Two-Way Relaying Networks with Wireless Power Transfer - IEEE Xplore

Globecom 2014 - Wireless Communications Symposium

Two-Way Relaying Networks with Wireless Power Transfer: Policies Design and Throughput Analysis Yuanwei Liu∗ , Lifeng wang∗ , Maged Elkashlan∗ , Trung Q. Duong† , and Arumugam Nallanathan‡ ∗

Queen Mary University of London, London, UK † Queen’s University Belfast, Belfast, UK ‡ King’s College London, London, UK

Abstract—This paper exploits an amplify-and-forward (AF) two-way relaying network (TWRN), where an energy constrained relay node harvests energy with wireless power transfer. Two bidirectional protocols, multiple access broadcast (MABC) protocol and time division broadcast (TDBC) protocol, are considered. Three wireless power transfer policies, namely, 1) dual-source (DS) power transfer; 2) single-fixed-source (SFS) power transfer; and 3) single-best-source (SBS) power transfer are proposed and well-designed based on time switching receiver architecture. We derive analytical expressions to determine the throughput both for delay-limited transmission and delay-tolerant transmission. Numerical results corroborate our analysis and show that MABC protocol achieves a higher throughput than TDBC protocol. An important observation is that SBS policy offers a good tradeoff between throughput and power.

I. I NTRODUCTION Recently, it has been shown that ambient radio-frequency (RF) signals can be a new source for harvesting energy [1] to prolong the life of a wireless network and has received significant attention since it meets the requirements of green communications. The advantages of this approach lies in the fact that most devices are surrounded by RF signals, and potentially, energy and information can be carried at the same time by RF signals for transmitting. As a consequence, a new energy harvesting solution which can achieve simultaneously wireless information and power transfer (SWIPT) was proposed [2, 3], where it is assumed that the receiver could decode the information and harvest the energy from the same signal. However, this assumption does not hold in practice due to circuit limitations [4]. To overcome this issue, two practical receiver designs were proposed for a multipleinput multiple-output (MIMO) wireless broadcast system to enable wireless information and power transfer [5]. In [6], optional designs were proposed to achieve tradeoffs between outage and energy as well as rate and energy in delay-limited and delay-tolerant transmission modes. In [7] and [8], an orthogonal frequency division multiplexing (OFDM) system and a cognitive radio system with wireless energy harvesting were considered, respectively. The aforementioned literature on energy harvesting considered the point-to-point system. For one-way relaying system, time switching-based relaying (TSR) protocol and power splitting-based relaying (PSR) protocol were proposed and the outage probability as well as throughput were analyzed in [9]. For two-way relaying system, a power splitting-based relaying

978-1-4799-3512-3/14/$31.00 ©2014 IEEE

protocol was analyzed in [10]. Moreover, two categories of two-way relaying bidirectional transmission protocols without energy harvesting, namely, multiple access broadcast (MABC) protocol and time division broadcast (TDBC) protocol was investigated in [11]. Compared with TDBC, MABC is more spectral efficient since it requires less time slots, however, TDBC is more reliable by applying maximal radio combining (MRC) to combine the direct link and the relay link. In this paper, we focus on amplify-and-forward (AF) twoway relaying network (TWRN) with an energy constrained relay. Particularly, based on the time switching receiver architechture [4], we propose three two-way relaying wireless power transfer policies, namely, 1) dual-source (DS) power transfer; 2) single-fixed-source (SFS) power transfer; and 3) single-best-source (SBS) power transfer to harvest energy at the relay node. Comparing the three policies, SFS and SBS cost less power but achieve less throughput. We also consider the two major bidirectional transmission protocols, MABC and TDBC, for TWRN, and take into account the two transmission modes, delay-limited transmission and delaytolerant transmission. With this in mind, we formulate new analytical expressions for the three proposed policies with MABC and TDBC protocols, together with the two transmission modes. Our analytical and numerical results show that MABC protocol achieves a higher throughput than TDBC protocol. The SBS policy offers a good throughput/power tradeoff. II. S YSTEM M ODEL We consider a half-duplex two-way relaying network, where the exchange of information between two single-antenna sources SA and SB is facilitated by an energy constrained intermediate amplify-and-forward (AF) relay R with single antenna. The time switching-based relay separates the energy harvesting (EH) and the information processing (IP) phases in time, i.e., during the EH phase, the relay harvests energy from the source signals with wireless power transfer, and during IP phase, the relay forwards information using the harvested energy. All the channels are modeled as quasi-static block Rayleigh fading channels. We denote hAR , hBR , and hAB as the channel coefficients of SA → R, SB → R, and SA → SB links, respectively. And the channel power 2 2 2 gains |hAR | , |hBR | , and |hAB | are exponentially distributed random variables (RVs) with the means ΩA = (dAR )−ζ ,

