text: | | for i, j = 0, 1, 2, if v + v + v = Ω , and if Ω satisﬁes an interior sphere condition, then 0 F1 2 { } | | there exists a minimizer to among permissible triples E with E = v . The same F SWP F F F j j j statement is true if is replaced by either or . ( is deﬁned below.) Assuming that SWP SP S S we allow a two sided trace of our BV characteristic functions on the boundary of our domain, and making the same assumptions as above, then there will also exist minimizers which satisfy given Dirichlet data. (Of course one should refer to the discussion above regarding the nature of Dirichlet data for this problem.) Remark 3.3 (Appropriate Problems) It seems worthwhile to observe here the necessity of prescribing Dirichlet data in any problem without a volume constraint. Indeed, without a volume constraint or Dirichlet data, one expects two of the three ﬂuids to vanish in any minimizer. On the other hand, once you have a volume constraint, you can study the minimizers both with and without Dirichlet data. At this point, we standardize our language for the type of minimizer that we are considering in order to prevent language from becoming too cumbersome. Deﬁnition 3.4 (Types of Minimizers) We will use the syntax: [ Qualiﬁer(s) ]-minimizer of [ functional ] in [ set ] . The “qualiﬁers” we will use are “D” and/or “V” to indicate a Dirichlet or a volume constraint { } F respectively. So a typical appearance might look like: E is a V-minimizer of in B , { } Fj SP 3 which means that E are V-permissible and minimize in B among all V-permissible j SP 3 sets. If the set is not speciﬁed, then we will assume that the minimization happens on Ω; If the F functional is not speciﬁed, then we assume that is the functional being minimized. The set S given will typically be bounded, but when it is not bounded we will assume that anything which we call any kind of minimizer will minimize the given functional when restricted to any compact subset of the unbounded domain. Remark 3.5 (On restrictions and rescalings) It is also worth remarking that after re- stricting and rescaling, a triple which used to V-minimize some functional will still V-minimize some functional in the new set, but except in the case of three cones, the new sets will typically be competing against V-permissible triples with diﬀerent restrictions on the volume of each set from the restrictions at the outset. Remark 3.6 (Reversal of inclusions) We also observe that the inclusions of types of min- imizers are also reversed from what one might assume before thinking about it. In typical set inclusions of this sort, one assumes that more constraints leads to a smaller set. Here, because it is the competitors which are being constrained, the inclusions work in reverse. Indeed, the set of all DV-minimizers contains both the set of V-minimizers and the set of D-minimizers insofar as if you take the DV-minimizer where you take the Dirichlet data to be rather “wiggly” then you only compete against other conﬁgurations with similarly wiggly boundary data. Thus, you are automatically the DV-minimizer by contruction, but you are not likely to be a V-minimizer, as any V-minimizer would prefer less wiggly boundary data. 8

text: for

text: i,

text: j

text: if

text: v

text: v

text: v

text: Ω

text: and

text: if

text: Ω

text: satisﬁes

text: an

text: interior

text: sphere

text: condition,

text: then

text: there

text: exists

text: a

text: minimizer

text: to

text: among

text: permissible

text: triples

text: E

text: with

text: E

text: v

text: The

text: same

text: F

text: SWP

text: F

text: F

text: F

text: j

text: j

text: j

text: statement

text: is

text: true

text: if

text: is

text: replaced

text: by

text: either

text: or

text: is

text: deﬁned

text: below.)

text: Assuming

text: that

text: SWP

text: SP

text: S

text: S

text: we

text: allow

text: a

text: two

text: sided

text: trace

text: of

text: our

text: BV

text: characteristic

text: functions

text: on

text: the

text: boundary

text: of

text: our

text: domain,

text: and

text: making

text: the

text: same

text: assumptions

text: as

text: above,

text: then

text: there

text: will

text: also

text: exist

text: minimizers

text: which

text: satisfy

text: given

text: Dirichlet

text: data.

text: (Of

text: course

text: one

text: should

text: refer

text: to

text: the

text: discussion

text: above

text: regarding

text: the

text: nature

text: of

text: Dirichlet

text: data

text: for

text: this

text: problem.)

text: Remark

text: (Appropriate

text: Problems)

text: It

text: seems

text: worthwhile

text: to

text: observe

text: here

text: the

text: necessity

text: of

text: prescribing

text: Dirichlet

text: data

text: in

text: any

text: problem

text: without

text: a

text: volume

text: constraint.

text: Indeed,

text: without

text: a

text: volume

text: constraint

text: or

text: Dirichlet

text: data,

text: one

text: expects

text: two

text: of

text: the

text: three

text: ﬂuids

text: to

text: vanish

text: in

text: any

text: minimizer.

text: On

text: the

text: other

text: hand,

text: once

text: you

text: have

text: a

text: volume

text: constraint,

text: you

text: can

text: study

text: the

text: minimizers

text: both

text: with

text: and

text: without

text: Dirichlet

text: data.

text: At

text: this

text: point,

text: we

text: standardize

text: our

text: language

text: for

text: the

text: type

text: of

text: minimizer

text: that

text: we

text: are

text: considering

text: in

text: order

text: to

text: prevent

text: language

text: from

text: becoming

text: too

text: cumbersome.

text: Deﬁnition

text: (Types

text: of

text: Minimizers)

text: We

text: will

text: use

text: the

text: syntax:

text: Qualiﬁer(s)

text: ]-minimizer

text: of

text: functional

text: in

text: set

text: The

text: “qualiﬁers”

text: we

text: will

text: use

text: are

text: “D”

text: and/or

text: “V”

text: to

text: indicate

text: a

text: Dirichlet

text: or

text: a

text: volume

text: constraint

text: F

text: respectively.

text: So

text: a

text: typical

text: appearance

text: might

text: look

text: like:

text: E

text: is

text: a

text: V-minimizer

text: of

text: in

text: B

text: Fj

text: SP

text: which

text: means

text: that

text: E

text: are

text: V-permissible

text: and

text: minimize

text: in

text: B

text: among

text: all

text: V-permissible

text: j

text: SP

text: sets.

text: If

text: the

text: set

text: is

text: not

text: speciﬁed,

text: then

text: we

text: will

text: assume

text: that

text: the

text: minimization

text: happens

text: on

text: Ω;

text: If

text: the

text: F

text: functional

text: is

text: not

text: speciﬁed,

text: then

text: we

text: assume

text: that

text: is

text: the

text: functional

text: being

text: minimized.

text: The

text: set

text: S

text: given

text: will

text: typically

text: be

text: bounded,

text: but

text: when

text: it

text: is

text: not

text: bounded

text: we

text: will

text: assume

text: that

text: anything

text: which

text: we

text: call

text: any

text: kind

text: of

text: minimizer

text: will

text: minimize

text: the

text: given

text: functional

text: when

text: restricted

text: to

text: any

text: compact

text: subset

text: of

text: the

text: unbounded

text: domain.

text: Remark

text: (On

text: restrictions

text: and

text: rescalings)

text: It

text: is

text: also

text: worth

text: remarking

text: that

text: after

text: re-

text: stricting

text: and

text: rescaling,

text: a

text: triple

text: which

text: used

text: to

text: V-minimize

text: some

text: functional

text: will

text: still

text: V-minimize

text: some

text: functional

text: in

text: the

text: new

text: set,

text: but

text: except

text: in

text: the

text: case

text: of

text: three

text: cones,

text: the

text: new

text: sets

text: will

text: typically

text: be

text: competing

text: against

text: V-permissible

text: triples

text: with

text: diﬀerent

text: restrictions

text: on

text: the

text: volume

text: of

text: each

text: set

text: from

text: the

text: restrictions

text: at

text: the

text: outset.

text: Remark

text: (Reversal

text: of

text: inclusions)

text: We

text: also

text: observe

text: that

text: the

text: inclusions

text: of

text: types

text: of

text: min-

text: imizers

text: are

text: also

text: reversed

text: from

text: what

text: one

text: might

text: assume

text: before

text: thinking

text: about

text: it.

text: In

text: typical

text: set

text: inclusions

text: of

text: this

text: sort,

text: one

text: assumes

text: that

text: more

text: constraints

text: leads

text: to

text: a

text: smaller

text: set.

text: Here,

text: because

text: it

text: is

text: the

text: competitors

text: which

text: are

text: being

text: constrained,

text: the

text: inclusions

text: work

text: in

text: reverse.

text: Indeed,

text: the

text: set

text: of

text: all

text: DV-minimizers

text: contains

text: both

text: the

text: set

text: of

text: V-minimizers

text: and

text: the

text: set

text: of

text: D-minimizers

text: insofar

text: as

text: if

text: you

text: take

text: the

text: DV-minimizer

text: where

text: you

text: take

text: the

text: Dirichlet

text: data

text: to

text: be

text: rather

text: “wiggly”

text: then

text: you

text: only

text: compete

text: against

text: other

text: conﬁgurations

text: with

text: similarly

text: wiggly

text: boundary

text: data.

text: Thus,

text: you

text: are

text: automatically

text: the

text: DV-minimizer

text: by

text: contruction,

text: but

text: you

text: are

text: not

text: likely

text: to

text: be

text: a

text: V-minimizer,

text: as

text: any

text: V-minimizer

text: would

text: prefer

text: less

text: wiggly

text: boundary

text: data.


