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Throughput Analysis for a Multi-user,Multi-channel ALOHA Cognitive Radio System

Xiaofan Li, Student Member, IEEE, Hui Liu, Fellow, IEEE, Sumit Roy, Fellow, IEEE, Jianhua Zhang,Member, IEEE, Ping Zhang, Member, IEEE, and Chittabrata Ghosh, Member, IEEE

Abstract—In this paper, we investigate a novel slotted ALOHA-based distributed access cognitive network in which a secondaryuser (SU) selects a random subset of channels for sensing, detectsan idle (unused by licensed users) subset therein, and transmits inany one of those detected idle channels. First, we derive a rangefor the number of channels to be sensed per SU access. Then,the analytical average system throughput is attained for caseswhere the number of idle channels is a random variable. Basedon that, a relationship between the average system throughputand the number of sensing channels is attained. Subsequently, ajoint optimization problem is formulated in order to maximizeaverage system throughput. The analytical results are validatedby substantial simulations.

Index Terms—Cognitive radio, distributed system, multi-channels, throughput analysis, number of sensing channels.

I. INTRODUCTION

THE surge in demand for high bandwidth applications onmobile devices is driving the current imperative for either

additional spectrum allocations and/or more efficient use ofexisting ones. Cognitive radios (CR) [1] performing dynamicspectrum access seems to be a natural pathway for realizingimproved spectrum efficiencies by allowing secondary userson hitherto licensed spectrum. Utilization of licensed bandimposes the constraint of sensing channel availability foropportunistic access by unlicensed (secondary) users (SUs),without imposing inadmissible interference to primary users(PUs).

Coexistence of SUs and PUs may be achieved using eithera scheduled (centralized) mechanism or a distributed scheme.For a scheduled mechanism, a central control channel isnecessary to schedule SUs on spectrum sensing and packetaccessing. Among the former, Cordeiro et al. [2] presenteda Cognitive MAC (Media Access Control) protocol overthe vacant TV broadcasting spectrum based on instructionsfrom base station and analyzed efficiency improvement of

Xiaofan Li, Jianhua Zhang, and Ping Zhang (xiaofanli, jhzhang,pzhang@bupt.edu.cn) are with key Laboratory of Universal Wireless Commu-nications for Ministry of Education, Wireless Technology Innovation Institute,Beijing University of Posts and Telecommunications, Beijing, 100876, China.

Hui Liu (huiliu@sjtu.edu.cn) is with the Department of Electrical Engi-neering, Shanghai JiaoTong University, Shanghai, 200240, China.

Sumit Roy (sroy@u.washington.edu) is with the Department of ElectricalEngineering, University of Washington, Box 352500 Seattle, WA 98195-2500.

Chittabrata Ghosh (chittabrata.ghosh@nokia.com) is with Nokia ResearchCenter, Berkeley, CA-94704.

The research is supported by the National Natural Science Foundationof China with NO. 61171105, Program for New Century Excellent Talentsin University, NCET-11-0598, National Basic Research Program of China(973Program) with NO.2009CB320400, and the National Science FoundationGoali Grant NO. 0801997.

the SU in terms of throughput, delay, and quality of service.Hamdaoui et al. [3] proposed an opportunistic spectrum MACprotocol through periodically listening to a control channeland undertook a simulation based performance evaluation.

For a distributed access, reliable (and fast) spectrum sensingis vital for overall system performance due to the absence ofcentral control channel or scheduling mechanism. In existingserial or random sensing mechanisms - the “classic sensingstrategies (CSS)” - each SU serially or randomly searches thechannels within the spectrum for an idle channel. The searchscheme terminates only when such a channel is identified. Theperformance of various medium access control (MAC) layerprotocols based on such CSS constitute the core of the cross-layer cognitive network performance evaluation literature. In[4] and [5], the authors proposed an opportunistic multi-channel MAC protocol and analyzed its throughput usingrandom sensing with negotiation, that required an extra controlchannel for coordination among SUs. In contrast, Choe et al.[6] and [7] provided analytical results for throughput of aslotted ALOHA-based multi-channel CR system in a proposedRandom Channel Selection scheme without any such controlcoordination channel.

The above were also limited to narrowband systems; morerecently, wideband dynamic spectrum access (DSA) systems -notably based on orthogonal frequency division multiplexing(OFDM) - have been explored for flexible spectrum poolingas in [8] and [9]. In such scenarios, the SUs should becapable of opportunistically detecting multiple non-contiguousidle OFDM sub-carriers and accessing them. This motivatesour present work where we consider a (generic) spectrumpool consisting of a random set of licensed channels that theSUs select for sensing until the first available (idle) channelis detected. However, sensing of multiple idle channels suc-cessfully is a more challenging problem, whose performance(as characterized by imperfect decisions with probability ofmis-detections and false alarms) in turn affects the MAC inwhich it is embedded. Novel sensing algorithms are neededthat balance the latency (number of samples needed) fordetection of primary user occupancy with desired accuracy(given detection error probability).

In this context, Liang et al. [10] studied the performancetradeoff between sensing time and achieved throughput ofSUs in point-to-point transmission. While, Quan et al. [11]developed an optimization approach to maximize the aggregatethroughput for optimal sensing thresholds for each sub-band.To extend the above research, Luo et al. [12] consideredjoint minimization of the average detection time for finding a

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spectrum hole as a function of both duration and threshold inthe constraint of certain detection and false alarm probabilities.In order to improve sensing performance, an extensive researchalso by Luo et al. [13] have been pursued based on two stagesensing, which involves coarse resolution detection in the firststage and finite resolution detection in the second stage.

We generalize prior art by allowing each of the SUs to selecta (randomly chosen) set of channels, for sensing and determin-ing channel status (idle/occupied). Each SU then undertakespacket transmission in any one of the idle channels fromits (detected) idle sub-set. This method is termed “extendedsensing strategy (ESS)” which reveals some interesting aspectsfor further investigation. One is the tradeoff between thenumber of channels to be sensed and the system throughput.Further, the optimal system throughput by jointly adjusting thepacket transmission probability and the number of channels tobe sensed by each SU is explored via analytical formulation.

In this paper, we consider the ESS applied to a slottedALOHA-based multi-channel random access CR system. Themajor new contributions of this paper are:

• Proposed the Extended Sensing Strategy for multi-channel ALOHA access;

• Derive a relationship between the average systemthroughput and the number of sensing channel, Ns,, findoptimal Ns;

• Consider imperfect sensing and attain the analyticalaverage system throughput;

• Optimize average system throughput jointly with respectto Ns and the packet transmission probability;

The rest of the paper is organized as follows. Section IIbriefly discusses the system model of multi-user multi-channelspectrum access. In Section III, an analytical derivation of theaverage throughput based on the ESS is provided. SectionIV deals with the joint optimization problem with respectto Ns and the packet transmission probability. In SectionV, the average system throughput under imperfect sensing isderived. Section VI discusses average throughput achieved bycomparing the simulation results with those obtained from ourtheoretical analysis. Section VII concludes the paper.

