Multi-Channel MAC Protocol for Full-Duplex Cognitive Radio Networks with Optimized Access Control and Load Balancing

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by  Tan Le Thanh

1
Multi-Channel MAC Protocol for Full-Duplex
Cognitive Radio Networks with Optimized Access
Control and Load Balancing
Le Thanh Tan and Long Bao Le
Abstract—Inthispaper,weproposeamulti-channelfull-duplex perform sensing and transmission simultaneously; however,
Medium Access Control (MAC) protocol for cognitive radio the work [6] assumes simultaneous spectrum access of the
networks (MFDC–MAC). Our design exploits the fact that full-
SU and PU networks. This design is, therefore, not applicable
duplex(FD)secondaryusers(SUs)canperformspectrumsensing
to the hierarchical spectrum access in the CRNs where PUs
6 and access simultaneously, and we employ the randomized
1 dynamic channel selection for load balancing among channels shouldhavehigherspectrumaccessprioritycomparedtoSUs.
0 andthestandardbackoffmechanismforcontentionresolutionon In this paper, we propose a novel MFDC–MAC protocol
2 each available channel. Then, we develop a mathematical model that allows concurrent spectrum sensing and transmission on
toanalyze thethroughput performanceofthe proposedMFDC– each channel as well as efficient access and load balancing
b MACprotocol.Furthermore,westudytheprotocolconfiguration
among the channels. In our design, each SU adopts the
e optimization to maximize the network throughput where we
F show that this optimization can be performed in two steps, randomized channel selection to choose its channel, which
namely optimization of access and transmission parameters on is slowly updated over time for load balancing. Moreover,
1
each channel and optimization of channel selection probabilities SUs employ the standard p-persistent CSMA mechanism for

of the users. Such optimization aims at achieving efficient self- contentionresolutionontheselectedchannel,andthewinning
]
interference management for FD transceivers, sensing overhead
T SU follows a two-stage procedure for spectrum sensing and
control, and load balancing among the channels. Numerical
I resultsdemonstratetheimpactsofdifferentprotocolparameters access. Specifically, the winning SU performs simultaneous
.
s andtheimportanceofparameteroptimizationonthethroughput sensing and transmission during the first stage and transmis-
c performance as well as the significant performance gain of the sion only in the second stage. This design enables appropriate
[
proposed design compared to traditional design.
protectionofPUsandefficientexploitationofwhitespaceson

1 Index Terms—MAC protocol, spectrum sensing, optimal sens- all the channels.
v ing, throughput maximization, full-duplex cognitive radios. We develop a mathematical model for throughput perfor-
6
mance analysis of the proposed MFDC-MAC protocol con-
6
3 I. INTRODUCTION sidering the imperfect sensing and self-interference effects.
Moreover, we study the optimal configuration of different
0
Design of MAC protocols for efficient sharing of white
0 protocol parameters for spectrum sensing, access, and load
spaces and appropriate protection of transmissions from pri-
. balancing (i.e., channel access probabilities) to achieve the
2 mary users (PUs) on licensed frequency in cognitive radio
maximum throughput. Extensive numerical results are then
0 networks (CRNs) is an important research topic. In the tra-
6 presented to illustrate the impacts of different protocol pa-
ditional design and analysis of a half-duplex (HD) MAC
1 rameters on the throughput performance and the significant
protocol [1], [2], [3], [4], [5], SUs typically employ a two-
: throughput gains of the proposed MFD-MAC protocol with
v stage sensing/access procedure due to the HD constraint [3],
respect to conventional designs.
i [4], [5]. This constraint also requires SUs be synchronized
X Theremainingofthispaperisorganizedasfollows.Section
during the spectrum sensing stage, which could be difficult
r IIdescribesthesystemandPUactivitymodels.MACprotocol
a to achieve in practice. Moreover, sophisticated design and
design and throughput analysis are performed in Section III.
parameterconfigurationofcognitiveMACprotocolscanresult
We discuss the protocol optimization in Section IV. Section
in significant performance enhancement while appropriately
V demonstrates numerical results followed by concluding
protecting SUs [4], [5]. Furthermore, different multi-channel
remarks in Section VI.
cognitive MAC protocols were proposed considering either
different spectrum sensing and access methods [1], [2].
