Joint Optimization of Power Splitting and Allocation for SWIPT in Interference Alignment Networks

1.2 MB·

by  Nan Zhao

1
Joint Optimization of Power Splitting and
Allocation for SWIPT in Interference Alignment
Networks
Nan Zhao, Senior Member, IEEE
Abstract—Interference alignment (IA) is a promising solution In wireless networks, another key issue is energy con-
7 for interference management in wirelessnetworks. On theother sumption. Due to the rapidly rising energy costs and global
1 hand, simultaneous wireless information and power transfer
CO emissions, green communicationshave attracted a lot of
0 (SWIPT) has become an emerging technique. Although some 2
2 works have been done on IA and SWIPT, these two important interest from both academia and industry [20], [21]. Energy
areas have traditionally been addressed separately in the liter- harvesting(EH)isanimportantmethodtoachievegreencom-
n
ature. In this paper, we propose to use a common framework munications [22]. In EH, the energy captured from external
a
J to jointly study IA and SWIPT. We analyze the performance sources is converted to electrical energy to support green
of SWIPT in IA networks. Specifically, we derive the upper
8 self-sufficientwirelessnodes[23]–[25].Sinceradio-frequency
bound of the power that can be harvested in IA networks. In
(RF) signals carryenergy,RF can be a new source for energy
addition, we show that, to improve the performance of wireless
T] power transfer and information transmission, users should be harvesting. Indeed, wireless power transfer (WPT) through
dynamically selected as energy harvesting (EH) or information RF signals can be applied to the scenarios with low-power
I
. decoding (ID) terminals. Furthermore, we design two easy- applications, and thus becomes an importantaspect of energy
s
implementedSWIPT-userselection(SWIPT-US)algorithmsinIA
c harvesting [26], [27]. As RF signals are commonly used as a
[ networks. To optimize the ID and EH performance of SWIPT vehicle for transmitting information in wireless networks, si-
in IA networks, a power-splitting optimization (PSO) algorithm

1 is proposed when power splitters are available, and its closed- multaneouswireless informationandpowertransfer (SWIPT)
v form optimal solutionsare derived. Powerallocation in thePSO has become an emerging technique attracting great attention
2 algorithm is also studied to further optimize the performance. [28]–[35].
5 Simulation results are presented to show the effectiveness of the
Some initial worksin SWIPT have been conductedin [28],
9 proposed algorithms.
[29] to analyze the maximal information rate versus (vs.)
1
0 Index Terms—Simultaneous wireless information and power energyperformanceinsingle-inputsingle-output(SISO)chan-
transfer, interference alignment, energy harvesting, information
. nel without and with frequency-selective fading, respectively.
1 decoding, power splitting, power-to-rate ratio.
Zhang et al. [30] studied information rate vs. energy perfor-
0
7 mance in a multi-input multi-output (MIMO) wireless broad-
1 I. INTRODUCTION castsystemconsistingofoneEHreceiverandoneinformation
v: INTERFERENCE management is one of the key issues in decoding(ID)receiver.In[31],theoptimalpowersplittingwas
i wireless networks. Recently, interference alignment (IA) performed in SISO and single-input multiple-output (SIMO)
X
has become a promising solution to the interference problem systems to achieve various trade-offs between information
r in wireless networks [1]–[3]. With IA, the transmitted signals capacity and energy harvested. Xiang et al. [32] studied
a
are designed to cooperatively constrain all the interferences the robust beamforming problem for three-node multiple-
into certain subspaces at the unintended receivers, and thus input single-output (MISO) broadcasting systems with one
the remaining interference-free subspaces can be exploited to energy receiver and one information receiver when the CSI
obtain the desired signal at each receiver [4]. is imperfect. A two-way communication system with two
Some challengesof applyingIA in practicalnetworkswere nodes communicating in an interactive fashion to achieve
presented in [5], and plenty of effort has been conducted SWIPT was studied in [33], where information “1” and “0”
to make IA more practical [6]–[19]. In [6], iterative IA correspond to one unit of energy and no energy transferred,
algorithmsbasedonthe reciprocityofwirelessnetworkswere respectively. In [34], a practical framework for SWIPT in
designed, which make IA easier to realize. The performance broadbandwirelesssystemswasdevelopedthroughexploiting
degradationin IAnetworksatlowsignal-to-noiseratio(SNR) orthogonal frequency division multiplexing (OFDM) systems
was analyzed in [9], and several research works have been todivideabroadbandchannelintodecouplednarrowbandsub-
presented to improve the sum rate or QoS of IA networks channels,wherefrequencydiversityisalsoutilizedtoimprove
[6]–[9].Sinceaccuratechannelstateinformation(CSI)should theefficiencyofSWIPT.Fouladgaretal.[35]proposedtouse
be available at the transmitters for IA, the authors of [10]– constrained run-length limited codes instead of conventional
[14] focused on solving the problem of imperfect CSI in IA unconstrained codes in SWIPT to limit battery overflow and
networks. control battery underflow.
Although some excellent works have been done on IA and
N.ZhaoiswiththeSchoolofInformationandCommunicationEngineering,
DalianUniversity ofTechnology, China(email:[email protected]). SWIPT, these two important areas have traditionally been
2
addressed separately in the literature [36]–[39]. For example, is introduced.
in IA networks, the interferences are usually leveraged to
separate out the desired signal instead of reutilization, which
A. Linear Interference Alignment Wireless Networks
is a great waste of energy in wireless networks. On the other
Consider a K-user interference channel with M[k] and
hand, in the existing SWIPT studies, recent advances in IA
N[k] antennas equipped at the kth transmitter and receiver,
are largely ignored.
respectively. Perfect CSI of the network is assumed to be
In this paper, we propose to use a common framework to
availableatallthetransceivers.IflinearIAisadoptedtoavoid
jointly study IA and SWIPT. The main contributions of this
interferences among users, the received signal with d[k] data
work can be summarized as follows.
streams at receiver k can be represented as
• SWIPTisbecominganimportantaspectintheresearchof
EH, however, to the best of our knowledge, the SWIPT y[k](n)=U[k]†(n)H[kk](n)V[k](n)x[k](n)
issue in IA networks is largely ignored in the existing K
works. Thus a unified framework of SWIPT in IA is + U[k]†(n)H[kj](n)V[j](n)x[j](n)+U[k]†(n)z[k](n),(1)
introduced, and some fundamental work is presented in j=X1,j6=k
this paper.