II. SYSTEM MODEL

As shown in Fig. 1, we consider a spectrum of N licensedchannels, out of which M random channels are idle orunoccupied by the PUs. Further, there are K SUs located inthe same local area and synchronized with the PUs that seekto estimate channel status so as to opportunistically access theidle channels without imposing interference to the PUs. Eachaccess frame (AF) has a fixed duration TAF, divided into twoparts - the sensing slot, TS , and packet transmission slot, TP ,depicted in Fig. 2.

A. Spectrum Sensing Strategy in one AF

During the sensing slot, each SU accomplishes sensing onelicensed channel in one unit slot TSm within TS . Each SUsenses Ns channels in sequence which are randomly selectedfrom the N channels, and detects/constructs its idle channelset. We name this as the “extended sensing strategy.” The time

Occupied Idle

ch1 ch2 ch3 chNchn chn+1

PUs

chn+2

t

Fig. 1. Channel states of PUs in one Slot

ST

SmT

1SU

t

t

t

tSU

K

Occupied Idle

Defer the Packet

2SU

3SU

Successful Transmision Collision

ch1 chn ch 1n +

chN ch3 ch 2n +

chN ch 2n + ch1

ch 2n + chnch2

ch1 ch1ch 1n +

chN chN

chN chN

ch3 ch3

ch1

ch1

PT

AFT

PmT

Fig. 2. Access frame for SUs based on the channel states in Fig. 1

required for sensing all channels is TS = TSmNs; clearlythe number of channels determined to be idle by the kth

SU, Mks ≤ min(Ns,M), is a random variable. Due to the

absence of any central control channel, one SU will not knowwhich channels are sensed idle by the other SUs. Since thedetermination of each individual channel status as busy/idleis subject to (occasional) error, determined by the probabilityof (correct) detection of the presence of PUs’ signals Pd andprobability of false alarm Pf (probability of falsely declaringa idle channel as busy), we first assume ideal detection, i.e.,Pd = 1 and Pf = 0 for simplicity in this work. The casesinvolving imperfect sensing, i.e., Pd ̸= 1 and Pf ̸= 0, will bestudied in Section V.

B. MAC for Packet Transmission in one AFFor packet transmission, slotted ALOHA access is applied.

As shown in Fig. 2, the kth SU transmits a single packetat the beginning of each unit transmission slot, TPm, withprobability pk

tra on any one of the Mks idle channels that has

been determined to be idle, during the sensing period TS .Thus, the number of transmitted packets in one slot, U , isa random variable. Take the fairness of packets access inconsideration, each SU has the same transmission probabilityptra (ptra ∈ [0, 1]). Thus, E[U ] = Kptra, due to the independentidentical binomial distribution of the packet transmission foreach SU.

Since there is no coordination among SUs, each SU accessesone idle channel through a random selection among its owndetected idle channel set. Thus, successful packet transmissionof the kth SU in a time slot only occurs when the followingtwo conditions are satisfied simultaneously:

• Mks ̸= 0, i.e., at least one idle channel exists within Ns

sensed channels;• The kth SU transmits a packet on an idle channel ran-

domly selected from its Mks idle channel set, that is NOT

accessed by any other SU in the same time slot.

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Correspondingly, the following two situations result infailed packet transmission:

• More than one packet is transmitted on the same idlechannel in one time slot (e.g., both SU1 and SU3 trans-mitting packets in ch1 in the first time slot in Fig. 2),defined as a collision.

• Any packet transmission is deferred when no idle channelis detected within the Ns sensed channels (e.g., SUK inFig. 2).

Assume there is a timer with each SU and the expiry ofthe timer identifies an unsuccessful transmission. Each lostpacket is re-queued and will be retransmitted in a future AFwhen an idle channel is found. We assume that an SU alwayshas at least one packet in its buffer. Further, the state of PUchannels changes sufficiently slowly, such that it can be viewedas constant within a TAF.

Consequently,

TAF = TS + TP = NsTSm + NpTPm, (1)

where we let TPm = ηTSm. For higher throughput, Np >>Ns is typical.

III. THROUGHPUT ANALYSIS BASED ON “EXTENDEDSENSING STRATEGY”

In this section, we will analyze the average system through-put based on the “extended sensing strategy”. According to thesystem model description in Section II, we will firstly providethe range of choosing Ns channels for sensing. Then therelationship between Ns and the average system throughputwill be investigated.

A. Choice of Ns

We assume that M (M ≤ N ) among N licensed channelsare idle. After selecting (randomly) an Ns subset, the kth

SU determines the status of Mks idle channels within the Ns

channels sensed, where Mks ≤ M .

Lemma 1. The probability, p(i)sac of the ith idle channel being

selected for access is given by the following (note that theresult is indep. of the index of the idle channel):

p(i)sac =

{1M

(1 − (N−Ns)[M]

N [M]

), if Ns ≤ N − M,

1M

, if Ns ≥ N − M + 1,(2)

Clearly, p(i)sac ∈ [1/N, 1/M ].

Proof: Refer to Appendix for the derivation of p(i)sac.

From Lemma 1, we find that a given idle channel selectedfor a packet access depends on Ns, but not on Mk

s . Moreover,since p

(i)sac is invariant w.r.t i, it implies that p

(1)sac = p

(2)sac = . . . =

p(M)sac and we may drop the superscript in the sequel. Note

that accessing an idle channel does not guarantee a successfulpacket transmission for reasons described in Section II-B.Based on the result in Lemma 1, the average number of packetsin successful transmission can be derived as followings, whenthere are U packets transmitted from all the SUs in a slot.When all users transmit packets with ptra = 1, i.e. they alwayshave a packet to send in each slot, U = K.

Theorem 1. When U packets are sent to access the Midle channels, the average number of successfully transmittedpackets is given by

Ssuc(U) = MUpsac(1 − psac)U−1. (3)

Additionally, Ssuc(U) is constant if Ns > N − M + 1.

