a global optimal solution pm∗nmaximizing Jmn can be got easily by an exhaustive searchsuch as clustering methods or enumerative methods [52] andit is computationally tractable [51], [53].

Substituting (34) and pm∗n into Jmn (δ,P SU ), the results aredenoted as Jm∗n . For any subcarrier m, it will be assigned tothe user who has the biggest Jm∗n (δ,P SU ). Let n∗m be theresult of subcarrier m’s assignment which is given by:

n∗m = argmaxn

Jmn ,∀n and $m∗n =

{1 if n = n∗m0 otherwise

(39)

Let E∗ =∑Nn=1

∑Mm=1 p

m∗n $m∗

n . As to the value of δ, weuse subgradient method to update it as in (40),

δ(i+ 1) = [δ(i)− ς4δ(i)]+ (40)

where 4δ(i) = Pmax − E∗(t, i). 4δ(i) is the subgradient ofH(δ) at δ and ς is the step size which should be a smallpositive constant. In addition, index i stands for iterationnumber. When the subgradient method converges, the resourceallocation is completed.

From the above description, we can find some principles ofresource allocation.

Remark 1: In (34), both virtual and actual queues of open aswell as private data reflect the gap between the correspondinguser’s demand on data rate and the data rate that the system

can provide. Thus, XonQon

qomaxand XpnQ

pn

qpmaxcan be regarded as the

transmission urgency of open data and private data. Onlywhen the transmission urgency of private data exceeds opendata, CBS would allocate some resource to transmit privatedata. Otherwise, CBS would use the user’s entire resource totransmit open data due to delay constraint. In PS, it is easy tofind that a bigger Y results in less power allocated to everyuser, which will reduce the system power consumption. Alsowe let Q0 to be the weights of RPU0 in PS. It means thatif the transmission pressure of PU is high, CBS will allocateless power in subcarrier set ΓPU0 to avoid causing too muchinterference on primary link.

Remark 2: In the sub-problem of PS, the transmission powerof PBS is assumed to be external variables. Even for theworst case that PBS does not control its transmission poweractively, the proposed resource allocation algorithm aims tomaximize Q0R

PU0 in PS by adjusting the interference from

the secondary networks to primary networks. Thus, it can befound that the proposed algorithm actually does not affect theenergy consumption of primary networks too much.

C. Control algorithm of Multi-PU case

Flow control algorithm is the same as (26), (27), (30) and(31).

Resource allocation of multi-PU implementation is thesolution to problem MPS:

MPS:Maximize:

N∑n=1

XonQ

on

qomaxRon +

N∑n=1

XpnQ

pn

qpmaxRpn +

K∑k=1

QkRPUk − Y E

(41)Subject to: (1), (12)

In next section, the algorithm performance with single PUis analysed. It is easy for readers to prove that multi-PUimplementation ensures primary data queue stability and fur-thermore enjoys a similar performance as single PU situation.

VI. ALGORITHM PERFORMANCE

Before the analysis it is necessary to introduce some aux-iliary variables. Let t∗ = (tp,∗n , to,∗n ) be the solution to thefollowing problem:

maxt:t∈Υ

∑Nn=1 θnt

pn + ϕnt

on,

Subject to: e ≤ PavgAnd t∗(ε) = (tp,∗n (ε), to,∗n (ε)) denotes the solution of:

maxt:t+ε∈Υ

∑Nn=1 θnt

pn + ϕnt

on

Subject to: e ≤ PavgAccording to [54], it is true that:

limε→0

N∑n=1

{θntp,∗n (ε)+ϕnto,∗n (ε)} =

N∑n=1

{θntp,∗n +ϕnto,∗n } (42)



9

TABLE IALGORITHM DESCRIPTIONS

Proposed online control algorithm in timeslot t

1) Flow control:Use (26), (27), (30), (31) to calculate T o

n , T pn , µon and µpn

respectively.2) Resource allocation:

a) Set the Lagrange multiplier δ = δini, (δini: An initial value of δ).b) For each (n,m)

i) Use (34) to calculate ζ∗n.ii) Use (38) or exhaustive search to find pm∗

n .iii) Use (39) to calculate $m∗

n .c) Use (40) to update δ and calculate 4δ(i).d) If |4δ(i)| > 4δc, goto b), else proceed.

