1. ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 3, May 2012
Secured communication technique for MIMO
based wireless network using codebook and
multiplexing methodology
1
R.RAICHEAL, 2C.ARUNACHALAPERUMAL,
Abstract--In this paper we study about the Secure The wire-tap channel, is one of the solution of
communication among wireless shared medium using information-theoretic security, was introduced in [1], the
secrecy performance of a codebook based ergodic secrecy capacity is calculated for fading wiretap
transmission beamforming with limited feedback. channels in [2]. In wireless channels, when the number
And avoid attacker from stealing the confidential of antenna increases the fading can be reduced, and
data. In the feedback method transmitter is using a transmission rates can be increased . In [3] the secrecy
predefined codebook known to transmitter and capacity of the Gaussian multiple-input multiple-output
receiver knows it after producing index value as (MIMO) wire-tap channel are found, when the source s
feedback during beamforming. The secrecy outage and the destination d have two antennas each and the
probability is analyzed to find whether it is stealed. attacker e has only a single antenna. Outage probability
The bound values are provided on the secrecy outage for a target secrecy rate is shown in [4], when s, d and e
probability. The fading in multiple antenna (MIMO) have CSI, and optimal power allocation minimize the
wire-tap channel is investigated under short term outage probability are calculated. The DMT is a high
power constraints. The secret diversity multiplexing SNR analysis. The diversity gain decays the rate of the
tradeoff (DMT) is found for no transmitter side probability of error, and the multiplexing gain is the rate
channel state information (CSI) and for full CSI. of increase of the transmission rate in the limit of high
When there is no CSI at the transmitter, while using SNR. In this paper we investigate the code generation
Gaussian codebooks, it seems that both transmitter and the cryptographic methods[5] in the multiple-
and receiver antennas are stealed, and the secret antenna wire-tap channel. Under CSIT, we study the
DMT depends on the other degrees of freedom. When effect on secrecy from a codebook based transmission
CSI is available at the transmitter (CSIT), then beamforming with limited receiver feedback. Codebook
transmitter antenna is only stealed. beamforming [6], [7] has become commonly adopted in
practice [8], [9] for reducing the amount of feedback
Index terms — Diversity multiplexing tradeoff overhead. The idea behind this scheme is the use of
MIMO, transmission beamforming, codebook, wiretap code. By using a stochastic encoder to map the
information-theoretic security, secrecy outage secret message into many codewords according to an
probability appropriate probability distribution, the sender can hide
the secret information in the noise on wiretapper‟s
I. INTRODUCTION: channel. We see about the secret outage probability in
As the wireless medium the communication is II.A, code book generation in III, and feedback method
being shared there is much more possibility of stealing in IV.
the confidential informations. In any region of the
transmitter the stealer can present and he can be more II. SYSTEM MODEL AND PRELIMINARIES:
advantageous than the information producer. The We consider fig1, multiple-antenna wire-tap
confidential information such as user IDs, passwords, or channel, in which s, d and e have 𝑚, 𝑛 and 𝑘 antennas.
credit card numbers become vulnerable if he is present Both d and e have CSI about their incoming channels.
near to the transmitter antenna. Then, wireless security is For each channel, the received signal is represented as
an essential system requirement. In existing wireless follows:
systems, protection against stealing is provided at higher
layers of the Open Systems Interconnection (OSI) Yd = HdX + Nd (1)
reference model. Therefore, key exchange and renewal Ye = HeX + Ne. (2)
may be difficult.