By employing the advanced FD transceiver, each SU can II. SYSTEMANDPUACTIVITYMODELS
transmit and receive data simultaneously on the same fre- A. System Model
quency band [7]. Practical FD transceivers, however, suffer
WeconsideranetworksettingwhereN pairsofSUsoppor-
from self-interference, which is caused by power leakage
tunistically exploit white spaces on M frequency channels for
from the transmitter to the receiver. The self-interference may
data transmission. We assume that each SU is equipped with
indeed lead to serious communication performance degrada-
one full-duplex transceiver, which can perform sensing and
tion of FD wireless systems. Employment of FD transceivers
transmission simultaneously. However, any SU suffers from
for more efficient spectrum access design in cognitive radio
self-interference from its transmission during sensing (i.e.,
networks has been very under explored in the literature. The
transmitted signals are leaked into the received signal). At
cognitive MAC design in one recent work [6] allows SUs to
channelj,wedenoteI astheaverageself-interferencepower,
j
whichisassumedtobemodeledasI =ζ(P )ξ [7]where
TheauthorsarewithINRS-EMT,UniversityofQuebec,Montre´al,Que´bec, j sen,j
Canada.Emails:{lethanh,long.le}@emt.inrs.ca. Psen,j is the SU transmit power, ζ and ξ (0 ≤ ξ ≤ 1) are
2
DIFS SIFS SIFS SIFS we consider the general heterogeneous scenario where the
statistical parameters τj and τj of different channel j can
DIFS RTS RTS CTS DATA ACK ac id
be different. This channel selection is repeated once after a
Collision RTS/CTS exchange Data Transmission
predetermined long period, which is an order of magnitude
. . . DATA . . . DATA . . . time larger than the average contention/access time to transmit one
I C C I U data frame (packet) on each channel (e.g., every Kmax data
Contention and access cycle Contention and access cycle frames).
Contention phase Data phase After channel selection, each SU employs the following
T T
ove T T T single-channelcontention,spectrumsensing,andtransmission
S S
to exploit the white space. Specifically, SUs choosing the
Channel is available Channel is not available
Case 1 same channel j is assumed to employ the p-persistent CSMA
Sensing stage Tx stage Sensing stage Tx stage PU activity h00 h00 h00,h00! principle[9]forcontentionresolutionwhereeachSUattempts
h h
00 01 Case 2 to capture the channel with a probability p after the channel
DATA 1 DATA 2 DATA 1 PU activity h ,h ! is sensed to be idle during the standard DIFS interval (DCF
t 00 01
FD T Teva FD T Teva 1 Interframe Space). If a particular SU decides not to transmit
Activesensing SU Activesensing SU h01 h11 Case 3 (with probability of 1−p), it will carrier sense the channel
Collision (C) Idle (I) PU acttivity h01,h11! and attempt to transmit again in the next slot with probability
Successful channel reservation (U) 1 p.
To complete the reservation, the four-way handshake with
Request-to-Send/Clear-to-Send (RTS/CST) exchanges [9] is
Fig.1. Timingdiagramoftheproposedfull-duplexMACprotocol.
employed to reserve the available channel for transmission
in the next phase. After each successful transmission of du-
ration T , an acknowledgment (ACK) from the SU’s receiver
predetermined coefficients which capture the self-interference j
is transmitted to its corresponding transmitter to notify the
cancellation quality. We design an asynchronous MAC pro-
successful reception of a packet. Furthermore, the standard
tocol where no synchronization is required between SUs and
small interval, namely SIFS (Short Interframe Space), is used
PUs as well as among SUs. We assume that different pairs
before the transmissions of CTS, ACK, and data frame as in
of SUs can overhear transmissions from the others (i.e., a
the standard 802.11 MAC protocol [9].
collocated network). In the following, we refer to pair i of
Then, the data phase after the channel contention phase
SUs simply as SU i.
comprisestwostageswherethewinningSUperformsconcur-
rent sensing and transmission in the first stage with duration
B. Primary User Activity T (called FD sensing stage) and transmission only in the
S,j
We assume that the PU’s idle/busy status follows two second stage with duration Tj − TS,j (called transmission
independent and identical distribution processes. In particular, stage).Here,theSUexploitstheFDcommunicationcapability
each channel is available and busy for the secondary access if ofitstransceivertorealizeconcurrentsensingandtransmission
the PU is in the idle and busy states, respectively. Let H the first stage where the sensing outcome at the end of this
0
and H denote the events that the PU is idle and active, stage (i.e., an idle or active channel status) determines its
1
respectively. To protect the PU, we assume that SUs must further actions as described in the following. If the sensing
stop their transmission and evacuate from the channel within outcome indicates an available channel then the SU transmits
the maximum delay of T , which is referred to as channel data in the second stage; otherwise, it remains silent for the
eva
evacuation time. remaining period of the data phase with duration Tj −TS,j.