whereH[kj](n) CN[k]×M[j] denotesthechannelgainmatrix
• We analyze the performance of SWIPT in IA networks. ∈
from transmitter j to receiver k in the nth time slot. For a
Specifically,wederivethelowerandupperboundsofthe
symmetricnetwork,each entryofH[kj](n) canbeassumedto
power that can be harvested in IA networks.
be independent and identically distributed (i.i.d.) (0,a ),
• To improve the performance of wireless power transfer CN p
where0<a 1,whichisdeterminedaccordingtothesignal
and informationtransmission, we show that users should p
≤
attenuation due to path loss. For the convenience of analysis,
be dynamically selected as EH or ID terminals. Then,
a is assumed to be 0.1 in this paper.Block fadingchannelis
we design two easy-implemented SWIPT-user selection p
adoptedinthispaper[40],andforclarity,thetimeslotnumber
(SWIPT-US) algorithms in IA networks. The first one is
n is henceforth suppressed unless stated otherwise. x[k] is
based on the round-robinprinciple, which is natural and
composedofd[k] datastreamsofuserk withpowerconstraint
simple. To further improvethe performance,we define a
P[k] = P for the symmetric network, except when power
parameter called power-to-rate radio (PRR), and design t t
a PRR-based SWIPT-US algorithm. allocationisconsideredinSectionV-B.V[k] CM[k]×d[k] and
• Writehmprotopooseptiampizoewethr-espIlDittinangdopEtHimipzeartfioonrm(aPnScOe)oaflgIoA- sUu[pk]pr∈essCioNn[k]m×adt[kr]icaerseotfheusuenritka,ryrepsrpeeccotidvienlgy∈.azn[dk]inteCrfNer[ekn]×c1e
∈
networks when power splitters are available, in which representsreceivernoisevectorwithdistributionCN(0,IN[k])
the specific rate and energy requirements of users are at receiver k.
taken into account. The closed-formoptimal solutions to When IA is feasible [41], the interferences among users
the PSO algorithm are derived. In addition, the power can be assumed to be perfectly eliminated if the following
allocation (PA) problemin the PSO algorithmis studied. conditions are satisfied [6].
• Simulationresultsarepresentedtoshowtheeffectiveness U[k]†H[kj]V[j] =0, j =k, (2)
of the proposed algorithms. ∀ 6
The rest of the paper is organizedas follows. In Section II, rank U[k]†H[kk]V[k] =d[k]. (3)
the system model is presented. The performance of SWIPT (cid:16) (cid:17)
Thus the desired signals of user k can be assumed to be
in IA networks is analyzed in Section III. In Section IV,
two SWIPT-US algorithms are proposed for SWIPT in IA receivedthroughad[k] d[k] fullrankchannelmatrixH[kk] ,
networks. In Section V, the PSO algorithm is proposed to U[k]†H[kk]V[k], and (1)×can be simplified as
optimize the ID and EH performance of IA networks, and y[k] =H[kk]x[k]+z[k], (4)
power allocation is also studied. Simulation results are dis-
cussedinSectionVI,andfinally,conclusionsandfuturework where z[k] =U[k]†z[k], following (0,I ).
are presented in Section VII. In pursuing the matrices of U[kC]Nand Vd[k[k]], IA only focuses
Notation: I represents the d d identity matrix. A† and on condition (2) to eliminate the interferences, and does not
d
×
A are the Hermitian transpose and determinant of matrix involvethedirectchannelH[kk] tomaximizethedesiredsignal
| |
A, respectively. a and A are the ℓ2-norm of vector power within the desired signal subspace [12]. Thus several
2 2
k k k k
a and matrix A, respectively. λ (A) means the maximal IA algorithms have been proposed to further improve the
max
eigenvalueofthematrixA. a istheabsolutevalueofcomplex performance of the conventionalIA algorithm [6]–[9].
| |
number a. For two integers b and c, b%c means b modulo c. Basedontheabovedescription,thetransmissionrateofuser
CM×N isthespaceofcomplexM N matrices. (a,A)is k in the IA network, if only the ID terminal at receiver k is
× CN
thecomplexGaussiandistributionwithmeanaandcovariance performed, can be expressed as
matrix A. E() stands for expectation.
· R[k] =log I + Pt H[kk]H[kk]† . (5)
II. SYSTEMDESCRIPTION 2(cid:12) d[k] d[k] (cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
Inthissection,wefirstpresentthemodelforlinearIAwire- Sincethispapermainl(cid:12)yconcentratesonthein(cid:12)formationand
less networks. Then, wireless power transfer in IA networks power transfer in IA networks instead of degrees of freedom
3
(DoFs), it is assumed that there is only one data stream
for each user in the rest of this paper1. Besides, symmetric
networksare considered, and thus all the users have the same
parameters, i.e., M[k] =M, N[k] =N and d[k] =1 for all k.
Thusthe interferencealignmentis feasible in this paperwhen
condition (2) is met if
M +N K+1. (6)
≥
B. Wireless Power Transfer in IA Networks
Each transmitter of the IA wireless network is assumed
to have a constant power source, while all the receivers
need to replenish energy from WPT or recharge the batteries
when WPT is insufficient. The received signal with one data
stream of user k in the IA network before processed by the
interference suppression vector u[k] can be expressed as
K
y[k] = H[kj]v[j]x[j]+z[k]. (7)
Fig.1. AK-userIAwirelessnetworkwithbothIDandEHterminalsthrough
Xj=1 powersplitter ateachreceiver.
b
In(7),eachelementofy[k] isthereceivedsignalonthecorre-
spondingantennaatreceiverk.v[j] andx[j] are theprecoding
b From the above description, we can see that both ID
vector and transmitted data stream of user j, respectively.
terminal and EH terminal can be equipped at each receiver
Denote
to transfer informationand power,respectively.Power splitter
2 2
E x[j] =PtE ξ[j] =Pt, (8) canbeusedtoinducethereceivedpowertoIDorEHterminals
(cid:18)(cid:12) (cid:12) (cid:19) (cid:18)(cid:12) (cid:12) (cid:19)
(cid:12) (cid:12) (cid:12) (cid:12) accordingto the requirementsof the system [30], as shownin
where ξ[j] = x[j(cid:12)] an(cid:12)d E ξ[j] 2 (cid:12)=1(cid:12). Fig. 1. ρ[k] ∈[0,1] is the portion of signal power split to the
√Pt (cid:16)(cid:12) (cid:12) (cid:17) ID terminal at receiverk, and correspondingly1−ρ[k] is that
If an EH terminal is also(cid:12) equ(cid:12)ipped at each receiver of the to the EH terminal.