(4δc: converge condition of 4δ)3) Update the queues:Use (6), (7), (8), (9), (22) and (23) to update all queues including Qo

n,

Qpn, Xo

n, Xpn, Y , Zn.

The algorithm performance will be listed in Theorem 1 andTheorem 2.

Theorem 1: Employing the proposed algorithm, both actualqueues of open data Qon(t) and private data Qpn(t) in CBShave deterministic worst-case bounds:

Qon(t) ≤ qomax, Qpn(t) ≤ qpmax,∀t,∀n (43)

Theorem 2: Given

qomax > µmax +Comax

2 + µ2max

2ε, (44)

qpmax ≥ Dmax +Cpmax

2 +D2max

2ε, (45)

ρn >qomaxνo,∗n (ε)

,∀n (46)

where ε is positive and can be chosen arbitrarily close to zero.The proposed algorithm performance is bounded by:

lim inft→∞

1

t

t−1∑τ=0

N∑n=1

{θnT pn(τ) + ϕnTon(τ)}

≥N∑n=1

{ϕnto,∗n (ε) + θntp,∗n (ε)} − B

V(47)

where B is a positive constant independent of V and itsexpression can be found in appendix B.

In addition, the algorithm also ensures that the long-termtime-average sum of PU queue Q0 and virtual queues Xo

n,Xpn, Zn, Y has an upper bound:

lim supt→∞

1

t

t−1∑τ=0

{N∑n=1

(Xon +Xp

n + Zn) + Y +Q0}

≤B + V

N∑n=1{[θntp,∗n + ϕnt

o,∗n ]}

σ(48)

where o ≤ σ ≤ ε. The proof of Theorem 1 is in appendix A.Theorem 2 and the definition of σ can be found in appendixB.

Remark 3 (Network stability): According to the definitionof strongly stability as shown in (4), (43) and (48) indicatethe stabilities of all queues in the network system. As aresult, the network system is stabilized and the long-term time-average constraints of delay and power are satisfied. Noticehere that Q0’s stability is proved means the PU queue stabilityconstraint is fulfilled. Q0’s stability means that the long-termthroughput performance is uninfluenced. In addition, if PU’sarrival rates are within the stability region of PU networks,Q0’s stability can be ensured by the proposed schedulingalgorithm for any transmission power of PU base station.Therefore, the transmission power of PU network is notaffected in this situation. Furthermore, (43) states that all theactual queues of open data and private data have deterministicupper bounds, and this characteristic means that the CBS canaccommodate the random arrival packets with finite buffer.

Remark 4 (Optimal throughput performance): (47) states alower-bound on the weighted throughput that our algorithmcan achieve. Since B is a constant independent of V , ouralgorithm would achieve a weighted throughput arbitrarilyclose to

∑Nn=1{ϕnto,∗n (ε) + θnt

p,∗n (ε)} for some ε ≥ 0.

Furthermore, given any ε ≥ 0, we can get a better algorithmperformance by choosing a larger V without improving thebuffer sizes. In addition, as it is shown in (42), when ε tendsto zero, our algorithm would achieve a weighted throughputarbitrarily close to

∑Nn=1{ϕnto,∗n + θnt

p,∗n } with a tradeoff

in queue length bounds and long-term time-average delayconstraints as shown in (44)-(46). Thus we can see that withsome certain finite buffer sizes, the proposed algorithm canprovide arbitrarily-close-to-optimal performance by choosingV , and V ’s influence on queue length is shifted from actualqueues to virtual queues.