4030


αT

(1 − α ) T / 2

EH at R

IP: S & S to R

(1 − α ) T / 2

beginning αT2 block time is the EH time, and the remaining (1 − α)T2 block time is the IP time. During the IP phase, each time slot will occupy (1 − α)T2 /3. Each source utilizes MRC to combine the signals from the relay link and the direct link, and the received SNR after MRC at Si is given by

IP: R to S & S

T

2

(a) MABC protocol αT

(1 − α )T / 3

EH at R

IP: S to R & S

γiM RC =

(1 − α )T / 3 IP: S to R & S

(1 − α )T / 3

2

G22 PR |hiR | 2σ 2 + σ 2

+

Pj |hAB | , σ2

2

IP: R to S & S

(b) TDBC protocol Fig. 1. Frame structures of energy harvesting for MABC and TDBC protocols.

−ζ

ΩB = (dBR ) , and ΩC = (dAB ) , respectively, where dAR , dBR , and dAB denote the distances of SA → R, SB → R, and SA → SB links, respectively, and ζ represents the path-loss exponent. We consider two practical two-way relaying protocols, namely, multiple access broadcast (MABC) and time division broadcast (TDBC). A. Multiple Access broadcast (MABC)

2

1

III. W IRELESS P OWER T RANSFER P OLICES D ESIGN AND T HROUGHPUT A NALYSIS In this section, based on the time switching receiver architecture, three different wireless power transfer polices, i.e., dual-source (DS) power transfer, single-fixed-source (SFS) power transfer and single-best-source (SBS) power transfer are considered for MABC and TDBC transmission protocols. A. DS power transfer policy for MABC In this subsection, we consider the DS power transfer policy for MABC. 1) End-to-End SNR: In this policy, both SA and SB transfer power to the relay simultaneously, and the energy harvested at the relay is expressed as 2

2

Eh = η(PA |hAR | + PB |hBR | )αT1 ,

2

G21 PR Pj |hiR | |hjR | 2

2

G21 PR |hiR | σ 2 + σ 2

,

(1)

where {i, j} ∈ {A, B} and i ̸= j, and G1 = 1 2 2 (PA |hAR | + PB |hBR | + σ 2 )− 2 is the scaling gain based on variable gain AF relaying. B. Time Division Broadcast (TDBC) In this protocol, apart from the time in the EH phase, three time slots are required in the IP phase. As shown in Fig.1(b), we denote the transmission time of a frame as T2 . The

(3)

where 0 < η ≤ 1 is the energy conversion efficiency. Based on (3), the transmit power at the relay is given by 2

In this protocol, apart from the time in the EH phase, two time slots are required in the IP phase. As shown in Fig.1(a), we denote the transmission time of a frame as T1 , where α is the fraction of time that the relay harvests energy from the source signals, where 0 < α < 1. The beginning αT1 block time is the EH time, and the remaining (1 − α)T1 block time is the IP time. Since the information length from sources to relay and relay to sources is identical, each of them will occupy (1 − α)T1 /2. We denote PA is the transmit power at SA and PB is the transmit power at SB . The relay’s transmit power PR depends on the amount of energy harvested during the energy harvest time and will be detailed in Section III. Assuming that all the nodes have the same noise level with variance σ 2 , the end-toend signal-to-noise ratio (SNR) at Si is given by γi =

(2)

where G2 = (PA |hAR | + PB |hBR | + 2σ 2 )− 2 is the scaling gain based on variable gain AF relaying.

