Multi-channel Sensing And Resource Allocation in Energy Constrained Cognitive Radio Networks

0.34 MB·

by  Kedar Kulkarni

Multi-channel Sensing And Resource Allocation in
Energy Constrained Cognitive Radio Networks
KedarKulkarni,AdrishBanerjee∗
7 DepartmentofElectricalEngineering,IndianInstituteofTechnology,Kanpur,208016,India
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J Abstract

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1 We consider a cognitive radio network in a multi-channel licensed environment.

Secondary user transmits in a channel if the channel is sensed to be vacant. This
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T resultsinatradeoffbetweensensingtimeandtransmissiontime. Whensecondary
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. users are energy constrained,energy availablefortransmissionis less ifmoreen-
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c ergyisusedinsensing. Thisgivesrisetoanenergytradeoff. Formultipleprimary
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channels, secondary users must decide appropriate sensing time and transmis-

1 sionpowerineachchanneltomaximizeaverageaggregate-bitthroughputineach
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frame duration while ensuring quality-of-service of primary users. Considering
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0 time and energy as limited resources, we formulate this problem as a resource
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allocation problem. Initially a single secondary user scenario is considered and
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0 solutionisobtainedusingdecompositionandalternatingoptimizationtechniques.
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1 Later we extend the analysis for the case of multiple secondary users. Simula-
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tionresultsarepresented to studyeffect ofchannel occupancy,fading andenergy
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1 availabilityonperformanceofproposedmethod.
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Keywords: Cognitiveradio, energy constrainednetworks,resourceallocation,
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X sensing-throughputtradeoff
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1. Introduction
Cognitiveradio(CR)facilitatesefficientspectrumuseofcurrentlicensedspec-
trum that is highly underutilized and is considered as a potential solution to the
∗Correspondingauthor
Emailaddresses: [email protected](KedarKulkarni),[email protected]
(AdrishBanerjee)
PreprintsubmittedtoPhysicalCommunication January19,2017
problemofspectrumscarcity[1,2]. InCRnetworks,secondaryusers(SU)oppor-
tunistically access spectrum allocated to licensed or primary users (PU) in such
a way that quality of service (QoS) requirements of PUs are satisfied. For this
purpose, SUs periodically sense the spectrum for presence of PUs. While many
spectrum sensing techniques exist, energy detection method is widely used due
to its low complexity and easy implementation [3–5] and is optimal when form
of signal to be detected is unknown [6]. SU transmits in a channel only if the
channel is sensed to be vacant. This method of spectrum access is widely known
as interweave-mode[7]. Due to channel fading and noise, spectrum sensing may
result in missed detection or false alarm. Longer sensing periods lead to better
sensingperformance,butatthecostofreducedtransmissiontimeasanodecannot
transmit and sense simultaneously. This sensing-throughputtradeoff necessitates
selection of optimal sensing time to maximize SU throughput while sufficiently
protectingPU [8].
Sensing throughput tradeoff where SU determines optimal sensing time has
beenstudiedundervariousPUQoSconstraintssuchasfixedtargetdetectionprob-
ability [8, 9], collision probability constraint [10] and PU outage constraint [11].
Kaushik et al. [12] studied effect of estimation time on the tradeoff considering
PU signal of unknown power. When multiple SUs are present, better sensing
performance can be achieved in less time using cooperative sensing. In [9] and
[11], authors optimized sensing time in cooperative sensing framework assum-
ing availability of a single PU band. Pei et al. [13] considered multiple PUs
multiplexedusingorthogonalfrequencydivisionmultipleaccess(OFDMA)anda
SU equipped with wideband antenna, which enabled simultaneous sensing of all
PU channels. The authors determined optimal sensing time to achieve given tar-
get detection probability and proposed power allocation method to maximizeSU
throughput. Using the same model, Sharkasi et al. [14] studied sensing through-
put tradeoff under PU outage constraint. In practice, maximum bandwidth that
canbescannedbySUislimitedbyitsradio-frequency(RF)frontendandanalog-
to-digital converter (ADC) sampling unit. For a SU device having narrowband
antenna or low sampling rate, simultaneous sensing of all bands in a wideband
spectrum is not possible, promptingSU to optimallyselect sensing and transmis-
sion time in each PU band. In this work, we aim to address this multi-channel
sensing-throughputtradeoff.
