Maged Elkashlan. â¡. , and Trung Q. Duong. â. â . Department of Electrical and Computer Engineering, The University of British Columbia, Canada. â¡. School of ...
Wireless Energy Harvesting and Spectrum Sharing in Cognitive Radio S. Ali Mousavifar† , Yuanwei Liu‡ , Cyril Leung† , Maged Elkashlan‡ , and Trung Q. Duong∗ † Department of Electrical and Computer Engineering, The University of British Columbia, Canada ‡ School of Electronic Engineering and Computer Science, Queen Mary University of London, UK ∗ School of Electronics, Electrical Engineering and Computer Science, Queen’s University, Belfast, UK
Abstract—A wireless energy harvesting protocol is proposed for a decode-and-forward relay-assisted secondary user (SU) network in a cognitive spectrum sharing paradigm. An expression for the outage probability of the relay-assisted cognitive network is derived subject to the following power constraints: 1) the maximum power that the source and the relay in the SU network can transmit from the harvested energy, 2) the peak interference power from the source and the relay in the SU network at the primary user (PU) network, and 3) the interference power of the PU network at the relay-assisted SU network. The results show that as the energy harvesting conversion efficiency improves, the relay-assisted network with the proposed wireless energy harvesting protocol can operate with outage probabilities below 20% for some practical applications.
I. I NTRODUCTION Energy harvesting has been proposed as a means to augment battery usage or as an alternative source of energy in a variety of applications. Energy harvesting refers to the process of extracting energy from the surrounding environment. Recently, with the emergence of embedded low power electronics such as Micro-electromechanical (MEM) and low power wireless sensor network (WSN) systems, batteries with limited energy capacity can no longer serve as the sole energy provider of the system over its life span [1][2]. Various sources of energy such as thermal, solar, mechanical, wind, acoustic, wave, and more recently wireless signals have been studied for energy harvesting [1]-[8]. Wireless energy harvesting strategies for point-to-point communication systems have been proposed in [4]-[6]. The results from the studies have shown that wireless energy harvesting can be a viable solution in prolonging the lifetime of energy constrained systems. In [7], a data packet scheduling (i.e. delay before transmission) is studied subject to arrival rate and energy harvesting constraints. However, the method for energy harvesting is not discussed. Two relaying protocols for wireless energy harvesting, namely power splitting receiver (PSR) and time switching relaying (TSR) protocols, are proposed in [8]. In PSR protocol, a fraction of signal power from the source is used for energy harvesting and the remaining portion is used to retrieve information. In TSR protocol, the relay harvests energy from the source signal during the energy harvesting period and receives the information and transmits the information to the destination during the remainder of the period. Expressions for the outage probability and signal-to-noise ratio (SNR) are derived for both protocols. In [8], only the relay is energy constrained and capable of harvesting energy from the wireless signal
transmitted by the source. The wireless energy can be harvested from a variety of signals in the surrounding environment, e.g., UHF and VHF signals. In the context of cognitive radio, secondary users (SUs), also known as unlicensed users, can use the energy from the primary user (PU) signal to harvest energy. In addition, the SUs can utilize the licensed spectrum under two defined paradigms: overlay and underlay. The SUs can transmit opportunistically, when the licensed spectrum is unused in the cognitive radio overlay paradigm [9]-[11]. In the cognitive radio underlay paradigm, the SU network shares the spectrum with the PU network as long as the interference from the SU network to the PU network does not exceed a predetermined threshold value [12][13]. The relay-assisted cognitive radio is proposed to decrease the system outage probability in [12]. The impact of power interference from one PU transmitter on the system outage probability of an SU network is also analyzed in [12]. The joint impact of the interference power from multiple PU transmitters on the SU network and that from the SU network on the PU network is studied in [13]. In addition to power interference constraints, the relay-assisted cognitive radio is constrained by the stored energy and may require an external recharging mechanism to sustain its operation. The cognitive radio in an underlay paradigm in conjunction with energy harvesting is studied in [14]-[16]. The capacity of a point-to-point SU network under imperfect CSI is investigated in [14] and the achievable rate in the SU network using opportunistic interference cancelation is studied in [15]. To the best of our knowledge, the outage probability in a cognitive relay network jointly with the use of energy harvesting has not been studied. In this paper we propose a wireless energy harvesting relaying protocol for a decode-and-forward relay-assisted cognitive network in a spectrum sharing paradigm. In the proposed protocol, the source and the relay in the cognitive network harvest energy from the PU signal. We consider three power constraints and their impact on the system outage probability: 1) the maximum power the SU source or relay can transmit from the harvested wireless energy, 2) the peak permissable power from the SU source and the relay at PU receiver, and 3) the interference power from the PU transmitter at the SU relay and destination. The results demonstrate that as the energy conversion efficiency rate increases, outage probabilities below 20% can be achieved. The terms “relay-assisted cognitive network” and “SU network” are used interchangeably in
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this paper. The remainder of this paper is organized as follows. In Section II, we present the system model for the energy harvesting relaying protocol and the transmit power constraints. In Section III, we derive an expression for the system outage probability of the relay-assisted cognitive radio network. Illustrative results and conclusions are provided in Sections IV and V, respectively.