Letτajc andτijd denotetherandomvariableswhichrepresent We assume that the duration of the SU’s data phase Tj
the durations of channel active and idle states on channel is smaller than the channel evacuation time Teva so timely
j, respectively. We assume that τj and τj are larger than evacuation from the busy channel can be realized. Therefore,
ac id
T with high probability. We denote probability density our design allows to protect the PU with evacuation delay
eva
pfaudrendsciettiinootnnt,shleoeftprτPoajcb(cid:16)aaHbnid0jli(cid:17)tτieijd=sathsτ¯iajdfτ¯t+τijdtτ¯ajhcajce(tac)nhadanndPnef(cid:16)lτHiijds(1jat(cid:17)v)a,=irleasb1plee−catPnivde(cid:16)lbHyu.s0jIy(cid:17)n, aaFletnuvdrmetlhostehsPrtemTosjrpeie,facnttwrhdueemPcaassrseruidnemusrirenisngegtnhsitainhntegttFhhbDeeefosdSeraUentastihntrpegahncaasonsmendtiettasrnarteniaostnmpepiprsohfsweiaocsetner.
sen,j dat
respectively. stages, respectively where the transmit power P will be
sen,j
chosentoeffectivelymitigatetheself-interferenceandachieve
III. MULTI-CHANNELFULL-DUPLEXCOGNITIVEMAC good sensing-throughput tradeoff. The timing diagram of the
PROTOCOL proposed MFDC–MAC protocol is illustrated in Fig. 1.
In this section, we describe our proposed MFDC-MAC
protocol and conduct its throughput analysis considering im- B. Throughput Analysis
perfect sensing and self-interference of the FD transceiver.
We now analyze the saturation throughput. Recall that for
eachchannelj,thePUisactiveandidlewiththecorrespond-
A. MFDC–MAC Protocol Design ing pdfs of τj and τj are f (cid:0)τj(cid:1) and f (cid:16)τj(cid:17). Moreover,
ac id τajc ac τijd id
InourMFDC-MACprotocol,eachSUrandomlyselectsone we assume that the received PU’s signal power at the SU’s
channel by using a randomized channel selection mechanism receiver for channel j is Pj. The throughput is a function of
p
wherechannelj isselectedwithprobabilitypsec.Inthispaper, following parameters: probability of transmission p, sensing
j
3
time T , frame length T , and SU transmit power P As being shown in Fig. 1, there can be several idle periods
S,j j sen,j
for each channel j. For brevity, we ignore the dependence and collisions before one successful channel reservation. Let
of throughput on p and T in the following. Ti denote the i-th idle duration between two consecutive
j idle,j
To calculate the throughput of the MFDC–MAC pro- RTS/CTS exchanges on channel j, which can be collisions
tocol, denoted as NT, we consider all possible cases or successful exchanges. Then, Ti can be calculated based
idle
where each case is represented by the corresponding sets on its probability mass function (pmf), which is derived as
of users selecting different channels (each set of users follows. In the following, all relevant quantities are defined
is for one channel). We now define the set Ω = in terms of the number of time slots. With n SUs joining
(cid:110) (cid:111) k,j
ωk={nk,1,...,nk,j,...,nk,M}:(cid:80)Mj=1nk,j=N where its the contention resolution on channel j, let Psucc,j, Pcoll,j and
P denote the probabilities that a particular generic slot
k-th element ω has its components n representing the idle,j
k k,j
corresponds to a successful transmission, a collision, and an
number of users who select channel j. The probability for
the set ω is (cid:81)M (cid:0)psec(cid:1)nk,j. Then, the network throughput idle slot, respectively. These probabilities can be calculated as
k j=1 j follows:
can be expressed as
NT(cid:16)P(cid:126)sec,T(cid:126) ,P(cid:126) (cid:17)=(cid:88)|Ω|(cid:32) N (cid:33)(cid:89)M(cid:0)psec(cid:1)nk,j PPsucc,j == n(1k,−jpp()1n−k,jp)nk,j−1 ((56))
S sen {n } j idle,j
k,j
k=1 j=1 P = 1−P −P , (7)
coll,j succ,j idle,j
M
(cid:88)NT (T ,P |n )I(n >0), (1) where p is the transmission probability of an SU in a generic
j S,j sen,j k,j k,j
slot. In general, the interval T , whose average value is
j=1 cont,j
T given in (3), consists of several intervals correspond-
cont,j
where NT (T ,P |n )I(n >0) represents the
j S,j sen,j k,j k,j ing to idle periods, collisions, and one successful RTS/CTS
throughput contributed by channel j given that n users
k,j transmission. Hence, this quantity can be expressed as
select this channel; and I(.) denotes the indicator func-
(cid:32) N (cid:33) Ncoll,j
tion. Moreover, is the multinomial coefficient T = (cid:88) (cid:0)T +Ti (cid:1)+TNcoll,j+1+T , (8)
{n } cont,j coll idle,j idle,j succ
k,j
(cid:32) (cid:33) (cid:32) (cid:33) i=1
N N
which is defined as = = where Ncoll,j is the number of collisions before the successful