text: three anomalies: missing satellites, cusp vs core, too big to fail. [14–16]. To solve these problems, it needs a proper self-interaction between dark matter that can give the non- relativistic self-scattering cross section.[17] The scattering cross section between DM can be described by quantum mechanics. In our model, interchanging h between singlino χ forms a Yukawa potential κ2 − V (r) = e mhr. (19) 2π Since mass of h can be tuned to any value, self interaction can be realized without right handed neutrino. we will check the case of participation of right handed neutrino. Also we will set N lighter than m /2 so that h can decay to the right handed neutrino N to satisfy h the BBN constraint. [20] The numerical results are shown in the following section. III. REALIZING THE SELF-INTERACTING DARK MATTER The numerical input for the simulation of small scales is the diﬀerential cross sec- (cid:82) tion dσ/dΩ as a function of the DM relative velocity v. The standard cross section σ = dΩ(dσ/dΩ) receives a strong enhancement in the forward backward scattering limit → ± (cos θ 1), which does not change the DM particle trajectories. Thus two additional cross sections are deﬁned to parameterize transport [21], the transfer cross section σ and (cid:90) (cid:90) T the viscosity (or conductivity) cross section σ :[17–19] V − dσ dσ σ = dΩ (1 cos θ) , σ = dΩ sin2 θ . (20) T V dΩ dΩ σ is for the estimation of the Dirac DM, while σ is for the Majorana DM. Since the singlino T T χ is a Majorana fermion, thus we should(cid:12) check the viscosity cross section which sh(cid:12)ould be (cid:12) (cid:12) (cid:12) (cid:88) (cid:12) deﬁned with two variables: (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) ∞ (cid:12)2 dσ | − | 1 − V S = f(θ) + f(π θ) 2 = (cid:12) (2(cid:96) + 1)(exp(2iδ ) 1)P (cos θ)(cid:12) (21) dΩ k2 (cid:12)(cid:12) (cid:88) l (cid:96) (cid:12)(cid:12) (cid:12)(cid:96)(EVEN number) (cid:12) (cid:12) (cid:12) (cid:12) ∞ (cid:12)2 dσ | − − | 1 − V A = f(θ) f(π θ) 2 = (2(cid:96) + 1)(exp(2iδ ) 1)P (cos θ) (22) dΩ k2 l (cid:96) (cid:88) (cid:96)(ODD number) Using the orthogonality relation for the Legendre polynomials, we can obtain ∞ σ k2 − V S = (cid:88) 4 sin2(δ(cid:96)+2 δ(cid:96))((cid:96) + 1)((cid:96) + 2)/(2(cid:96) + 3), (23) 4π (cid:96)(EVEN number) ∞ σ k2 − V A = 4 sin2(δ δ )((cid:96) + 1)((cid:96) + 2)/(2(cid:96) + 3). (24) (cid:96)+2 (cid:96) 4π (cid:96)(ODD number) 6 ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: three

label: paragraph

text: anomalies:

text: missing

text: satellites,

text: cusp

text: vs

text: core,

text: too

text: big

text: to

text: fail.

text: To

text: solve

text: these

text: problems,

text: it

text: needs

text: a

text: proper

text: self-interaction

text: between

text: dark

text: matter

text: that

text: can

text: give

text: the

text: non-

text: relativistic

text: self-scattering

text: cross

text: The

text: scattering

text: cross

text: section

text: between

text: DM

text: can

text: be

text: described

text: by

text: quantum

text: mechanics.

text: In

text: our

text: model,

text: interchanging

text: h

text: between

text: singlino

text: χ

text: forms

text: a

text: Yukawa

text: potential

text: κ2

text: V

text: (r)

text: e

text: mhr.

text: 2π

text: Since

text: mass

text: of

text: h

text: can

text: be

text: tuned

text: to

text: any

text: value,

text: self

text: interaction

text: can

text: be

text: realized

text: without

text: right

text: handed

text: neutrino.

text: we

text: will

text: check

text: the

text: case

text: of

text: participation

text: of

text: right

text: handed

text: neutrino.

text: Also

text: we

text: will

text: set

text: N

text: lighter

text: than

text: m

text: so

text: that

text: h

text: can

text: decay

text: to

text: the

text: right

text: handed

text: neutrino

text: N

text: to

text: satisfy

text: h

text: the

text: BBN

text: constraint.

text: The

text: numerical

text: results

text: are

text: shown

text: in

text: the

text: following

text: section.

text: III.

text: REALIZING

text: THE

text: SELF-INTERACTING

text: DARK

text: MATTER

text: The

text: numerical

text: input

text: for

text: the

text: simulation

text: of

text: small

text: scales

text: is

text: the

text: diﬀerential

text: cross

text: sec-

text: tion

text: dσ/dΩ

text: as

text: a

text: function

text: of

text: the

text: DM

text: relative

text: velocity

text: v.

text: The

text: standard

text: cross

text: section

text: σ

text: dΩ(dσ/dΩ)

text: receives

text: a

text: strong

text: enhancement

text: in

text: the

text: forward

text: backward

text: scattering

text: limit

text: (cos

text: θ

text: which

text: does

text: not

text: change

text: the

text: DM

text: particle

text: trajectories.

text: Thus

text: two

text: additional

text: cross

text: sections

text: are

text: deﬁned

text: to

text: parameterize

text: transport

text: the

text: transfer

text: cross

text: section

text: σ

text: and

text: T

text: the

text: viscosity

text: (or

text: conductivity)

text: cross

text: section

text: σ

text: V

text: dσ

text: dσ

text: σ

text: dΩ

text: cos

text: θ)

text: σ

text: dΩ

text: θ

text: T

text: V

text: dΩ

text: dΩ

text: σ

text: is

text: for

text: the

text: estimation

text: of

text: the

text: Dirac

text: DM,

text: while

text: σ

text: is

text: for

text: the

text: Majorana

text: DM.

text: Since

text: the

text: singlino

text: T

text: T

text: χ

text: is

text: a

text: Majorana

text: fermion,

text: thus

text: we

text: check

text: the

text: viscosity

text: cross

text: section

text: which

text: be

text: deﬁned

text: with

text: two

text: variables:

text: dσ

text: V

text: S

text: f(θ)

text: f(π

text: θ)

text: (cos

text: dΩ

text: l

text: number)

text: dσ

text: V

text: A

text: f(θ)

text: f(π

text: θ)

text: (cos

text: θ)

text: dΩ

text: l

text: number)

text: Using

text: the

text: orthogonality

text: relation

text: for

text: the

text: Legendre

text: polynomials,

text: we

text: can

text: obtain

text: σ

text: V

text: S

text: 4π

text: number)

text: σ

text: V

text: A

text: δ

text: 4π

text: number)

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 34, NO. X, JAN. 2016 2 regarded as a promising solution to highly energy-efﬁcient which is known as the harvest-store-use model. This model networking. Note that, due to the dual-purpose of RF signals, has been incorporated with time switching-based relaying in i.e., wireless power transfer (WPT) and wireless information three-node relaying networks in [15], where data relaying was transfer (WIT), fundamental changes to the designs of green realized when sufﬁcient power was collected through time communication networks are entailed. switching technique, and the remaining power was stored for A. Related Works future usage. The outage probability of the proposed strategy As concluded in [7], energy harvesting receiving archi- was studied. Besides, a similar strategy was discussed for tectures and power management models are two essential user equipment relay in device-to-device communications units to realize wireless-powered cooperative relay commu- in [16]. nications. The energy harvesting unit is for energy collection, Note that, it is still an open problem to allow energy and there are mainly two types of energy harvesting receiving accumulation in PS-based relaying strategy. Furthermore, architectures in the literature. In particular, the ﬁrst type is the harvest-store-use mode is well justiﬁed if the battery based on power splitting (PS) technique, which splits the has perfect efﬁciency. However, nearly all practical batteries received RF signal into two different power streams for suffer a storage loss to varying extents, ranging from 10% to separate WPT and WIT, and the other is based on time 30% [17]. From the perspective of energy efﬁciency, a new switching technique, where the received signal at one time harvest-use-store model has been proposed in [18], where slot is used for either WPT or WIT [8]. Note that, the the harvest energy is prioritized for use in data transmission signal received at one time slot is used for both information while its balance/debt is stored in or extracted from the processing and power transfer in the PS technique, which is battery, which avoids unnecessary energy loss in storing. This not allowed in the time switching technique [10]. Therefore, new model has been combined with the conventional energy the time switching technique is suboptimal in terms of harvesting techniques in [18]. B. Motivations and Contributions efﬁciently using the available signal power [9], and the PS technique is more suitable for applications with critical delay To realize an efﬁcient utilization of harvested energy and constraints [10]. Besides, the power management unit aims at improve spectral efﬁciency, energy accumulation is realized utilizing the harvested power effectively. Most of the research in PS-based relaying in this paper. In particular, the com- works conducted so far assumes either harvest-use or harvest- bining of PS based-relaying and harvest-use-store model store-use model. In the former model, the harvested energy to improve throughput performance is considered. Different is directly used and energy accumulation is not allowed from the previous works with time switching-based case due to lack of storage units, while in the later model, the in [15], [16], information transfer and battery operations harvested energy is ﬁrst accumulated and stored with the including the charging and discharging happen at the same help of a battery and then adaptively utilized in information time slot in the PS-based case. Moreover, the enhanced transmission [7]. PS technique needs to be designed to support the battery The incorporation of harvest-use model and PS-based operations. To address these challenging issues is the main relaying has been studied in [11]–[13], where harvested concern of this paper, and the main contributions can be energy through PS is used up at each information relaying. summarized as follows: In particular, in [11], a harvest-use PS-based relaying strat- • To realize an efﬁcient utilization of harvested energy egy was realized in two-way amplify-and-forward relaying with the help of a battery, a harvest-use-store PS relaying systems, and the outage probability and ergodic capacity strategy with distributed beamforming is proposed for were analyzed. In [13], a multiple relay system was con- the wireless-powered multiple-relay scenario. Speciﬁ- sidered, where several randomly located energy harvesting cally, each relay obtains both information and power relays help the transmission between a source-destination from the received signals transmitted by the source pair. The proposed strategy was shown to achieve the same node via power splitting. Subsequently, with the help diversity gain as the case with conventional self-powered of a battery, the harvested power is used to amplify- relays. The multiple antenna conﬁgurations were considered and-forward the information to the destination through in [12], where a sophisticated relaying strategy that jointly distributed beamforming with adaptive power allocation. utilizes harvest-use PS and antenna selection was designed • To reveal a theoretical bound of the proposed strat- and optimized to improve the achievable rate. Besides, the egy, a throughput maximization problem is formulated harvest-use time switching-based relaying was studied in and solved with an ideal non-causal channel state in- multi-tier uplink cellular networks in [14], where each user formation (CSI) assumption. Though the formulated transmits only when the harvested energy at one time slot optimization problem is intractable looking, a layered is sufﬁcient for the designed power control scheme, and no optimization method that derives the optimal solution is user can save the extra harvested energy for the next time developed. In particular, the joint PS and battery oper- slot. Though the harvest-use model is easy to implement, it ation design in the proposed strategy is decomposed in would perform better if energy accumulation is allowed to two layers, such that the original optimization problem store a part of the harvested power for future usage [13], is transformed to a dynamic programming problem with

text: IEEE

text: JOURNAL

text: ON

text: SELECTED

text: AREAS

text: IN

text: COMMUNICATIONS,

text: VOL.