IA network, energy can be harvested through wireless power
transfer. Although the energy is captured in RF band at EH
III. PERFORMANCE ANALYSIS OF SIMULTANEOUS
terminals, the harvested energy in RF band is proportional to
WIRELESS INFORMATION AND POWERTRANSFER IN
thecorrespondingenergyfrombasebandsignalduetothelaw
of energy conservation. Assume that the received signal y[k] INTERFERENCEALIGNMENT NETWORKS
on the antennas of receiver k is intended only for WPT, and Inthissection,we firstanalyzetheperformanceofwireless
theharvestedenergyduetothebackgroundnoiseisnegligibble power transfer in IA networks. Then, we analyze the perfor-
and can be ignored. Thus the instantaneous power harvested mance of information transfer in IA networks.
in a certain time slot at receiver k when the blocking fading
is adopted can be calculated as
A. Performance Analysis of Wireless Power Transfer in IA
† Networks
K K
Q[k] = ζ H[kj]v[j]x[j]  H[kj]v[j]x[j] We analyze performance of energy harvesting in IA net-
·
Xj=1 Xj=1 works when a user is dedicated to wireless power transfer.
   
2 Lemma 1: For a given channel gain matrix H[kj] as in (1)
K
= ζ(cid:13) H[kj]v[j]x[j](cid:13) and an arbitrary unitary vector v[j], it abides by
(cid:13) (cid:13)
(cid:13)Xj=1 (cid:13)
(cid:13)(cid:13)(cid:13) K (cid:13)(cid:13)(cid:13)2 2 (cid:13)H[kj]v[j](cid:13)2 ≤(cid:13)H[kj](cid:13)2 =rλmax(cid:16)H[kj]†H[kj](cid:17).
= ζPt(cid:13) H[kj]v[j]ξ[j](cid:13) , (9) (cid:13)(cid:13) (cid:13)(cid:13) (cid:13)(cid:13) (cid:13)(cid:13)
(cid:13) (cid:13) Proof: v[j] is unitary, and thus we have v[j] = 1.
(cid:13)Xj=1 (cid:13) 2
(cid:13) (cid:13)2 Basedonthedefinitionoftheinducednorm,itca(cid:13)nbe(cid:13)obtained
(cid:13) (cid:13) (cid:13) (cid:13)
where ζ (0,1(cid:13)) is a constant(cid:13)representing the loss in that
∈
the energy transducer for converting the harvested energy to
H[kj]v[j]
electrical energy to be stored [30]. ζ is assumed to be 0.5
H[kj] = max (cid:13) (cid:13)2
throughoutthis paper for the convenience of analysis. (cid:13)(cid:13) (cid:13)(cid:13)2 v[j]6=0(cid:13)(cid:13) v[j] 2(cid:13)(cid:13)
1Theconclusionforthesituationwithmorestreamscanbeeasilyextended, (cid:13) (cid:13) = max (cid:13)(cid:13)H[k(cid:13)(cid:13)j]v[j] . (10)
anditisoutofthescopeofthispaper. v[j] =1(cid:13) (cid:13)2
k k2 (cid:13) (cid:13)
(cid:13) (cid:13)
4
Fig.3. Demonstration oflower andupperbounds ofpower harvested ofa
certain userinIAnetworks.
Fig.2. Illustration ofdesiredsignal,interferences, andu[k] atreceiverkin
IAnetworks.
We can also define the desired of user k as
Thus we have
H[kj]v[j] H[kj] . (11) H[kk]v[k]x[k] =s[k]. (16)
(cid:13) (cid:13)2 ≤(cid:13) (cid:13)2
(cid:13) (cid:13) (cid:13) (cid:13)
According to th(cid:13)e definitio(cid:13)n of(cid:13)spectra(cid:13)l norm, we can also
obtain From Fig. 2, we can see that the interferences at receiver k,
H[kj] = λ H[kj]†H[kj] . (12) g[k] lyingin [k],areorthogonaltou[k],andthedesiredsignal
(cid:13) (cid:13)2 r max(cid:16) (cid:17) s[jk] is randomZly distributed in CN×1.
(cid:13) (cid:13)
From (11) a(cid:13)nd (12(cid:13)), the conclusion can be obtained as
From (9), we can know that
H[kj]v[j] H[kj] = λ H[kj]†H[kj] . (13)
(cid:13) (cid:13)2 ≤(cid:13) (cid:13)2 r max(cid:16) (cid:17) 2
(cid:13) (cid:13) (cid:13) (cid:13) K
T(cid:13)hus the up(cid:13)per b(cid:13)ound o(cid:13)f H[kj]v[j] can be expressed as Q[k] = ζ(cid:13) H[kj]v[j]x[j](cid:13)
(cid:13) (cid:13)
(cid:13) (cid:13)2 (cid:13)Xj=1 (cid:13)
(cid:13) (cid:13) (cid:13) (cid:13)2
rλmax H[kj]†H[kj] . (cid:13) (cid:13) (cid:13)(cid:13) K (cid:13)(cid:13) 2
(cid:16) (cid:17)
Based on Lemma 1, Theorem 1 can be derived, which = ζ(cid:13) g[k]+s[k](cid:13)
(cid:13) j (cid:13)
defines the lower and upper bounds of power harvested at (cid:13)j=X1,j6=k (cid:13)
(cid:13) (cid:13)2
receiver k in the IA wireless network. (cid:13) 2 (cid:13)
Theorem 1: In a K-user IA wireless network with one = ζ(cid:13)g[k]+s[k] . (cid:13) (17)
(cid:13) (cid:13)2
data stream for each user, if receiver k is dedicated to WPT (cid:13) (cid:13)
(cid:13) (cid:13)
utilization, its harvested power should follow
Thusduetothe propertyofvectornorm,thefollowingcanbe
K 2 achieved
0≤Q[k] ≤ζPtXj=1rλmax(cid:16)H[kj]†H[kj](cid:17) . 2
  0 Q[k] ζ g[k] + s[k] . (18)
Proof:Asdemonstratedin(7),thedesiredsignalreceived ≤ ≤ (cid:16)(cid:13) (cid:13)2 (cid:13) (cid:13)2(cid:17)
(cid:13) (cid:13) (cid:13) (cid:13)
on antennas of receiver k can be expressed as H[kk]v[k]x[k], (cid:13) (cid:13) (cid:13) (cid:13)
and interferences can be denoted as H[kj]v[j]x[j], j = In (18), Q[k] =0 when g[k] = s[k], which means that the
1,2,...,K, j = k. According to the condition (2) of IA, −
sum of interferences and desired signal have the same length
6
interferencesareconstrainedintoacertainsubspaceatreceiver
with angleθ (thatequalsto π) between them, as illustrated in
k, which is differentfromthat of the desiredsignal H[kk]v[k].