In energy harvesting (EH) wireless networks, users are often energy con-
strained [15, 16]. In this case, in addition to tradeoff arising from sensing and
transmission time, tradeoff in energy becomes critical. In energy constrained
CR networks, as sensing time increases, more energy is used in sensing, leav-
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ing less energy available for transmission. Considering EH-CR network, Park et
al. [17] determined optimal sensing threshold for SU under energy causality and
collision probability constraints. In [18], authors found optimal sensing time to
minimize average energy cost under constraints on SU transmission rate. Yin et
al. [19] divided SU frame duration in three parts for— harvesting, sensing and
transmission— and proposed optimal time division to maximize SU throughput
under a fixed target detection probability. A fractional programming framework
was proposed in [20] to find optimal sensing time and power allocation to max-
imize energy efficiency of SU. In [21–23], authors proposed energy efficient dy-
namiccontrolpoliciesusingMarkovdecisionprocess(MDP)approachwhereSU
canchoosetostaysilent,carryoutsensingortransmitbasedonitsbeliefaboutPU
occupancy. MDP based techniques have high computational complexity and re-
quireknowledgeoftransitionprobabilitiesbetweendifferentPUoccupancystates.
Inpractice,informationofstatetransitionprobabilitiesisnotreadilyavailabledue
to sparse spectrum activity overlong term. Existing spectrum availabilitystudies
only document duty cycle of a channel which is the probability of a channel be-
ing occupied by a PU [24–27]. Also, the works mentioned above considered CR
systems with a single PU channel with fixed target detection probability as PU’s
QoScriteria. AvailabilityofmultiplePU channels posesachallengeasSU hasto
allocateavailabletimeandenergyappropriatelyinsensingandtransmissiontasks
ineach channel.
In multi-channelenvironment, if channel conditionsare such that the channel
does not yield good throughput, SUs should not transmit in the channel. Hence
SUs should not be required to sense it. Further, choice of channels for sensing
and transmissioncan bemadebased on occupancy probabilityof thechannel. To
maximize average SU throughput, SU must appropriately allocate limited time
and energy for tasks of sensing and transmission in each channel. In this paper,
we address the problem of finding optimal sensing time and power allocation in
a multi-channel PU environment where channels have to be sensed sequentially
such that expected bit-throughput of SU is maximized in a given duration. We
considertwomainconstraints—averagerateconstraintofPUtomaintainQoSof
PU and total energy constraint that results from limited energy availability. Our
contributioninthiswork isas follows.
• We first consider a single SU case and formulate the joint sensing time-
energy-throughputtradeoffproblemtomaximizeaggregateaveragebit-throughput
of SU. The optimization problem is a non-convex one. We decompose the
probleminsubproblemswithseparableobjectives. Weproposesensingand
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Sensing Transmission
Figure1: Framestructureformulti-channelsensingandtransmission
resourceallocation(SRA)methodwhichiterativelysolvesthesubproblems
and finds optimal sensing time, transmission time and transmission energy
foreach channel.
• We then extend SRA method for multiple SU scenario to maximize sum-
throughputofSU network.
• We present numerical results to study performance of proposed approach
undervariouschannel and energy availabilityconditions. We also compare
SRA with heuristics based best channel selection (BCS) and proportional
energy-timeallocation(PETA)methods.
Restofthepaperisorganizedasfollows. InSection2, systemmodelispresented
and optimization problem is formulated. In Section 3, we propose SRA and find
solutionto the optimizationproblem. In Section 4, we proposeSRA for themul-
tiple SU case. Simulation results are presented in Section 5. We conclude in
Section 6.
2. System model andproblem formulation
Initially we consider a cognitive radio system with one SU that opportunisti-
callyaccesses PU spectrum ofM non-overlappingnarrowbandchannels ofequal
bandwidth. The model for multiple SU scenario is explained later in Section 4.