text: NO.

text: X,

text: JAN.

text: regarded

text: as

text: a

text: promising

text: solution

text: to

text: highly

text: energy-efﬁcient

text: which

text: is

text: known

text: as

text: the

text: harvest-store-use

text: model.

text: This

text: model

text: networking.

text: Note

text: that,

text: due

text: to

text: the

text: dual-purpose

text: of

text: RF

text: signals,

text: has

text: been

text: incorporated

text: with

text: time

text: switching-based

text: relaying

text: in

text: i.e.,

text: wireless

text: power

text: transfer

text: (WPT)

text: and

text: wireless

text: information

text: three-node

text: relaying

text: networks

text: in

text: where

text: data

text: relaying

text: was

text: transfer

text: (WIT),

text: fundamental

text: changes

text: to

text: the

text: designs

text: of

text: green

text: realized

text: when

text: sufﬁcient

text: power

text: was

text: collected

text: through

text: time

text: communication

text: networks

text: are

text: entailed.

text: switching

text: technique,

text: and

text: the

text: remaining

text: power

text: was

text: stored

text: for

text: A.

label: section

text: Related

text: Works

text: future

text: usage.

text: The

text: outage

text: probability

text: of

text: the

text: proposed

text: strategy

text: As

text: concluded

text: in

text: energy

text: harvesting

text: receiving

text: archi-

text: was

text: studied.

text: Besides,

text: a

text: similar

text: strategy

text: was

text: discussed

text: for

text: tectures

text: and

text: power

text: management

text: models

text: are

text: two

text: essential

text: user

text: equipment

text: relay

text: in

text: device-to-device

text: communications

text: units

text: to

text: realize

text: wireless-powered

text: cooperative

text: relay

text: commu-

text: in

text: nications.

text: The

text: energy

text: harvesting

text: unit

text: is

text: for

text: energy

text: collection,

text: Note

text: that,

text: it

text: is

text: still

text: an

text: open

text: problem

text: to

text: allow

text: energy

text: and

text: there

text: are

text: mainly

text: two

text: types

text: of

text: energy

text: harvesting

text: receiving

text: accumulation

text: in

text: PS-based

text: relaying

text: strategy.

text: Furthermore,

text: architectures

text: in

text: the

text: literature.

text: In

text: particular,

text: the

text: ﬁrst

text: type

text: is

text: the

text: harvest-store-use

text: mode

text: is

text: well

text: justiﬁed

text: if

text: the

text: battery

text: based

text: on

text: power

text: splitting

text: (PS)

text: technique,

text: which

text: splits

text: the

text: has

text: perfect

text: efﬁciency.

text: However,

text: nearly

text: all

text: practical

text: batteries

text: received

text: RF

text: signal

text: into

text: two

text: different

text: power

text: streams

text: for

text: suffer

text: a

text: storage

text: loss

text: to

text: varying

text: extents,

text: ranging

text: from

text: to

text: separate

text: WPT

text: and

text: WIT,

text: and

text: the

text: other

text: is

text: based

text: on

text: time

text: From

text: the

text: perspective

text: of

text: energy

text: efﬁciency,

text: a

text: new

text: switching

text: technique,

text: where

text: the

text: received

text: signal

text: at

text: one

text: time

text: harvest-use-store

text: model

text: has

text: been

text: proposed

text: in

text: where

text: slot

text: is

text: used

text: for

text: either

text: WPT

text: or

text: WIT

text: Note

text: that,

text: the

text: the

text: harvest

text: energy

text: is

text: prioritized

text: for

text: use

text: in

text: data

text: transmission

text: signal

text: received

text: at

text: one

text: time

text: slot

text: is

text: used

text: for

text: both

text: information

text: while

text: its

text: balance/debt

text: is

text: stored

text: in

text: or

text: extracted

text: from

text: the

text: processing

text: and

text: power

text: transfer

text: in

text: the

text: PS

text: technique,

text: which

text: is

text: battery,

text: which

text: avoids

text: unnecessary

text: energy

text: loss

text: in

text: storing.

text: This

text: not

text: allowed

text: in

text: the

text: time

text: switching

text: technique

text: Therefore,

text: new

text: model

text: has

text: been

text: combined

text: with

text: the

text: conventional

text: energy

text: the

text: time

text: switching

text: technique

text: is

text: suboptimal

text: in

text: terms

text: of

text: harvesting

text: techniques

text: in

text: B.

text: Motivations

text: and

text: Contributions

text: efﬁciently

text: using

text: the

text: available

text: signal

text: power

text: and

text: the

text: PS

text: technique

text: is

text: more

text: suitable

text: for

text: applications

text: with

text: critical

text: delay

text: To

text: realize

text: an

text: efﬁcient

text: utilization

text: of

text: harvested

text: energy

text: and

text: constraints

text: Besides,

text: the

text: power

text: management

text: unit

text: aims

text: at

text: improve

text: spectral

text: efﬁciency,

text: energy

text: accumulation

text: is

text: realized

text: utilizing

text: the

text: harvested

text: power

text: effectively.

text: Most

text: of

text: the

text: research

text: in

text: PS-based

text: relaying

text: in

text: this

text: paper.

text: In

text: particular,

text: the

text: com-

text: works

text: conducted

text: so

text: far

text: assumes

text: either

text: harvest-use

text: or

text: harvest-

text: bining

text: of

text: PS

text: based-relaying

text: and

text: harvest-use-store

text: model

text: store-use

text: model.

text: In

text: the

text: former

text: model,

text: the

text: harvested

text: energy

text: to

text: improve

text: throughput

text: performance

text: is

text: considered.

text: Different

text: is

text: directly

text: used

text: and

text: energy

text: accumulation

text: is

text: not

text: allowed

text: from

text: the

text: previous

text: works

text: with

text: time

text: switching-based

text: case

text: due

text: to

text: lack

text: of

text: storage

text: units,

text: while

text: in

text: the

text: later

text: model,

text: the

text: in

text: information

text: transfer

text: and

text: battery

text: operations

text: harvested

text: energy

text: is

text: ﬁrst

text: accumulated

text: and

text: stored

text: with

text: the

text: including

text: the

text: charging

text: and

text: discharging

text: happen

text: at

text: the

text: same

text: help

text: of

text: a

text: battery

text: and

text: then

text: adaptively

text: utilized

text: in

text: information

text: time

text: slot

text: in

text: the

text: PS-based

text: case.

text: Moreover,

text: the

text: enhanced

text: transmission

text: PS

text: technique

text: needs

text: to

text: be

text: designed

text: to

text: support

text: the

text: battery

text: The

text: incorporation

text: of

text: harvest-use

text: model

text: and

text: PS-based

text: operations.

text: To

text: address

text: these

text: challenging

text: issues

text: is

text: the

text: main

text: relaying

text: has

text: been

text: studied

text: in

text: where

text: harvested

text: concern

text: of

text: this

text: paper,

text: and

text: the

text: main

text: contributions

text: can

text: be

text: energy

text: through

text: PS

text: is

text: used

text: up

text: at

text: each

text: information

text: relaying.

text: summarized

text: as

text: follows:

text: In

text: particular,

text: in

text: a

text: harvest-use

text: PS-based

text: relaying

text: strat-

text: To

text: realize

text: an

text: efﬁcient

text: utilization

text: of

text: harvested

text: energy

text: egy

text: was

text: realized

text: in

text: two-way

text: amplify-and-forward

text: relaying

text: with

text: the

text: help

text: of

text: a

text: battery,

text: a

text: harvest-use-store

text: PS

text: relaying

text: systems,

text: and

text: the

text: outage

text: probability

text: and

text: ergodic

text: capacity

text: strategy

text: with

text: distributed

text: beamforming

text: is

text: proposed

text: for

text: were

text: analyzed.

text: In

text: a

text: multiple

text: relay

text: system

text: was

text: con-

text: the

text: wireless-powered

text: multiple-relay

text: scenario.

text: Speciﬁ-

text: sidered,

text: where

text: several

text: randomly

text: located

text: energy

text: harvesting

text: cally,

text: each

text: relay

text: obtains

text: both

text: information

text: and

text: power

text: relays

text: help

text: the

text: transmission

text: between

text: a

text: source-destination

text: from

text: the

text: received

text: signals

text: transmitted

text: by

text: the

text: source

text: pair.

text: The

text: proposed

text: strategy

text: was

text: shown

text: to

text: achieve

text: the

text: same

text: node

text: via

text: power

text: splitting.

text: Subsequently,

text: with

text: the

text: help

text: diversity

text: gain

text: as

text: the

text: case

text: with

text: conventional

text: self-powered

text: of

text: a

text: battery,

text: the

text: harvested

text: power

text: is

text: used

text: to

text: amplify-

text: relays.

text: The

text: multiple

text: antenna

text: conﬁgurations

text: were

text: considered

text: and-forward

text: the

text: information

text: to

text: the

text: destination

text: through

text: in

text: where

text: a

text: sophisticated

text: relaying

text: strategy

text: that

text: jointly

text: distributed

text: beamforming

text: with

text: adaptive

text: power

text: allocation.

text: utilizes

text: harvest-use

text: PS

text: and

text: antenna

text: selection

text: was

text: designed

text: To

text: reveal

text: a

text: theoretical

text: bound

text: of

text: the

text: proposed

text: strat-

text: and

text: optimized

text: to

text: improve

text: the

text: achievable

text: rate.