VII. IMPLEMENTATION WITH IMPERFECT ESTIMATION

CBS needs the information of queue length from primarynetworks to decide the resource allocation among SUs. [17]considers a situation that queue length information is sharedamong all the nodes, but in CR environment it is impossible toknow the non-cooperative PU’s queue information precisely.Compared with getting perfect information about Qk, it ismore realistic to know the time-average packet arrival rateof PUs. Considering this, in this section, we propose animperfect estimation of Qk by CBS. And the performanceof this estimation will be showed in simulation section. If thePU k is busy, the estimated queue length in CBS is:

Qk(t+ 1) = [Qk(t)−RPUk (t)]+ + (λk + ι) (49)

where ι is an over-estimated slack variable to promise primarylink stability. CBS can get the precise information when PU isidle by listening to primary link ACK to find that no power isused to transmit PU k’s data packets. In this situation, Qk =Qk = 0 perfectly holds.

As to the control algorithm, we use Qk to substitute Qkin resource allocation algorithm. For simplicity, we name thisimplementation COCA-E (CBS-side online control algorithmwith estimated PU queue).



10

0 500 1000 1500 2000 2500 3000 3500 4000 45000

200

400

600

800

1000Q

8p,Q

8o,Q

0 a

nd

Z8

Time slot

(A) Actual &Virtual Queues of SU 8 and PU Queue,V=50

Q8

pQ

8

o Q0

Z8

0 500 1000 1500 2000 2500 3000 3500 4000 45000

10

20

30

40

50

60

X8o,X

8p a

nd

Y

Time slot

(B) Virtual queues of SU 8,V=50

X8

pX

8

oY

Fig. 3. Queue evolutions over 4500 slots

VIII. SIMULATION

In this section, we firstly simulate COCA performance inan examplary CR system with a single primary link andsecondary network consisting of one CBS, eight SUs and64 subcarriers. All weights of open data and private dataare set to be 0.8 and 1 respectively. The main algorithmparameters of secondary network are set as: Pavg = 0.8W ,Pmax = 1W , ρn = 60,∀n, qomax = 200, qpmax = 1000,µmax = 50, Dmax = 20 and λon = n ∗ 0.1 ∗ Dmax, λ

pn =

n ∗ 0.1 ∗ µmax, for n ∈ {1, 2, · · · , 8}. The long-term time-average arrival rate of PU λ0 is set to be 140 and DPU

max = 200.We simulate the multipath channel of primary and secondarynetworks as Rayleigh fading channels and the shadowingeffect variances are 10 dB. The cross-link channels betweenPBS to SUs and CBS to PU are simulated as long-scale fading.All parameters in the following parts are set the same as thesementioned here, except for other specification.

In Fig. 3 and Fig. 4, we set average value of am0S , a0S =0.35, and average value of amnP , anP = 21, V = 50 and weshow both primary and secondary networks’ queue evolutionover 4500 slots. Because all SUs’ data queues (Qon, Q

pn) and

virtual queues (Xon, X

pn, Zn) enjoy similar trends, we take SU

8 as an example. Fig. 3 (A) shows the dynamics of SU 8’sdata queues Qo8, Qp8, virtual delay queue Z8 and PU queueQ0. It is observed that both actual data queues are strictlylower than their own deterministic worst case upper bound,which verifies Theorem 1. That Q0 is stable in Fig. 3 (A)illustrates that our algorithm can ensure PU queues stabilityfrom simulation aspect. Besides, in Fig. 3(B), we can alsosee that virtual queues Xo

8 , Xp8 and Y are bounded. So Fig.

3 shows that all queues are bounded, which means that thenetwork system is stabilized and the long-term time-averageconstraints of delay and power are satisfied.

Fig. 4 directly shows eight SUs’ long-term time-averageadmitted rates and service rates of open data and private data,respectively. Notice that, every user’s admitted rate is smallerthan service rate and this promises the stabilities of actual dataqueues.