{n } n ,n ,...,n
k,j k,1 k,2 k,M RTS/CTS exchange on channel j and N is a geometric
coll,j
nkF,1u!nrkth,N2e!.r.m.nok,rMe,!. the throughput of channel j rPaniddleo,jm=va1r−iabPleidl(eR,jV.)Twheitrhefpoarera,mitsetperm1f−caPncoblle,je/xPpirdeles,sjewdhaesre
NTj(TS,j,Psen,j|nk,j) can be calculated as (cid:18)P (cid:19)x(cid:18) P (cid:19)
fNcoll,j(x)= coll,j 1− coll,j , x=0,1,2,... (9)
NT (T ,P |n )= Bj . (2) X Pidle,j Pidle,j
j S,j sen,j k,j T +T
ove,j j Also, T represents the number of consecutive idle slots
idle,j
where Tove,j represents the time overhead required for one on channel j, which is also a geometric RV with parameter
successful channel reservation on channel j (i.e., successful 1−P with the following pmf
idle,j
RTS/CTS exchanges), B (bits/Hz) denotes the average num-
j
ber of bits transmitted per one unit of system bandwidth for fXTidle,j(x)=(Pidle,j)x(1−Pidle,j), x=0,1,2,... (10)
one contention/access (CA) cycle on channel j. To complete
Therefore,T (theaveragevalueofT )canbewritten
thethroughputanalysis,wederivethequantitiesT andB , cont,j cont,j
ove,j j as follows [9]:
which are conducted in the following.
1) Derivation of Tove,j: The average time overhead for one Tcont,j =Ncoll,jTcoll+Tidle,j(cid:0)Ncoll,j +1(cid:1)+Tsucc, (11)
successful channel reservation can be written as
where T and N can be calculated as
idle,j coll,j
T =T +2SIFS+2PD+ACK, (3)
ove,j cont,j (1−p)nk,j
where ACK is the length of an ACK message, SIFS is Tidle,j = 1−(1−p)nk,j (12)
the length of a short interframe space, and PD is the prop-
1−(1−p)nk,j
agation delay where PD is usually small compared to the N = −1. (13)
slot size σ, and T denotes the average time overhead coll,j n p(1−p)nk,j−1
cont,j k,j
due to idle periods, collisions, and successful transmissions
These expressions are obtained by using the pmfs of the
of RTS/CTS messages in one CA cycle. To calculate T ,
cont,j corresponding RVs given in (9) and (10), respectively [9].
we define some further parameters as follows. Denote T as
coll 2) Derivation of B : To calculate B , we consider all pos-
the duration of the collision and T as the required time j j
succ siblecasesthatcapturetheactivitiesofSUsandstatuschanges
for successful RTS/CTS transmission. These quantities can be
of the PU in the data phase of duration T . Because the PU’s
calculated as follows [9]: j
activity is not synchronized with the SU’s transmission, the
(cid:40)
T =DIFS+RTS+SIFS+CTS+2PD PU can change its active/inactive status any time. We assume
succ
T =DIFS+RTS+PD, (4) that there can be at most one transition between the idle and
coll
activestatesofthePUduringtheintervalT .Thisisconsistent
j
where DIFS is the length of a distributed interframe space, with the assumption on the slow status changes of the PU as
RTS and CTS denote the lengths of the RTS and CTS described in Section II-B since T < T . Furthermore, we
j eva
messages, respectively. assume that the carrier sensing of the MFDC-MAC protocol
4
(cid:16) (cid:17)
is perfect; therefore, the PU is idle at the beginning of the max NT P(cid:126)sec,T(cid:126) ,P(cid:126)
S sen
data phase. Note that the PU may change its status during the p,P(cid:126)sec,T(cid:126)S,P(cid:126)sen
SU’s sensing or access stage, which requires us to consider s.t. Pˆdj(cid:0)εj,TS,j(cid:1)≥Pjd, 0≤Psen,j ≤Pmax, (15)
different possible events in the data phase. 0≤T ≤T , 0≤psec ≤1, (cid:80)M psec =1
S,j j j j=1 j
We use h (k,l ∈ {0,1}) to represent events captur-
kl
ing status changes of the PU in the FD sensing stage and where psec is the probability of channel selection (P(cid:126)sec =
transmission stage where i = 0 and i = 1 represent the idle (cid:8)psec(cid:9)),jP is the SU’s transmit power on channel j and
and active states of the PU, respectively. For example, if the j sen,j
P is the maximum power for SUs, and T is upper
PU is idle during the FD sensing stage and becomes active bomuanxdedbyT .Infact,thefirstconstraintonPˆj(cid:0)Sε,jj,T (cid:1)im-
during the transmission stage, then we represent this event j d S,j
plies that the spectrum sensing should be sufficiently reliable
as (h ,h ) where sub-events h and h represent the
00 01 00 01 to protect the PU. Moreover, the SU’s transmit power P
status changes in the FD sensing and transmission stages, sen,j
must be appropriately set to achieve good tradeoff between
respectively. Moreover, if the PU changes from the idle to the
the network throughput and self-interference mitigation.