text: Besides,

text: the

text: egy,

text: a

text: throughput

text: maximization

text: problem

text: is

text: formulated

text: harvest-use

text: time

text: switching-based

text: relaying

text: was

text: studied

text: in

text: and

text: solved

text: with

text: an

text: ideal

text: non-causal

text: channel

text: state

text: in-

text: multi-tier

text: uplink

text: cellular

text: networks

text: in

text: where

text: each

text: user

text: formation

text: (CSI)

text: assumption.

text: Though

text: the

text: formulated

text: transmits

text: only

text: when

text: the

text: harvested

text: energy

text: at

text: one

text: time

text: slot

text: optimization

text: problem

text: is

text: intractable

text: looking,

text: a

text: layered

text: is

text: sufﬁcient

text: for

text: the

text: designed

text: power

text: control

text: scheme,

text: and

text: no

text: optimization

text: method

text: that

text: derives

text: the

text: optimal

text: solution

text: is

text: user

text: can

text: save

text: the

text: extra

text: harvested

text: energy

text: for

text: the

text: next

text: time

text: developed.

text: In

text: particular,

text: the

text: joint

text: PS

text: and

text: battery

text: oper-

text: slot.

text: Though

text: the

text: harvest-use

text: model

text: is

text: easy

text: to

text: implement,

text: it

text: ation

text: design

text: in

text: the

text: proposed

text: strategy

text: is

text: decomposed

text: in

text: would

text: perform

text: better

text: if

text: energy

text: accumulation

text: is

text: allowed

text: to

text: two

text: layers,

text: such

text: that

text: the

text: original

text: optimization

text: problem

text: store

text: a

text: part

text: of

text: the

text: harvested

text: power

text: for

text: future

text: usage

text: is

text: transformed

text: to

text: a

text: dynamic

text: programming

text: problem

text: with


text: IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 34, NO. X, JAN. 2016 15 [1] M. Peng, C. Wang, V. Lau, H. V.Poor, “Fronthaul-constrained cloud [22] W. J. Huang, Y. W. P. Hong, and C. C. J. Kuo, “Lifetime maximization radio access networks: insights and challenges,”IEEE Wireless Com- for amplify-and-forward cooperative networks,” IEEE Trans. Wireless mun., vol.22, no.2, pp.152–160, April 2015. Commun., vol. 7, no. 5, pp. 1800–1805, May 2008. [2] B. Bangerter, S. Talwar, R. Areﬁ, and K. Stewart, “Networks and [23] W. Dinkelbach, “On nonlinear fractional programming, ” Manage- Devices for the 5G Era,”IEEE Commun. Mag., vol. 52, no. 2, pp. ment Science, vol. 13, pp. 492–498, Mar. 1967. Available: [Online] 90–96, Feb. 2014. http://www.jstor.org/stable/2627691. [3] E. Hossain, M. Rasti, H. Tabassum, A. Abdelnasser, “Evolution toward [24] S. Boyd and L. Vandenberghe, Convex optimization, 2nd ed. Cam- 5G multi-tier cellular wireless networks: An interference management bridge University Press, Cambridge, England, UK, 2004. perspective,”IEEE Wireless Commun., vol. 21, no. 3, pp. 118–127, June [25] M. L. Puterman, Markov decision processes: discrete stochastic 2014. dynamic programming, 1st ed. John Wiley & Sons, Inc., New York, [4] C. Huang, J. Zhang, P. Zhang, and S. Cui, “Threshold-based transmis- NY, USA, 1994. sions for large relay networks powered by renewable energy,” in Proc. [26] X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power IEEE Global Commun. Conf. (Globecom), Atlanta, GA, USA, Dec. transfer: architecture design and rate-energy tradeoff,” IEEE Trans. 2013, pp. 1921–1926. Wireless Commun., vol. 61, no. 11, pp. 4754–4767, Nov. 2013. [5] Z. Ding, C. Zhong, D. Wing, M. Peng, H. A. Suraweera, R. Schober, [27] P. Sadeghi, R. A. Kennedy, P. B. Rapajic, and R. Shams, “Finitestate and H. V. Poor, “Application of smart antenna technologies in simulta- Markov modeling of fading channels – a survey of principles and neous wireless information and power transfer,” IEEE Commun. Mag., applications,” IEEE Signal Processing Magazine, vol. 25, pp. 57–80, vol. 53, no. 4, pp. 86–93, Apr. 2015. Sep. 2008. [6] H. Tabassum, E. Hossain, A. Ogundipe, and D. I. Kim, “Wireless- powered cellular networks: Key challenges and solution techniques,” IEEE Commun. Mag., 2015 (to appear). [Online]. Available: http: //wireless.skku.edu/english/UserFiles/File/ﬁnal [7] X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z. Han, “Wireless networks with RF energy harvesting: A contemporary survey,” IEEE Commun. Surveys & Tutorials, 2014, DOI: 10.1109/COMST.2014.2368999. Zheng Zhou received the B.S. degree in Informa- [8] R. Zhang and C. K. Ho, “MIMO broadcasting for simultaneous wire- tion Engineering from Beijing University of Posts less information and power transfer,” IEEE Trans. Wireless Commun., and Telecommunications (BUPT), Beijing, China, vol. 12, no. 5, pp. 1989–2001, May 2013. in 2012. He is currently working toward the Ph.D. [9] K. Huang, E. Larsson, “Simultaneous Information and Power Transfer degree at BUPT. His research interests include for Broadband Wireless Systems,” IEEE Trans. Sig. Proc., vol.61, simultaneous information and power transfer and no.23, pp.5972–5986, Dec. 2013. cloud radio access networks. [10] I. Krikidis, S. Timotheou, S. Nikolaou, G. Zheng, D.W.K. Ng, R. Schober, “Simultaneous wireless information and power transfer in modern communication systems,” IEEE Commun. Mag., vol.52, no.11, pp.104–110, Nov. 2014. [11] A. A. Nasir, X. Zhou, S. Durrani, and R. A. Kennedy, “Relaying protocols for wireless energy harvesting and information processing,” IEEE Trans. Wireless Commun., vol. 12, no. 7, pp. 3622–3636, July 2013. [12] Z. Zhou, M. Peng, Z. Zhao and Y. Li, “Joint power splitting and Mugen Peng (M’05–SM’11) received the B.E. antenna selection in energy harvesting relay channels,” IEEE Sig. Proc. degree in Electronics Engineering from Nanjing Lett., vol. 22, no. 7, pp.823–827, July 2015. University of Posts & Telecommunications, China [13] Z. Ding, I. Krikidis, B. Sharif, and H. V. Poor, “Wireless information in 2000 and a PhD degree in Communication and and power transfer in cooperative networks with spatially random Information System from the Beijing University relays,” IEEE Trans. Wireless Commun., vol. 13, no. 8, pp. 4440–4453, of Posts & Telecommunications (BUPT), China Aug. 2014. in 2005. After the PhD graduation, he joined in [14] A. H. Sakr and E. Hossain, “Analysis of multi-tier uplink cellular BUPT, and has become a full professor with the networks with energy harvesting and ﬂexible cell association,” in Proc. school of information and communication engi- IEEE Global Commun. Conf. (Globecom), Austin, TX, USA, Dec. neering in BUPT since Oct. 2012. During 2014, 2014, pp. 4525–4530. he is also an academic visiting fellow in Princeton [15] I. Krikidis, S. Timotheou, and S. Sasaki, “RF energy transfer for University, USA. He is leading a research group focusing on wireless trans- cooperative networks: Data relaying or energy harvesting?,” IEEE mission and networking technologies in the Key Laboratory of Universal Commun. Lett., vol. 16, no. 11, pp.1772–1775, Nov. 2012. Wireless Communications (Ministry of Education) at BUPT, China. His [16] H. Yang, J. Lee, and T. Q. S. Quek, “Heterogeneous cellular main research areas include wireless communication theory, radio signal network with energy harvesting based D2D communication,” sub- processing and convex optimizations, with particular interests in cooperative mitted to IEEE Trans. Wireless Commun. Available: [Online] communication, radio network coding, self-organization networking, hetero- http://www.researchgate.net/publication/263848668. geneous networking, and cloud communication. He has authored/coauthored [17] S. Sudevalayam and P. Kulkarni, “Energy harvesting sensor nodes: over 40 refereed IEEE journal papers and over 200 conference proceeding Survey and implications,” IEEE Commun. Surveys Tuts., vol. 13, no. papers. 3, pp. 443–461, 2011. Dr. Peng is currently on the Editorial/Associate Editorial Board of IEEE [18] F. Yuan, Q. T. Zhang, S. Jin, and H. Zhu, “Optimal harvest-use-store Communications Magazine, IEEE Access, International Journal of Antennas strategy for energy harvesting wireless systems,” IEEE Trans. Wireless and Propagation (IJAP), and China Communications. He has been the guest Commun., vol. 14, no. 2, pp. 698–710, Feb. 2015. leading editor for the special issues in IEEE Wireless Communications, IJAP [19] Y. Jing and H. Jafarkhani, “Network beamforming using relays with and International Journal of Distributed Sensor Net- works (IJDSN). He perfect channel information,” IEEE Trans. Inf. Theory, vol. 55, no. 6, received the 2014 IEEE ComSoc AP Outstanding Young Researcher Award, pp. 2499–2517, June 2009. and the Best Paper Award in IEEE WCNC 2015, WASA 2015, GameNets [20] R. Wang and M. Tao, “Joint Source and Relay Precoding Designs for 2014, IEEE CIT 2014, ICCTA 2011, IC-BNMT 2010, and IET CCWMC MIMO Two-Way Relaying Based on MSE Criterion,” IEEE Trans. Sig. 2009. He was awarded the First Grade Award of Technological Invention Proc., vol.60, no.3, pp.1352–1365, March 2012. Award in Ministry of Education of China, and the Second Grade Award of [21] L. Liu, R. Zhang, and K.-C. Chua, “Wireless information and power Scientiﬁc & Technical Progress from China Institute of Communications. transfer: A dynamic power splitting approach,” IEEE Trans. Commun., vol. 61, no. 9, pp. 3990–4001, Sept. 2013. ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure##

text: IEEE

text: JOURNAL

text: ON

text: SELECTED

text: AREAS

text: IN

text: COMMUNICATIONS,

text: VOL.