T

−ζ

2

2

G22 PR Pj |hiR | |hjR |

2

Eh 2η(PA |hAR | + PB |hBR | )α = . (4) (1 − α)T1 /2 (1 − α) Substituting (4) into (1), we obtain a tight high SNR approximation [9, 12] for the end-to-end SNR at Si as PR =

Pj γi = 2 σ

2 2 2ηα (1−α) |hiR | |hjR | . 2 2ηα (1−α) |hiR | + 1 P 2ηα

(5) 2

2ηα j Lemma 1: Let ϖj = σ2 (1−α) , ϑ = (1−α) , X = |hiR | , and 2 Y = |hjR | , (5) can be re-expressed as ϖj XY γi = , (6) ϑX + 1 and the cumulative distribution function (CDF) of γi is √ ( √ ) − γϑ 2e Ωj ϖj γΩi γ Fγi (γ) = 1 − K1 2 , (7) Ωi ϖj Ω j ϖj Ωi Ωj

where γ is the threshold value of the SNR and Kn (•) is the modified Bessel function of the second kind with order n. Proof: The CDF of γi is expressed as [ ] γ (ϑX + 1) Fγi (γ) = Pr Y ≤ ϖj X ∫ − Ωγϑ ∞ e j ϖj − γ − y =1 − e Ωj ϖj y Ωi dy. (8) Ωi 0 Using [13, Eq. (3.324.1)], we obtain the desired result in (7).

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2) Throughput analysis: a) Delay-limited Transmission: In delay-limited transmission, the source transmits information at a fixed rate and outage probability plays a pivotal role in the throughput. Given 0 that SA and SB transmit information with fixed (rates R)A 0 0 0 and RB bits/sec/Hz, ( )respectively, where RA , log2 1 + γA , 0 RB , log2 1 + γB , the throughput is calculated as ) 0 ( ) 0) (1 − α) T1 /2 (( A B τ= 1 − Pout RA + 1 − Pout RB , (9) T1 ( 0) A where Pout , F(γA )γA is the outage probability at SA , B 0 and (Pout , F γ is the outage probability at SB , with γB ) (B 0 ) 0 FγA γA and FγB γB given in (7). b) Delay-Tolerant Transmission: In delay-tolerant transmission, the throughput is determined by evaluating the ergodic rate. Using (7), the throughput is calculated as (1 − α) T1 /2 (E {log2 (1 + γA )} + E {log2 (1 + γB )}) T1 ) (∫ ∫ ∞ ∞ 1−α 1 − FγB (λ) 1 − FγA (λ) = dλ + dλ 2 ln 2 1+λ 1+λ 0 0 ( √ ) √ λ λ ∫ ∞ K 2 ∑ ϖj Ωi Ωj 1 ϖj Ω i Ω j 1−α = dλ, λϑ ln 2 (1 + λ) e Ωj ϖj {i,j}∈{A,B} 0

τ=

√ where a1 = ΩC4Ψj ϖj Ω1i Ωj , b1 = ( ) √ ϑ 1 , and t1 = ϖj Ω4i Ωj . Ωj ϖj − ΩC Ψj

Proof: The CDF of γiM RC is expressed as [ ] ϖj XY FγiM RC (γ) = Pr + Ψj Z ≤ γ ϑX + 1 = Pr [γi ≤ γ − Ψj Z] .

(1 − α) T2 /3 (E {log2 (1 + γA )} + E {log2 (1 + γB )}) T2 ( ∑ 1−α e−b1 Ei (b1 ) + a1 e−b1 =− 3 ln 2 {i,j}∈{A,B}

∫

where E {·} is the expectation operator.

∞

×

B. DS power transfer policy for TDBC

(

i̸=j

) (( ) ) ) 2 e−c1 λ λ2 K1 (t1 λ) Ei λ2 + 1 b1 dλ , (18)

0

In this subsection, we consider the DS power transfer policy for TDBC. 1) End-to-End SNR: As suggested in Section III-A1, the energy harvested at the relay is expressed as 2

Eh = η(PA |hAR | + PB |hBR | )αT2 .