h2
h1 S
D
R
f1
g1
f3
f2
g2
II. S YSTEM M ODEL As shown in Fig. 1, the PU network consists of a PU transmitter (P Utx ) and a PU receiver, (P Urx ). The SU network consists of one source (S), one relay (R), and one destination (D) where information is transferred from an energy constrained source to the destination only via an energy constrained relay. There is no direct link between the source and destination. The source and the relay can harvest energy from the PU. However, we assume that the SU network incapable of storing the harvested energy for a long time. This assumption is reasonable for SUs which are equipped with inexpensive capacitors for energy storage due to to energy leakage. The SU network shares the spectrum with the PU network in an underlay mode. The channel gain coefficients from the source to the relay and from the relay to the destination are denoted by h1 and h2 , respectively. The transmission power from the SU network can cause interference at the receiver of the PU; therefore, a power constraint on the SU network is imposed such that its interference power does not exceed the peak permissable interference power, denoted by PI . The channel gain coefficients from the source and the relay to the PU receiver are denoted by g1 and g2 , respectively. The amount of power that the source and the relay can use during transmission period is constrained by the amount of energy they have harvested, denoted by Ehs and Ehr , respectively. The channel gain coefficients from the PU transmitter to the source, relay, and destination receiver are denoted by f1 , f2 , and f3 , respectively. The distances from the PU transmitter to the source, relay, and destinations are d1 , d2 , and d3 respectively. The PU network interference power received at the relay and the destination are
PUrx
Figure 1.
PI,R and
PI,D =
PP Utx |f3 |2 , dm 3
where PP Utx is the PU transmitter power, m is the path loss exponent. The relay and the source harvest energy from the PU signal for a duration of αT at the beginning of each time slot, where T is the duration of one time slot and 0 < α < 1. By changing the value of α, the source and relay have the flexibility to trade-off harvesting more energy against the reduction in throughput at the destination, in a time slot. The choice of α and its impact on the relay network throughput is beyond the scope of this paper. We are currently studying the scenario in which the relay can also harvest energy from the source. Subsequent to the harvesting period, the source transmits information to the relay for a duration . The relay then forwards, the information to equal to (1−α)T 2
Energy Harvesting at the Source (S)
Information Transmission from the Source to the Relay S ------ > R
(b)
Energy Harvesting at the Relay (R)
Information Transmission from the Source to the Relay S ------ > R
Figure 2.
Information Transmission from the Relay to the Destination R ------ > D
(1 − α )T / 2
(1 − α )T / 2
The proposed protocol: (a) at the source (b) at the relay
the destination. The protocol is illustrated in Fig. 2. Note that of the protocol the source is idle during the last slot (1−α)T 2 in Fig. 2 (a). It is natural to assume that the source can store energy during this period for the next transmission. However, due to leakage and a long time to the energy harvested in the next transmission any such energy will be depleted. The energy harvested using the time switching receiver (TSR) architecture at the source and the relay are [17] Ehs =
ηPP Utx |f1 |2 αT dm 1
(3)
Ehr =
ηPP Utx |f2 |2 αT, dm 2
(4)
and
(1)
(2)
System Model
(a)
αT
2
PP Utx |f2 | = dm 2
PUtx