Fig. 3(a).
We can assume that the interference from transmitter j to
From Lemma 1, we can know that
receiver k can be expressed as
H[kj]v[j]x[j] =g[k],j =1,2,...,K, j =k, (14)
j 6 g[k] = H[kj]v[j]x[j] P λ H[kj]†H[kj] ,
which lies in the subspace [k] of CN×1 that is orthogonal (cid:13) j (cid:13)2 (cid:13) (cid:13)2 ≤r t· max(cid:16) (cid:17)
to u[k] according to (2), as sZhown in Fig. 2. Thus the sum of (cid:13)(cid:13) (cid:13)(cid:13) (cid:13)(cid:13) (cid:13)(cid:13) (19)
where j =1,2,...,K, j =k, and
interferencesduetoalltheothertransmittersatreceiverk can 6
be denoted as
K K
H[kj]v[j]x[j] = g[jk] =g[k]. (15) (cid:13)s[k](cid:13)2 =(cid:13)H[kk]v[k]x[k](cid:13)2 ≤rPt·λmax(cid:16)H[kk]†H[kk](cid:17).
j=X1,j6=k j=X1,j6=k (cid:13)(cid:13) (cid:13)(cid:13) (cid:13)(cid:13) (cid:13)(cid:13) (20)
5
From (19) and (20), it can also be obtained that 15
Upper Bound of Q[k]
2
ζ g[k] + s[k] Q[k]
(cid:16)(cid:13) (cid:13)2 (cid:13) (cid:13)2(cid:17)
(cid:13) (cid:13) (cid:13) (cid:13) 2
(cid:13) K(cid:13) (cid:13) (cid:13)
= ζ(cid:13)(cid:13)(cid:13)(cid:13)(cid:13)j=X1,j6=kg[jk](cid:13)(cid:13)(cid:13)(cid:13)(cid:13)2+(cid:13)(cid:13)(cid:13)s[k](cid:13)(cid:13)(cid:13)22 P)t 10
ζ(cid:13) K g[k](cid:13) + s[k]  [k]Q (
≤ j=X1,j6=k(cid:13)(cid:13) j (cid:13)(cid:13)2 (cid:13)(cid:13) (cid:13)(cid:13)2
 (cid:13) (cid:13) (cid:13) (cid:13)  5
2
K
≤ ζPtXj=1rλmax(cid:16)H[kj]†H[kj](cid:17) . (21)
 
The upper bound of Q[k] in (21) can be achieved only
0
when all the interferences and desired signal are all in the 0 2000 4000 6000 8000 10000
same direction, i.e., θ = 0, and every vector v[j] can make Time Slot (n)
H[kj]v[j] achieve the largest value as in (13), which is
Fig.4. ComparisonofupperboundandsimulatedvalueofQ[k]ina5-user
(cid:13) (cid:13)2
i(cid:13)llustrated(cid:13)in Fig. 3(b). IAnetworkwith1datastreameachuser.
(cid:13) (cid:13)
From (18) and (21), we can have the following conclusion
2 1.5 6
K Q[k]
ζTatPhRette(cid:18)0hmeP≤laorwKjQkk=et1[hr1kr]:≤rTaλenhmcζdeePaixvtloe(cid:16)urwHpXjep=[Qkre1jr[]brk†oH]ubλ[nokmcdjuaa]nn(cid:17)xod(cid:19)(cid:16)fsHb2Q,e[kro[kejf]]ds†peHiennpc[okott(jiwev2]d(cid:17)e2elr)y,.a0sh.,arc0vaen(sa2tnbe2dde) sted at receiver k (P)t 1 R[k] 4 ate of User k (Bits/s/Hz)
e R
adpifp•fircodIuatelctsihistreoedddaificfinshicigsuenovlatmelfedosur[ckee]artltotlaoittnhhleieecafionsineltlesor,twfheweirnehgsnialcermeesiaetssgod[jnukir]spe,.pcjetiro6=nb,okuw,nhdaincihds Power Harv 0.5 2 Transmission
means the angle between these vectors should be 0.
• Each vector v[j] of transmitter j is designed according 0 0
to the requirement of IA in (2), instead of intending to 00 1100 2200 3300 4400 5500
Time Slot (n)
achieve the goal in (13). Thus it is difficult to require
all the precoding vectors to achieve the upper bound of
Fig. 5. Comparison ofR[k] and Q[k] in a 5-user IA network with 1 data
H[kj]v[j] in (13).
streameachuser,whentheaverage received SNRis10dB.
(cid:13) (cid:13)2
Fig(cid:13). 4 shows(cid:13)the upper bound of Q[k], which is defined in
(cid:13) (cid:13)
(22),comparedwithitssimulatedvalueina5-userIAnetwork
and desired signal. The transmission rate of user k can be
over10000timeslots.FromFig.4,wecanseethat,withalow
expressed as
probability,thesimulatedvalueofQ[k] canapproachitsupper
bound described in (22). On the other hand, the simulated 2
valueofQ[k] cangetclose to itslowerbound,0,with a much R[k] = log2(cid:18)1+Pt(cid:12)u[k]†H[kk]v[k](cid:12) (cid:19)
largerprobability.ThustheresultsinFig.4areconsistentwith (cid:12) (cid:12)
= log 1+P c(cid:12)2cos2δ , (cid:12) (23)
Remark 1. 2 t k k
(cid:0) (cid:1)
where c = H[kk]v[k] and δ is the angle between u[k] and
k k
B. Performance of Information Transmission of IA H[kk]v[k]. (cid:12)(cid:12) (cid:12)(cid:12)
(cid:12) (cid:12)
Whenauserisdedicatedtoinformationtransmissioninthe In Fig. 5, the transmission rate of user k when receiver k
IA network,its performancewillalso be varyingaccordingto is used as an ID terminal, R[k], and the power harvested of
the CSI of the network. In our previouswork [9], it is proved user k when receiver k is EH terminal, Q[k], are compared
that the information transmission performance of user k in in a 5-user IA network over 50 time slots, when the average
the IA network with one data stream each user is determined received SNR is 10dB. The average received SNR for user k
by the length of the desired signal c , and the angle δ 2
k k can be expressed as 10lg P E u[k]†H[kk]v[k] .
between the directions of interference suppression vector u[k] (cid:18) t (cid:18)(cid:12) (cid:12) (cid:19)(cid:19)
(cid:12) (cid:12)
(cid:12) (cid:12)
6
From [9] and Theorem 1, we can see that, for the CSI in 6) After duration , time slot n ends, n = n+1, and go
T
a time slot, the performance of information transmission and back to Step 1).
that of WPT may be quite different,as shown in Fig. 5. Thus The RRS algorithmfor SWIPT-US is simple to implement.
we should determine carefully to which extent a receiver is Nevertheless, both of the energy harvested and the transmis-
selectedtoharvestenergyaccordingtothedifferencebetween sion rate of the IA network can be further improved with the
theperformanceofinformationtransmissionandthatofWPT. same number of EH users L.