(11)

Based on (11), the transmit power at relay is given by 2

2

Eh 3ηα(PA |hAR | + PB |hBR | ) = . (12) (1 − α)T2 /3 (1 − α)

where Ei (·) is the exponential integral function [13, eq. (8.211.1)]. C. SFS power transfer policy for MABC In this subsection, we consider the SFS power transfer policy for MABC. 1) End-to-End SNR: In this policy, only a fixed source SA or SB transfers power to the relay. Without loss of generality, we assume this source is SA , and the energy harvested at the relay is expressed as

Substituting (12) into (2), we obtain a tight high SNR approximation for the end-to-end SNR at Si as γi =

2 2 3ηα Pj (1−α) σ 2 |hiR | |hjR | 2 6ηα (1−α) |hiR | + 1 3ηαPj σ 2 (1−α) ,

Lemma 2: Let ϖj = 2

Y = |hjR | , Ψj = expressed as

Pj σ2 ,

γiM RC

6ηα (1−α) , X = 2 |hAB | , (13) can

ϖj XY + Ψj Z, = ϑX + 1

2

Eh = ηPA |hAR | αT1 .

(13)

2

PR = 2

|hiR | , be re-

γ j ΩC

∫

√ γ

− a1 e

0

e−c1 λ λ2 K1 (d1 λ)dλ, 2

(20)

γA =

a2 ΨA ΨB X 2 Y , b2 ΨA X 2 + ΨB Y + ΨA X

(21)

γB =

a2 Ψ2A X 2 Y , b2 ΨA XY + ΨA X + ΨB Y

(22)

and

−Ψ

b1 γ

Eh 2ηαPA |hAR | = . (1 − α)T1 /2 (1 − α)

Substituting (20) into (1), we obtain tight high SNR approximations for the end-to-end SNR at SA and SB as

(14)

and the CDF of γiM RC is FγiM RC (γ) =1 − e

(19)

Based on (19), the transmit power at relay is given by

2

Pj |hAB | + . σ2

ϑ =

and Z =

(16)

τ=

(10)

PR =

=

With the help of (7), we can obtain the result in (15). 2) Throughput Analysis: a) Delay-Limited Transmission: As suggested in Section III-A2, in delay-limited transmission, the throughput is calculated as ) 0 ( ) 0) (1 − α) T2 /3 (( A B τ= 1 − Pout RA + 1 − Pout RB , (17) T2 ( 0) ( 0) B ∆ A ∆ and Pout , with = FγBM RC γB where Pout = FγAM RC γA ( 0) ( 0) FγAM RC γA and FγBM RC γB given in (15). b) Delay-Tolerant Transmission: In delay-tolerant transmission, using (15), the throughput is calculated as

i̸=j

2

− ΩC1Ψj , c1

2

(15)

2

respectively, where X = |hAR | , Y = |hBR | , a2 = 2ηα b2 = (1−α) , ΨA = PσA2 , and ΨB = PσB2 .

4032

2ηα (1−α) ,


√ Lemma 3: The CDF of γA in (21) is ) ∫ ∞ ( γb2 ΨA x2 +γΨA x − + Ωx 1 ΩB (a2 ΨA ΨB x2 −γΨB ) A FγA (γ) =1 − e dx, ΩA X2 (23) √ with X1 = a2γΨA , and the CDF of γB in (22) is 1 ΩA

FγB (γ) = 1 −

√

b γ+

∫

( ∞ −

e

ΨA xγ ΩB a2 Ψ2 x2 −b2 ΨA xγ−ΨB γ A

(

)

+ Ωx

A

(24) 2

(b γ) +4a Ψ γ

where FγA (λ) and FγB (λ) are given in (23) and (24), respectively. D. SFS power transfer policy for TDBC In this subsection, we consider the SFS power transfer policy for TDBC. 1) End-to-End SNR: As suggested in Section III-C1, the energy harvested at the relay is expressed as 2

Eh = ηPA |hAR | αT2 .