In the above equations X is an 𝑚 × 1 vector, which is
the transmitted s signal. Yd and Ye are 𝑛×1 and 𝑘×1
Manuscript received on April 2012
1
M.E(Communication systems) S.A Engineering College, Chennai -
vectors, shows the received signals at d and e. Then Nd
77. and Ne are 𝑛×1, and 𝑘×1 vectors that indicate the
2
Asst. Professor,,Dept of P.G. Studies,S.A Engineering College, independent additive noise at d and e. Both (Nd , Ne)
Chennai -77. and (Hd, He) have independent and identically
distributed (i.i.d.) complex Gaussian entries with zero
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2. ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 3, May 2012
mean and unit variance. Hd, He are of size 𝑛× 𝑚, and channel codeword X 𝑛1 . Note that 𝐵 is the number of
𝑘× 𝑚. They indicate the channel gains between s and d dummy code words used to confuse e for each 𝑎 ∈ 𝒜.
and the s and e. Since the fading is slow, Hd and He are With full CSI at s and d, 𝑅( 𝑠) is set to 𝑅 𝑠, and R( 𝑑) =
fixed for the whole duration of the communication.
𝐼(X;Ye). The total number of code words in the s
When there is no secrecy, the error probability
is dominated by the outage event. The DMT,d ( 𝑟), codebook is 𝐴 × 𝐵 = 2 𝑁𝐼(X;Yd), and the d can decode
establishes a relation between the target transmission W using a. The attacker can decode only the index b and
rate 𝑅( 𝑇)(SNR) and probability of error 𝑃 𝑒(SNR), where 𝑟 there will no information about the secret message a.
is the multiplexing gain. Therefore the secrecy depends Thus secrecy is achieved. For average power constraint
on the remaining degrees of freedom in this system is m-SNR that the transmitter has to satisfy for each
min{ 𝑚, 𝑛}, and 𝑟 can increase up to this value. The codeword transmitted. The secret multiplexing gain is
maximum diversity gain is 𝑚𝑛, and it decreases as the
defined as,
multiplexing gain increases.
Under secrecy constraints, the source has to
send the message 𝑊, So the secrecy rate, 𝑅 𝑠 is achieved lim ≜ 𝑟𝑠. (6)
if the secrecy constraint is satisfied; i.e.
SNR→∞
𝑅𝑠 = lim (3)
𝑁→∞ the above equation shows how fast the target secrecy
rate scales with increasing SNR. The secret diversity
=lim (4) gain, ds, is equal to
𝑁→∞
The probability of decoding error at the d approaches Lim ≜ −ds, (7)
zero as 𝑁 approaches infinity. The term lim
SNR→∞
1
𝑁→∞ 𝐻( 𝑊∣𝑌e 𝑁 ) is also known as the equivocation
N where Pe(SNR) denotes the probability of error under
rate. secrecy constraints. Two events are considered :Either
the destination does not receive the secret message
reliably, or secrecy is not achieved. Then
Pe(SNR) = P (secrecy not achieved, main
Destination D
channel decoding error) (8)
D ≤ (secrecy not achieved)+
(main channel decoding error), (9)
Source S
Where (secrecy not achieved)
1
≜ 𝑃 ( lim 𝐻( 𝑊∣𝑌 𝑁
e
) < 𝑅( 𝑇) 𝑠 (SNR))
Attacker E N
𝑁→∞ (10)
𝐵 = 2 𝑁𝑅( 𝑑)(SNR) and
𝐴 × 𝐵 = 2 𝑁 𝑠 𝑅( 𝑇)(SNR)
=2 𝑁𝑅( 𝑇) (SNR)+ 𝑁𝑅( 𝑑)(SNR),
Fig1: Basic System Model 𝑃(secrecy not achieved) defined in (8) can be calculated
as
𝑃(secrecy not achieved)
The H( ) denotes the mutual sharing information = 𝑃( 𝑅( 𝑇)(SNR) − 𝐼(X;Ye) < 𝑅( 𝑇) 𝑠(SNR))
= 𝑃 ( 𝐼(X;Ye) > 𝑅( 𝑑)(SNR)). (11)
between e. The papers, prove that the secrecy rate.
