secrecy in multiuser wireless communications: flirting with

Outline Introduction System Model Performance Upper Bounds Imperfect CSIT Ongoing Research

Secrecy in Multiuser Wireless Communications:Flirting with Many Girls or Boys at the Same

Time

Giovanni Geraci and Jinhong Yuan

Feb 18, 2013

Jinhong Yuan:

Secrecy in Multiuser MISO Wireless Communications


Outline

Introduction: Physical Layer Security

System Model and Proposed Scheme

Performance

Upper Bounds

Imperfect Channel State Information

Ongoing Research

Jinhong Yuan:



Security in Wireless Networks

I Security is crucial for wireless communications:users rely on wireless devices to transmit sensitive data.

I Due to the broadcast nature of the physical medium,every node in the network is a potential eavesdropper.

Jinhong Yuan:



Classical Cryptography

I Symmetric key: a secret key must be distributed

Jinhong Yuan:



Classical Cryptography

I Asymmetric key:the eavesdropper must have limited computational power

Jinhong Yuan:



Physical Layer Security

I Physical layer security exploits the randomness of the channel

I No secret key is needed

I Even an eavesdropper with unlimited computational powercannot extract any information from the received signal

I How? Example:

I Eavesdropper’s channel is noisier than the intended receiver’s

I Message is encoded in such a way that the intended receivercan recover it, but the eavesdropper cannot

I Some of the bits are used to “confuse” the eavesdropper

Jinhong Yuan:



Secrecy Rates

I The secrecy rate is the rate at which:

I The message is transmitted reliably to the intended user

I No information is leaked at the eavesdropper

I The secrecy rates achievable in multi-user networks withpractical transmission schemes remain an open problem.

Jinhong Yuan:



Code construction: random binning

I Generate a message m out of 2nR possible messages.

I Associate m to a bin of size 2nR′, and select a message m′

inside the bin. Transmit the codeword (m,m′).

I If Cm are Ce are capacities to intended user and eavesdropper,then choose R + R ′ < Cm and R ′ > Ce ⇒ R < Cm − Ce .

Jinhong Yuan:



Code construction: random binning

I The intended receiver can correctly decode

I The eavesdropper can decode within each bin,but he cannot distinguish between different bins!

Jinhong Yuan:



Outline



Performance

Upper Bounds


Ongoing Research

Jinhong Yuan:



Multi-User MIMO with Malicious Users

How do we define the secrecy rates for this scenario?

Jinhong Yuan:



Worst-case Scenario

I The BS cannot predict the behavior of the users. We assumethat users can cooperate to jointly eavesdrop on other users.

I Worst-case for message uk : the K − 1 unintended users forman alliance k and jointly eavesdrop on user k.

Jinhong Yuan:



Worst-case Scenario

I Secrecy rate Rs,k : reliable transmission to user k without

allowing k to obtain any information about uk .

I The secrecy sum-rate is given by Rs =∑K

k=1 Rs,k .

Jinhong Yuan:



System Model

One Base Station (BS) with M transmit antennas serves Ksingle-antenna users. The vector of received signals y is given by

y = Hx + n

where

I x = 1√γWu is the vector of transmitted signals

I W = [w1, . . . ,wK ] is the linear precoding matrix

I H = [h1, . . . ,hK ]† is the Rayleigh fading channel matrix

I n is complex Gaussian noise with E[nn†]

= σ2I

I ρ = 1σ2 is the SNR.

Jinhong Yuan:



Equivalent MISOME wiretap channel

I Each user k, with its own eavesdropper k and the transmitter,forms an equivalent MISOME wiretap channel[1]

I The eavesdropper k can cancel interference from uj , j 6= k

[1] A. Khisti and G. Wornell, ”Secure transmission with multiple antennas I: The MISOME wiretap channel,” IEEETrans. Inf. Theory, vol. 56, no. 7, pp. 3088−3104, Jul. 2010.

Jinhong Yuan:



Equivalent MISOME wiretap channel

I For the k-th MISOME with linear precoding we obtain[2]

Rs,k = log2

(1 + SINRk

)− log2

(1 + SINR

k

)[2] I. Csiszar and J. Korner, ”Broadcast channels with confidential messages,” IEEE Trans. Inf. Theory, vol. 24,no. 3, pp. 339−348, May 1978.

Jinhong Yuan:



Secrecy sum-rates

I The secrecy sum-rate achievable by linear precoding is

Rs =K∑

k=1

[log2

(1+

∣∣∣h†kwk

∣∣∣2γσ2 +

∑j 6=k

∣∣∣h†kwj

∣∣∣2︸︷︷︸SINR term

)−log2

(1+

∑j 6=k |h

†jwk |2

γσ2

︸︷︷︸leakage term

)]

I We need to choose the precoding matrix W = [w1, . . . ,wK ]

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Regularized Channel Inversion

I RCI precoding is better than plain CI, particularly at low SNR

W = H†(HH† + αIK

)−1

I We look for the αopt that maximizes

Rs =K∑

k=1

[log2

(1+

∣∣∣h†kwk

∣∣∣2γσ2 +

∑j 6=k

∣∣∣h†kwj

∣∣∣2)−log2

(1+

∑j 6=k |h

†jwk |2

γσ2

)]

I We study the RCI precoder in the large-system regime:M,K →∞, with their ratio β = K/M being held constant.