text: NO.

text: X,

text: JAN.

label: reference

text: M.

text: Peng,

text: C.

text: Wang,

text: V.

text: Lau,

text: H.

text: V.Poor,

text: “Fronthaul-constrained

text: cloud

text: W.

text: J.

text: Huang,

text: Y.

text: W.

text: P.

text: Hong,

text: and

text: C.

text: C.

text: J.

text: Kuo,

text: “Lifetime

text: maximization

text: radio

text: access

text: networks:

text: insights

text: and

text: challenges,”IEEE

text: Wireless

text: Com-

text: for

text: amplify-and-forward

text: cooperative

text: networks,”

text: IEEE

text: Trans.

text: Wireless

text: mun.,

text: April

text: Commun.,

text: vol.

text: no.

text: pp.

text: May

text: B.

text: Bangerter,

text: S.

text: Talwar,

text: R.

text: Areﬁ,

text: and

text: K.

text: Stewart,

text: “Networks

text: and

text: W.

text: Dinkelbach,

text: “On

text: nonlinear

text: fractional

text: programming,

text: Manage-

text: Devices

text: for

text: the

text: Era,”IEEE

text: Commun.

text: Mag.,

text: vol.

text: no.

text: pp.

text: ment

text: Science,

text: vol.

text: pp.

text: Mar.

text: Available:

text: [Online]

text: Feb.

text: E.

text: Hossain,

text: M.

text: Rasti,

text: H.

text: Tabassum,

text: A.

text: Abdelnasser,

text: “Evolution

text: toward

text: S.

text: Boyd

text: and

text: L.

text: Vandenberghe,

text: Convex

text: optimization,

text: ed.

text: Cam-

text: multi-tier

text: cellular

text: wireless

text: networks:

text: An

text: interference

text: management

text: bridge

text: University

text: Press,

text: Cambridge,

text: England,

text: UK,

text: perspective,”IEEE

text: Wireless

text: Commun.,

text: vol.

text: no.

text: pp.

text: June

text: M.

text: L.

text: Puterman,

text: Markov

text: decision

text: processes:

text: discrete

text: stochastic

text: dynamic

text: programming,

text: ed.

text: John

text: Wiley

text: Sons,

text: Inc.,

text: New

text: York,

text: C.

text: Huang,

text: J.

text: Zhang,

text: P.

text: Zhang,

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text: S.

text: Cui,

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text: NY,

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text: sions

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text: relay

text: networks

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text: energy,”

text: in

text: Proc.

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text: R.

text: Zhang,

text: and

text: C.

text: K.

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text: power

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text: Global

text: Commun.

text: Conf.

text: (Globecom),

text: Atlanta,

text: GA,

text: USA,

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text: transfer:

text: architecture

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text: and

text: rate-energy

text: tradeoff,”

text: IEEE

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text: Commun.,

text: vol.

text: no.

text: pp.

text: Nov.

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text: C.

text: Zhong,

text: D.

text: Wing,

text: M.

text: Peng,

text: H.

text: A.

text: Suraweera,

text: R.

text: Schober,

text: P.

text: Sadeghi,

text: R.

text: A.

text: Kennedy,

text: P.

text: B.

text: Rapajic,

text: and

text: R.

text: Shams,

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text: Poor,

text: “Application

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text: technologies

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text: Markov

text: modeling

text: of

text: fading

text: channels

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text: survey

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text: principles

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text: neous

text: wireless

text: information

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text: power

text: transfer,”

text: IEEE

text: Commun.

text: Mag.,

text: applications,”

text: IEEE

text: Signal

text: Processing

text: Magazine,

text: vol.

text: pp.

text: vol.

text: no.

text: pp.

text: Apr.

text: Sep.

text: H.

text: Tabassum,

text: E.

text: Hossain,

text: A.

text: Ogundipe,

text: and

text: D.

text: I.

text: Kim,

text: “Wireless-

text: powered

text: cellular

text: networks:

text: Key

text: challenges

text: and

text: solution

text: techniques,”

text: IEEE

text: Commun.

text: Mag.,

text: (to

text: appear).

text: [Online].

text: Available:

text: http:

text: X.

text: Lu,

text: P.

text: Wang,

text: D.

text: Niyato,

text: D.

text: I.

text: Kim,

text: and

text: Z.

text: Han,

text: “Wireless

text: networks

text: with

text: RF

text: energy

text: harvesting:

text: A

text: contemporary

text: survey,”

text: IEEE

text: Commun.

text: Surveys

text: Tutorials,

text: DOI:

text: Zheng

text: Zhou

text: received

text: the

text: B.S.

text: degree

text: in

text: Informa-

text: R.

text: Zhang

text: and

text: C.

text: K.

text: Ho,

text: “MIMO

text: broadcasting

text: for

text: simultaneous

text: wire-

text: tion

text: Engineering

text: from

text: Beijing

text: University

text: of

text: Posts

text: less

text: information

text: and

text: power

text: transfer,”

text: IEEE

text: Trans.

text: Wireless

text: Commun.,

text: and

text: Telecommunications

text: (BUPT),

text: Beijing,

text: China,

text: vol.

text: no.

text: pp.

text: May

text: in

text: He

text: is

text: currently

text: working

text: toward

text: the

text: Ph.D.

text: K.

text: Huang,

text: E.

text: Larsson,

text: “Simultaneous

text: Information

text: and

text: Power

text: Transfer

text: degree

text: at

text: BUPT.

text: His

text: research

text: interests

text: include

text: for

text: Broadband

text: Wireless

text: Systems,”

text: IEEE

text: Trans.

text: Sig.

text: Proc.,

text: simultaneous

text: information

text: and

text: power

text: transfer

text: and

text: Dec.

text: cloud

text: radio

text: access

text: networks.

text: I.

text: Krikidis,

text: S.

text: Timotheou,

text: S.

text: Nikolaou,

text: G.

text: Zheng,

text: D.W.K.

text: Ng,

text: R.

text: Schober,

text: “Simultaneous

text: wireless

text: information

text: and

text: power

text: transfer

text: in

text: modern

text: communication

text: systems,”

text: IEEE

text: Commun.

text: Mag.,

text: Nov.

text: A.

text: A.

text: Nasir,

text: X.

text: Zhou,

text: S.

text: Durrani,

text: and

text: R.

text: A.

text: Kennedy,

text: “Relaying

text: protocols

text: for

text: wireless

text: energy

text: harvesting

text: and

text: information

text: processing,”

text: IEEE

text: Trans.

text: Wireless

text: Commun.,

text: vol.

text: no.

text: pp.

text: July

text: Z.

text: Zhou,

text: M.

text: Peng,

text: Z.

text: Zhao

text: and

text: Y.

text: Li,

text: “Joint

text: power

text: splitting

text: and

text: Mugen

text: Peng

text: received

text: the

text: B.E.

text: antenna

text: selection

text: in

text: energy

text: harvesting

text: relay

text: channels,”

text: IEEE

text: Sig.

text: Proc.

text: degree

text: in

text: Electronics

text: Engineering

text: from

text: Nanjing

text: Lett.,

text: vol.

text: no.

text: July

text: University

text: of

text: Posts

text: Telecommunications,

text: China

text: Z.

text: Ding,

text: I.

text: Krikidis,

text: B.

text: Sharif,

text: and

text: H.

text: V.

text: Poor,

text: “Wireless

text: information

text: in

text: and

text: a

text: PhD

text: degree

text: in

text: Communication

text: and

text: and

text: power

text: transfer

text: in

text: cooperative

text: networks

text: with

text: spatially

text: random

text: Information

text: System

text: from

text: the

text: Beijing

text: University

text: relays,”

text: IEEE

text: Trans.

text: Wireless

text: Commun.,

text: vol.

text: no.

text: pp.

text: of

text: Posts

text: Telecommunications

text: (BUPT),

text: China

text: Aug.

text: in

text: After

text: the

text: PhD

text: graduation,

text: he

text: joined

text: in

text: A.

text: H.

text: Sakr

text: and

text: E.

text: Hossain,

text: “Analysis

text: of

text: multi-tier

text: uplink

text: cellular

text: BUPT,

text: and

text: has

text: become

text: a

text: full

text: professor

text: with

text: the

text: networks

text: with

text: energy

text: harvesting

text: and

text: ﬂexible

text: cell

text: association,”

text: in

text: Proc.

text: school

text: of

text: information

text: and

text: communication

text: engi-

text: IEEE

text: Global

text: Commun.

text: Conf.

text: (Globecom),

text: Austin,

text: TX,

text: USA,

text: Dec.

text: neering

text: in

text: BUPT

text: since

text: Oct.

text: During

text: pp.

text: he

text: is

text: also

text: an

text: academic

text: visiting

text: fellow

text: in

text: Princeton

text: I.

text: Krikidis,

text: S.

text: Timotheou,

text: and

text: S.

text: Sasaki,

text: “RF

text: energy

text: transfer

text: for

text: University,

text: USA.

text: He

text: is

text: leading

text: a

text: research

text: group

text: focusing

text: on

text: wireless

text: trans-

text: cooperative

text: networks:

text: Data

text: relaying

text: or

text: energy

text: harvesting?,”

text: IEEE

text: mission

text: and

text: networking

text: technologies

text: in

text: the

text: Key

text: Laboratory

text: of

text: Universal

text: Commun.

text: Lett.,

text: vol.

text: no.

text: Nov.

text: Wireless

text: Communications

text: (Ministry

text: of

text: Education)

text: at

text: BUPT,

text: China.

text: His

text: H.

text: Yang,

text: J.

text: Lee,

text: and

text: T.