IV. SWIPT-USER SELECTIONSCHEME IN IA NETWORKS
B. PRR-Based Selection Algorithm for SWIPT-US
In Fig. 1, one power splitter is equipped at each receiver;
however, it is improper to still adopt power splitters due to In order to further improve EH and ID efficiency of the
the limitation of the size and complexity of the receivers in IA network, we define a parameter called power-to-rate ratio
somepracticalsystems.Inthissection,aSWIPT-userselection (PRR) to compare the instantaneous EH capability to ID
schemeisproposedforsimultaneouswirelessinformationand capabilityofanIAuser.ThePRRofuserk intheIAnetwork
power transfer in IA networks. In the SWIPT-US scheme, a in a time slot can be denoted as
numberofreceiversareselectedforEHdedicatedly,whichare 2
K
similartothosewithρ=0inFig.1,whiletheotherreceivers ζP H[kj]v[j]ξ[j]
t(cid:13) (cid:13)
aredevotedtoID,whicharesimilartothosewithρ=1.Thus η[k]=Q[k]= (cid:13)(cid:13)jP=1 (cid:13)(cid:13)2 (24)
theSWIPT-USschemeismucheasiertobeimplementedthan R[k] (cid:13) (cid:13) 2
log 1+(cid:13) P u[k]†H[kk]v(cid:13)[k]
the one with power splitters. Two algorithms to realize the 2(cid:18) t(cid:12) (cid:12) (cid:19)
SWIPT-US scheme are proposed. (cid:12) (cid:12)
ThePRRofuserk,η[k],definest(cid:12)heratiobetwee(cid:12)nthepower
A. Round-Robin Selection Algorithm for SWIPT-US transferredifuserkisonlyassignedasanEHterminalandthe
information rate if it is specially selected as an ID terminal.
In the IA wireless network, every receiver can act as an
When the PRR of user k is large, it means that it is better for
EH or ID terminal in a time slot, and simultaneous wireless
user k to harvest energy than to transmit information. With
information and power transfer can be achieved. In practical
PRR,weproposeaPRR-basedselection(PRRS)algorithmfor
systems,weshouldnotadoptallthereceiversasEHterminals,
SWIPT-US,inwhichtheuserswithlargerPRRareselectedas
because information transmission of the network should not
EH receivers in a time slot. The PRRS algorithm for SWIPT-
be terminated; on the other hand, the receivers should not
US can be expressed by the following steps:
be all dedicated to ID either, as the receivers need to collect
1) When time slot n starts, the solutions of IA are calcu-
energyto supporttheir operation,and prolongthe life time of
lated through using MinIL IA algorithms.
theirbatteries.Thus,onlyafractionofthereceiversshouldbe
2) The PRRs of all the users are calculated according to
devoted to EH in a time slot, and the SWIPT-US scheme for
(24), and we can obtain η[1],η[2],...,η[K].
SWIPT-based IA networks can be leveraged.
A simple idea of SWIPT-US is to select a number of 3) Select L users with the largest PRRs as EH receivers,
and devote the other users to ID.
receivers as EH terminals in a round-robin principle, i.e.,
to assign SWIPT users in successive time slots in circular 4) The portion of signal power split to the ID terminal, ρ,
order without priority, which is called round-robin selection is set to be 0 at the selected L EH receivers, and ρ is
set to 1 at all the other ID receivers.
(RRS) algorithm for the SWIPT-US scheme. Assume that
L receivers are switched to EH terminals in the SWIPT-US 5) Information transmission begins at the K L ID re-
−
ceivers according to (23), and energy harvesting is also
scheme,L<K.InaK-userIAnetworkwithbothIDandEH
terminals at each receiver as shown in Fig. 1, RRS algorithm performed at the L EH receivers according to (9).
for SWIPT-US can be represented by the following steps: 6) After duration , time slot n ends, n = n+1, and go
T
back to Step 1).
1) When time slot n starts, the solutions of IA are calcu-
lated throughusing the minimizinginterferenceleakage Remark 2: Comparing RRS and PRRS algorithms for
(MinIL) IA algorithms [6]. SWIPT-US, we can have the following observations.
2) The largest user number of dedicated EH users in time • The RRS algorithm is easy to implement, as it adopts
slot n 1 is , and thus the users with number round-robin principle to select EH receivers, and no
n−1
− I
( +1)%K,( +2)%K,...,( +L)%K are additional calculation is needed. By contrast, the PRRS
n−1 n−1 n−1
I I I
selected as EH users in time slot n (user 0 is equal to algorithmis more complex,because it needs to calculate
user K). The other K L users are assigned to be ID thePRRparameterofalltheuserstoselectEHreceivers.
−
users. • Both EH and ID performance of the PRRS algorithm
3) Set =( +L)%K. is better than that of the RRS algorithm with the same
n n−1
I I
4) The portion of signal power split to the ID terminal, ρ, number of EH receivers, due to the selection according
is set to be 0 at the selected L EH receivers, and ρ is to the PRR parameter in the PRRS algorithm.
set to 1 at all the other ID receivers. • In both RRS and PRRS algorithms, a receiver may be
5) Information transmission begins at the K L ID re- dedicated to be either an EH terminal or an ID terminal,
−
ceivers according to (23), and energy harvesting is also and the EH and ID performanceof the network may not
performed at the L EH receivers according to (9). be continuouslyoptimized accordingto the requirements
7
of the systems, e.g., battery status. In addition, they do β[k] = ϕ[k]·Q[rke]q , (29)
notconsider the specific requirementsof rate and energy υ[k] R[k] +ϕ[k] Q[k]
req req
for the users. Thus, if power splitters can be equippedat · ·
thereceivers,theEH andID performanceofthe network whereRr[ke]q andQ[rke]q areinstantaneousrequestedtransmission
canbeimprovedsignificantly,andtherequirementsofthe rate and requested power by user k. υ[k] and ϕ[k] are two
userscanbebettersatisfied.Nevertheless,theSWIPT-US constants to make rate correspondto power to achieve proper
scheme is much easier to be implemented. values of α[k] and β[k].