Proof: From Appendix, Xi =∑U

j=1 Xij is the numberof packets accessing the ith idle channel in one time slot. Weintroduce a new binary random variable Zi, that equals 1 ifthe ith idle channel is accessed by only one packet, otherwise,Zi = 0, if no packet or more than one packet accesses the ith

idle channel. That means p(Zi = 1) = p(Xi = 1).Since successful transmissions only occur if an idle channel

is accessed by a single packet, the average number of success-ful transmissions in a slot Ssuc(U) is expressed as

Ssuc(U) = E[Z|U ] = E[

M∑i=1

Zi|U ]

=

M∑i=1

E[Zi|U ] =

M∑i=1

p(Zi = 1|U),

(4)

where Z =∑M

i=1 Zi is the number of idle channels with onlyone packet access. Since p(X1 = 1|U) = p(X2 = 1|U) =. . . = p(XM = 1|U) and each Xij represents a independentBernoulli trial, we can reformulate (4) as,

Ssuc(U) =

M∑i=1

p(Xi = 1|U) = Mp(Xi = 1|U)

=Mp(∑U

j=1Xij = 1|U)=M

(U

1

)psac(1−psac)

U−1,

(5)

yielding (3).From (3), we deduce that Ns is independent of Ssuc when

Ns > N − M + 1. It implies that the number of successfulpacket transmissions will not always increase with increasingvalues of Ns, i.e. it is not necessary to choose more thanN −M +1 channels for sensing. We will verify this fact fromthe simulation results discussed in Section VI.

B. Average System Throughput

Define the average system throughput as the average numberof packets in successful transmission per slot. FollowingTheorem 1, we first derive the expression of the averagesystem throughput, when each SU transmits the packet withptra < 1 and U is a random variable. Then the average systemthroughput under a random M is obtained.

Theorem 2. The average system throughput conditioned onM is

Ssys(Ns, ptra) =ηNp

Ns + ηNpMKpsacptra(1 − ptrapsac)

K−1. (6)

Proof: From Theorem 1:

Ssys(Ns, ptra) = E[NpTPmSsuc(U)

NsTSm + NpTPm]

=NpTPm

NsTSm + NpTPmE[Ssuc(U)]

=ηNp

Ns + ηNpE[Ssuc(U)].

(7)

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We define Save = E[Ssuc(U)] as the average number of thepackets in successful transmission. Using Theorem 1, Save fora given M can be written as,

Save = E[MUpsac(1 − psac)(U−1)]

= MpsacE[U(1 − psac)(U−1)]

= Mpsac

K∑U=1

U(1 − psac)U−1pnum(U),

(8)

where pnum(U) is the probability that there are U packetstransmitted from K SUs. Since the packet transmission ofeach SU is the independent Binomial distribution, pnum(U)can be obtained as

pnum(U) =

(K

U

)(ptra)

U (1 − ptra)K−U . (9)

Substituting (9) into (8) simplifies to

Save = MpsacKptra

K∑U=1

(1−psac)U−1

(K − 1

U − 1

)(ptra)

U−1(1−ptra)K−U

= MKpsacptra(ptra(1 − psac) + 1 − ptra)K−1

= MKpsacptra(1 − ptrapsac)K−1.

(10)

yielding (6).Note that (6) is dependent on N , M and K whereby

each SU senses the idle channels and transmits the packetwith a fixed (Ns, ptra). Indeed, in a distributed system, thenumber of idling channels and the number of SUs are generallynot known to the SUs. Hence, these parameters need to beestimated at the SU side without a control channel. In thepractical system, N is generally known by each SU due toawareness of the range of the spectrum allowed for SUs access.Thus, the remaining question is how to obtain K and Mbased on the outputs of the initial access period (IAP). Itis noted that each SU is aware of the packet in successful(failed) transmission and can count the total number of theidle channels detected during all the sensing slots in IAP. Thus,K and M can be estimated based on individual SU’s meanthroughput value [14]. In this paper, we assume each SUs hasthe perfect knowledge about the system parameters K and M .

In a dynamic environment, the PU is silent on a channel withprobability q and active with probability 1 − q. That impliesthat the number of idle channels M is a random variable. Toavoid interference from SU to the PUs, we assume that thePU’s state is fixed within the access period. Accordingly wehave the following result.

Corollary 1. The average system throughput under a randomM, Srm(Ns, ptra), is

Srm(Ns, ptra) =ηNp

Ns + ηNpKptra

·N∑

m=1

mpsac(m)(1−ptrapsac(m))K−1

(N

m

)qm(1−q)N−m.

(11)

Proof: Since the PU channels are iid, the probability ofM = m idle channels among N PU channels is given by

Pnumidl(M = m) =

(N

m

)qm(1 − q)N−m. (12)

According to (6), the average system throughput under arandom M can be derived as

Srm(Ns, ptra) = E[Ssys(Ns, ptra|M)]

=

N∑m=1

ηNpmKptrapsac(m)

Ns + ηNp(1−ptrapsac(m))K−1Pnumidl(m)

=ηNpKptra

Ns + ηNp

N∑m=1

mpsac(m)(1−ptrapsac(m))K−1Pnumidl(m),

(13)

yielding (11).In several scenarios, M is slowly varying relative to the SU

access frame duration. Hence for throughput maximization, wefirst fix the number of idle channels so that other system pa-rameters (e.g., the SU’s access rate) can be jointly optimized.Subsequently, we average over the distribution of a random Mto explore the impact of varying M over a sufficiently longperiod.

C. Relationship between Ns and Average System Throughput

From (6), it is observed that the average system throughputwill be affected by both Ns and ptra. Since Ns is a discrete andfinite variable, we can in principle obtain the optimal Ns viaexhaustive search in (6) and selecting the Ns correspondingto the maximal Save. However, this is not effective for Ns

increasing or variable ptra.

Proposition 1. For the maximal average system throughput,Ns and Ssys for a given ptra are related via

N∗s =

{1, Kptra ≥ N ;

argNs

{min{Ssys(Ns) − Ssys(N̂s)}}, otherwise, (14)

where N̂s satisfies ∂Ssys

∂N̄s

∣∣∣N̂s

= 0 and N̄s ∈ [0, N − M + 1].

Proof: We relax Ns as N̄s ∈ [0, N − M + 1] anddifferentiate Ssys in (6) with respect to N̄s.

i) When Kptra > N , which means 1Kptra

< 1N ≤ psac,

then 1 − Kptrapsac < 0 and ∂Ssys

∂N̄s< 0. That indicates Ssys

decreases with psac. Further, psac is an increasing functionof Ns as proved in Appendix. Therefore, Save achieves themaximal value at N∗

s = 1.ii) Kptra < N , i.e., 1

N ≤ 1Kptra

, then ∂Ssys

∂N̄s> 0 at N̄s = 0

and ∂Ssys

∂N̄s< 0 at N̄s = N − M + 1. Due to the continuity of

∂Ssys

∂N̄son N̄s ∈ [0, N−M +1], there exists a N̂s which satisfies

∂Ssys

∂N̄s

∣∣∣N̂s

= 0. Further, once ∂Ssys

∂N̄s

∣∣∣N̂s

= 0, ∂2Ssys

∂N̄2s

∣∣∣N̂s

< 0(K >

2), which means Ssys(N̂s) is the only maximal point on thedomain. Thus, N∗

s = argNs

{min{Ssys(Ns) − Ssys(N̂s)}}.