(26)

Based on (26), the transmit power at relay is given by 2

Eh 3ηαPA |hAR | = . (1 − α)T2 /3 (1 − α)

(27)

Substituting (27) into (2), we obtain tight high SNR approximations for the end-to-end SNR at SA and SB as M RC γA =

a3 ΨA ΨB X 2 Y + ΨB Z, b3 ΨA X 2 + ΨB Y + ΨA X

(28)

M RC γB =

a3 Ψ2A X 2 Y + ΨA Z, b3 ΨA XY + ΨA X + ΨB Y

(29)

and

2

3ηα 6ηα respectively, where a3 = (1−α) , b3 = (1−α) , X = |hAR | , 2 2 Y = |hBR | , and Z = |hAB | . M RC Lemma 4: The CDF of γA in (28) is

1 × ΩA ΩC γA (z)(b3 ΨA x2 +ΨA x) − x − Ω γΨ C B

∫ 0

γ ΨB

∫

∞

−

e X1

M RC and the CDF of γB in (29) is γ C ΨA

−Ω

FγBM RC (γ) = 1 − e ∫

γ ΨA

0

− Ωz

e

∫

∞ −

e

C

−

ΩB (a3 ΨA ΨB x2 −γA (z)ΨB )

ΩA

− Ωz

C

dxdz,

(30)

−

1 × ΩA ΩC

ΨA xγB (z) ΩB a3 Ψ2 x2 −γB (z)(b3 ΨA x+ΨB ) A

(

)

− Ωx

A

dxdz,

X2

b γ (z)+

dx,

X2

FγAM RC (γ) = 1 − e

γA (z) a3 ΨA ,

)

2 2 B . with X2 = 2 2a2 ΨA Proof: The proof is accomplished in the similar method as the proof of Lemma 1. 2) Throughput analysis: a) Delay-Limited Transmission: In this mode, the expression for the throughput is the same as (9), where ( 0) ( 0) ( 0) B ∆ A ∆ Pout (=0F)γA γA and Pout = FγB γB , with FγA γA and FγB γB given in (23) and (24), respectively. b) Delay-Tolerant Transmission: In this mode, similar to (10), the throughput is calculated as (∫ ∞ ) ∫ ∞ 1−α 1 − FγA (λ) 1 − FγB (λ) τ= dλ + dλ , 2 ln 2 1+λ 1+λ 0 0 (25)

PR =

with X1 =

√

(31) (b γ (z))2 +4a Ψ γ (z)

3 B 3 B B where X2 = 3 B , γA (z) = γ − 2a3 ΨA ΨB z and γB (z) = γ − ΨA z. 2) Throughput Analysis: a) Delay-Limited Transmission: In this mode, the exA ∆ pression for the throughput is the same as (17), where Pout = ( 0) ( ) ( ) 0 B ∆ 0 , with FγAM RC γA and FγAM RC γA and Pout = FγBM RC γB ( 0) given in (30) and (31), respectively. FγBM RC γB b) Delay-Tolerant Transmission: In this mode, similar to (18), the throughput is calculated as (∫ ∫ ∞ 1 − F M RC (γ) ) ∞ 1 − F M RC (γ) 1−α γA γB τ= dλ + dλ , 3 ln 2 1 1 + λ +λ 0 0 (32)

where FγAM RC (λ) and FγBM RC (λ) are given in (30) and (31), respectively. E. SBS power transfer policy for MABC In this subsection, we consider the SBS power transfer policy for MABC. 1) End-to-End SNR: In this policy, we select the strongest channel to transfer power to the relay, and the energy harvested at the relay is expressed as { } 2 2 Eh = ηPk max |hAR | , |hBR | αT1 , (33) { 2 2 A, |hAR | > |hBR | where k = . Based on (34), the trans2 2 B, |hAR | < |hBR | mit power at relay is given by { } 2 2 2ηαPk max |hAR | , |hBR | Eh PR = = . (34) (1 − α)T1 /2 (1 − α) Substituting (34) into (1), we obtain a tight high SNR approximation for the end-to-end SNR at Si as { } 2 2 2 2 a4 Ψk Ψj max |hiR | , |hjR | |hiR | |hjR | { } γi = , 2 2 2 2 2 b4 Ψk max |hiR | , |hjR | |hiR | + Ψi |hiR | + Ψj |hjR | (35) P

2ηα 2ηα , b4 = (1−α) , Ψi = σP2i , Ψj = σ2j , and where a4 = (1−α) Pk Ψk = σ2 . Lemma 5: The CDF of γi in (35) is given as (36) at the top of the next page, √where U (x) is the b γ+