The optimization problem in (27) is a convex optimization
problem, and its optimal solutions can be calculated as in
V. OPTIMIZATIONOF BOTH IDAND EH PERFORMANCE
Theorem 2.
USING POWERSPLITTING
Theorem 2: The optimization problem in (27) is a con-
In Section IV, SWIPT-US algorithms for IA networks are
vex optimization problem in each time slot, and k
proposed, and they are simple and easy-implemented. How- ∀ ∈
1,2,...,K , its closed-form optimal solutions can be ex-
ever, the EH and ID performance may not be continuously { }
pressed as
optimized, and the specific requirements of the users are not
considered.Thusinthissection,apower-splittingoptimization 0, ψ[k] 0
≤
algorithm is proposed, when power splitters are available, to ρ∗[k] = 1, ψ[k] 1
optimize the performance of the network over the portion of  ψ[k], other≥wise,
signal power splitting ρ. Transmitted power allocation among where 
users in the PSO algorithm is also studied.
α[k] 1
ψ[k] = .
2 − 2
A. Power-Splitting Optimization for SWIPT in IA Networks K P u[k]†H[kk]v[k]
β[k]ζP H[kj]v[j]ξ[j] ln2 t
t(cid:13) (cid:13) (cid:12) (cid:12)
In this section, it is assumed that each receiver in the IA (cid:13)(cid:13)jP=1 (cid:13)(cid:13)2 (cid:12)(cid:12) (cid:12)(cid:12)
network can serve as EH and ID terminals simultaneously (cid:13) (cid:13)
Proof: In a(cid:13)time slot, the so(cid:13)lutionsof the IA network are
according to Fig. 1. ρ[k] is no long 1 or 0 for user k,
determined by the channel state information of the network,
instead, the received power is split into two portions, which
and thus ρ[k],k =1,2,...,K, are the only variables in (27).
are induced to EH and ID terminals, respectively. According
k 1,2,...,K ,ρ[k] [0,1]in(27)isaconvexset.Itcan
to ρ[k],k = 1,2,...,K, the sum rate of the IA network can ∀ ∈{ } ∈
also easily obtained that
be represented as
∂2
K F <0, (30)
= [k] ∂ρ[k]2
SR Rρ[k]
kX=1 and the objective function of (27) is convex. Thus the op-
F
K timization problem of (27) is a convex optimization problem.
2
= log 1+ρ[k]P u[k]†H[kk]v[k] . (25) We can obtain the derivative of with ρ[k] as (31) (on the
kX=1 2(cid:18) t(cid:12)(cid:12) (cid:12)(cid:12) (cid:19) next page). Because the solutionsFto (27) should satisfy that
The sum power harvested in the(cid:12)IA network sh(cid:12)ould also be 0 ρ[k] 1, thus from (31), we can achieve the closed-form
≤ ≤
updated as optimal solutions of (27) as
K 0, ψ[k] 0
= [k] ρ∗[k] = 1, ψ[k] ≤1 (32)
SQ Xk=1Qρ[k]  ψ[k], other≥wise,
2
K K where 
= Xk=1(cid:16)1−ρ[k](cid:17)ζPt(cid:13)(cid:13)(cid:13)Xj=1H[kj]v[j]ξ[j](cid:13)(cid:13)(cid:13) . (26) ψ[k] = α[k] 1 .
(cid:13) (cid:13)2 2 − 2
(cid:13) (cid:13) K P u[k]†H[kk]v[k]
Thus the optimization problem o(cid:13)f the PSO algori(cid:13)thm con- β[k]ζP H[kj]v[j]ξ[j] ln2 t
t(cid:13) (cid:13) (cid:12) (cid:12)
sidering both EH and ID performancesimultaneously at each (cid:13)(cid:13)jP=1 (cid:13)(cid:13)2 (cid:12)(cid:12) (cid:12)(cid:12)
receiver can be defined as (27) (on the next page). (cid:13) (cid:13) (33)
(cid:13) (cid:13)
In (27), α[k] and β[k] are two nonnegative design param-
eters, which denote the weights for the requirements of rate Equations (32) and (33) present the easy-implemented
andenergyneededofuserk,respectively,andα[k]+β[k] =1. closed-from solutions to (27), and thus the EH and ID per-
When α[k] becomeslarger,it meansthatthe transmission-rate formance of the IA network can be optimized simultaneously
requirementof user k is high or the battery power of receiver accordingtothespecificrequirementsoftheusersrepresented
k is sufficient; when α[k] is smaller, it means that the rate by α[k] and β[k], k =1,2,...,K.
requirement of user k is low or the battery is running out. Remark3: From(32) and(33), we canfind thatthe closed-
For example, we can define α[k] and β[k] as form optimal solution ρ∗[k] of user k is not affected by α
and β parameters of other users, i.e., the specific power and
α[k] = υ[k]·Rr[ke]q , (28) rate requirementsof the users in the network will not interact
υ[k] R[k] +ϕ[k] Q[k] among users.