From Proposition 1, if Kptra ≥ N , each SU can directlyset N∗

s = 1 without extra searching. While, if Kptra < N ,each SU can obtain N∗

s by calculating N̂s. When it is notconvenient to compute N̂s directly, we apply the first order andsecond order partial derivatives for the optimal Ssys as in theproof of Proposition 1, i.e., ∂2Ssys

∂N̄2s

∣∣∣N̂s

< 0, once ∂Ssys

∂N̄s

∣∣∣N̂s

= 0.This implies that when the first order derivative of Ssys at twoadjacent Ns values are different in sign, N∗

s corresponds to

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the larger Ssys. Choice of a proper initial value for Ns willresult in more effective searching in such cases, but is beyondthe scope of our paper.

Moreover, as E[U ] = Kptra, that means when the averagenumber of transmitted packets is larger than N , each SU doesnot need to sense the channels for more than one TSm. That isbecause it will introduce more collisions and thereby reducethe system throughput, although each SU incurs more time andresources on sensing the channels. For E[U ] = Kptra < N ,it is worth investing more time on sensing the idle channelfor each SU and the optimal Ns can be decided accordingto Proposition 1. With this understanding, let us focus on thesystem throughput optimization with respect to both Ns andptra in the next section.

IV. JOINT OPTIMIZATION ON SYSTEM THROUGHPUTMAXIMIZATION THROUGH (Ns, ptra)

In this section, we focus on the throughput maximizationjointly w.r.t. Ns and ptra. According to (6), the problem canbe presented as

arg(Ns,ptra)

max Ssys =ηNp

Ns + ηNpMKpsacptra(1 − ptrapsac)

K−1 (15a)

s.t. 0 ≤ ptra ≤ 1 (15b)Ns ∈ {1, 2, . . . , N − M + 1}. (15c)

Since the above is neither convex nor concave on the domainof Ns or ptra, that implies the Karush-Kuhn-Tucker conditionswill only provide locally optimal solution. Thus, in the follow-ing, we analyze the optimal ptra according to the relationshipbetween N∗

s and throughput for a given ptra which we haveobtained in Proposition 1, and finally obtain the optimal pair(Ns, ptra).

Proposition 2. For a given Ns, the optimal ptra for maximizingthe system average throughput in (15a) is given by,

p∗tra =

{1

Kpsac, psac > 1 − 1/K; (16a)

1, psac ≤ 1 − 1/K. (16b)

Proof: Differentiate Ssys in (15a) with respect to ptra.When ∂Ssys

∂ptra

∣∣∣p̃tra

= 0, p̃tra = 1Kpsac

and ∂2Ssys

∂ptra2

∣∣∣p̃tra

< 0. Thus,

Ssys(p̃tra) is the only maximum value on the given Ns. Further,when ptra < p̃tra, ∂Ssys

∂ptra

∣∣∣<p̃tra

> 0, implying that (15a) is

an increasing function in this rang. Thus, the optimal ptra isattained at p∗tra = min{ 1

Kpsac, 1}.

In terms of Proposition 2, for psac ≤ 1/K, each SU shouldalways transmit the packet in each TSm slot. For psac > 1/K,each SU will reduce the transmission probability to 1

Kpsacto

reduce the chance of collisions. Moreover, N , M , and K alsoaffects the optimal packet transmission probability in the rangepsac ∈ [1/N, 1/M ]. Take all this in consideration, we developthe optimal (Ns, ptra) as follows.

Theorem 3. The maximal average system throughput can beattained at the optimal values of (Ns, ptra) given by

Smax =

Ssys(N

∗s1, p

∗tra1), K ≤ M ; (17a)

Ssys(N∗s2, p

∗tra2), K ≥ N ; (17b)

max(Ssys(N∗s1, p

∗tra1), Ssys(N

∗s2, p

∗tra2)), others, (17c)

where (N∗s1, p

∗tra1) = (arg

Ns

minptra=1

{Ssys(Ns) − Ssys(N̂s)}, 1) and

(N∗s2, p

∗tra2) = (1, N/K).

Proof: From Proposition 2, we see that the optimal(N∗

s , P ∗tra) depends on the relationship between the range

psac ∈ [1/N, 1/M ] and K.a) If K ≤ M , then there is psac ≤ 1/M ≤ 1/K. Thus,

ptra = 1 at any Ns value to maximize the average systemthroughput based on the Proposition 2. Substituting ptra = 1into (15a), the maximal system throughput can be attained atNs = arg

Ns

minptra=1

{Ssys(Ns)−Ssys(N̂s)} in terms of Proposition

1. Hence, the optimal point is

(N∗s1, p

∗tra1) = (arg

Ns

minptra=1

{Ssys(Ns) − Ssys(N̂s)}, 1). (18)

b) If K ≥ N , then psac > 1/N > 1/K. From Proposition 2,Ssys attains the maximal point at ptra = 1

Kpsacon a given Ns.

That implies for each feasible Ns that satisfies ptra = 1Kpsac

,the system can achieve the maximal average throughput byadjusting the probability of packet transmission according to(15a). Substituting ptra = 1

Kpsacinto (15a), the maximal system

throughput will be at Ns = 1. Hence, Ssys attains the maximalpoint given by,

(N∗s2, p

∗tra2) = (1,

N

K). (19)

c) For M < K < N , we exam psac for two cases. For thecase when 1/N < psac ≤ 1/K, the local maximal point isattained at Ssys(N∗

s1, p∗tra1). For the other case 1/K < psac <

1/M , the system throughput achieves a local maximal pointrepresented as Ssys(N∗

s2, p∗tra2). Thus, the maximal point will

be the maximum value of the above two situations.Based on Theorem 3, the optimal parameters (Ns, ptra)

can be decided according to the relationship among K, M ,and N . On the other hand, the SUs are able to adjust itsown parameters (Ns, ptra) in order to optimize the systemthroughput even without the central control channel. We willalso verify this conclusion in Theorem 3 through the simulationresults.

V. SYSTEM THROUGHPUT ANALYSIS UNDER IMPERFECTSPECTRUM SENSING

To consider the imperfect sensing [10], [12] and [15], denoteτ as the spectrum sensing time, fs the sampling frequency, andγ the received signal-to-noise ratio (SNR) from PU to SUs.The false alarm probability Pf can be calculated ([10]) by

Pf (τ) = Q(√

2γ + 1Q−1(Pd) +√

τfsγ)

, (20)

where Q(·) is the complementary function of a standard Gaus-sian variable and Pd is the predefined detection probability.