PU and SU follow time slotted synchronous communication with frame dura-
tion T [28]. PU is active in ith channel with occupancy probability π , i =
1,i
1, 2,..., M. Thus, probabilityof ith channel being vacant is π = 1−π . SU
0,i 1,i
hasa-prioriknowledgeofchanneloccupancyprobabilitieswhichcanbeobtained
by observing the spectrum for long duration or from existing spectrum database
[24,27, 29]. All channelsbetween different source-destinationpairsare indepen-
dent Rayleigh block fading, that is, channel gains remain constant in one frame
and vary independently from frame to frame. Instantaneous channel gain of SU
source to SU destination link on ith channel is denoted as g , i = 1, 2,..., M.
i
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π ProbabilityofithPU channel being vacant
0,i
g Channel powergainofSU-SU linkonith channel
i
σ2 AWGN noisepower
N
τ Sensingtimeallocated toith channel
s,i
τ Transmissiontimeallocated toith channel
t,i
p SU transmitpowerinith channel
t,i
p Sensingpower
s
f Samplingfrequency
s
T Frametime
Table1:Keynotationusedinthispaper
Noise at SU receiver is additive white Gaussian (AWGN) with variance σ2 . PU
N
transmit power in each channel is p . In Table 1, we list key notation used in
PU
thispaper.
2.1. Sensingandspectrumaccess
SU is equipped with a single narrowband antenna that limits the sensing ca-
pability to one channel at a time. At the beginning of each frame, SU performs
spectrum sensing using energy detection with sampling frequency f . Sensing
s
takes place at a constant power p [18]. SU senses ith PU channel for time τ .
s s,i
Assuming PU signal to be complex valued phase-shift keying (PSK) signal, we
writedetection probabilityP andfalsealarm probabilityP as [8]
d,i f,i
ǫ f τ
i s s,i
P = Q −γ −1 , (1)
d,i (cid:18)σN2 i (cid:19)s2γi +1!
ǫ
i
P = Q −1 f τ , (2)
f,i σ2 s s,i
(cid:18)(cid:18) N (cid:19) (cid:19)
p
where ǫ is the detection threshold and γ is the average PU signal-to-noise ratio
i i
(SNR) received at SU source over ith channel. For a target detection probability
P , wecan writefalsealarm probabilityas [8]
d,i
P = Q 2γ +1Q−1(P )+γ f τ . (3)
f,i i d,i i s s,i
(cid:16)p p (cid:17)
Note that depending on channel occupancy probabilities, channel conditions and
available energy, SU may not sense a PU channel, which results in τ = 0.
s,i
After the sensing phase is over, for the remaining frame duration, SU transmits
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invacantPUchannels(interweavemode)withappropriatepowersoasmaximize
bit-throughput. Forithchannel,timespentintransmissionandtransmitpowerare
denotedasτ andp respectively. TheframestructureofSU isshowninFig. 1.
t,i t,i
2.2. System constraints
2.2.1. Primaryrateconstraint
Quality of service (QoS) criterion of ith PU demands that the PU should be
abletotransmitB¯ bitsonaverageineachframeduration. IfSUcorrectlysenses
p,i
achannelasactive,thereisnointerferencewiththePUtransmission. Inthiscase,
averagenumberofbitstransmittedbyithPUisgivenbyTE[R ]whereE[R ]
p,i p,i
is the average transmission rate that depends on PU source-PU destination link.
In case of missed detection, SU transmits and interferes with ith PU for time τ .
t,i
ThereisnointerferencetothePU transmissionfortime(T −τ ). Weconsidera
t,i
stronginterferencechannelbetweenSUandPU.Thus,transmissionrateachieved
under interference is negligible. Then average number of bits transmitted in a
frameby ithPU is
B ∼= P TE[R ]+(1−P )(T −τ )E[R ]. (4)
p,i d,i p,i d,i t,i p,i
Let τ = B¯ /E[R ] where τ ∈ [0, T]. Higher value of τ indicates that
p,i p,i p,i p,i p,i
requiredaveragebit-throughputB¯ ishigher. ThentheQoSconstraintB ≥ B¯
p,i p,i p,i
can bewrittenas
T −τ
P ≥ P¯ = max 0, 1− p,i . (5)
d,i d,i
τ
(cid:20) t,i (cid:21)
Thus, to transmit in ith channel, detection probability should be greater than de-
tection probability threshold P¯ which depends on transmission time τ . As
d,i t,i
τ increases, requireddetectionprobabilityincreases. ToachieveincreasingP ,
t,i d,i
sensing time τ increases, leaving less time available for transmission. This re-
s,i
sults in the sensing-throughput tradeoff. Optimal sensing time is such that con-
straintin(5)is satisfiedwithequality[8].
