Analyze the impact of energy arrival on average secrecy rate of wireless network and optimization the system for improving the secrecy rate

1. Security of Wireless Networks
with rechargeable Energy Harvesting
Transmitters
Arvin Moeini - 504151332

2. Motivation
Security is an important issue in wireless networks due to the open
wireless medium. Security against an eavesdropper is typically
achieved via cryptographic algorithms that are implemented at
higher network layers.

3. Motivation
Wiretap channel
(Wyner, 1975)
Physical layer based security was pioneered by Wyner, who
introduced the wiretap channel and established the possibility of
creating perfectly secure communication links without relying on
private keys.

4. Motivation
Radio frequency (RF) energy harvesting technique is the
capability of converting the received RF signals into electricity.
This technique becomes a promising
solution to power energy constrained
wireless networks.
Conventionally, the energy
constrained wireless networks, such as
wireless sensor networks, have a
limited lifetime which largely confines
the network performance.

5. Outline
• Analyze Impact of the energy arrival rate on the system’s
secrecy rate
• Optimize the data transmission time to improve the
secrecy rate
• Optimize the weight vector to improve the secrecy rate
• Propose to use subset of jammer’s antenna for jamming
• Batteries queuing analyses
• Simulate the system on MATLAB

6. Background information
We consider a scenario in which a source communicates with a
destination in the presence of one eavesdropper. The
communication is aided by a relay that is equipped with multiple
antennas that provide more degrees of freedom for the relay
channel.

7. Background information
The secrecy outage happens when the transmission rate exceeds
the secrecy rate. Letting Cn-m L denote the channel capacity of the
n−m link when the event L is true, the secrecy rate of the Alice-
Bob link is given by
where [ ]+ denotes the maximum between the enclosed value in·
the brackets and zero
L {{∈ BJ > 0}, {BJ = 0}} represents the state of
Jimmy’s battery.
If L = {BJ > 0} Jimmy’s battery has energy
if L = {BJ = 0} Jimmy’s battery has no energy and
hence he cannot help in jamming Eve.

8. New Methods

9. New Methods
Optimize Alice’s transmission times to enhance the achievable
secrecy rate due to the increase of the transmit and jamming powers.
αA = TA/T [0∈ , 1]
analyze the energy arrival randomness at Alice and Jimmy
and show their impact on the average secrecy rate.

10. New Methods
Our proposed jamming scheme is summarized as follows

11. Secrecy Capacity
Let ΓA = eA/T and Γ J = eJ/ T. For given channel realizations,
the rates of the Alice-Bob and Alice-Eve links are
The secrecy rate is Cs A (B j >0) =[CA,B − CA,E (BJ >0]+
The superscript ∗ denotes the complex-conjugate transpose
| · | denotes the absolute value, θj,k = |hj,k|2 denotes channel gain between
Node j ∈ {A, 1, 2, 3, . . . , N } and Node k ∈ {E, B, 1, 2, . . . , N }

12. We aim at maximizing the secrecy rate in a given time slot over
the weight vector used at Jimmy and the transmission time. That is,
g = [g1, g2, . . . , gK ]T, where the superscript T denotes the vector
transpose, is the BF weight vector whose dimension is K × 1 with gj as the
weight used at Antenna j ∈ J .
For a given (fixed) αA, the optimization problem becomes independent of αA.
This implies that the optimal weight vector is independent of αA.
Secrecy Capacity

13. Optimization
for a fixed αA, maximizing Cs ,A (B ,J>0) over the weight vector g is
equivalent to minimizing
Since the logarithmic function is a monotonically increasing function,
the problem reduces to the maximization of the following objective function
The optimal weight vector g that maximizes |g*hE|2 =
subject to (s.t.) the normalization constraint ||g ||^2 = 1, where || · || represents
the l2-norm.

14. Optimization
the total elimination of the interference at Bob, i.e., |g hB| = 0,∗
can be achieved by solving the following optimization problem
Since g has a unit norm, we must divide the projection vector by its
magnitude. Thus,
where is the projection matrix which is given by
we substitute with g = g* into the objective function of secrecy rate and optimize it
over αA.