active state during the FD sensing stage and remains active in
To solve problem (15), we propose the two-step approach
the remaining of the data phase, then we represent this event
where we solve the following two subproblems P2 and P3 in
as (h ,h )
01 11 the two steps, respectively. In the first stage, we optimize the
It can be verified that we must consider the following three
parameters for each individual channel j and n contending
cases with the corresponding status changes of the PU during k,j
SUs on this channel to achieve maximum throughput of each
the FDC-MAC data phase to analyze B .
j channel j, i.e., NT (T ,P |n ). This problem can be
j S,j sen,j k,j
• Case 1: The PU is idle for the whole FDC-MAC data presented as
phase (i.e., there is no PU’s signal in both FD sens- P2:
ing and transmission stages) and we denote this event
as (h00,h00). The average number of bits (in bits/Hz) max NTj(TS,j,Psen,j|nk,j)
transmitted during the data phase in this case is denoted TS,j,Psen,j
s.t. Pˆj(cid:0)εj,T (cid:1)≥Pj, 0≤P ≤P , (16)
as Bj,1. d S,j d sen,j max
• Case 2: The PU is idle during the FD sensing stage but 0≤TS,j ≤Tj
the PU changes from the idle to the active status in the
transmissionstage.Wedenotetheeventcorrespondingto After solving problem P2 with optimal results
thiscaseas(h00,h01)whereh00andh01capturethesub- NT∗j(cid:0)TS∗,j(nk,j),Ps∗en,j(nk,j)|nk,j(cid:1) for all channels j
eventsintheFDsensingandtransmissionstages,respec- and possible cases with different nk,j contending SUs. Then,
tively.Theaveragenumberofbits(inbits/Hz)transmitted the network throughput with given T(cid:126)∗,P(cid:126)∗ only depends
S sen
during the data phase in this case is represented by B . on the channel selection probabilities in P(cid:126)sec. Problem P3
j,2
• Case 3: The PU is first idle then becomes active during maximizes the throughput with respect to P(cid:126)sec as
the FD sensing stage and it remains active during the P3:
whole transmission stage. Similarly we denote this event max NT (cid:16)P(cid:126)sec(cid:17)
as (h01,h11) and the average number of bits (in bits/Hz) P(cid:126)sec (17)
transmitted during the data phase in this case is denoted s.t. 0≤psec ≤1 (cid:80)M psec =1.
j j=1 j
as B .
j,3
(cid:16) (cid:17)
Then, we can calculate Bj as follows: Here, NT P(cid:126)sec can be written as
B =B +B +B . (14)
j j,1 j,2 j,3 |Ω| M
NT(cid:16)P(cid:126)sec(cid:17)=(cid:88)(cid:89)(cid:0)psec(cid:1)nk,jB({n }) (18)
Theoretical derivation for B , B , and B is given in the j k,j
j,1 j,2 j,3
k=1j=1
online technical report [8] due to the space constraint.
where
(cid:32) N (cid:33) M
IV. MFDC–MACPROTOCOLCONFIGURATIONFOR (cid:88)
B(ω )=B({n })= I(n >0)×
THROUGHPUTMAXIMIZATION k k,j {nk,j} k,j
j=1
In this section, we study the optimal configuration of the NT∗(cid:0)T∗ (n ),P∗ (n )|n (cid:1). (19)
j S,j k,j sen,j k,j k,j
proposed MFDC–MAC protocol to achieve the maximum
secondary throughput while satisfactorily protecting the PU. Duetothedecomposedstructureofthethroughputexpression
(cid:16) (cid:17)
NT P(cid:126)sec,T(cid:126) ,P(cid:126) in (1), it can be seen that the proposed
S sen
two-step approach does not loose optimality.