Finally, as the main channel outage event dominates the
𝑅𝑠 = [ 𝐼(X;Yd) − 𝐼(X;Ye)]+ (5)
main channel decoding error when the channel block
length-N is long enough and good codes are used ,
is achievable for any input distribution 𝑝(X), where 𝑥+
denotes max{0, 𝑥}. 𝑃(main channel decoding error)
=˙ 𝑃(main channel outage)
Define 𝐴 = 2𝑁𝑅( 𝑠) , 𝐵=2𝑁𝑅( 𝑑)and the sets 𝒜 = = 𝑃( 𝐼(X;Yd) < 𝑅( 𝑇)(SNR)). (12)
{1, ...,} and ℬ = {1, ..., 𝐵}. The source generates 𝐴 × 𝐵 Lower bound is given as follows
channel codewords X 𝑁1 i.i.d. with 𝑝(X). In order to send
a secret message a ∈ 𝒜, the source chooses 𝑏 uniformly 𝑃 𝑒(SNR) ≥ 𝑃(secrecy not achieved)
from the set ℬ, forms 𝑊 = ( 𝑎, 𝑏) and maps 𝑊 into the ≥ 𝑃([ 𝐼(X;Yd) − 𝐼(X;Ye)]+ < 𝑅( 𝑇) 𝑠 (SNR))
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3. ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 3, May 2012
≥ 𝑃( 𝐼(X;Yd) − 𝐼(X;Ye) < 𝑅( 𝑇) 𝑠 (SNR))
≜ 𝑃(secrecy rate outage), (13)
for the chosen achievable scheme with 𝑝(X). If many
antennas are considered power constraint will be larger.
Key CB Code
A. Definition Of Secrecy Outage Probability:
Generator Generator
book
To achieve secrecy, s encodes the secret
message using a scalar Gaussian wiretap code and
transmits in the direction of q. When the input signaling
is Gaussian, then the difference of mutual information
between s-to-d is Rd and between s-to-e Re is an
Character
achievable rate. This implies that when s knows the
set
channel information to both d and e, she can design a
wiretap code such that d can receive data at a rate Re –
Rb, whereas d receives no secret information. When no Fig. 2 : Code book generation
channel information is present from e, s can give
information to d. Without e‟s channel information, s will
set the wiretap code to operate at an arbitrary rate R. If Group Group code
Rb − Re ≥ R, then secrecy is achieved. If, Rb − Re < R, AJS J
then e can eavesdrop at a positive rate so no secrecy is BKT T
there it is also known as secrecy outage. For any positive
CLU C
R, the secrecy outage probability characterizes an
achievable secrecy rate which is also decodable by d. DMV V
For a target secrecy rate R and transmission power R, ENW E
secrecy outage probability can be expressed as FOX O
GPY P
𝑃so ( 𝑅, 𝑃) = Prob [ 𝑅d − 𝑅 𝑒 ≤ 𝑅] (14) HQZ Z
= P[|H 𝑒q|2 ≥(( 𝜏 ∣⟨hd, q⟩∣2 − 𝛾 𝑒)/2 𝑅) ] (15) IR R
Table 1 :Group of element generated
We denote 𝛾d = 2 𝑅−(1/ 𝑃 𝑏) and 𝛾 𝑒 = 2 𝑅−(1/ 𝑃 𝑒), and we
set 𝜏 = 𝑃 𝑏/ 𝑃 𝑒 = 𝛾 𝑒/ 𝛾d. • E is coded as E1, since „E‟ belongs to the
group that is having a group code „E‟ and „E‟ is in 1st
III. CODE BOOK GENERATION: position from right.
In our system it works by the basis of a Code- • L is coded as C2, since „L‟ belongs to the
book (CB), without the needing of a key to be shared. group that is having a group code „C‟ and „L‟ is in 2nd
Maintaining of sessions is done to renew the code-book position from right.
from time-to-time. The proposed Methodology works as Likewise the total message is coded as -
follows: “Z1E1C2C2O2”.
• Generation of CB. This message is coded in such a way that a
• Encryption of CB using WEP and exchange of group code is followed by the position of that character
CB. in that group.