(b γ)2 +4a Ψ γ

4 4 j 4 unit step function, K1 = , K2 = 2a4 Ψi √ √ 2 b γ+ (b γ) +4a γ(Ψ +Ψ ) 4 4 4 i j γ , and K4 = = a4 Ψj , K3 2a4 Ψi √ b4 Ψj γ+ (b4 Ψj γ)2 +4a4 Ψi Ψj γ(Ψi +Ψj ) . Due to limited space, the 2a4 Ψi Ψj detailed derivation of (36) is not included.

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∫ Fγi (γ) =

(

∞

max{K1 ,K3 }

−

1−e (

)

Ψj κγ

(

Ωi a4 Ψ2 κ2 −b4 Ψj κγ−Ψi γ j

)

∫

− Ωκ

e

j

Ωj

(

∞

−

1−e

dκ +

b4 Ψi κ2 γ+Ψi γκ Ωi (aΨi Ψj κ2 −Ψj γ )

j

K

− Ω3 j

2) Throughput analysis: a) Delay-Limited Transmission: In this mode, the expression for the throughput is the same as (9), where ( 0) ( 0) ( 0) A ∆ B ∆ Pout (=0F)γA γA and Pout = FγB γB , with FγA γA and FγB γB given in (36), respectively. b) Delay-Tolerant Transmission: In this mode, similar to (10), the throughput is calculated using (25), where FγA (λ) and FγB (λ) are given in (36) at the top of this page, respectively.

Throughput (bits/s/Hz)

0.5 0.45

F. SBS power transfer policy for TDBC In this subsection, we consider the SBS power transfer policy for TDBC protocol. 1) End-to-End SNR: As suggested in Section III-E1, the energy harvested at the relay is expressed as { } 2 2 Eh = ηPk max |hAR | , |hBR | αT2 . (37) Based on (37), the transmit power at relay is given by { } 2 2 3ηαPk max |hAR | , |hBR | Eh PR = = . (38) (1 − α)T2 /3 (1 − α) Substituting (38) into (2), we obtain a tight high SNR approximation for the end-to-end SNR at Si as 2

γiM RC = Ψj |hAB | + { } 2 2 2 2 a5 Ψk Ψj max |hiR | , |hiR | |hiR | |hjR | { } , 2 2 2 2 2 b5 Ψk max |hiR | , |hjR | |hiR | + Ψi |hiR | + Ψj |hjR | (39) 3ηα 6ηα where a5 = (1−α) , b5 = (1−α) , Ψi = σP2i , Ψj = Ψk = Pσk2 . Lemma 6: The CDF of γiM RC in (39) is ∫ Ψγ − z j e ΩC FγiM RC (γ) = Fγi (γ − Ψj z) dz, ΩC 0

Pj σ2 ,

and

(40)

where Fγi is given in (36). 2) Throughput Analysis: a) Delay-Limited Transmission: In this mode, the exA ∆ pression for the throughput is the same as (17), where Pout = ( 0) ( ) ( ) ∆ B 0 0 FγAM RC γA and Pout = FγBM RC γB , with FγAM RC γA and ( 0) FγBM RC γB given in (40), respectively.

− Ωκ

e

i

Ωi

max{K2 ,K4 } )) ( Ω +Ω ) ( Ω +Ω ) i j − Ω Ω K1 − Ωi Ω j K3

( Ωi i j i j + U (K3 − K1 ) e −e − e −e Ωi + Ωj ( ( ( Ωi +Ωj ) )) ( Ω +Ω ) i j K K Ωj − K2 − K4 − 2 − 4 + U (K4 − K2 ) e Ωi − e Ωi − e Ωi Ωj − e Ωi Ωj Ωi + Ωj ( Ω +Ω ) ( Ω +Ω ) K1 i j i j K2 Ωj Ω − − K1 − K2 i − e Ωi Ωj + e Ωi Ωj . + 1 − e Ωj − e Ωi + Ω i + Ωj Ωi + Ωj K

− Ω1

)

dκ

(36)