where |f1 |2 is the channel gain coefficients from P Utx to the source and 0 < η < 1 is the energy conversion efficiency [17]. The distances from the source and the relay to the receiver of the PU are d4 and d5 . The distances from the source to the relay and from the relay to the destination are d6 and d7 . The maximum power that the source and the relay can transmit Ehs Ehr based on the harvested energy are: (1−α)T /2 and (1−α)T /2 . Therefore, the transmit power at the source and the relay are: PI Ps = min( |g |2 ,
Ehs ) (1 − α)T /2
(5)
PI Pr = min( |g |2 ,
Ehr ), (1 − α)T /2
(6)
1 dm 4
and
2 dm 5
respectively. Flat Rayleigh fading channel is assumed for all links. Hence, |h1 |2 , |h2 |2 , |g1 |2 , |g2 |2 , |f1 |2 , |f2 |2 , and
|f3 |2 are random variables (RV) distributed exponentially with parameters λ1 , λ2 , ω1 , ω2 , ν1 , ν2 , and ν3 . We have summarized the main used parameters for the derivation of outage probability: • η: the energy efficiency (0 < η < 1). • α: the fraction of a time slot in which relay and the source harvest energy from PU transmitter signal (0 < α < 1). • PI : the peak permissable interference power at the PU receiver • γth : the threshold SNR at the relay and destination • PP Utx : the primary user transmit power • Ps : the source transmit power • Pr : the relay transmit power • d1 , d2 , and d3 : the distances from the PU transmitter to the source, relay, and destination, respectively. 2 2 2 • |f1 | , |f2 | , and |f3 | : the channel gain RVs for the links from PU transmitter to the source, relay, and destination, respectively. • ν1 , ν2 , and ν3 : the exponential parameters corresponding to |f1 |2 , |f2 |2 , and |f3 |2 RVs, respectively. • d4 and d5 : the distances from the source and relay to the PU receiver, respectively. 2 2 • |g1 | and |g2 | : the channel gain RVs for the links from the source and relay to the PU receiver, respectively. • ω1 and ω2 : the exponential parameters corresponding to |g1 |2 and |g2 |2 RVs, respectively. • d6 and d7 : the source-relay and the relay-destination distances, respectively. 2 2 • |h1 | and |h2 | : the channel gain RVs for the links from the PU transmitter to the relay and destination, respectively. • λ1 and λ2 : the exponential parameters corresponding to |h1 |2 and |h2 |2 RVs, respectively. III. O UTAGE P ROBABILITY The outage probability, denoted by Pout , is defined as the probability that the equivalent signal to interference ratio (SIR) at each hop is below a threshold value, γth . In this study, we have neglected the effect of noise. In our system model, the decode-and-forward relay-assisted cognitive network is considered to be in outage when at least one of the links is suffering from link outage, i.e. the RV SIR at the relay, denoted by ΓR , or the RV SIR at the destination, denoted by ΓD , are below γth : Pout
=
1 − Pr{ΓR ≥ γth , ΓD ≥ γth },
(7)
|g1 |2 , |g2 |2 , |f1 |2 , |f2 |2 , and |f3 |2 , with X1 , X2 , Y1 , Y2 , Z1 , Z2 , and Z3 hereafter. Conditioning the term P r{ΓR ≥ γth , ΓD ≥ γth } in (7) on Z2 , we have ∞ Pout = 1 − Pr{ΓR ≥ γth |Z2 = z2 } × 0
Pr{ΓD ≥ γth |Z2 = z2 }fZ2 (z2 )dz2 , (10) where Pr{ΓR ≥ γth |Z2 = z2 } and Pr{ΓD ≥ γth |Z2 = z2 } are two independent event probabilities for a given Z2 = z2 . The term P r{ΓR ≥ γth |Z2 = z2 } can be obtained as Pr{ΓR ≥ γth |Z2 } X1 β2,6 PI dm 4 ≥ γth = Pr min ρR Z1 , Y1 PP Utx Z2 Z2 PP Utx γth PI dm 4 , Y1 ≤ = Pr X1 ≥ Z1 ρR β2,6 Z1 ρR
JR,I
Y1 Z2 γth PP Utx PI dm 4 + Pr X1 ≥ , ≤ Z1 PI β2,6 Y1 ρR
JR,II
(11) Conditioning JR,I in (11) on Z1 and taking the expected value of the results over the distribution of Z1 , we have ∞ Z2 PP U γth P dm z1 tx 1 − − I 4 e z1 ρR λ1 β2,6 (1 − e z1 ρR ω1 )e− ν1 dz1 (12) JR,I = ν1 0 Similarly, we condition JR,II in (11) on Y1 and we take the expected value of the result over the distribution of Y1 ∞ y1 Z2 γth PP Utx P dm y1 − P mλ β 1 − I 4 1 2,6 Id4 JR,II = e e y1 ρR ν1 e− ω1 dy1 ω1 0 (13) In the same manner, the term P r{ΓD ≥ γth |Z2 } in (10) can be obtained as Pr{ΓD ≥ γth |Z2 } X2 β3,7 PI dm 5 ≥ γth = Pr min ρD Z2 , Y2 PP Utx Z3 PP Utx γth Z3 PI dm 5 , Y2 ≤ = Pr X2 ≥ Z2 ρD β3,7 Z2 ρD