A. Problem Formulation
We are interested in determining suitable configuration for
B. Configuration for MFDC–MAC Protocol
P(cid:126)sec, T(cid:126) , and P(cid:126) to maximize the secondary throughput,
NT (cid:16)P(cid:126)Ssec,T(cid:126) ,P(cid:126)sen(cid:17). Suppose that the PU requires that the 1) Configuration for Sensing and Access Stages: We will
S sen solve problem P2 in the following. In the following analysis,
averagedetectionprobabilitybeatleastPj.Then,thethrough- we assume the exponential distribution for τj and τj where
d ac id
put maximization problem can be stated as follows: τ¯j and τ¯ denote the corresponding average values of these
ac id
P1: active and idle intervals on channel j. Specifically, let f (t)
τxj
5
denote the pdf of τj (x represents ac or id in the pdf of τj ThroughputvsPsen,1andTS,1
or τijd, respectively)xthen ac Hz) NT*(3 ms, 5.689 dB) = 8.5723 8
/10 7
1 t /s
fτxj(t)= τ¯xj exp(−τ¯xj). (20) NT,bits 5 56
We assume a homogeneous case with same frame length ( 4
Tj. We are interested in determining suitable configuration hput 3
for TS,j, and Psen,j to maximize the secondary throughput, oug 0 2
NT (T ,P |n ). To gain insights into the parameter hr 10
j S,j sen,j k,j T 1
configuration of the MFDC–MAC protocol, we first study the 0 0.01
−10 0.005
optimization with respect to the sensing time TS,j for a given Psen,1(dB) 0 TS,1(s)
P .
sen,j
ForafixedTS,j,wewouldneedtosetthesensingdetection Fig.2. ThroughputversusSUtransmitpowerPsenandsensingtimeTS for
threshold εj so that the detection probability constraint is met p=0.0022,N =50,ξ=0.95,ζ=0.2andPdat=15dB.
with equality, i.e., Pˆj(cid:0)εj,T (cid:1)=Pj as in [3], [4]. Since the
d S,j d
detectionprobabilityissmallerinCase3(i.e.,thePUchanges max NT (cid:16)X(cid:126)(cid:17)=(cid:80)|Ω| X B(ω )
from the idle to active status during the FD sensing stage of X(cid:126) k=1 M+k k
durationT )comparedtothatinCase1andCase2(i.e.,the s.t. 0≤X ≤1,i∈{1,...,M +|Ω|} (25)
S,j i
PUremainsidleduringtheFDsensingstage)consideredinthe (cid:80)M X =1
previoussection,weonlyneedtoconsiderCase3tomaintain i=1 i
thedetectionprobabilityconstraint.Theaverageprobabilityof where B(ω ) is the constant, which is given in (19). Recall
k
detection for the FD sensing in Case 3 can be expressed as that B(ω ) can be determined from the optimal solution of
k
(cid:90) TS,j ProblemP2instep1.TosolveproblemP4instep2,standard
Pˆj = Pj,01(t)f (t|0≤t≤T )dt, (21) methods in [10] such as cutting-plane method, branch and
d d τj S,j
0 id bound,branchandcut,branchandpricecanbeemployed.We
where t denotes the duration from the beginning of the FD use the branch and bound method [11] to solve this problem.
sensingstagetotheinstantwhenthePUchangestotheactive
state, and fτj(t|A) is the pdf of τijd conditioned on event A V. NUMERICALRESULTS
capturing theidcondition 0≤t≤TS,j, which is given as To obtain numerical results, we take key parameters for
the MAC protocol from Table II in [4]. All other parameters
f (t) 1 exp(− t )
τj τ¯j τ¯j are chosen as follows unless stated otherwise: mini-slot is
f (t|A)= id = id id . (22)
τijd Pr{A} 1−exp(−TS,j) σ = 20µs; sampling frequency for sensing is fs = 6MHz;
τ¯ijd bandwidth of PU’s QPSK signal is 6MHz; Pd = 0.8; the
Ngiovteentihnat(2P0)dj.,01(t) is derived in Appendix A and fτijd(t) is SinNteRrfeorfenPcUe spiagrnaamlsetaetrsSUζsaγnPd =ξ. NPWp0it=ho−ut2l0odsBs;ovfargyeinnegrasleitlyf-,
the noise power is normalized to one; hence, the SU transmit
We consider the following single-variable optimization
power, P becomes P = SNR ; and P = 15dB.
problem for a given P : sen sen s max
sen,j
For one specific channel, we investigate the effect of self-
max NT (T ,P |n ). (23) interference on the throughput performance and the single-
j S,j sen,j k,j
0<TS,j≤T channel throughput performance versus SU transmit power
We characterize the properties of function Psen and sensing time TS for different cases with varying
NT (T ,P |n ) with respect to T for given self-interference parameters. Detailed results are shown in the
j S,j sen,j k,j S,j
P in Proposition 1 in technical report [8], whose details online technical report [8] due to the space constraint.