2.2.2. Energyconstraint
SU is energy constrained i.e. in each frame, SU has limited energy to spend
in sensing and transmission. This may happen when SU is not powered by con-
ventional sources and harvests energy from surroundings. SU employs a greedy
policy where it uses all the available energy in one frame for sensing and trans-
mission subject to maximum power constraint. Suppose energy e is available
tot
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at SU in each frame. Then total energy spent in sensing and transmission cannot
exceed e , thatis,
tot
M M
p τ + p τ ≤ e . (6)
s s,i t,i t,i tot
i=1 i=1
X X
2.2.3. Peaktransmitpower constraint
Asresponseofpoweramplifierisnon-linearathighvaluesoftransmitpower,
therealimitp onallowedmaximumtransmitpower. Thus, wehave
max
p ≤ p , i = 1, 2,..., M. (7)
t,i max
2.2.4. Totaltimeconstraint
In a frame, total time spent in sensing and transmission cannot exceed frame
duration. Thus,wehave
M M
τ + τ ≤ T. (8)
s,i t,i
i=1 i=1
X X
2.3. Problemformulation
If ith channel is vacant, instantaneous rate achieved by SU on the channel is
log 1+ gipt,i bits/s assuming normalized bandwidth. In case of missed detec-
2 σ2
N
tion,(cid:16)PU interfe(cid:17)res with SU transmission. Our interest is in maximizing through-
put achieved in transmissionover a vacant band. Thus, we consider transmission
rate achieved under interference as negligible. This is especially true when inter-
ferencechannelbetweenPUandSUisstrong. Thenaveragebit-throughputofSU
over ith channel, which is defined as average number of bits transmitted over ith
channel inaframeby SU, iswrittenas
g p
B = π 1−P P¯ , τ τ log 1+ i t,i . (9)
s,i 0,i f,i d,i s,i t,i 2 σ2
(cid:18) N (cid:19)
(cid:0) (cid:0) (cid:1)(cid:1)
In this paper, our objective is to maximize average aggregate bit-throughput
of SU in a frame duration, given by B = M B under aforementioned con-
s i=1 s,i
straintsinSection 2.2. Thus,wecan writethemaximizationproblemas
P
M
g p
i t,i
max π (1−P (τ , τ ))τ log 1+ (10)
τs,τt,pt i=1 0,i f,i t,i s,i t,i 2(cid:18) σN2 (cid:19)
X
s. t. (5), (6), (7), (8),
τ , τ , p ≥ 0, i = 1, 2,..., M,
s,i t,i t,i
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whereτ = [τ ,..., τ ]T,τ = [τ ,..., τ ]T andp = [p , p ,..., p ]T.
s s,1 s,M t t,1 t,M t t,1 t,2 t,M
The optimization problem in (10) is non-convex due to non-convex nature of
P (τ , τ ). Also,theenergyconstraintgivenby(6)isnon-convexduetoprod-
f,i t,i s,i
uct terms of optimization variables p and τ . In following section, we refor-
t,i t,i
mulate the problem so that all constraints are affine and the objective function is
separable.
3. Sensing andresource allocation(SRA): Singleuserscenario
Tomakeconstraint(6)affine,wereconstituteproblem(10)asenergyandtime
allocation problem. Suppose SU uses energy e to transmit in ith channel. Then
t,i
energy constraintin(6)can bewritten as
M M
e +p τ ≤ e . (11)
t,i s s,i tot
i=1 i=1
X X
Transmit power in ith channel is p = e /τ . Thus, we write peak power
t,i t,i t,i
constraintin(7)as
e ≤ p τ , i = 1, 2,..., M. (12)
t,i max t,i
Suppose SU allocates time t = αT, α ∈ [0, 1] for sensing and time t =
s t
(1−α)T fortransmission. Thenwecanwritetimeconstraint(8)astwoseparate
constraintsgivenby
M
τ ≤ αT, (13)
s,i
i=1
X
M
τ ≤ (1−α)T. (14)
t,i
i=1
X
Let B = f (τ , τ )·f (τ , e ) where
s,i 1,i t,i s,i 2,i t,i t,i
f (τ , τ ) = 1−P (τ , τ ), (15)
1,i t,i s,i f,i t,i s,i
g e
i t,i
f (τ , e ) = π τ log 1+ . (16)
2,i t,i t,i 0,i t,i 2 σ2 τ
(cid:18) N t,i(cid:19)
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Nowwecan reformulateoptimizationproblemin (10)as follows:
M
max f (τ , τ )f (τ , e ) (17a)
1,i t,i s,i 2,i t,i t,i
α,{τs,τt,et}
i=1
X
M M
s. t. e +p τ ≤ e , (17b)
t,i s s,i tot
i=1 i=1
X X
e ≤ p τ , i = 1, 2,..., M, (17c)
t,i max t,i
M
τ ≤ αT, (17d)
s,i
i=1
X
M
τ ≤ (1−α)T, (17e)
t,i
i=1
X
e , τ , τ ≥ 0, i = 1, 2,..., M, (17f)
t,i s,i t,i
α ∈ [0, 1], (17g)
where τ = [τ ,..., τ ]T, τ = [τ ,..., τ ]T and e = [e ,..., e ]T.