JD,I
where ΓR
|h1 |2 β2,6 PI dm 4 = min ρR |f1 |2 , , |g1 |2 PP Utx |f2 |2
(8)
|h2 |2 β3,7 PI dm 5 = min ρD |f2 |2 , , |g2 |2 PP Utx |f3 |2
(9)
γth PP Utx Y2 Z3 PI dm 5 + Pr X2 ≥ , Y ≥ 2 PI β3,7 dm Z2 ρD 5
JD,II
and ΓD
are functions of RV |f2 |2 and therefore, ΓR and ΓD are 2ηPP Utx α , dependent. Note that we have replaced the constants dm (1−α) 2ηPP Utx α dm , d2m , dm 2 (1−α) 6
dm
(14)
1
and d3m with ρR , ρD , β2,6 , and β3,7 . respec7 tively. For notation simplicity, we will replace |h1 |2 , |h2 |2 ,
Since JD,I is conditioned on Z2 , the joint probability can be presented as the product of two independent probabilities JD,I
=
PP Utx γth Z3 PI dm 5 Pr{X2 ≥ } Pr{Y2 ≤ } ρD Z2 β3,7 ρD Z2
I1
I2
(15)
1
=
1 ν3
=
ρD Z2 β3,7 λ2 γth PP Utx ν3 + ρD Z2 β3,7 λ2
and I2 = 1 − e
γth PP U Z3 − ρ Z β tx λ D 2 3,7 2
e 0
P dm − ρ IZ 5ω D 2 2
JD,II |Z3
∞
0.9
z3
e− ν3 dz3
0.8
(16)
PI dm 5
PP Utx Y2 Z3 γth = Pr{X2 ≥ , Y2 ≥ } PI β3,7 dm ρD Z2 5 ∞ PP U y2 Z3 γth y 1 − P λtx β dm − ω2 I 2 3,7 5 2 dy = e e 2 m ω2 PρI dZ5 =
−
P Iλ2 β3,7 dm 5 +γth Z3 PP Utx ω2 ρD Z2 λ2 β3,7 ω2
.
Averaging JD,II over the PDF of Z3 we have, ∞ JD,II = JD,II |Z3 fZ3 (z3 )dz3 0 ∞ PI λ2 β3,7 dm 1 5 = ν3 0 PI λ2 β3,7 dm + γ Z th 3 PP Utx ω2 5 ×e
0.3 0.2 0
0.1
0.2
0.3
0.4 0.5 0.6 0.7 X−coordinante of PUtx (XPU )
0.8
0.9
1
tx
P Iλ2 β3,7 dm 5 +γth Z3 PP Utx ω2 ρD Z2 λ2 β3,7 ω2
z3
e− ν3 dz3 (18)
each scenario, the outage probability increases as X-coordinate of P Utx increases because P Utx interference power at the relay and destination increases. In addition, as the distances from the P Utx to the source and the relay increase, the amount of energy which can be harvested from the PU signal decreases. For XP Utx = 0.75, the outage probability in Scenario 2 surpasses that of Scenario 1. In Scenario 1 at XP Utx = 0.75, the PU receiver is located farther from both the relay and the destination compared to Scenario 2 and therefore, the relay can transmit at higher transmit power (i.e. without imposing higher than PI interference power at P Urx ) than in Scenario 2. Fig. 4 shows the outage probability as a function
Using (12), (13), (15), and (18), we can obtain the outage probability as ∞ 1 Pout = 1 − (JR,I + JR,II ) ν2 0 ×(JD,I + JD,II )e
2
1
[Theo.] γth=0dB
0.9
[Sim.] γth=0dB
0.8
[Sim.] γth=5dB
0.7
[Sim.] γth=10dB
[Theo.] γ =5dB th
[Theo.] γ =10dB th
dz2
0.6
(19) IV. N UMERICAL R ESULTS In this section, numerical and analytical results are presented. The outage probability with respect to η, γth , PI , P Urx location, and P Utx location is studied here. The analytical results are validated via computer simulations. The noise power is assumed to be negligible in the following simulations. A two dimensional network topology is assumed, where the locations of nodes are denoted by (X, Y ). The source, relay, and destination are located at (0, 0), (0.5, 0), and (1, 0) on the X-Y plane. The mean of all the channel gain coefficients are assumed to be equal to 5, i.e. λ1 = 5, λ2 = 5, ω1 = 5, ω2 = 5, ν1 = 5, ν2 = 5, ν3 = 5, and they remain the same hereafter, unless it is stated otherwise. Fig. 3 shows the outage probability in the SU network as a function of the X-coordinate of P Utx location (denoted by XP Utx on Fig. 3), where Ycoordinate remains constant at 0.5. We show the results for three P Urx location scenarios: • Scenario 1: P Urx at (0, 0.5). • Scenario 2: P Urx at (0.5, 0.5). • Scenario 3: P Urx at (1, 0.5). The parameter values used for the results in Fig. 3) are: η = 10%, PP Utx = 2 dB, PI = 20 dB, and γth = 5 dB. For
Pout
z
− ν2
The outage probability as a function of the P Utx X-cooridinate.