Assume the detection result indicator of the nth channelsis Dn (n ∈ {1, 2, ..., N}). It is noted that Dn indicates thedetection results of the idle channels when n ∈ {1, 2, ..., M},and the occupied channels when n ∈ {M+1,M+2, ..., N}. IfDn = 1, the nth channel is detected as idle channel, otherwise,Dn = 0. The probability of one idle channel detected withno false alarm is 1 − Pf and the probability for an occupiedchannels detected as an idle channel is 1−Pd. In other words,

Pr(Dn = 1) =

{V0 = 1 − Pf , if nth channel is idle;V1 = 1 − Pd, if nth channel is occupied. (21)

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And the probability of the ith idle channel is detected with nofalse alarm by one SU is Pr(Di = 1) = V0.

To obtain the analytical result on the average systemthroughput under imperfect sensing, we start by rederiving theprobability of the ith idle channel selected for packet accessingby one SU in Lemma 1, psac, im. Define Φ as the set of thedetected channels by one SU. First, the probability that theith channel is scanned and included in the Ms idle channelsout of the Ns sensed channels is expressed as,

Pr(the ith idle channel is scanned|Ms)

=

(M − 1

Ms − 1

)(N − M

Ns − Ms

)/

(N

Ns

).

(22)

Assume MD (MD ∈ [1, Ns]) channels are detected as idlechannels within the Ns sensed channels. Out of the MDdetected idle channels, the number of the idle channelsdetected correctly is mID (mID ∈ [max{1, Ms − (Ns −MD)},min{Ms, MD}]) and the number of the occupied chan-nels detected as idle status is mOD (mOD = MD−mID). Thus,conditioning on MD and Ms, the probability of the ith idlechannel being detected as idling is,

Pr(Di = 1|Ms, MD)

= Pr(Di = 1) · Pr(∑

n̸=i,n∈Φ

Dn =MD − 1|Ms)

= V0 ·min{MD,Ms}∑

mID=max{1,MD−(Ns−Ms)}

(Ms − 1

mID − 1

)(V0)

mID−1

· (1−V0)Ms−mID

(Ns − Ms

mOD

)(V1)

mOD(1−V1)Ns−Ms−mOD .

(23)

Substituting mOD = MD − mID into (23),

Pr(Di = 1|Ms, MD)

=

min{MD,Ms}∑mID=max{1,MD−Ns+Ms}

(Ms−1

mID−1

)V0

MID(1−V0)Ms−mID

·(

Ns − Ms

MD − mID

)(V1)

MD−mID(1 − V1)Ns−Ms−(MD−mID).

(24)

With the MD detected idle channels (including the ith idlechannel), the probability of a packet accessing the ith idlechannel is 1/MD. Then, with Ms scanned channels and MDdetected channels, the probability of the ith idle channel isselected for packet access is obtained as following,

pisac, im|(Ms,MD) = Pr(the ith idle channel is scanned|Ms)

· 1

MD· Pr(Di = 1|Ms, MD).

(25)

Hence, the probability of the packet from one SU accessing aspecific idle channels is

pisac, im =

min{Ns,M}∑Ms=max{1,Ns−(N−M)}

Ns∑MD=1

pisac, im|(Ms,MD).

It is observed that pisac, im is invariant w.r.t i. We may drop the

superscript for simplicity: psac, im. Given psac, im, the averagesystem throughput under imperfect spectrum sensing Ssys, imcan be presented as following, according to (6),

Ssys, im =ηNp

Ns + ηNpMKptrapsac, im(1 − psac, im)Kptra−1. (26)

VI. SIMULATION RESULTS

In this section, we present the results of the average systemthroughput via Monte-Carlo simulation. In our simulation, Wehave considered N = 10 licensed channels. The samplingfrequency fs is set as 6MHz. The overall detection probabilityfor SU is always kept at Pd = 0.9 under imperfect spectrumsensing. The length of one sensing unit, TSm, is set at 2ms. The duration of one unit transmission time is set to be2TSm, i.e., η = 2. Since the actual spectrum sensing timeτ ∈ (0, TSm] may vary, we only consider the minimum Pf

attained at τ = TSm in our simulations. And the numberof packet transmission slots is set as Np = 30. The M idlechannels are randomly located within the N channels. Withinan access frame duration TAF, each SU randomly selects Ns

channels for sensing in TS and transmits the packet on any oneof the idle channels identified as idle among the Ns channelsselected.

The average throughput is obtained by counting the numberof the idle channels which have only one packet access ineach time slot within Np packet transmissions slots. We applythe free space propagation model with the path-loss exponentβ = 2 in our simulations as in [16]. The SNR at SU receivercan be expressed as,

γ = PS,PU · Dsu−β/N0, (27)

where PS,PU is the transmission power from the PU and Dsu

is the distance between the SUs and PU. N0 is the averagepower of noise, which is assumed to be the same for each SU.Moreover, we assume the worst γ at an SU receiver is −20dB.

Fig. 3 and Fig. 4 present the average number of packets insuccessful transmissions when each SU transmits the packetwith ptra = 1. First, we see that the analytical results in (3) fitwell with the simulation results in Fig. 3 and Fig. 4, respec-tively. The average number of successful transmitted packetsis constant when Ns > N −M as circled points in Fig. 3 andFig. 4, which means it is independent on Ns as specified inLemma 1. It is intuitive that the average number of successfultransmitted packets increases with M . Further, when K < M ,the average number of packets in successful transmissionincreases with Ns until Ns = N − M + 1. Conversely, whenK > N , the average number of successful transmitted packetsdeclines as Ns increases. For M ≤ K ≤ N , it is noted thatthe number of successful transmitted packets first increaseswith Ns, then decreases after the maximum point. This occursbecause increasing Ns ultimately brings more collisions andreduces successful transmissions.

In Fig. 5 and Fig. 6, the average system throughput aredepicted when the probability of packet transmission is given.The analytical results in (6) and the simulation results al-most coincide with each other. It can been observed that ifKptra > N , e.g. K = 15, the throughput is decreasing withNs raising, thus the optimal N∗

s = 1. For Kptra ≤ N , thethroughput achieves the maximal point according to Proposi-tion 1. Further, the throughput in K = 3 and K = 6 are largerthan that in K = 15 as Ns growing shown in Fig. 6, sincemore collisions result.