Fig. 5 shows the relationship between the weighting param-

1 2 3 4 5 6 7 81

2

3

4

5

6

SU index

Tim

e-a

ve

rge

da

ta r

ate

(b

its/

slo

t)

(B)Time-average admitted & service rate of private data of different SU

Admitted rate of private rate

Service rate of private rate

1 2 3 4 5 6 7 80

10

20

30

40

50

SU index

Tim

e-a

ve

rge

da

ta r

ate

(b

its/

slo

t) (A)Time-average admitted & service rate of open data of different SU

Admitted rate of open data

Service rate of open data

Fig. 4. Long-term time-average admitted and service rate of all SUs

eters and long-term time-average service rates. To show theeffects more clearly, we consider the scenario consisting ofonly one SU and one PU with fixed ϕ1 = 450 and variationalθ1 ∈ {0, 90.180, 270, 360, 450}. The long-term time-averagearrival rate of SU is set as: λp1 = 8 and λo1 = 260. The controlparameter V is set to be 380. Each value in Fig. 5 is obtainedby averaging the converged results of 5000 times. Fig. 5 showswith the increase of θ1 the long-term time-average service rateof private data increases while the one of open data decreases,which illustrates the effect of throughput weights on long-termtime-average service rates.

Fig. 6 demonstrates the relationship between different long-term time-average network performance versus control pa-rameter V . In order to compare PU and SU performance,the similar scenario including one PU and one SU is alsoconsidered here. The average data arrival rates of SU areset as: λo1 = 250 and λp1 = 10. In general, the bigger Vresults in the higher SU open and private transmission ratesas Fig. 6 (B) and Fig. 6 (C) respectively show. Fig. 6 (A)demonstrates PU transmission rate decreases as V increases.Notice here, although rPU0 decreases, even when V = 380,rPU0 approximates 146 and is greater than λ0 = 140, whichpreserves PU queue stability. Fig. 6 (D) shows the queuingdelay performance also improves as V increases.

The implementation of COCA-E with imperfect estimatedQ0 is simulated. We set the over-estimated slack variableι to be 0.01. We show the differences of the sum servicerate of SUs and RPU0 between COCA and COCA-E in Fig.7 (A), Fig. 7 (B) and Fig. 7 (C), respectively. We can seethat all the differences are around zero, and SU sum rateis more effected than RPU0 by the imperfect estimation ofPU queue information. More directly, the influence of ι onthe long-term time-average rate difference between COCAand COCA-E is simulated in Fig. 8, where each record isan averaged result of 1000 converged results. Fig. 8 (C)shows that rCOCA0 − rCOCA−E0 becomes more negative asι increases, which means that the rate decline of PU causedby SU transmissions decreases as ι increases. More directly,if we want to make sure PU transmission is less influenced,we should choose a larger ι. While a larger ι inevitably makes



11

0 45 90 135 180 225 270 315 360 405 450266

268

270

272

274

276

Weights of private data throughput θ1

Se

rvic

e ra

te o

f o

pe

n d

ata

r1o

0 45 90 135 180 225 270 315 360 405 4500

2

4

6

8

10

12

Weights of private data throughput θ1

Se

rvic

e ra

te o

f

pri

va

te d

ata

r1p

Fig. 5. The time average service rate (rp1 and ro1) versus the weights ofprivate data θ1

30 80 180 280 380144

146

148

150

152

154

156

158

r 0PU

Parameter V

(A) PU time-average rate versus different V

30 80 180 280 380280

300

320

340

360

380

r o

Parameter V

(B) SU time-average open

transmission rate versus different V

30 80 180 280 38014.4

14.6

14.8

15

15.2

15.4

r p

Parameter V

(C) SU time-average private

transmission rate versus different V

30 80 180 280 3801

1.01

1.02

1.03

1.04

1.05

1.06

1.07

ρo

Parameter V

(D) SU time-average queuing delay versus different V

Fig. 6. COCA performances (long-term time-average PU rate, SU rates andSU queuing delay) versus control parameter V .

SUs’ transmission rates decrease as Fig. 8 (A) and Fig. 8 (B)show.