Figure 3.
(17)
−
[Theo.] Scenario 1 [Sim.] Scenario 1 [Theo.] Scenario 2 [Sim.] Scenario 2 [Theo.] Scenario 3 [Sim.] Scenario 3
0.4
2
PI λ2 β3,7 dm 5 PI λ2 β3,7 dm 5 + γth Z3 PP Utx ω2 ×e
0.6 0.5
. We condition JD,II on Z3
D
0.7 out
I1
P
where
0.5 0.4 0.3 0.2 0.1 0
10
Figure 4.
20
30
40
50 η (%)
60
70
80
90
100
The outage probability as a function of η
of η for γth = 0, 5 and 10 dB. The parameter values used for the results in Fig. 4 are: PP Utx = 2 dB, PI = 20 dB, and the P Utx and P Urx locations are (0.5, 0.5) and (1, 0.5), respectively. For a given γth , the outage probability decreases as η increases. As η increases, more wireless energy is being harvested at the source and the relay and therefore, more energy is available for wireless transmission to the next hop. For a given value of η, the outage probability increases as the minimum SIR requirement (i.e. γth ) at the source and the relay increases. Fig. 5 shows the outage probability as a function of PI for PP Utx = 2, 5 and 10 dB. The parameter values used for the results in Fig. 5 are: η = 20%, γth = 5 dB, and the P Utx and P Urx locations are (0.5, 0.5) and (1, 0.5), respectively. For a given value of PP Utx , the outage probability decreases as PI increases. The relay and the source can transmit at higher
constraints on the primary user network, and an interference imposed by primary user network on the secondary user cognitive network. A sensitivity analysis for the outage probability was presented and validated using computer simulations. The results demonstrate that as the energy conversion efficiency rate is improved, the outage probabilities below 20% can be achieved.
1 0.95
[Theo.] PPU = 2 dB
0.9
[Sim.] PPU = 2 dB
tx
tx
[Theo.] PPU = 5 dB
0.85
tx
[Sim.] P out
P
= 5 dB
PU
0.8
tx
[Theo.] P 0.75
PU
= 10 dB tx
[Sim.] PPU = 10 dB tx
0.7 0.65
ACKNOWLEDGMENT
0.6 0.55 −10
−5
0 5 10 15 Maximum Interference SU may Incure at PU [P ] (dB) rx
20
I
This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada under Grant RGPIN 1731-2013.
The outage probability as a PI
Figure 5.
R EFERENCES transmit power before they impose higher than PI interference power at P Urx . For a given value of PI , it is shown that as PP Utx increases, so does the interference at the relay and destination and hence, Pout increases. The interference power imposed on the relay and destination offsets the energy harvested at the source and the relay for large PP Utx values. Fig. 6 shows the outage probability as a function of γth for 1 0.9 0.8 0.7
P
out
0.6 0.5 [Theo.] Case 1 [Sim.] Case 1 [Theo.] Case 2 [Sim.] Case 2 [Theo.] Case 3 [Sim.] Case 3
0.4 0.3 0.2 0.1 0 −40
−30
−20
−10
γ (dB)
0
10
20
30
th
Figure 6.
The outage probability as a function of γth
three cases: • Case 1: λ1 = λ2 = ω1 = ω2 = ν1 = ν2 = ν3 = 1 • Case 2: λ1 = λ2 = ω1 = ω2 = ν1 = ν2 = ν3 = 2 • Case 3: λ1 = λ2 = ω1 = ω2 = ν1 = ν2 = ν3 = 5 The parameter values used for the results in Fig. 6 are: η = 10%, PI = 20 dB, PP Utx = 2 dB, and the P Utx and P Urx locations are (0.5, 0.5) and (1, 0.5), respectively.In each case, as γth increases, the probability that the γth is unsatisfied in at least one link (i.e. source-to-relay and relay-todestination) increases and consequently, the outage probability of the system increases. For a given value of γth , the outage probability decreases as the channel gain coefficient increase. V. C ONCLUSIONS A wireless energy harvesting protocol for a relay-assisted network in a cognitive spectrum sharing paradigm was proposed. The outage probability of the relay-assisted cognitive network with the proposed protocol was analyzed, subject to the energy harvesting constraint, the interference power
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