A. Generation of CB: B. Encryption Of CB Using WEP And Exchange Of CB:
The code-book is generated as follows: The CB has to be exchanged between the two
The Key Generator generates a key, based on communication parties. The WEP is used to encrypt the
which the Code- Book generator generates a Code-Book code book and is sent to the receiver. Since, initially CB
for the given Character- Set. The key generation process will be only at one side, so there is a need of exchange of
is delaying sensitive, and keys generated this way are CB between both the parties.
used to protect the delay-sensitive secret messages.
The working is as follows:
Each group is identified or denoted by a single
member (character) of that group. Now, the generated
CB may look like Table-1. Fig. 3 : Packet format for CB
Let us suppose that “HELLO” is the message,
and then it is coded as: Fig.3.Packet that contains CB and is
• H is coded as Z1, since „H‟ belongs to the encapsulated using WEP encryption and sent to the other
group that is having a group code. „Z‟ and „H‟ is in 1st party. Then the communication begins.
position from right.
IV BEAM FORMING AND FEEDBACK
METHODOLOGY:
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4. ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 3, May 2012
VI. DISCUSSIONS:
A. Effect Of Codebook Size:
If the codebook size increases, then the chosen codeword A. Secrecy Outage Probability:
q will be closer to the naive beam forming vector. For
large 𝑁, the value of 𝛿 is dominated by the term Equal noise power received at both d and e
receivers. For codebook beam forming, we use a MISO
Max ∣⟨c 𝑖, c 𝑗 ⟩∣2 (16) system with M = 4 transmit antennas. We apply two
𝑖, 𝑗, 𝑖≠ 𝑗. different codebooks for this system.. Fig. 5 presents the
secrecy outage probability with different number of
For any given codebook with 𝑁 ≥ 𝑀s, receive antennas at Attacker. The simulation also shows
max ∣⟨c 𝑖, c 𝑗 ⟩∣ can be lower bounded as the performance of another non-security centric
𝑖, 𝑗, 𝑖≠ 𝑗 beamforming strategy - equal gain beamforming strategy
max ∣⟨c 𝑖, c 𝑗 ⟩∣≥ max{√ ( 𝑁 – 𝑀s)/( 𝑁 -1) 𝑀s, probability with
1 − 2 𝑁− 1/( 𝑀s−1)} (17)
𝑖, 𝑗, 𝑖≠ 𝑗
1.2
R=0.5b/sHz, P b=Pe=20dB,
where, for large value of 𝑁, the bound is dominated by Mt=4
Secracy outage probability
the second term. As 𝑁 →∞, this lower bound becomes 1 8, 1
Equal gain
max ∣⟨c 𝑖, c 𝑗 ⟩∣ ≥ 1 − 2 𝑁− 1/ 𝑀s−1 →1 0.8
beamfor
𝑖, 𝑗, 𝑖≠ 𝑗 0.6 ming
Therefore, 𝛿 → 1 for large 𝑁 and hence as 𝑁 →
∞, That is, for large 𝑁, the secrecy outage probability 𝑃cb 0.4 LB(Naïve
so approaches the secrecy outage probability 𝑃nb so from Beamfor
naive beam forming. 0.2 ming)
0 UB(N=8)
CODE BOOK
MESSAGE
ALGORITHM
0 5
Me 10
CIPHER (USING Fig .5 Comparison of secrecy outage probability
CB)
between naive beamforming
increasing SNR, where we kept the number of transmit
WEP ALGORITHM FINAL CIPHER antenna at User1 fixed to Me = 4. The simulation is
performed for target secrecy rate of R = 0.5 b/s/Hz when
Fig. 4 :Encoding method Pb = Pe = 20 dB. It can be seen that at very low SNR,
the secrecy outage probability is close to 1, here we
B. Positive Secrecy cannot expect any secrecy when the channel condition is
Positive secrecy is achievable when 𝑅 𝑏 ≥ 𝑅 𝑒. In very poor. At moderate to high SNR, the secrecy outage
terms of secrecy outage probability, probability increases with an increase in the number of
receive antennas at e, which is expected. The simulation
Prob [ 𝑅d ≥ 𝑅 𝑒] = 1 – 𝑃nbso ( 𝑅 = 0, 𝑃) ≥ 0. result presented in Fig. 6 shows the effects of increasing
both the number of transmit antennas at s, and the
Using Eq, we now have number of receive antennas at e on the secrecy outage
probability. The simulation is performed for Pe = Pb =
Prob [ 𝑅d ≥ 𝑅 𝑒] = 1 – 𝑃nb so (0, 𝑃) 20 dB for a target secrecy rate R = 2 b/s/Hz. The
= 1−1/Γ ( 𝑀 𝑒) ∫ Γ ( 𝑀 𝑒, 𝜏 𝛼) 𝑓𝛼 ( 𝛼) 𝑑𝛼 simulation is performed for different value of Me.