s s,1 s,M t t,1 t,M t t,1 t,M
In the problem above, all constraints are affine. Objective in (17a) is concave in
optimizationvariablee . But theproblemis stillnon-convexinτ andτ .
t,i s,i t,i
To solve (17a), we first fix α and decompose the problem into three subprob-
lemsas follows.
SubproblemP1
We first fix (τ , e ) and find optimal sensing time τ subject to constraints
t t s
(11),(17d)and(27f). Objectivein(17a)ismonotonicallyincreasingwithτ , i =
s,i
1, 2,..., M. Forfixed (τ , e ), wecan writeproblemoffindingoptimalτ as
t t s
M
max B (τ ) (18)
s,i s,i
i=1
X
M M
e − e
s. t. τ ≤ min αT, tot i=1 t,i ,
s,i
p
i=1 " Ps #
X
Problemin(18)canbemodelledasageneralnon-linearknapsackproblem(NKP).
We use greedy algorithm [30, 31] to solve it with complexity O(M log(f T)).
s
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Wedefine u = 1/f as thesmallesttimeunitthat can beallocated to thesensing
s s
timeofachannel. Incidentallyu isalsothetimebetweensuccessivesamples. We
s
initialize sensing time as τ = 0, i = 1, 2,..., M. Increase in bit-throughput
s,i
due to addition of one sensing time unit can be viewed as reward of the action.
Thus,reward ofaddingaunittoith channel inkth iterationisgivenby
r(k) = B τ(k) +u −B τ(k) . (19)
s,i s,i s,i s s,i s,i
(cid:16) (cid:17) (cid:16) (cid:17)
In each iteration, one time unit is added to the channel ˆi whereˆi is the channel
that gives maximum reward, i.e. ˆi = arg max r(k) . Thus, in each iteration,
i s,i
sensingtimeisupdatedas n o
τ(k) +u for i =ˆi(k)
τ(k+1) = s,i s . (20)
s,i (τs(,ki) for i 6=ˆi(k)
Theprocesscontinuesuntil M τ(k) ≤ min αT, etot−PMi=1et,i .
i=1 s,i ps
h i
SubproblemP2 P
Keeping optimal (τ , e ) in P1 fixed, we now optimize τ subject to con-
s t t
straints(17e)and(17f). Theproblemofoptimizingτ is
t,i
M
max B (τ ) (21)
s,i t,i
i=1
X
M
s. t. τ ≤ (1−α)T.
t,i
i=1
X
OnsimilarlinesofsubproblemP1,wecanfindoptimalτ bygreedymethodfor
t,i
NKP using u = 1/f as the smallest time unit. From (15) and (16), we see that
t s
f is a monotonically decreasing function of τ while f is a monotonically
1,i t,i 2,i
increasingfunctionof τ . Thus, ina regionwhereB (τ ) is monotonicallyde-
t,i s,i t,i
creasingwithτ ,additionofaunitu totransmissiontimeofithchannelresultsin
t,i t
negativereward value. When reward values for all channel are negative, any fur-
ther increase in transmission time τ results in decreasing bit-throughput. Thus,
t,i
the greedy algorithm stops when all rewards become negativeor when constraint
(17e)isviolated. Usingrewardr(k) = B τ(k) +u −B τ(k) ,transmission
t,i s,i t,i t s,i t,i
(cid:16) (cid:17) (cid:16) (cid:17)
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