sen,j
are omitted due to the space constraint. In fact, we prove We now investigate the multichannel scenario where we
that there exists the optimal solution for (cid:0)T∗ ,P∗ (cid:1) to consider a network consisting of N =50 SUs and 3 channels
S,j sen,j
maximize the throughput NT (T ,P |n ). Therefore, with following parameter settings: τ¯1 =τ¯2 =τ¯3 =1000 ms,
we can determine the optimaljvaSlu,jes (sTen,j ,Pk,j ) by using (cid:8)τ¯1,τ¯2,τ¯3(cid:9)=50,250,50ms.Morideoveri,dwesiedtp=0.0022
S,j sen,j ac ac ac
bi-section search of Psen,j for given corresponding optimal and Pdat = 15 dB. Fig. 2 illustrates the throughput perfor-
TS,j on each channel with the corresponding number of mance versusSU transmit power Psen,1 and sensingtime TS,1
contending SUs. for channel 1 for the case with ξ = 0.95 and ζ = 0.2. The
2) Configuration for Channel Selection Probabilities: optimal configuration of SU transmit power P∗ = 5.689
sen,1
We now solve problem P3 by employing the polyno- dB and sensing time T∗ = 3 ms is shown to achieve the
S,1
mial optimization technique (for details of this technique, maximum throughput NT (cid:0)T∗ ,P∗ (cid:1) = 8.5723, which is
S,1 sen,1
please see [10]). Let us define the variables X(cid:126) = again indicated by a star symbol.
(cid:8) (cid:9)
X ,...,X ,X ,...,X as follows: Toinvestigatetheimpactsofchannelselectionprobabilities,
1 M M+1 M+|Ω|
we also consider the above network with following parameter
Xi =(cid:40) p(cid:81)sieMc (cid:0)psec(cid:1)nk,j iiff 11≤≤ik≤=Mi−M ≤|Ω| (24) {se5t0ti,n2g5s0:,5τ¯i01d}=ms,τ¯i2dξ == 0τ¯.i39d5,=ζ 1=0000.2masn,d(cid:8)τP¯a1dca,tτ¯a2=c,τ¯1a3c5(cid:9)dB=.
j=1 j
Fig. 3 demonstrates the throughput performance versus chan-
Then, problem P3 can be transformed into the linear program nel selection probabilities for channels 1 and 2 ({psec,psec}).
1 2
P4: Theoptimalconfigurationofchannelselectionprobabilitiesis
6
Throughputvsps1ecandps2ec Throughputvsζ
8
bits/s/Hz)180 NT*(0.3571, 0.2857) = 8.5723 78 bits/s/Hz)7.75 PAArlloggp.. o12sed Alg.
NT, 6 6 NT,6.5
Throughput( 124 1 345 Throughput(5.56
0.5
0.5 5
ps2ec 0 0 ps1ec 0.1 0.2 0.3ζ 0.4 0.5 0.6
Fig. 3. Throughput versus SU transmit power psec and psec for N = 50, Fig.5. Throughputversusζ forM×N =3×30,ξ=0.95,τ¯j =1000
ξ=0.95,ζ=0.2andPdat=15dB. 1 2 ms,(cid:0)τ¯a1c,τ¯a2c,τ¯a3c(cid:1)=(50,150,500)msandPdat=15dB. id
Throughputvspsec
1
9
In Alg. 1, we use equal channel selection probabilities for
Hz)8 different channels, i.e., psec =psec. In Alg. 2, a fixed channel
bits/s/7 acsosrirgenspmoenndtinigssuetseodf,SUi.es,1wehaecrhe2ecahcahnnseetlhiasstahsesisganmedentuomobneer
NT,6 of SUs. For the channels with (cid:8)τ¯i(cid:9) = {100,500,1000} ms,
ut(5 we obtain the corresponding throuidghput values of {NTi} =
p
h4 {0.6992,2.2815,2.9937},respectively.Sothetotalthroughput
g
u
o is the sum of two throughput values for the two channels.
Thr3 ps2ec = 0, 0.0714, 0.2856, 0.7854, 0.9286 Note that we also perform optimization of sensing and access
2
0 0.2 0.4 0.6 0.8 1 parameters for each channel in calculating the throughput of
psec
1 Algs. 1 and 2. The results shown in Table I demonstrate that
our proposed algorithm outperforms Algs. 1 and 2. Moreover,
Fig. 4. Throughput versus SU transmit power psec and psec for N = 50,
ξ=0.95,ζ=0.2andPdat=15dB. 1 2 the throughput gains between our proposed algorithm and
Algs. 1 and 2 (which are ∆NT and ∆NT , respectively)
1 2
are about 10%, which is quite significant.
psec,∗ =0.3571 and psec,∗ =0.2857, which is again indicated We now consider the scenario with 30 SUs and 3 channels.