text: Q.

text: S.

text: Quek,

text: “Heterogeneous

text: cellular

text: main

text: research

text: areas

text: include

text: wireless

text: communication

text: theory,

text: radio

text: signal

text: network

text: with

text: energy

text: harvesting

text: based

text: communication,”

text: sub-

text: processing

text: and

text: convex

text: optimizations,

text: with

text: particular

text: interests

text: in

text: cooperative

text: mitted

text: to

text: IEEE

text: Trans.

text: Wireless

text: Commun.

text: Available:

text: [Online]

text: communication,

text: radio

text: network

text: coding,

text: self-organization

text: networking,

text: hetero-

text: geneous

text: networking,

text: and

text: cloud

text: communication.

text: He

text: has

text: authored/coauthored

text: S.

text: Sudevalayam

text: and

text: P.

text: Kulkarni,

text: “Energy

text: harvesting

text: sensor

text: nodes:

text: over

text: refereed

text: IEEE

text: journal

text: papers

text: and

text: over

text: conference

text: proceeding

text: Survey

text: and

text: implications,”

text: IEEE

text: Commun.

text: Surveys

text: Tuts.,

text: vol.

text: no.

text: papers.

text: pp.

text: Dr.

text: Peng

text: is

text: currently

text: on

text: the

text: Editorial/Associate

text: Editorial

text: Board

text: of

text: IEEE

text: F.

text: Yuan,

text: Q.

text: T.

text: Zhang,

text: S.

text: Jin,

text: and

text: H.

text: Zhu,

text: “Optimal

text: harvest-use-store

text: Communications

text: Magazine,

text: IEEE

text: Access,

text: International

text: Journal

text: of

text: Antennas

text: strategy

text: for

text: energy

text: harvesting

text: wireless

text: systems,”

text: IEEE

text: Trans.

text: Wireless

text: and

text: Propagation

text: (IJAP),

text: and

text: China

text: Communications.

text: He

text: has

text: been

text: the

text: guest

text: Commun.,

text: vol.

text: no.

text: pp.

text: Feb.

text: leading

text: editor

text: for

text: the

text: special

text: issues

text: in

text: IEEE

text: Wireless

text: Communications,

text: IJAP

text: Y.

text: Jing

text: and

text: H.

text: Jafarkhani,

text: “Network

text: beamforming

text: using

text: relays

text: with

text: and

text: International

text: Journal

text: of

text: Distributed

text: Sensor

text: Net-

text: works

text: (IJDSN).

text: He

text: perfect

text: channel

text: information,”

text: IEEE

text: Trans.

text: Inf.

text: Theory,

text: vol.

text: no.

text: received

text: the

text: IEEE

text: ComSoc

text: AP

text: Outstanding

text: Young

text: Researcher

text: Award,

text: pp.

text: June

text: and

text: the

text: Best

text: Paper

text: Award

text: in

text: IEEE

text: WCNC

text: WASA

text: GameNets

text: R.

text: Wang

text: and

text: M.

text: Tao,

text: “Joint

text: Source

text: and

text: Relay

text: Precoding

text: Designs

text: for

text: IEEE

text: CIT

text: ICCTA

text: IC-BNMT

text: and

text: IET

text: CCWMC

text: MIMO

text: Two-Way

text: Relaying

text: Based

text: on

text: MSE

text: Criterion,”

text: IEEE

text: Trans.

text: Sig.

text: He

text: was

text: awarded

text: the

text: First

text: Grade

text: Award

text: of

text: Technological

text: Invention

text: Proc.,

text: March

text: Award

text: in

text: Ministry

text: of

text: Education

text: of

text: China,

text: and

text: the

text: Second

text: Grade

text: Award

text: of

text: L.

text: Liu,

text: R.

text: Zhang,

text: and

text: K.-C.

text: Chua,

text: “Wireless

text: information

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text: power

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text: Technical

text: Progress

text: from

text: China

text: Institute

text: of

text: Communications.

text: transfer:

text: A

text: dynamic

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text: approach,”

text: IEEE

text: Trans.

text: Commun.,

text: vol.

text: no.

text: pp.

text: Sept.

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##


text: IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 34, NO. X, JAN. 2016 16 Zhongyuan Zhao received the B.S. degree in applied mathematics and the Ph.D. degree in com- munication and information systems from Bei- jing University of Posts and Telecommunications (BUPT), Beijing, China, in 2009 and 2014, re- spectively. He is currently a Lecturer with the Key Laboratory of Universal Wireless Communication (Ministry of Education) at BUPT. His research interests include network coding, MIMO, relay transmissions, and large-scale cooperation in future communication networks. Wenbo Wang is currently the dean of Telecommu- nication Engineering at Beijing University of Posts and Telecommunications (BUPT). He received the BS degree, the MS and Ph.D. Degrees from BUPT in 1986, 1989 and 1992 respectively. Now he is the Assistant Director of academic committee of Key Laboratory of Universal Wireless Communication (Ministry of Education) in BUPT. His research interests include radio transmission technology, Wireless network theory, Broadband wireless ac- cess and Software radio technology. Prof. Wenbo Wang has published more than 200 journal and international conference papers and holds 12 patents and has published six books. Rick S. Blum (S’83–M’84–SM’94–F’05) received the B.S. degree in electrical engineering from the Pennsylvania State University in 1984 and the M.S. and Ph.D. degrees in electrical engineering from the University of Pennsylvania in 1987 and 1991, respectively. From 1984 to 1991, he was a member of technical staff at General Electric Aerospace, Val- leyForge, PA, USA, and he graduated from GEs Advanced Course in Engineering. Since 1991, he has been with the Electrical and Computer Engi- neering Department at Lehigh University, Bethlehem, PA, USA, where he is currently a Professor and holds the Robert W. Wieseman Chaired Research Professorship in Electrical Engineering. His research interests include signal processing for smart grid, communications, sensor networking, radar and sensor processing. He is on the editorial board for the Journal of Advances in Information Fusion of the International Society of Information Fusion. He was an Associate Editor for IEEE TRANSACTIONS ON SIGNAL PROCESSING and for IEEE COMMUNICATIONS LETTERS. He has edited special issues for IEEE TRANSACTIONS ON SIGNAL PROCESSING, IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, and IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. He is a member of the SAM Technical Committee (TC) of the IEEE Signal Processing Society. He was a member of the Signal Processing for Communications TC of the IEEE Signal Processing Society and is a member of the Communications Theory TC of the IEEE Communication Society. He was on the awards committee of the IEEE Communication Society. Dr. Blum is a former IEEE Signal Processing Society Distinguished Lecturer, an IEEE Third Millennium Medal winner, a member of Eta Kappa Nu and Sigma Xi, and holds several patents. He was awarded an ONR Young Investigator Award and an NSF Research Initiation Award. His IEEE Fellow Citation “for scientiﬁc contributions to detection, data fusion and signal processing with multiple sensors” acknowledges contributions to the ﬁeld of sensor networking. ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure##

text: IEEE

text: JOURNAL

text: ON

text: SELECTED

text: AREAS

text: IN

text: COMMUNICATIONS,

text: VOL.

text: NO.

text: X,

text: JAN.

text: Zhongyuan

text: Zhao

text: received

text: the

text: B.S.

text: degree

text: in

text: applied

text: mathematics

text: and

text: the

text: Ph.D.

text: degree

text: in

text: com-

text: munication

text: and

text: information

text: systems

text: from

text: Bei-

text: jing

text: University

text: of

text: Posts

text: and

text: Telecommunications

text: (BUPT),

text: Beijing,

text: China,

text: in

text: and

text: re-

text: spectively.

text: He

text: is

text: currently

text: a

text: Lecturer

text: with

text: the

text: Key

text: Laboratory

text: of

text: Universal

text: Wireless

text: Communication

text: (Ministry

text: of

text: Education)

text: at

text: BUPT.

text: His

text: research

text: interests

text: include

text: network

text: coding,

text: MIMO,

text: relay

text: transmissions,

text: and

text: large-scale

text: cooperation

text: in

text: future

text: communication

text: networks.

text: Wenbo

text: Wang

text: is

text: currently

text: the

text: dean

text: of

text: Telecommu-

text: nication

text: Engineering

text: at

text: Beijing

text: University

text: of

text: Posts

text: and

text: Telecommunications

text: (BUPT).

text: He

text: received

text: the

text: BS

text: degree,

text: the

text: MS

text: and

text: Ph.D.

text: Degrees

text: from

text: BUPT

text: in

text: and

text: respectively.

text: Now

text: he

text: is

text: the

text: Assistant

text: Director

text: of

text: academic

text: committee

text: of

text: Key

text: Laboratory

text: of

text: Universal

text: Wireless

text: Communication

text: (Ministry

text: of

text: Education)

text: in

text: BUPT.

text: His

text: research

text: interests

text: include

text: radio

text: transmission

text: technology,

text: Wireless

text: network

text: theory,

text: Broadband

text: wireless

text: ac-

text: cess

text: and

text: Software

text: radio

text: technology.

text: Prof.

text: Wenbo

text: Wang

text: has

text: published

text: more

text: than

text: journal

text: and

text: international

text: conference

text: papers

text: and

text: holds

text: patents

text: and

text: has

text: published

text: six

text: books.

text: Rick

text: S.

text: Blum

text: received

text: the

text: B.S.

text: degree

text: in

text: electrical

text: engineering

text: from

text: the

text: Pennsylvania

text: State

text: University

text: in

text: and

text: the

text: M.S.

text: and

text: Ph.D.

text: degrees

text: in

text: electrical

text: engineering

text: from

text: the

text: University

text: of

text: Pennsylvania

text: in

text: and

text: respectively.

text: From

text: to

text: he

text: was

text: a

text: member

text: of

text: technical

text: staff

text: at

text: General

text: Electric

text: Aerospace,

text: Val-

text: leyForge,

text: PA,

text: USA,

text: and

text: he

text: graduated

text: from

text: GEs

text: Advanced

text: Course

text: in

text: Engineering.