req req
· ·
8
2
K K
2
ρ[1],ρm[2]a,.x..,ρ[K]kX=1α[k]log2(cid:18)1+ρ[k]Pt(cid:12)(cid:12)u[k]†H[kk]v[k](cid:12)(cid:12) (cid:19)+β[k](cid:16)1−ρ[k](cid:17)ζPt(cid:13)(cid:13)(cid:13)(cid:13)Xj=1H[kj]v[j]ξ[j](cid:13)(cid:13)(cid:13)(cid:13)2=F
 (cid:12) (cid:12) (cid:13) (cid:13) 
s.t. 0 ρ[k] 1, k =1,2,...,K. (cid:13) (cid:13) (27)
≤ ≤ ∀
2 2
α[k]P u[k]†H[kk]v[k] K
∂ t
∂ρF[k] = (cid:12)(cid:12) 2 (cid:12)(cid:12) −β[k]ζPt(cid:13)(cid:13) H[kj]v[j]ξ[j](cid:13)(cid:13) =0. (31)
(cid:18)1+Pt(cid:12)u[k](cid:12)†H[kk]v[k](cid:12) ρ[(cid:12)k](cid:19)ln2 (cid:13)(cid:13)(cid:13)Xj=1 (cid:13)(cid:13)(cid:13)2
(cid:12) (cid:12) (cid:13) (cid:13)
(cid:12) (cid:12)
B. PSO Algorithm with Power Allocation where x+ ,max(x,0), and should satisfy
V
+
In the above discussions, we assume that equal transmitted
K
power is allocated to each user, Pt[k] = Pt,k = 1,2,...,K, V − 1 2 =K·Pt. (37)
i.e., power allocation is not involved. In practical systems, Xk=1 u[k]†H[kk]v[k] 
the channel is usually not symmetric, and power allocation  (cid:12) (cid:12) 
(cid:12) (cid:12)
should be considered to guarantee the performance of the Remark 5: When α(cid:12)[k] = 0,k =(cid:12)1,2,...,K, ρ[k] is equal
whole network. Thus in this subsection, power allocation is to 0, k 1,2,...,K , and all the receivers work as EH
∀ ∈ { }
studiedinPSOtofurtherimprovetheIDandEHperformance terminals. This can happen when the batteries at receiversare
of SWIPT in IA networks. all at low levels and need to be recharged, and (34) becomes
Weassumethatthesumtransmittedpowerofalltheusersis
2
constrainedtobelowerthanaconstant,i.e., K P[k] K K K
k=1 t ≤ · max (cid:13) P[j]H[kj]v[j]ξ[j](cid:13)
Puste,ra.nWdthheunspPotwiserthaellaovceartaiogneoisftchoentsriadnesrmedit,tPethdepoowpteirmoizfaetaiochn Pt[1],Pt[2],...,Pt[K]Xk=1(cid:13)(cid:13)(cid:13)Xj=1q t (cid:13)(cid:13)(cid:13)2
problemin(27) forthe PSO algorithmcanbe updatedas(34) s.t. K (cid:13)(cid:13)P[k] K P , (cid:13)(cid:13)
(on the next page). t ≤ · t
kP=1
The optimization problem in (34) is not convex due to the P[k] 0. (38)
product of ρ[k] and P[k], and thus the closed-form optimal t ≥
solutionsaredifficulttot obtain.Therearemanysimplebutef- In practical systems, the extreme cases when all the α[k]
equalto1 or0 willappearwith lowprobability.Thecommon
fectivemethodsforsolvingcontinuousoptimizationproblems.
Inthesimulationsofthispaper,theinterior-pointmethod[42] situation is that some receivers with low level battery will
harvest more energy with low transmission rate, while some
is adopted.
others may have sufficient power supply, and they want to
Remark 4: Thepower allocationin the PSO algorithmwith
transmit more information instead of energy harvesting.
two extremes, k, α[k] = 1 and α[k] = 0, is interesting
∀
and worth noting. When α[k] = 1,k = 1,2,...,K, only
ID terminals are active at the receivers, and (34) becomes a VI. SIMULATION RESULTS ANDDISCUSSIONS
conventional power allocation problem that can be solved by We consider a 5-user IA wireless network with one data
the standard “water-filling” power allocation strategy. stream for each user. Three antennas are equipped at each
When α[k] =1,k=1,2,...,K, (34) becomes transceiver (i.e., M = N = 3). Rayleigh block channel
fading [40] is adopted, and perfect CSI is available at each
max K log 1+P[k] u[k]†H[kk]v[k] 2 node. ap due to the path loss is 0.1 (i.e., each element in the
Pt[1],Pt[2],...,Pt[K]kP=1 2(cid:18) t (cid:12)(cid:12) (cid:12)(cid:12) (cid:19) cthheansnimelumlataitornixs.follows CN(0,0.1)), and ζ is 0.5 throughout
K (cid:12) (cid:12)
s.t. P[k] K P , Fig. 6 shows the sum harvested power and sum rate of the
kP=1 t ≤ · t 5-user IA network using the PRRS and RRS algorithms for
P[k] 0. (35) theSWIPT-USschemewithdifferentnumbersofdedicatedID
t ≥
receivers, when the average received SNR is 10dB. From the
results,wecanseethatthesumharvestedpowerincreasesand
The closed-form solutions to (35) can be easily achieved by
the sum rate decreases as the number of dedicated ID users
“water-filling” as [43]
becomes smaller. Both ID performance and EH performance
+ ofthePRRSalgorithmarebetterthanoratleastequaltothose
1 of the RRS algorithm due to the selection according to PRR
Pt[ko]pt =V − 2 , (36) in (24). For example, when there are 3 dedicated ID users,
 u[k]†H[kk]v[k]  the sum powerharvestedincreasesfrom1.34Pt with the RRS
 (cid:12) (cid:12) 
(cid:12) (cid:12)
(cid:12) (cid:12)
9
2
K K
2
max α[k]log 1+ρ[k]P[k] u[k]†H[kk]v[k] +β[k] 1 ρ[k] ζ(cid:13) P[j]H[kj]v[j]ξ[j](cid:13) 
ρ[1],ρ[2],...,ρ[K],Pt[1],Pt[2],...,Pt[K]Xk=1 2(cid:18) t (cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12) (cid:19) (cid:16) − (cid:17) (cid:13)(cid:13)(cid:13)(cid:13)Xj=1q t (cid:13)(cid:13)(cid:13)(cid:13)2
s.t. 0 ρ[k] 1, k =1,2,...,K, (cid:13) (cid:13)
≤ ≤ ∀
K
P[k] K P ,
t ≤ · t
kP=1
P[k] 0, k =1,2,...,K. (34)
t ≥ ∀
4 1166 4 16
Sum Power in PRRS
Sum Power in RRS
3.5 14 3.5 14
Sum Rate in PRRS
Sum Rate in RRS
3 1122 3 12
m Power (P)t 2.25 8180 Rate (Bits/s/Hz) m Power (P)t 2.25 810 Rate (Bits/s/Hz)
Su 1.5 6 m Su 1.5 6 m
Su Su
1 44 1 4
Sum Power in PSO Scheme
0.5 2 0.5 Sum Rate in PSO Scheme 2
0 00 0 0
000 111 222 333 444 555 00 00..22 00..44 00..66 00..88 11
Number of Dedicated ID Users α
Fig. 6. Comparison of sum harvested power and sum rate of the 5-user Fig. 7. Comparison of sum harvested power and sum rate of the PSO
IA network using the PRRS and RRS algorithms with different numbers of algorithm withdifferent valuesofαin5-userIAnetwork,whentheaverage
dedicated IDreceivers, whentheaverage received SNRis10dB. received SNRis10dB.
algorithm to 1.83P with the PRRS algorithm, and the sum EH terminals. Thus, α[k] =α, k 1,2,...,K , can be set
t
∀ ∈{ }
rate increases from 8.63 bits/s/Hz with the RRS algorithm to in a reduced domain of [0.4,1].