IX. CONCLUSIONS

In this paper, we propose a cross-layer scheduling anddynamic spectrum access algorithm for maximizing the long-term average throughput of open and private information in anOFDMA-based CR network. We derive the sufficient conditionto guarantee that full overlay is optimal in this system. Theproposed algorithm can provide a flexible scheduling imple-mentation of open and private information while ensuring thestability of primary networks as well as performance require-ments in CR systems with finite buffer size. Furthermore, theproposed algorithm is proved to be close to optimality withcurrent network states in time-varying environments.

APPENDIX APROOF OF THEOREM 1

Supposing there exists a slot t satisfying Qon(t) ≤ qomax, itis obviously true for all queues initialized to zero. We prove

0 500 1000 1500 2000 2500 3000 3500 4000 4500-0.06

-0.04

-0.02

0

0.02

0.04

0.06

R0C

OC

A-R

0CO

CA

-E

Time slot

(C) The difference of PU rate under under two implementations

0 1000 2000 3000 40004500-40

-20

0

20

40

Ro

,CO

CA

-Ro

,CO

CA

-E

Time slot

(A) The difference of SUs sum open

transmission rate between two implementations

0 1000 2000 3000 40004500-10

-5

0

5

10

Rp

,CO

CA

-Rp

,CO

CA

-E

Time slot

(B) The difference of SUs sum private

transmission rate between two implementations

Fig. 7. The rate difference of COCA and COCA-E implementation during4500 slots.

0.01 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

1

2

3

4

5

ro,C

OC

A-r

o,C

OC

A-E

Slack variable ι

(A) Time-average SU open

rate difference versus ι

0.01 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.05

0.1

0.15

0.2

rp,C

OC

A-r

p,C

OC

A-E

Slack variable ι

(B) Time-averge SU private

rate differences versus ι

0.01 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-0.02

-0.015

-0.01

-0.005

0

r 0CO

CA

-r0C

OC

A-E

Slack variable ι

(C) Time-averge PU rate difference betwenn COCA and COCA-E

Fig. 8. The long-term time-average rate differences of COCA and COCA-Eimplementation versus different over-estimated slack variable ι .

that for t+1 the same holds. Obviously, there exists two cases.Firstly, we suppose Qon(t) ≤ qomax − µmax and we can easilyget Qon(t + 1) ≤ qomax. Else, if Qon(t) > qomax − µmax, thenaccording to (26), T on(t) = 0. Then

Qon(t+ 1) ≤ Qon(t) ≤ qomax.

The proof of Qpn ≤ qpmax is similar and omitted here.

APPENDIX BPROOF OF THEOREM 2

Let Q = {Q0, Qon, Q

pn, X

on, X

pn, Y, Zn}. We define Lya-

punov function L(Q) as:

L(Q) =1

2{N∑n=1

[qomax − µmax

qomaxXon2 + Z2

n +1

qomaxQon

2(t)Xon+

qpmax −Dmax

qpmaxXpn2 +

1

qpmaxQpn

2Xpn] + Y 2 +Q2

0}

(50)

According to [47], 4L(Q) is defined as the conditionalLyapunov drift for slot t:

4L(Q) , E{L(Q(t+ 1))− L(Q(t))|Q(t)} (51)



12

According to (|x− y|+ z)2 ≤ x2 + y2 + z2 − 2x(y − z), wecan get the results below:

qomax − µmaxqomax

[Xon2(t+ 1)−Xo

n2(t)] ≤

qomax − µmaxqomax

{2µ2max − 2Xo

n(t)[Ton(t)− µon(t)]} (52)

[Qo2

n (t+ 1)Xon(t+ 1)−Qo2n (t)Xo

n(t)]

qomax≤ qomaxµmax+

(µ2max + Co

2

max)− 2Qon(t)[Ron(t)− T on(t)]

qomaxXon(t) (53)

The queues of private data have similar inequalities above.Furthermore, we can derive that:

4L(Q)− VN∑n=1

E{θnµpn + ϕnµon|Q} ≤ B −Q0E{RPU0 −

DPU0 |Q} − Y E{Pavg − E|Q}+

N∑n=1

{Xon(C

o2

max + µ2max)

2qomax

+Xpn(C

p2

max +D2max)