Fig. 7 depicts the maximal throughput of the system withincreasing K and the optimal pair (Ns, ptra) corresponding to

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 7

1 2 3 4 5 6 7 8 9 10

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

Ns (Number of sensing channels)

Ave

rage

num

ber

of s

ucce

ssfu

lly t

rans

mit

ted

pack

ets

Simulation Result, M=4Analysis Result of (3), M=4Simulation Result, M=6Analysis Result of (3), M=6Simulation Result, M=8Analysis Result of (3), M=8

Fig. 3. Average number of successfully transmitted packets in ptra = 1 andK = 6.

1 2 3 4 5 6 7 8 9 100.4

0.6

0.8

1

1.2

1.4

1.6

Ns (Number of sensed channels)

Ave

rage

num

ber

of s

ucce

ssfu

lly t

rans

mit

ted

pack

ets

Simulation Result, K=3Analysis Result of (3), K=3Simulation Result, K=6Analysis Result of (3), K=6Simulation Result, K=12Analysis Result of (3), K=12

Fig. 4. Average number of successfully transmitted packets in ptra = 1 andM = 4.

1 2 3 4 5 6 7 8 9 10

1.4

1.6

1.8

2

2.2

2.4

2.6

Ns (Number of sensed channels)

Ave

rage

sys

tem

thr

ough

put

Simulation result, M=4Analytical result of (6), M=4Simulation result, M=6Analytical result of (6), M=6Simulation result, M=8Analytical result of (6), M=8

Fig. 5. Average system throughput when K = 6 and ptra = 0.8.

the maximal throughput are enumerated in Table I. From Fig.7, the analytical results of the system throughput are matchingclosely with that of the simulation results. Moreover, the

1 2 3 4 5 6 7 8 9 100.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Ns (Number of sensed channels)

Ave

rage

sys

tem

thr

ough

put

Simulation result, K=3Analytical result of (6), K=3Simulation result, K=6Analytical result of (6), K=6Simulation result, K=15Analytical result of (6), K=15

Fig. 6. Average system throughput when M = 4 and ptra = 0.8.

2 4 6 8 10 12 14 161.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

K (Number of SUs)

Ave

rage

Sys

tem

Thr

oghp

ut

Maximal throughput (simulation), M=4

Optimized throughput (analysis), M=4

Maximal throughput (simulation), M=6

Optimized throughput (analysis), M=6

Maximal throughput (simulation), M=8

Optimized throughput (analysis), M=8

Fig. 7. Optimal average system throughput.

throughput improves with increasing number of idle channelsin the spectrum. Moreover, there exists an optimal number ofSUs for each M value. As depicted in Fig. 7, the optimalnumber of SUs is equal or close to M .

Fig. 8 and Fig. 9 illustrate the system throughput under fixedM and random M with increasing values of Ns, respectively.The analytical results under a random M match closely withthe simulation results. It is observed that the system throughputunder a fixed M and a random M follow the same trend whenE[M] = qN = M . That means Theorem 3 can be also appliedto the situations with random number of idle channels basedon E[M]. Specifically, the system throughputs under a fixedM and a random M attain the same value when Ns = 1. Inaddition, the system throughput curve under a random M isparallel with that under a fixed M when Ns ≥ N − M + 1.

In Fig. 10, the average system throughput under imperfectsensing is plotted as a function of the distance Dsu. It isnoted that the growing Dsu will reduce the SNR, γ, at the SUreceiver, which in turn leads to an increasing Pf accordingto (20). The results show the effects of the physical fadingchannel on the SU spectrum sensing performance. At theoptimal point (N∗

s , p∗tra) attained based on Theorem 3, thesystem throughput under perfect sensing is constant under

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 8

1 2 3 4 5 6 7 8 90.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Ns (Number of sensed channels)

Ave

rage

sys

tem

thr

ough

put

Simulation result, M=4, K=6Simulation result, M=4, K=12Simulation result, E[M]=4, K=6Simulation result, E[M]=4, K=12Analytical result, E[M]=4, K=6Analytical result, E[M]=4, K=12

Fig. 8. Average system throughput when E[M] = 4.

1 2 3 4 5 6 7 8 9

2.5

2.6

2.7

2.8

2.9

3

3.1

3.2

Ns (Number of sensed channels)

Ave

rage

sys

tem

thr

ough

put

Simulation result, M=8, K=6Simulation result, M=8, K=12Simulation result, E[M]=8, K=6Simulation result, E[M]=8, K=12Analytical result, E[M]=8, K=6Analytical result, E[M]=8, K=12

Fig. 9. Average system throughput when E[M] = 8.

10 20 30 40 50 60 70 80 90 1001

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Distance from SUs to PU (m)

Ave

rage

Sys

tem

Thr

ough

put

Optimal throughput (simulation), perfect sensing, K=3Optimal throughput (analysis), perfect sensing, K=3Simulation result, imperfect sensing, K=3Analytical result, imperfect sensing, K=3Optimal throughput (simulation), perfect sensing, K=15Optimal throughput (analysis), perfect sensing, K=15Simulation result, imperfect sensing, K=15Analytical result, imperfect sensing, K=15

Fig. 10. Average system throughput under perfect and imperfect sensing.

different Dsu, while the system throughput under imperfectsensing reduces as Dsu grows. That implies it is also beneficialto reduce the false alarm probability Pf to maximize thesystem throughput.

TABLE IOPTIMAL (Ns, pTRA) FOR THROUGHPUT MAXIMIZATION

K = 3 K = 6 K = 9 K = 12 K = 15

M = 4 (5, 1) (2, 1) (1, 1) (1, 0.83) (1, 0.67)

M = 6 (4, 1) (2, 1) (1, 1) (1, 0.83) (1, 0.67)

M = 8 (3, 1) (2, 1) (1, 1) (1, 0.83) (1, 0.67)

VII. CONCLUSION

In this paper, we have introduced the “extended sensingstrategy” in which each SU randomly selects a subset ofchannels out of a spectrum of N channels for sensing. Fol-lowing that, each SU transmits the packet in any one of thedetected idle channels. The slotted ALOHA scheme is utilizedfor access to idle channels. From the analysis, we concludethat the effective number of sensing channels Ns is dependenton the total number of licensed channels N and the numberof the idle channels M , i.e., Ns ≤ N − M + 1. The systemthroughput under a random number of idle channel M isalso analyzed and compared with that under a fixed numberof idle channels M . Then, the optimal Ns is analyzed andreveals the relationship between Ns and the average systemthroughput. Later on, we formulated a joint optimizationproblem with respect to (Ns, ptra) and obtained the optimalsystem throughput. Thus, notice that sensing strategy is relatedto the packet transmission probability. That means to improvethe system throughput, each SU should take both Ns andptra in consideration. Finally, we have analyzed the averagesystem throughput under the imperfect sensing. Comparingthe simulation and analytical results, it is concluded thatthe system throughput from our analysis almost arrives atthe simulation results. Further, besides the slotted ALOHAscheme, we can also apply the “extended sensing strategy” toother effective MAC schemes, which will be one of our futureresearches.