9.94 bits/s/Hz with the PRRS algorithm. ThePSOalgorithmcanoptimizeEHandIDperformanceof
In the PSO algorithm,α[k] is a key parameter,whichdeter- IA networkssimultaneously,and the performancewith differ-
mines the trade-off between the rate and energy performance entpowerandrate requirementsofusersshouldbe discussed.
of user k. Assume α[1] = α[2] = = α[K] = α, Fig. 7 In Fig. 8, we compare the average performance of power
···
shows the sum harvested power and sum rate in a 5-user IA harvested, rate transmitted, and corresponding parameter ρ
networkwithdifferentvaluesofα, whentheaveragereceived of the users in a 5-user IA network with different values
SNR is 10dB. From the results, we can observe that, when of α, when the average received SNR is 10dB. α[1] = 0.6,
α becomes larger in the PSO algorithm, the sum rate of the α[2] = 0.8, α[3] = 0.95, α[4] = 0.975, α[5] = 0.99. From
networkincreases,andthesumharvestedpowerofthenetwork the results, it is shown that the different power and rate
decreases. From (32), (33) and α[k]+β[k] =1, we can know requirements of the users can be traded off with different
that, when values of α in the PSO algorithm for SWIPT in IA networks.
Besides, when the value of α of a user becomes larger, its
2
K transmissionratebecomeslarger,itsharvestedpowerbecomes
ζ H[kj]v[j]ξ[j] ln2
(cid:13) (cid:13) smaller, and its corresponding ρ becomes larger.
α[k] ≤ (cid:13)(cid:13)(cid:13)jP=1 2 (cid:13)(cid:13)(cid:13)2 , (39) PowerallocationcanimprovebothEH andIDperformance
ζ K H[kj](cid:13)v[j]ξ[j] ln2+(cid:13)u[k]†H[kk]v[k] 2 in the PSO algorithm of IA networks significantly. Power-
(cid:13) (cid:13)
(cid:13)(cid:13)jP=1 (cid:13)(cid:13)2 (cid:12)(cid:12) (cid:12)(cid:12) rate region can characterize all the achievable power and
(cid:13) (cid:13) (cid:12) (cid:12) rate pairs under a given transmit power constraint. Fig. 9
the optimal(cid:13)solution ρ∗[k] w(cid:13)ill be 0, and receiver k will be shows the power-rate trade-offs of the PSO algorithm with
dedicated to EH. From Fig. 7, we can also find that, when PA, PSO algorithm without PA, PRRS and RRS algorithms
α[k] = α, k 1,2,...,K , is set below 0.4, the sum rate for the SWIPT-US scheme in the 5-user IA network with the
∀ ∈ { }
of the network will be 0, and all the receivers are adopted as same values of α of all the users, i.e, α[1] = α[2] = =
···
10
3.5
3 Q[k] (P)
Q[k] (P) t
R[k] (Bitts/s/Hz) 3 R[k] (Bits/s/Hz)
2.5 P[k] (P)
ρ[k] t t
ρ[k]
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
1 2 3 4 5 0
1 2 3 4 5
User k
User k
Fig. 8. The average performance comparison of the power harvested, rate
Fig.10. Theaveragepowerharvested,transmissionrate,transmitted power
transmitted, and corresponding parameter ρ of users in the PSO algorithm
allocated, and corresponding parameter ρ of users in the power-allocation
withdifferentvaluesofαofusers,whentheaveragereceivedSNRis10dB.
α[1]=0.6,α[2]=0.8,α[3]=0.95,α[4]=0.975,α[5]=0.99. PSOalgorithmwithdifferentvaluesofα,whentheaveragereceivedSNRis
10dB.α[1]=0.05,α[2]=0.2,α[3]=0.35,α[4]=0.5,α[5]=0.65.
6
PSO Scheme with PA calculationof therate, while sumof thedesiredsignalandall
PSO Scheme
the interferences is adopted to calculate the power harvested.
5 PRRS Algorithm
In Fig. 10, we show the average power harvested, trans-
RRS Algorithm
mission rate, transmitted power allocated, and corresponding
4 parameterρoftheusersinthepower-allocationPSOalgorithm
P)t with differentvalues of α, when the average received SNR is
er ( 10dB. α[1] = 0.05, α[2] = 0.2, α[3] = 0.35, α[4] = 0.5,
ow 3 α[5] = 0.65. From the results, we can see that the average
P
m powerallocatedtoeachuserandparameterρofeachusercan
u
S
be adjustedaccordingto the valuesof α set by each user,and
2
thus the expected ID and EH performance can be achieved.
Theoptimaltransmittedpowerofa userbecomeslargerwhen
1 its expected rate is larger, and has little relationship with its
harvested power. This is because one user can harvest power
fromall the otherusersin the network,on the other hand,the
0
rateofauserisalmostonlydeterminedbyitsowntransmitted
0 5 10 15
Sum Rate (Bits/s/Hz) power. Besides, the values of α in the PSO algorithm with
power allocation are quite different from those in the PSO
Fig.9. Power-ratetradeoffs ofthePSOalgorithm withPA,PSOalgorithm algorithm without power allocation according to the ID and
withoutPA,andPRRSandRRSalgorithmsfortheSWIPT-USscheme,when EH performance of the users.
theaverage received SNRis10dB.
VII. CONCLUSIONS AND FUTURE WORK
α[5]. The average received SNR is 10dB, and the average In this paper, we have presented a common framework of
received SNR with power allocation can be calculated as simultaneous wireless information and power transfer in IA
2 networks, and analyzed the performance of SWIPT in IA
10lgE K P[k] u[k]†H[kk]v[k] /K . From the re-
(cid:18) k=1(cid:18) t (cid:12) (cid:12) (cid:19) (cid:19) networks.Wederivedthelowerandupperboundsofthepower
sults in FPig. 9, we ca(cid:12)n observe that(cid:12)power-rate performance that can be harvested in IA networks. An easy-implemented
(cid:12) (cid:12)
of the PSO algorithm is better than that of the SWIPT-US SWIPT-US scheme for IA networks was proposed, in which
scheme.WhenPAisadoptedinthePSOalgorithm,itspower- a number of receivers are selected for EH dedicatedly and
rate performance can be significantly improved, especially the others are devoted to ID solely in a time slot. Two
the performance of EH, which is consistent with Remark algorithms,RRS andPRRS, weredesignedforSWIPT-US. In
4 and Remark 5. The enhancement of the EH performance thePRRSalgorithm,power-to-rateratioisdefinedandadopted
is much more obvious than that of the ID performance by to select EH receivers. To continuously optimize the EH and
PA in the PSO algorithm, because log function is used in ID performance of each user according to the requirements