= 1−1/Γ ( 𝑀 𝑡) (1+ 𝜏) 𝑀𝑡 𝑀𝑒−1Σ 𝑘=0 ( 𝜏/(1 An interesting observation is that for a ≤ 4.2,
+ 𝜏) ) 𝑘 Γ ( 𝑘 + 𝑀 𝑡 − 1)/Γ ( 𝑘 + 1) secrecy outage probability increases with an increasing
Me, while for a ≥ 4.2, secrecy outage probability actually
This means that the additional gain in secrecy decreases with an increasing Me. It shows that, when a is
probability due to naive beam forming decays large, a change in Me also means many more transmit
exponentially with the number of received antennas antennas.
employed at Attacker. In practical cases, it is not We have performed additional simulation for
possible to estimate the number of receive antennas different values of SNR and target secrecy rate, and
Attacker uses. Therefore, we focus on the case of observed that the cross-off point as seen in Fig. 6 is a
Attacker with very large number of antennas and function of both SNR and target rate. Fig. 5 also shows
investigate the effect of different number of transmit the secrecy performance when the codeword
antennas in this situation. corresponding to CDI is used as beam forming vector.
When the attacker channel information at source is
accurate (i.e. low 𝜎𝑒), However, for high value of 𝜎𝑒,
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5. ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 3, May 2012
beam forming in the direction of destination provides REFERENCES:
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Authors profile:
R.Raicheal received B.E Electronics and communication
Fig.6 Effect of received SNR on secrecy outage Engineering in the year 2010. Currently doing M.E
probability for different values of Pb. Here, received Communication systems Engineering.
SNR of both Bob and Eve are assumed to be same,
VII. CONCLUSION: C.Arunachala Perumal received B.E Electronics and
In this work, we have analyzed the performance communication Engineering in the year 1997.Pursed M.E
of codebook based beam forming transmission with the degree in 2004 and completed MBA Production
management in 2005 MPhil in Management in 2007.
help of finite bit receiver feedback in a security setting. Currently working as Assistant professor.
We presented the naive beam forming scheme in the
direction of the intended receiver in presence of multi-
antenna attacker.In this paper we study the MIMO wire-
tap channel when there are stringent delay constraints
and short-term power constraint. First, we study no CSIT
case with isotropic Gaussian codebook. Our results show
that the eavesdropper decreases the degrees of freedom
in the direct link, min{m,n}, by the degrees of freedom in
the source-eavesdropper channel, min{m,k}. Therefore,
if k ≥ m, then no degrees of freedom is left. Otherwise,
the secret DMT is equivalent to that of a (m − k) × (n −
k) MIMO without secrecy constraints. In this paper when
there is CSIT, we assumed the source knows both the
main channel CSI and the eavesdropper channel CSI to
find the fundamental limits.
ACKNOWLEDGMENT
I thank Jesus almighty for extending my
opportunity to do this work and I thank everyone who
supported me internally and externally for doing this
work. I forward my thanks to my parents and director,
chairman, principal, HOD, Guide for boosting my talents
to do this work.
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