APPENDIX

Let Xij be the indicator random variable, where i ∈{1, 2, . . . ,M}, j ∈ {1, 2, . . . , U}, and U is the total numberof packets to be transmitted from all SUs within one TPm. Sothat Xij = 1 if jth the packet selects the ith idle channel foraccess, otherwise Xij = 0, and Xi =

∑Kj=1 Xij indicates the

number of packets which select the ith idle channel. For eachXij represents a Bernoulli trial, the probability that jth packet(or any one packet) selects the ith idle channel (any givenchannel) for access when Ms idle channels are detected, canbe presented as,

p(i)

sac|Ms= pidl(Ms) ·

(M − 1

Ms − 1

)/(M

Ms

)· 1

Ms(28a)

= pidl(Ms) ·1

M(28b)

,where

pidl(Ms) =

(M

Ms

)(N − M

Ns − Ms

)/(N

Ns

)(29)

is the probability of Ms idle channels sensed by one SUand the second term in (28a) is the probability of ith idlechannel included in the Ms idle channels. The probability of

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 9

the packet selecting the ith idle channel out of the Ms idlechannels is 1/Ms as presented in the third term in (28a), sincethe probability of selecting any one idle channel within Msidle channels is equal to each other. Hence, the probability ofthe jth packet selecting the ith channel, p

(i)sac, is

p(i)sac = p(Xij = 1) =

min{M,Ns}∑Ms=1

p(i)

sac|Ms(30a)

=1

M

min{M,Ns}∑Ms=1

pidl(Ms) =1

Mpidl(Ms ≥ 1) (30b)

=1

M(1 − pidl(Ms = 0)), (30c)

Thus, if Ns ≥ N − M + 1, it will always contains at leastone idle channel within the Ns detected channels which meanspidl(Ms = 0) = 0. While, if Ns ≤ N−M , the packet will failto access when the channels included in Ns sensed channelare all occupied by PUs, which implies no idle channel withinNs channels, so

pidl(Ms =0)=

(

N−M

Ns

)/(N

Ns

), if Ns ≤ N − M ;

0, if Ns ≥ N − M + 1;

=

{(N−Ns)[M]

N [M] , if Ns ≤ N − M ;0, if Ns ≥ N − M + 1; ,

(31)

where L[k] = L(L − 1) · · · (L − (k − 1)). Consequently, theprobability, p

(i)sac, of one packet selecting the ith idle channel

accessing is

p(i)sac =

1 − pidl(Ms = 0)

M

=

{1M

(1 − (N−Ns)[M]

N [M]

), if N − M ≥ Ns,

1M

, else.

(32)

From (32), it can be observed that p(i)sac is not related to Ms.

That implies that accessing a given idle channel will not beaffected by the number of the idle channels sensed by an SU.

To prove the monotonic property of p(i)sac, we first relax Ns

as 0 < N̄s ≤ N − M . Then we can differentiate p(i)sac as

followings,

∂p(i)sac

∂N̄s

= Υ

M−1∑j=0

1

(N − N̄s − j)> 0, (33a)

∂2p(i)sac

∂N̄2s

= Υ

M−1∑j=0

1

(N − N̄s − j)2−

(∂p

(i)sac

∂N̄s)2

Υ< 0, (33b)

where Υ = (N−N̄s)[M]

M ·N [M] . Through differentiating (32) withrespect N̄s, we can know the probability psac is an increasingfunction versus Ns.

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[1] J. M. III, Cognitive radio: An Integrated Agent Architecture for SoftwareDefined Radio. Ph.D. Thesis, KTH (Royal Institute of Technology),2000.

[2] C. Cordeiro, K. Challapali, and M. Ghosh, “Cognitive phy and maclayers for dynamic spectrum access and sharing of tv bands,” in Proc.1st ACM international workshop on Technology and policy for accessingspectrum (TAPAS 06), 2006, p. 3.

[3] B. Hamdaoui and K. Shin, “Os-mac: An efficient mac protocol forspectrum-agile wireless networks,” IEEE Transactions on Mobile Com-puting, vol. 7, no. 8, pp. 915–930, 2008.

[4] H. Su and X. Zhang, “Cross-layer based opportunistic mac protocols forqos provisionings over cognitive radio wireless networks,” IEEE Journalon Selected Areas in Communications, vol. 26, no. 1, pp. 118 –129, 2008.

[5] ——, “Design and analysis of a multi-channel cognitive mac protocolfor dynamic access spectrum networks,” in Proc. IEEE Military Com-munications Conference (MILCOM), 2008, pp. 1 –7.

[6] S. Choe and S.-K. Park, “Throughput of slotted aloha based cognitiveradio mac,” in Proc. 4th International Conference on Ubiquitous Infor-mation Technologies Applications (ICUT ’09), 2009, pp. 1 –4.

[7] S. Choe, “Performance analysis of slotted aloha based multi-channelcognitive packet radio network,” in Proc. 6th IEEE Consumer Commu-nications and Networking Conference (CCNC), 2009, pp. 1 –5.

[8] R. Rajbanshi, “Ofdm-based cognitive radio for dsa networks,” Infor-mation and Telecommunication Technology Center, The University ofKansas, Tech. Rep., 2007.

[9] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, “Next genera-tion/dynamic spectrum access/cognitive radio wireless networks: A sur-vey,” Computer Networks, vol. 50, no. 13, pp. 2127 – 2159, 2006. [On-line]. Available: http://www.sciencedirect.com/science/article/B6VRG-4K00C5M-4/2/3ad0ce34d1af95ffc509bf0ccaa455ab

[10] Y.-C. Liang, Y. Zeng, E. Peh, and A. T. Hoang, “Sensing-throughputtradeoff for cognitive radio networks,” IEEE Transactions on WirelessCommunications, vol. 7, no. 4, pp. 1326 –1337, 2008.

[11] Z. Quan, S. Cui, A. Sayed, and H. Poor, “Optimal multiband jointdetection for spectrum sensing in cognitive radio networks,” IEEETransactions on Signal Processing, vol. 57, no. 3, pp. 1128 –1140, 2009.

[12] L. Luo, C. Ghosh, and S. Roy, “Joint optimization of spectrum sensingfor cognitive radio networks,” in Proc. IEEE Global TelecommunicationsConference (GLOBECOM), dec. 2010, pp. 1 –5.