15. Optimization
Finally, we have the case when Alice’s battery has energy and Jimmy’s
battery has no energy. When Jimmy’s battery is empty, the secrecy rate
is given by

16. Batteries Queueing Analyses
Average secrecy rate of Alice transmission when Jimmy has no
energy and has energy to help
Average number of securely decoded bits/sec/Hz at Bob is given by
Two important special cases to gain some insights
A. The Case of Large Batteries Capacities and λA =1 or λJ =1
B. B. Geo/D/1 Queueing Model

17. Large Batteries Capacities
1) The Case of λA = 1 :
When λA = 1, Alice always has energy to
transmit data.
Pr{BA = 0} = 0 and Pr{BA > 0} = 1
The average secrecy rate is given by
When BJ max is very large, the probability that Jimmy’s battery is nonempty is
given by Pr{BJ > 0} = min{λj / β ,1}
By Substituting two above formula, the average secrecy rate of the system is
given by

18. 2) The Case of λj = 1 :
When Jimmy has a reliable energy supply, Pr{BJ = 0} = 0 and Pr{BJ > 0} = 1.
In this case, the average secrecy rate of the system is given by
Geo/D/1 Queueing Model
the probability of the Geo/D/1 energy queue with unity service rate being
empty is equal to 1 − λk for Bk. Applying this model to our scenario, we
can write
B. Geo/D/1 Queueing Model
Since CA, B (BJ >0) ≥ CA, B (BJ >0) , as the energy arriving at Jimmy increases,
the secrecy rate increases.

19. Simulation result
We simulated the system using 4000 channel realizations and assumed that
each channel coefficient is modeled as a circularly-symmetric Gaussian
random variable with zero mean and unit variance.
Moreover, we assume N = 6, eA/ /κ
(TW) = eJ/ /(κ TW) = 20 dB, and BA max =
BJ max = 10. Figure 1 shows the
average secrecy rate for our
proposed jamming scheme with and
without optimization over g and αA.

20. Simulation result
After optimization the weight vector we saw that our secrecy rate increased
because maximizing Cs B ,JA >0 over the weight vector g

21. Simulation result
If the arrival rate of a battery is high enough to saturate the battery with
energy packets, the average secrecy rate becomes fixed with that arrival rate.
According the results average secrecy rate increases linearly with both λA and λJ.

22. Simulation result
Instead of using all of Jimmy’s antennas for jamming Eve, which requires N radio-
frequency (RF) chains, we assume that only a set of K RF chains is available at
Jimmy (or he only activates any K ≤ N)

23. Conclusion
• investigated the impact of the batteries at a source node and a jammer on
the achievable average secrecy rates.
We showed that the average secrecy rate is nondecreasing with the
arrival rates at the energy batteries and it becomes constant when these
batteries are saturated with energy packets.
• In addition, we showed that the optimization over the transmission time, TA,
can significantly enhance the average secrecy rate.
• proposed a cooperative jamming scheme and showed that the jammer
does not need to use all of its antennas for jamming Eve.
The achievable performance is comparable with the case of using all
antennas, which requires complex hardware design since it increases
the number of transmit RF chains and antennas and also complicates
system design since the number of estimated channels increases.

24. References
• X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z. Han, “Wireless networks with RF energy
harvesting: A contemporary survey,” IEEE Commun. Surveys Tuts., vol. 17, no. 2, pp.
757–789, Jun. 2015.
• C. Alippi and C. Galperti, “An adaptive system for optimal solar energy harvesting in
wireless sensor network nodes,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55,
no. 6, pp. 1742–1750, Jul. 2008.
• L. Dong, Z. Han, A. P. Petropulu, and H. V. Poor, “Cooperative jamming for wireless
physical layer security,” in Proc. IEEE/SP 15th Workshop Stat. Signal Process.,
Cardiff, U.K., Aug./Sep. 2009, pp. 417–420.
• A. Mukherjee and J. Huang, “Deploying multi-antenna energy-harvesting cooperative
jammers in the MIMO wiretap channel,” in Proc. IEEE ASILOMAR, Pacific Grove, CA,
USA, 2012, pp. 1886–1890.
• I. Krikidis, G. Zheng, and B. Ottersten, “Protocols and stability analysis for energy
harvesting TDMA systems with/without relaying,” in Proc. IEEE GLOBECOM, Atlanta,
GA, USA, Dec. 2013, pp. 4536–4541.
• A. El Shafie, D. Niyato and N. Al-Dhahir, "Security of Rechargeable Energy-
Harvesting Transmitters in Wireless Networks," in IEEE Wireless Communications
Letters, vol. 5, no. 4, pp. 384-387, Aug. 2016.

25. Any Question?
THANK YOU FOR YOUR ATTENTION…