SFS, SBS, DS

0.4 0.35 0.3 0.25

Simulation

SFS, SBS, DS

0.2

TDBC MABC

0.15

Asymptotic

0.1 0.05

5

10

15

20 SNR (dB)

25

30

Fig. 2. Throughput in delay-limited transmission mode for different policies.

b) Delay-Tolerant Transmission: In this mode, similar to (18), the throughput is calculated using (32), where FγAM RC (λ) and FγBM RC (λ) are given in (40), respectively. IV. N UMERICAL R ESULTS In this section, we present numerical results to examine the throughput in the TWRN for delay-limited transmission and delay-tolerant transmission modes. In a two-dimensional topology, we assume that the co-ordinates of the relays (R), the source (A), and (B). are (1; 0.5), (0; 0), (2; 0), respec√ tively. √ Hence, the distances are calculated as dAR = 5/2, dBR = 5/2, and dAB = 2. In the simulations, we set ζ = 4, 0 0 γA = γB = 0 dB, α = 0.5 and η = 1. We denote PA = PB = P and SNR = σP2 . Fig. 2 shows the throughput versus SNR in delay-limited transmission mode for MABC and TDBC protocols with DS, SFS, and SBS policies respectively. The dashed lines for DS, SFS, and SBS policies are obtained from (9) with different ( 0) ( 0) A ∆ B ∆ Pout = FγA γA and Pout = FγB γB , respectively. The solid lines for DS, SFS, and SBS policies are obtained from ( 0) ( 0) A ∆ B ∆ (17) with different Pout = FγA γA and Pout = FγB γB ,

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V. C ONCLUSION

Throughput (bits/s/Hz)

3.5

In this paper, an amplify-and-forward two-way relaying network with multiple access broadcasting protocol and time division broadcasting protocol is considered. We proposed three different wireless power transfer policies, namely, dualsource power transfer, single-fixed-source power transfer, and single-best-source power transfer based on the recently widely adopted time switching receiver architectures. From the perspective of delay-limited and delay-tolerant transmission modes, the throughput was examined and analytical expressions for different power transfer policies were derived. Numerical results were presented to verify the analysis and compare the three policies for multiple access broadcasting protocol and time division broadcasting protocol.

Simulation

3 2.5

TDBC MABC

SFS, SBS, DS

2 1.5 1

SFS, SBS, DS

0.5

R EFERENCES

0 5

10

15

20 SNR (dB)

25

30

Fig. 3. Throughput in delay-tolerant transmission mode for different policies.

respectively. We can see that all the lines can be precise agreement with Monte Carlo simulations. In this mode, we assume that the sources SA and SB transmit the signals at 0 0 the same fixed rate RA = RB = 1 bits/s/Hz. It is shown that the MABC protocol achieves a higher throughput than TDBC protocol, since MABC requires less time slots to transmit information. For MABC protocol, we can see that DS policy achieves the highest throughput, since it transfers the largest power to the relay. The throughput of SBS policy is close to that of DS policy and higher than that of SFS policy, which indicates that SBS policy can offer a tradeoff between the performance and the system power cost. For TDBC protocol, we see that the achievable throughput of the proposed policies is still DS > SBS > SFS. Moreover, it is shown that the throughput ceilings exist in the high SNR regime. The reason is that at high SNRs, the outage probability is small and has little impact on the throughput, which solely depends on the fixed transmission rates at the sources. Fig. 3 shows the throughput versus SNR in delay-tolerant transmission mode for MABC and TDBC protocols with DS, SFS, and SBS policies respectively. The dashed lines for DS policy is obtained from (10) and for SFS and SBS policies are obtained from (25) with different FγA (λ) and FγB (λ), respectively. The solid lines for DS policy is obtained from (18) and for SFS and SBS policies are obtained from (32) with different FγAM RC (λ) and FγBM RC (λ), respectively. We can see that all the lines can be precise agreement with Monte Carlo simulations. We can see that MABC protocol achieves higher throughput than TDBC protocol. The throughput of the proposed policies is DS > SBS > SFS in both MABC and TDBC protocols. For TDBC protocol, SBS policy performs almost the same as DS policy, therefore, we can select SBS policy in this scenario, in order to reduce the system power cost.

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