text: Since

text: he

text: has

text: been

text: with

text: the

text: Electrical

text: and

text: Computer

text: Engi-

text: neering

text: Department

text: at

text: Lehigh

text: University,

text: Bethlehem,

text: PA,

text: USA,

text: where

text: he

text: is

text: currently

text: a

text: Professor

text: and

text: holds

text: the

text: Robert

text: W.

text: Wieseman

text: Chaired

text: Research

text: Professorship

text: in

text: Electrical

text: Engineering.

text: His

text: research

text: interests

text: include

text: signal

text: processing

text: for

text: smart

text: grid,

text: communications,

text: sensor

text: networking,

text: radar

text: and

text: sensor

text: processing.

text: He

text: is

text: on

text: the

text: editorial

text: board

text: for

text: the

text: Journal

text: of

text: Advances

text: in

text: Information

text: Fusion

text: of

text: the

text: International

text: Society

text: of

text: Information

text: Fusion.

text: He

text: was

text: an

text: Associate

text: Editor

text: for

text: IEEE

text: TRANSACTIONS

text: ON

text: SIGNAL

text: PROCESSING

text: and

text: for

text: IEEE

text: COMMUNICATIONS

text: LETTERS.

text: He

text: has

text: edited

text: special

text: issues

text: for

text: IEEE

text: TRANSACTIONS

text: ON

text: SIGNAL

text: PROCESSING,

text: IEEE

text: JOURNAL

text: OF

text: SELECTED

text: TOPICS

text: IN

text: SIGNAL

text: PROCESSING,

text: and

text: IEEE

text: JOURNAL

text: ON

text: SELECTED

text: AREAS

text: IN

text: COMMUNICATIONS.

text: He

text: is

text: a

text: member

text: of

text: the

text: SAM

text: Technical

text: Committee

text: (TC)

text: of

text: the

text: IEEE

text: Signal

text: Processing

text: Society.

text: He

text: was

text: a

text: member

text: of

text: the

text: Signal

text: Processing

text: for

text: Communications

text: TC

text: of

text: the

text: IEEE

text: Signal

text: Processing

text: Society

text: and

text: is

text: a

text: member

text: of

text: the

text: Communications

text: Theory

text: TC

text: of

text: the

text: IEEE

text: Communication

text: Society.

text: He

text: was

text: on

text: the

text: awards

text: committee

text: of

text: the

text: IEEE

text: Communication

text: Society.

text: Dr.

text: Blum

text: is

text: a

text: former

text: IEEE

text: Signal

text: Processing

text: Society

text: Distinguished

text: Lecturer,

text: an

text: IEEE

text: Third

text: Millennium

text: Medal

text: winner,

text: a

text: member

text: of

text: Eta

text: Kappa

text: Nu

text: and

text: Sigma

text: Xi,

text: and

text: holds

text: several

text: patents.

text: He

text: was

text: awarded

text: an

text: ONR

text: Young

text: Investigator

text: Award

text: and

text: an

text: NSF

text: Research

text: Initiation

text: Award.

text: His

text: IEEE

text: Fellow

text: Citation

text: “for

text: scientiﬁc

text: contributions

text: to

text: detection,

text: data

text: fusion

text: and

text: signal

text: processing

text: with

text: multiple

text: sensors”

text: acknowledges

text: contributions

text: to

text: the

text: ﬁeld

text: of

text: sensor

text: networking.

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##


text: IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 34, NO. X, JAN. 2016 3 (cid:0) (cid:1) a subproblem requiring optimization embedded in it. Finally, z˜a(t) is the additive zero mean variance σ2 white k a Then, to address the non-convex embedded subproblem, Gaussian noise (AWGN) in the received signal [11], thus ∼ an alternating-Dinkelbach optimization is proposed to z˜a(t) CN 0, σ2 . k a transfer the subproblem to a convex form. Further, the dynamic programming problem can be solved by using Signal conversion noise Power backward induction. x (t) amplifier unit • To study the throughput performance of the proposed Antenna noise k,R y (t) p (t) p (t) harvest-use-store PS relaying strategy in a general sce- k k,F k,R nario with causal CSI, the proposed layered optimization p (t) b (t) k,B k,F method is extended by utilizing the statistical properties of the CSI via incorporating a ﬁnite-state Markov Chain Power splitting unit Battery model. Further, a greedy method is proposed, which The first phase The second phase requires no information about subsequent time slots. It’s shown that the adopted greedy method will use up the Fig. 1. Processing at the energy harvesting relay Rk during the t-th time slot. harvested energy at each transmission. Simulation re- sults reveal that the advantages of the proposed strategy The received RF signal y (t) is then divided into three k over the conventional battery-free ones depend on the different power streams through PS, which is depicted in utilization of information about subsequent time slots. Fig. 1. Speciﬁcally, the ﬁrst part of the received signal, ∈ The remainder of this paper is outlined as follows. In which uses a PS ratio λ (t) [0, 1], is down-converted to k,I Section II, the system model will be presented and the pro- baseband and will be ampliﬁed and transmitted in the next posed strategy will be described. Following that, the optimal phase. The(cid:113)sampled (cid:16)baseban(cid:112)d signal is given by (cid:17) joint PS and battery operation design will be developed with the non-causal CSI assumption in Section III. Then, the causal CSI case will be analyzed in Section IV, followed by x (t) = λ (t) h (t) p (t)x (t) + za (t) +zb(t), k,R k,I k(cid:0) (cid:1) S S k k numerical results in Section V and conclusions in the ﬁnal (2) (cid:0) (cid:1) section. ∼ where za(t) CN 0, σ2 is the baseband equivalent k a ∼ II. SYSTEM MODEL AND PROTOCOL DESCRIPTION noise of the pass band noise z˜a(t), and zb(t) CN 0, σ2 k k b The system under consideration is a wireless-powered is the sampled AWGN introduced by RF band to baseband cooperative relay network consisting of a source (S), a desti- signal conversion [11]. The sec∈ond par−t of signal power, natio·n· ·(D), and a set of K energy harvesting relays (Rk, k = which uses a PS ratio λk,F (t) [0, 1 λk,I(t)], will be 1, 2, , K), where each relay is equipped with a battery. used to power the amplify-and-forward process in the next (cid:16) (cid:17) No direct link exists between S and D. Considering a half- phase. This part of power is described by duplex relay model and a total of T equal length time slots. | | A harvest-use-store PS strategy is proposed and implemented p (t) = η λ (t) h (t) 2p (t) + σ2 , (3) k,F 1 k,F k S a at each time slot, each of which consists of two equal length phases. In the ﬁrst phase, each relay obtains both information ∈ and power from its received RF signal transmitted by S where η (0, 1] is a constant denoting the energy 1 via power splitting. In the second phase, with the help of conversion efﬁciency from signal power to DC power. The battery, the harvested energy is used to amplify-and-forward last part of signal power, which uses a PS ratio λ (t) = − − k,B the information to D through distributed beamforming with (1 λ (t) λ (t)), will be used to charge the battery. k,I k,F (cid:16) (cid:17) adaptive power allocation. This part of power is denoted by A. Simultaneous Information and Power Transfer via Power Splitting (cid:48) | | In the ﬁrst phase of time slot t, the received RF signal at pk,B (t) = η1λk,B (t) hk (t) 2pS (t) + σa2 . (4) (cid:112) the R can be expressed by k A ﬁnite and discrete battery model is adopted in this y (t) = h (t) p (t)x (t) + z˜a (t) , (1) k k S S k paper, where the battery is of size B = αP, (α > max 0) and is discretized into L + 1 energy levels Γ = { · · · } where t denotes the time index, and k is the index 0, B /L, , B . Note that, this model can closely max max for relays, h (t) denotes the complex link gain between approximate a continuous battery model when the number of k S and R , x (t) denotes the signal transmitted from S energy levels is sufﬁciently large [22]. Due to this ﬁnite and k S | | during time slot t with normalized power E( x (t) 2) = 1, discrete battery model, the charged power at R during time S ≤ k and p (t) is the transmit power at S with p (t) P. slot t is given by S S ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: IEEE

text: JOURNAL

text: ON

text: SELECTED

text: AREAS

text: IN

text: COMMUNICATIONS,

text: VOL.

text: NO.

text: X,

text: JAN.