[13] L. Luo, N. Neihart, S. Roy, and D. Allstot, “A two-stage sensingtechnique for dynamic spectrum access,” IEEE Transactions on WirelessCommunications, vol. 8, no. 6, pp. 3028 –3037, jun. 2009.

[14] X. Li, H. Liu, J. Zhang, and P. Zhang, “A novel method for systemparameters estimation in distributed cognitive radio networks,” submittedto IEEE Communications Letters, 2012.

[15] Q. Chen, M. Motani, W.-C. Wong, and Y.-C. Liang, “Opportunisticspectrum access protocol for cognitive radio networks,” in Proc. IEEEInternational Conference on Communications (ICC), jun. 2011, pp. 1–6.

[16] T. Rappaport et al., Wireless communications: principles and practice.Prentice Hall PTR New Jersey, 1996, vol. 207.

Xiaofan Li received the B.S. degrees from Bei-jing University of Posts and Telecommunications(BUPT), Beijing, China. She is currently workingtowards her Ph.D degree at Key Lab of UniversalWireless Communications, Ministry of Education inBUPT. From September 2010 to September 2011,she studied in University of Washington as anexchanged Ph.D student. She was awarded ”Out-standing Graduate Student” of BUPT. Her currentresearch interests include resource management incooperative communication and throughput analysis

in distributed cognitive radio system.

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Hui Liu , ZhiYuan Chair Professor, received his B.S.in 1988 from Fudan University, Shanghai, China,, and a Ph.D. degree in 1995 from the Univ. ofTexas at Austin, all in electrical engineering. He waspreviously an assistant professor at the Dept. of EEat Univ. of Virginia and a full professor at the Dept.of EE, Univ. of Washington. Dr. Liu was one of theprincipal designers of the TD-SCDMA technologies.He founded Adaptix in 2000 and pioneered thedevelopment of OFDMA-based mobile broadbandnetworks (mobile WiMAX and 3G LTE). Dr. Liu

is the creator of CMMB transmission technology which enables the deliveryof mobile TV services to more than a billion of population in different regionsof the world.

Dr. Liu has published 45 journal articles and has 67 awarded patents. Heis the author of ”OFDM-Based Broadband Wireless Networks C Design andOptimization,” Wiley 2005, and ”Signal Processing Applications in CDMACommunications,” Artech House, 2000. He was selected Fellow of IEEEfor contributions to global standards for broadband cellular and mobilebroadcasting. He is the General Chairman for the 2005 Asilomar conferenceon Signals, Systems, and Computers. He is a recipient of 1997 NationalScience Foundation (NSF) CAREER Award, the Gold Prize Patent Award inChina, and 2000 Office of Naval Research (ONR) Young Investigator Award.

Sumit Roy received the B. Tech. degree from theIndian Institute of Technology (Kanpur) in 1983, andthe M. S. and Ph. D. degrees from the Universityof California (Santa Barbara), all in Electrical Engi-neering in 1985 and 1988 respectively, as well as anM. A. in Statistics and Applied Probability in 1988.Presently he is Professor of Electrical Engineering,Univ. of Washington where his research interestsinclude analysis/design of wireless communicationand sensor network systems with a diverse emphasison various technologies: wireless LANs (802.11)

and emerging 4G standards, multi-standard wireless inter-networking andcognitive radio platforms, vehicular and underwater networks, and sensornetworking involving RFID technology.

He spent 2001-03 on academic leave at Intel Wireless Technology Lab as aSenior Researcher engaged in systems architecture and standards developmentfor ultra-wideband systems (Wireless PANs) and next generation high-speedwireless LANs. During Jan-July 2008, he was Science Foundation of Ireland’sE.T.S. Walton Awardee for a sabbatical at University College, Dublin andwas the recipient of a Royal Acad. Engineering (UK) Distinguished VisitingFellowship during summer 2011. His activities for the IEEE CommunicationsSociety (ComSoc) includes membership of several technical and conferenceprogram committees, notably the Technical Committee on Cognitive Net-works. He currently serves on the Editorial Board for IEEE Trans. Communi-cations and IEEE Intelligent Transportation Systems. He was elevated to IEEEFellow by Communications Society in 2007 for his “contributions to multi-user communications theory and cross-layer design of wireless networkingstandards”.

Jianhua Zhang received her Ph.D. degree in cir-cuit and system from Beijing University of Postsand Telecommunication (BUPT) in 2003. She isan associate professor from 2005 and now she isprofessor of BUPT. She has published more than100 articles in referred journals and conferences.She was awarded ”2008 Best Paper” of Journal ofCommunication and Network. In 2009, she receivedsecond prize award by CCSA for her contributions toITU-R and 3GPP in IMT-Advanced channel model.In 2011, she was awarded the ”New Century Ex-

cellent Talents in University” by MOE and ”Young Talent Teachers” byFok Ying Tung Education Foundation. Her current research interests includepropagation models, green techniques for IMT-Advanced and beyond system,Relay, CoMP and Cognitive Radio techniques, etc.

Ping Zhang Ph.D and Prof. of BUPT, focusesresearch on wireless communication, new technolo-gies for cognitive radio, cognitive wireless networks,TD−LTE, MIMO, OFDM and etc. He is ExecutiveAssociate Editor-in-chief on information sciencesof Chinese Science Bulletin, a Member of next-generation broadband wireless communication net-work in National Science and Technology MajorProject committee, a Member of the 5th Advi-sory Committee of NSFC(National Natural ScienceFoundation of China), the Chief Scientist of ”973“

National Basic Research Program of China, He applied over 114 patents with51 authorized patents.

He received award of National Science and Technology Advance Prizetwice, Award of National Science and Technology Invention Prize once, theProvincial Science and Technology Awards many times,and was given theTitle of Outstanding Scientific and Technological Workers in 2010.

Chittabrata Ghosh is currently a Senior Researcherat Nokia Research Center (NRC), Berkeley, CAsince July 2011. Before joining NRC, he was aPostdoctoral Researcher at University of Washing-ton, Seattle since July 2009. He had received Ph.D.degree from Department of Computer Science, Uni-versity of Cincinnati, OH in 2009. He is activelyinvolved in IEEE standardization activities focusingon system design and architecture for low power Wi-Fi networks. Apart from this, his research interestsinclude analysis of coexistence issues among various

cooperating wireless networks and MAC layer optimization techniques forwireless sensor networks. He is also leading Nokia’s university researchcollaborations on multi-faceted research and policy issues in the TV WhiteSpaces. His activities for the IEEE Communications Society (ComSoc)include membership of several technical and conference program commit-tees. He is also the Vice Chair and Co-Editor of Technical Committee onSimulations under the IEEE Computer Society.