2qpmax− Xp

nQpn

qpmaxE{Rpn − T pn |Q}−

XonQ

on

qomaxE{Ron − T on |Q} − (1− Dmax

qpmax)Xp

nE{T pn − µpn|Q}−

(1− µmaxqomax

)XonE{T on − µon|Q} − ZnE{ρnµon −Qon|Q}

− V E{θnµpn + ϕnµon|Q}} (54)

where B = 12 (D

PU2

max + R20max + P 2

max + P 2avg) +

N [ 12qomaxµmax + (1 − µmax

qomax)µ2max + (1 − Dmax

qpmax)D2

max +

12qpmaxDmax] + 1

2

N∑n=1

(ρ2nµ2max + qo

2

max) and Cpmax =

maxn{Rpn}, Comax = max

n{Ron}, R0max = max{RPU0 }. Here

we can find that our algorithm minimizes the right hand side(RHS) of (54).

In order to prove Theorem 2, we introduce Lemma 3.Lemma 3: For any feasible rate vector t ∈ Υ, there exists a

a-only policy SR which stabilizes the network with the dataadmitted rate vector, (µpn,SR(t), t

pn,SR(t), µ

on,SR(t), t

on,SR(t)),

and the service vector, (Rpn,SR(t), Ron,SR(t)), independent of

data queues. For all t and all n ∈ {1, 2, ..., N}, the flowconstraints are satisfied:

E{µon,SR(t)} = E{T on,SR(t)} = E{Ron,SR}E{µpn,SR(t)} = E{T pn,SR(t)} = E{Rpn,SR}

Notice that, the stationary randomized policy SR makes de-cisions only depending on channel condition and independentof queue backlogs. Furthermore it may not fulfill the delayconstraints. Similar proof of a-only policy is given in [17]and the proof of Lemma 3 is omitted here.

We can control the admitted rate of t ranging from t∗(ε) tot∗(ε)+ε arbitrarily and resulting in that both t∗(ε) and t∗(ε)+ε are within Υ. It is assumed that the sufficient conditionof full overlay optimum (21) is satisfied in our system, soaccording to Lemma 2, full overlay can achieve the optimal

result. Besides, according to Lemma 3, it is true that there existtwo different a-only policies SR1 and SR2 which satisfy:

E{T on,SR1} = E{Ron,SR1

} = E{µon,SR1} = to,∗n (ε) (55)

E{T pn,SR1} = E{Rpn,SR1

} = E{µpn,SR1} = tp,∗n (ε) (56)

E{T on,SR2} = E{Ron,SR2

} = E{µon,SR2} = to,∗n (ε) + ε (57)

E{T pn,SR2} = E{Rpn,SR2

} = E{µpn,SR2} = tp,∗n (ε) + ε (58)

In addition, for policy SR1 and SR2, it is easy to provethat:

E{RPU0,SR1} ≥ λ0 + ε (59)

E{ESR2} ≤ Pavg − ε (60)

Our algorithm minimizes RHS of (54) among all possiblepolicies including SR policy, thus we can get :

4L(Q)− VN∑n=1

E{θnµpn + ϕnµon} ≤ B+

Y {E{ESR2} − Pavg} −Q0{E{RPU0,SR1

} − λ0}+N∑n=1

{ZnQon +Co

2

max + µ2max

2qomaxXon +

Cp2

max +D2max

2qpmaxXpn+

[qomax − µmax

qomaxXon − Znρn − V ϕn]Xo

nE{µon,SR1}+

E{T on,SR2} X

on

qomax[Qon + µmax − qomax]−

XonQ

on

qomaxE{Ron,SR2

}+

E{T pn,SR2} X

pn

qpmax[Qpn − qpmax +Dmax]−

XpnQ

pn

qpmaxE{Rpn,SR2

}+

E{µpn,SR1}[q

pmax −Dmax

qpmaxXpn − V θn]

}(61)

After substituting (55)-(58) , (59) and (60) into the RHS of(61) and transforming it, we can derive that:

4L(Q)− VN∑n=1

E{θnµpn + ϕnµon} ≤ B − ε(Y +Q0)−

∑{to,∗n (ε)ρ− qmax}Z − V

N∑n=1

{ϕnto,∗n (ε) + θntp,∗n (ε)}−

N∑n=1

Xon

qomax{ε(qomax − µmax)−

Co2

max + µ2max

2}−

N∑n=1

Xpn

qpmax{ε(qpmax −Dmax)−

Cp2

max +D2max

2} (62)

So when (44)-(46) hold, we can find ε1 > 0 that ε1 ≤ε(qomax−µmax)−

Co2max+µ2max

2

qomax, ε1 ≤ to,∗n (ε)ρn − qmax and ε1 ≤

ε(qpmax−Dmax)−Cp2max+D2

max2

qpmax. Thus:

4L(Q)− VN∑n=1

E{θnµpn + ϕnµon} ≤ B − V

N∑n=1

{ϕto,∗n (ε)+

θntp,∗n (ε)} − σ(

N∑n=1

{Xon +Xp

n + Zn}+ Y +Q0) (63)



13

where σ = min{ε, ε1}.It can be got that when (44), (45) and (46) hold, (48) and

lim inft→∞

1

t

t−1∑τ=0

N∑n=1

{θnµpn(τ) + ϕnµon(τ)} ≥

N∑n=1

{ϕnto,∗n (ε) + θntp,∗n (ε)} − B

V(64)

are satisfied by applying the theorem of Lyapunov Optimiza-tion, Theorem 4.2 in [47], on (63) directly. Furthermore, (48)implies that (10) and (11) hold since Xo

n and Xpn are kept

stable. So after substituting (10) and (11) into (64), (47) holds.Hence the proof of Theorem 2 is completed.

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Xingzheng Zhu received the B.S. degree in Au-tomation from Harbin Institute of Technology,Harbin, China, in 2011, the M.S. degree in ControlScience and Control Engineering from Shanghai JiaoTong University, Shanghai, China, in 2014. She iscurrently pursuing a Ph.D. degree in the Departmentof Electrical and Electronic Engineering, The Uni-versity of Hong Kong. Her research interests includewireless communication networks and smart grids.

Bo Yang (M’09) obtained his PhD in Electrical En-gineering from the City University of Hong Kong in2009. Prior to joining Shanghai Jiao Tong Universityin 2010, he was a postdoctoral researcher at theRoyal Institute of Technology (KTH), Sweden, from2009 to 2010 and a visiting scholar at the Poly-technic Institute of New York University in 2007.He is now an associate professor in Shanghai JiaoTong University. He is also a cyber scholar with theCyber Joint Innovation Center founded by ZhejiangUniversity, Tsinghua University, and Shanghai Jiao

Tong University.His current research interest includes game theoretical analysis and non-

linear optimization of communication networks and smart grid. He is on theeditorial board of Digital Signal Processing-Elsevier and in the TPC of severalinternational conferences. Dr. Yang has been the principle/co-investigator inseveral research projects funded by NSF of China, Swedish GovernmentalAgency for Innovation Systems, and the US air force. He is a Member ofIEEE and ACM.

Cailian Chen (S’03-M’06) received the B.Eng. andM.Eng. degrees in Automatic Control from YanshanUniversity, China in 2000 and 2002, respectively,and the Ph.D. degree in Control and Systems fromCity University of Hong Kong, Hong Kong SAR in2006. She joined Department of Automation, Shang-hai Jiao Tong University in 2008 as an AssociateProfessor. She is now a Full Professor.

Dr. Chen’s research interests include DistributedEstimation and Control of Network Systems, Wire-less Sensor and Actuator Network, Multi-agent Sys-

tems and Intelligent Control Systems. She has authored and/or coauthored 2research monographs and over 80 referred international journal and conferencepapers. She is the inventor of 20 patents. Dr. Chen received the ”IEEETransactions on Fuzzy Systems Outstanding Paper Award” in 2008. She wasone of the First Prize Winners of Natural Science Award from The Ministryof Education of China in 2007. She was honored as ”New Century ExcellentTalents in University of China” and ”Shanghai Rising Star” in 2013, ”ShanghaiPujiang Scholar”, ”Chenguang Scholar” and ”SMC Outstanding Young Staffof Shanghai Jiao Tong University” in 2009.