text: a

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text: IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 34, NO. X, JAN. 2016 4 (cid:18) (cid:19) (cid:80) (cid:112) { − ∗ } p (t) = min B B (t) , n (t)B , K | | 2 nk∗,(Bt) = arg mmaxax {nk(t) : n(tL)B max≤ η p (cid:48)(t)}, pS (t) (cid:80) βk(t) hk (t) gk (t) λk,I (t) n(t)∈{0,···,L} L max 2 k,B SNR(t) = k=1 . (5) K | | β (t)2 g (t) 2σ2 + σ2 k k b D where B (t) ∈ Γ denotes the energy level at the beginning k=1 (11) k ∈ of time slot t, η (0, 1] is the storage efﬁciency describing 2 the power loss in battery charging [7], the ﬁrst equation is The overall system throughput after T transmissions is due to the ﬁnite property of the battery, and the second one described by (cid:88) is due to the discrete property of the battery. T 1 R = log (1 + SNR (t)), (12) B. Distributed Beamforming with Adaptive Power Allocation total 2 t=1 In the second phase, the destination D receives a signal transmitted from all relays as where the factor 1/2 is due to the half-duplex relaying (cid:88) mode. According to (8), (9), (11), and (12), four key K factors should be jointly considered to optimize the y (t) = βk (t) gk (t) ejθk(t)xk,R(t) + z (t) , (6) overall throughput, including information transfer (i.e., (cid:0) (cid:1) k=1 designing λ (t), ∀k, ∀t), power transfer (i.e., design- ∼ k,∀I ∀ where gk(t) denotes the link gain for Rk to D and z(t) ing λk,F∀(t)∀, k, t), battery charging (i.e., designing CN 0, σD2 is the AWGN at D, ejθk(t) is derived from the λk,B(t),∀ k,∀ t), and battery discharging (i.e., designing distributed beamforming design [19], where b (t), k, t). The ﬁrst three factors are mainly deter- k,F mined by the PS, while the last one is only determined by − θk(t) = (arg hk (t) + arg gk (t)), (7) the batte∀ry o∀peration. Moreover, the harvested energy (i.e., p (t), k, t) obtained from the PS affects the throughput k,B during the subsequent time slots via battery charging and which cancels the phases of the two links between Rk and discharging. To this end, the PS and battery operations are S, D respective(cid:118)(cid:117)ly, βk(t) is the ampliﬁcation gain depicted by coupled with distributed beamforming, which makes the (cid:117) (cid:116) (cid:16) (cid:17) throughput maximization problem intractable. p (t) III. OPTIMAL JOINT POWER SPLITTING AND BATTERY βk(t) = | |k,R , (8) OPERATION DESIGN λ (t) h (t) 2p (t) + σ2 + σ2 k,I k S a b In this section, the proposed harvest-use-store PS relaying strategy is optimized toward the goal of throughput maxi- where pk,R(t) is the transmit power at Rk, this power is mization with the CSI of T time slots known before transmis- composed of two different parts: sion, which is commonly known as non-causal CSI assump- tion. To solve the resulting intractable looking problem, the pk,R(t) = pk,F (t) + bk,F (t) , (9) throughput maximization problem is described by a dynamic programming problem equivalently. However, such a solution where p is provided by the PS operation in (3), and is computationally prohibitive to implement since the number b (t) ∈ kΓ,Fis provided by the battery discharging. As a of possible joint PS and battery operations to be evaluated k,F result, the energy level at R at the end of time slot t (which is inﬁnite. Therefore, the joint PS and battery operations k is also the beginning of time slot (t + 1)) is are decomposed equivalently, and the resulting embedded problem and overall problem are formulated. Moreover, the B (t + 1) = B (t) + p (t) − b (t) . (10) optimal solutions to the embedded and overall problems can k k k,B k,F be approached through iterative algorithms and backward induction. In this way, the optimal solution toward throughput Note that, any power consumption at the relays for pur- maximization is approached. A. Decoupling of the Throughput Maximization Problem poses other than for transmission is assumed negligible [11], [15]. Due to the fact that the antenna noise za (t) has a We ﬁrst simplify the formulation of the throughput maxi- k negligible impact on both the information processing and mization problem by utilizing insights about the optimization energy harvesting [21], it is ignored in the following analysis variables. According to (11) and (12), the throughput R ∀ total by setting σ2 = 0. Substituting (1) and (2) into (6), the is a strictly increasing function of p (t), t, when other a ≤ S received signal-to-noise-ratio (SNR) at D at time slot t can variables are ﬁxed. Since p (t) P, the optimum choice S be expressed as is ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: IEEE

text: JOURNAL

text: ON

text: SELECTED

text: AREAS

text: IN

text: COMMUNICATIONS,

text: VOL.

text: NO.

text: X,

text: JAN.

label: equation

text: p

text: (t)

text: min

text: B

text: B

text: (t)

text: n

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text: as

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text: the

text: factor

text: is

text: due

text: to

text: the

text: half-duplex

text: relaying

text: mode.

text: According

text: to

text: and

text: four

text: key

text: K

text: factors

text: should

text: be

text: jointly

text: considered

text: to

text: optimize

text: the

text: y

text: (t)

text: βk

text: (t)

text: gk

text: (t)

text: ejθk(t)xk,R(t)

text: z

text: (t)

text: overall

text: throughput,

text: including

text: information

text: transfer

text: (i.e.,

text: designing

text: λ

text: (t),

text: ∀k,

text: ∀t),

text: power

text: transfer

text: (i.e.,

text: design-

text: k,∀I

text: where

text: gk(t)

text: denotes

text: the

text: link

text: gain

text: for

text: Rk

text: to

text: D

text: and

text: z(t)

text: ing

text: λk,F∀(t)∀,

text: k,

text: t),

text: battery

text: charging

text: (i.e.,

text: designing

text: CN

text: is

text: the

text: AWGN

text: at

text: D,

text: ejθk(t)

text: is

text: derived

text: from

text: the

text: λk,B(t),∀

text: k,∀

text: t),

text: and

text: battery

text: discharging

text: (i.e.,

text: designing

text: distributed

text: beamforming

text: design

text: where

text: b

text: (t),

text: k,

text: t).

text: The

text: ﬁrst

text: three

text: factors

text: are

text: mainly

text: deter-

text: k,F

text: mined

text: by

text: the

text: PS,

text: while

text: the

text: last

text: one

text: is

text: only

text: determined

text: by

text: θk(t)

text: (arg

text: hk

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text: arg

text: gk

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text: the

text: batte∀ry

text: o∀peration.

text: Moreover,

text: the

text: harvested

text: energy

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text: p

text: (t),

text: k,

text: t)

text: obtained

text: from

text: the

text: PS

text: affects

text: the

text: throughput

text: k,B

text: during

text: the

text: subsequent

text: time

text: slots

text: via

text: battery

text: charging

text: and

text: which

text: cancels

text: the

text: phases

text: of

text: the

text: two

text: links

text: between

text: Rk

text: and

text: discharging.

text: To

text: this

text: end,

text: the

text: PS

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text: battery

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text: S,

text: D

text: βk(t)

text: is

text: the

text: ampliﬁcation

text: gain

text: depicted

text: by

text: coupled

text: with

text: distributed

text: beamforming,

text: which

text: makes

text: the

text: throughput

text: maximization

text: problem

text: intractable.

text: p

text: (t)

text: III.

text: OPTIMAL

text: JOINT

text: POWER

text: SPLITTING

text: AND

text: BATTERY

text: βk(t)

text: |k,R

text: OPERATION

text: DESIGN

text: λ

text: (t)

text: h

text: (t)

text: (t)

text: σ2

text: σ2

text: k,I

text: k

text: S

text: a

text: b

text: In

text: this

text: section,

text: the

text: proposed

text: harvest-use-store

text: PS

text: relaying

text: strategy

text: is

text: optimized

text: toward

text: the

text: goal

text: of

text: throughput

text: maxi-

text: where

text: pk,R(t)

text: is

text: the

text: transmit

text: power

text: at

text: Rk,

text: this

text: power

text: is

text: mization

text: with

text: the

text: CSI

text: of

text: T

text: time

text: slots

text: known

text: before

text: transmis-

text: composed

text: of

text: two

text: different

text: parts:

text: sion,

text: which

text: is

text: commonly

text: known

text: as

text: non-causal

text: CSI

text: assump-

text: tion.

text: To

text: solve

text: the

text: resulting

text: intractable

text: looking

text: problem,

text: the

text: pk,R(t)

text: pk,F

text: (t)

text: bk,F

text: (t)

text: throughput

text: maximization

text: problem

text: is

text: described

text: by

text: a

text: dynamic

text: programming

text: problem

text: equivalently.

text: However,

text: such

text: a

text: solution

text: where

text: p

text: is

text: provided

text: by

text: the

text: PS

text: operation

text: in

text: and

text: is

text: computationally

text: prohibitive

text: to

text: implement

text: since

text: the

text: number

text: b

text: (t)

text: kΓ,Fis

text: provided

text: by

text: the

text: battery

text: discharging.

text: As

text: a

text: of

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text: joint

text: PS

text: and

text: battery

text: operations

text: to

text: be

text: evaluated

text: k,F

text: result,

text: the

text: energy

text: level

text: at

text: R

text: at

text: the

text: end

text: of

text: time

text: slot

text: t

text: (which

text: is

text: inﬁnite.

text: Therefore,

text: the

text: joint

text: PS

text: and

text: battery

text: operations

text: k

text: is

text: also

text: the

text: beginning

text: of

text: time

text: slot

text: (t

text: is

text: are

text: decomposed

text: equivalently,

text: and

text: the

text: resulting

text: embedded

text: problem

text: and

text: overall

text: problem

text: are

text: formulated.

text: Moreover,

text: the

text: B

text: (t

text: B

text: (t)

text: p

text: (t)

text: b

text: (t)

text: optimal

text: solutions

text: to

text: the

text: embedded

text: and

text: overall

text: problems

text: can

text: k

text: k

text: k,B

text: k,F

text: be

text: approached

text: through

text: iterative

text: algorithms

text: and

text: backward

text: induction.

text: In

text: this

text: way,

text: the

text: optimal

text: solution

text: toward

text: throughput

text: Note

text: that,

text: any

text: power

text: consumption

text: at

text: the

text: relays

text: for

text: pur-

text: maximization

text: is

text: approached.

text: A.

text: Decoupling

text: of

text: the

text: Throughput

text: Maximization

text: Problem

text: poses

text: other

text: than

text: for

text: transmission

text: is

text: assumed

text: negligible

text: Due

text: to

text: the

text: fact

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text: the

text: antenna

text: noise

text: za

text: (t)

text: has

text: a

text: We

text: ﬁrst

text: simplify

text: the

text: formulation

text: of

text: the

text: throughput

text: maxi-

text: k

text: negligible

text: impact

text: on

text: both

text: the

text: information

text: processing

text: and

text: mization

text: problem

text: by

text: utilizing

text: insights

text: about

text: the

text: optimization

text: energy

text: harvesting

text: it

text: is

text: ignored

text: in

text: the

text: following

text: analysis

text: variables.

text: According

text: to

text: and

text: the

text: throughput

text: R

text: total

text: by

text: setting

text: σ2

text: Substituting

text: and

text: into

text: the

text: is

text: a

text: strictly

text: increasing

text: function

text: of

text: p

text: (t),

text: t,

text: when

text: other

text: a

text: S

text: received

text: signal-to-noise-ratio

text: (SNR)

text: at

text: D

text: at

text: time

text: slot

text: t

text: can

text: variables

text: are

text: ﬁxed.

text: Since

text: p

text: (t)

text: P,

text: the

text: optimum

text: choice

text: S

text: be

text: expressed

text: as

text: is

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