1 2
by a star symbol (i.e., the probability of channel selection for We set τ¯3 = 1000 ms, τ¯1 = τ¯2 = τ¯3 = 50 ms, varying
id ac ac ac
the last channel is ps3ec,∗ = 1 − ps1ec,∗ − ps2ec,∗ = 0.3572). τ¯i1d and τ¯i2d, ξ = 0.95, ζ = 0.4 and Pdat = 15 dB. We
We can observe that the SUs choose a more busy channel will also compare our proposed design with Algs. 1 and
with lower channel selection probability at optimality, which 2. For the channels with (cid:8)τ¯i(cid:9) = {50,500,1000} ms, we
id
is quite intuitive. obtain the corresponding throughput values of {NTi} =
To better observe the relationship of throughput vs channel {0.7952,2.5471,3.1707}.Again,thetotalthroughputforAlg.
selection probabilities, we show the throughput performance 2 is the sum of throughput values achieved for the three
versus channel selection probabilities for channels 1 and 2 channels. The results summarized in Table II show that our
({psec,psec}) in Fig. 4. We set the network parameters as proposed design again outperforms Algs. 1 and 2. Note that
foll1ows:2τ¯1 = τ¯2 = τ¯3 = 1000 ms, (cid:8)τ¯1,τ¯2,τ¯3(cid:9) = forthecaseofτ¯1 =τ¯2 =τ¯3,allalgorithmsachievethesame
id id id ac ac ac id id id
{50,250,50} ms, ξ = 0.95, ζ = 0.2, and P = 15 dB. throughput because all the channels have the same statistics
dat
This figure shows that the throughput curve for each value of and we do not need to optimize the load balancing.
psec first increases to the maximum value (which is indicated InFig.5,wecompareourproposeddesignwithAlgs.1and
2
by the asterisk) and then decreases as we increase psec. 2 for varying self-interference parameters. Here, we consider
1
We now consider the scenario with 20 SUs and 2 channels. the network of 60 SUs and 3 channels where ξ = 0.95,
Wesetτ¯i2d =1000ms,τ¯a1c =τ¯a2c =100ms,varyingτ¯i1d,ξ =1, τ¯ijd = 1000 ms, (cid:0)τ¯a1c,τ¯a2c,τ¯a3c(cid:1) = (50,150,500) ms and
ζ = 0.3, and Pdat = 15 dB. We would like to compare our Pdat = 15 dB. Again, our proposed design leads to higher
proposed design with other two schemes (called Algs. 1 and throughput than those under Algs. 1 and 2. Moreover, the
2) which do not optimize the channel selection probabilities. throughputgapsbetweenourdesignandAlgs.1and2become
larger with lower self-interference cancellation quality. These
resultsconfirmthatoptimalconfigurationoftheMACprotocol
TABLEI and load balancing parameters is indeed important to achieve
THROUGHPUTVS(cid:0)τi1d,τi2d(cid:1)(MXN=2X20) the largest throughput performance.
τ¯1 ms 100 500 1000
id
Alg.1 NT 3.7202 5.3001 5.9873 VI. CONCLUSION
Alg.2 NT 3.6930 5.2752 5.9873
In this paper, we have proposed the MFDC–MAC protocol
Proposed psec 0.3218 0.4138 0.5
1 for CRNs, analyzed its throughput performance, and studied
Alg. NT 4.0893 5.5870 5.9873
∆NT1(%) 9.0260 5.1351 0 its optimal parameter configuration. The design and analysis
∆NT2(%) 9.6924 5.5808 0 have taken into account the FDcommunication capability and
7
TABLEII
THROUGHPUTVS(cid:0)τ¯i1d,τ¯i2d(cid:1)(MXN=3X30)
(cid:0)τ¯1,τ¯2(cid:1)ms (50,50) (500,50) (1000,50) (500,500) (1000,1000)
id id
Alg.1 NT 4.8111 6.6440 7.2786 8.3649 9.5121
Alg.2 NT 4.7611 6.5130 7.1366 8.2649 9.5121
(cid:0)psec,psec(cid:1) (0.2511,0.2511) (0.3888,0.2012) (0.4244,0.1512) (0.3011,0.3011) (0.3333,0.3333)
1 2
Proposed NT 5.4150 7.3515 7.9532 8.8231 9.5121
Alg. ∆NT1(%) 11.1524 9.6239 8.4821 5.1932 0
∆NT2(%) 12.0757 11.4058 10.2676 6.3266 0
the self-interference of the FD transceiver. In addition, we the signal-to-interference-plus-noise ratio (SINR) of the PU’s
proposed the mechanism of channel selection to effectively signal at the SU.
balance the load among channels. Finally, we have presented
extensivenumericalresultstodemonstratetheimpactsofself-
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