She is a Member of IEEE. She serves as an Associate Editor of Peer-topeer Networking and Applications (Springer), ISRN Sensor Networks, andScientific World Journal (Computer Science), and TPC member of severalflagship conferences including IEEE Globecom, IEEE ICC and IEEE WCCI.

Liang Xue received the B.S., M.S., and Ph.D.degrees in control theory and engineering from Yan-shan University, Qinhuangdao, China, in 2006, 2009,and 2012, respectively. He is currently an associateprofessor with the School of Information and Elec-trical Engineering and the chair of the Department ofInternet of Things, Hebei University of Engineering,Handan, China. He is also the Outstanding YoungScholar of Hebei Education Department and Hebeinew century ” 333 talent project ” third level suitableperson. He is now in charge of several research

projects including the National Natural Science Foundation of China, theScientific Research Plan of Hebei Education Department, etc. His researchinterests include the clustering design, hierarchical topology control, and datarouting in wireless sensor networks and wireless cognitive radio networks.

Xinping Guan (M’02-SM’04) received the Ph.D.degree in control and systems from Harbin Instituteof Technology, Harbin, China in 1999. In 2007,he joined the Department of Automation, ShanghaiJiao Tong University, Shanghai, China, where heis currently a Distinguished University Professor,the Executive Deputy Dean of University Officeof Research Management, and the Director of theKey Laboratory of Systems Control and InformationProcessing, Ministry of Education of China. Beforethat, he was the Professor and Dean of Electrical

Engineering, Yanshan University, China in 1998-2008.Dr. Guan’s current research interests include cyber-physical systems, mul-

tiagent systems, wireless networking and applications in smart city and smartfactory, and underwater sensor networks. He has authored and/or coauthored4 research monographs, more than 180 papers in IEEE Transactions andother peer-reviewed journals, and numerous conference papers. As a PrincipalInvestigator, he has finished/been working on many national key projects.He is the leader of the prestigious Innovative Research Team awarded byNational Natural Science Foundation of China (NSFC). Dr. Guan is anExecutive Committee Member of Chinese Automation Association Counciland the Chinese Artificial Intelligence Association Council. He was on theeditorial board of IEEE Trans. System, Man and Cybernetics?Part C andseveral Chinese journals. He received the First Prize of Natural Science Awardfrom the Ministry of Education of China in 2006 and the Second Prize ofthe National Natural Science Award of China in 2008. He was a recipientof the ”IEEE Transactions on Fuzzy Systems Outstanding Paper Award” in2008. He is a ”National Outstanding Youth” honored by NSFC, ”ChangjiangScholar” by the Ministry of Education of China and ”State-level Scholar” of”New Century Bai Qianwan Talent Program” of China.



15

Fan Wu is an associate professor in the Departmentof Computer Science and Engineering, ShanghaiJiao Tong University. He received his B.S. in Com-puter Science from Nanjing University in 2004, andPh.D. in Computer Science and Engineering fromthe State University of New York at Buffalo in2009. He has visited the University of Illinois atUrbana-Champaign (UIUC) as a Post Doc ResearchAssociate. His research interests include wirelessnetworking and mobile computing, algorithmic net-work economics, and privacy preservation. He has

published more than 70 peer-reviewed papers in leading technical journalsand conference proceedings. He is a receipt of China National Natural ScienceFund for Outstanding Young Scientists, CCF-Intel Young Faculty ResearcherProgram Award, CCF-Tencent ”Rhinoceros bird” Open Fund, and PujiangScholar. He has served as the chair of CCF YOCSEF Shanghai, on theeditorial board of Elsevier Computer Communications, and as the memberof technical program committees of more than 40 academic conferences. Formore information, please visit http://www.cs.sjtu.edu.cn/∼fwu/.

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