Jinhong Yuan:



Proposed SchemeTransmitted signal generated as x = Wu, where

W =

1√γH

H(HHH + MξIK

)−1for β ≤ 1

1√rγ

(HHH + MξIM

)−1HH for 1 < β < 2

0 for β ≥ 2

ξ =−2ρ2 (1− β)2 + 6ρβ + 2β2 − 2 [β (ρ+ 1)− ρ] ·

√· · ·

6ρ2 (β + 2) + 6ρβ

ρ is the transmit SNRβ = K/M is the number of users per antenna

r = max

(ρ

K log2β2

4(β−1)

, 1

)is a power reduction constant.

Jinhong Yuan:



Outline



Performance

Upper Bounds


Ongoing Research

Jinhong Yuan:



Achievable Secrecy Sum-Rate

We showed that an achievable secrecy sum-rate for our scheme is

Rs (H) =K∑

k=1

log2

1 +ρ|hHk wk |2

1+ρ∑

j 6=k |hHk wj |2

1 + ρ∥∥H

kwk

∥∥2

+

We study Rs in the large-system regime (Random Matrix Theory):

I M,K →∞I The ratio β = K/M is held constant

Jinhong Yuan:



Large-System Analysis

In the large-system regime

R◦s = K

log2

1 + g (β, ξ)ρ+ ρξ

β[1+g(β,ξ)]2

ρ+[1+g(β,ξ)]2

1 + ρ

(1+g(β,ξ))2

+

with

g (β, ξ) =1

2

sgn(ξ) ·

√(1− β)2

ξ2+

2 (1 + β)

ξ+ 1 +

1− βξ− 1

Jinhong Yuan:



Asymptotic Sum-RatesFor large SNR, the secrecy sum-rate Rs simplifies to

Rs ≈

K log2

1−ββ + K log2 ρ for β < 1

K2 log2

2764 + K

2 log2 ρ for β = 1

3K log2ββ−1 − K log2 ρ for β > 1

whereas the sum-rate R without secrecy is[3]

R ≈

K log2


K2 log2 ρ for β = 1

K log2ββ−1 for β > 1.

[3] V. Nguyen and J. Evans, ”Multiuser transmit beamforming via regularized channel inversion: A large systemanalysis,” in Proc. IEEE Global Commun. Conf. (GLOBECOM), Dec. 2008, pp. 1 4.

Jinhong Yuan:



Asymptotic Sum-RatesFor large SNR, the secrecy sum-rate Rs simplifies to

Rs ≈

K log2


K2 log2

2764 + K

2 log2 ρ for β = 1

3K log2ββ−1 − K log2 ρ for β > 1

whereas the sum-rate R without secrecy is

R ≈

K log2


K2 log2 ρ for β = 1

K log2ββ−1 for β > 1.

I For β < 1 secrecy can be achieved at no costI For β = 1 secrecy can be achieved at a cost of less than 4dBI For β > 1 the secrecy requirements result in a poor sum-rate

Jinhong Yuan:



Simulations vs Large-system analysis

0 5 10 15 200

1

2

3

4

ρ [dB]

Per-antennasecrecysum-rate

Simulations, M = 10

Simulations, M = 20

Simulations, M = 40

Large-system analysis

β = 0.8

β = 1.2

β = 1

The analysis is accurate even for finite-size systems

Jinhong Yuan:



Outline



Performance

Upper Bounds


Ongoing Research

Jinhong Yuan:



Upper Bounds

We consider two upper bounds:

I Sum-rate R without secrecy requirementsI The gap R − Rs represents the secrecy lossI i.e. the loss due to the secrecy requirements

I Secrecy capacity Cs,SU of a single-user systemI The gap Cs,SU − Rs represents the multi-user lossI i.e. the loss due to the requirement of serving multiple users at

the same time

Jinhong Yuan:



Cost of Secrecy in Multi-User Systems [bits]

Users per antenna Secrecy Loss Multi-User Loss

β < 1 0 ∼ 0

β = 1 0.62 0.62

1 < β < 2 2− log2 β 2− 2 log2 β

β ≥ 2 log2ββ−1 0

Jinhong Yuan:



Proposed Scheme vs Upper Bounds

0 5 10 15 20 250

2

4

6

8

ρ [dB]

Per-userrate

Proposed scheme

Upper bound (no secrecy)

Upper bound (single user)

β = 1

β = 1.2

β = 0.8

No multiplexing gain loss!

Jinhong Yuan:



Outline



Performance

Upper Bounds


Ongoing Research

Jinhong Yuan:



Imperfect CSIT

H = H + E, var(hij

)= 1− τ2, var(eij) = τ2

τ2 can significantly degrade Rs , especially at high SNR.

Jinhong Yuan:



Secrecy Sum-Rate under Imperfect CSIT

In the large-system regime

R◦s = K

log2

1 + g(β, ξ)ρ+ ξρ

β [1+g(β,ξ)]2

ρ+[1+g(β,ξ)]2

1 + ρ

[τ2 + 1−τ2

(1+g(β,ξ))2

]

+

with

ρ4=ρ(1− τ2

)ρτ2 + 1

and ξ4=

ξ

1− τ2

Jinhong Yuan:



Minimum Required CSIT quality

I For β ≤ 1, a CSI distortion τ2 = Cρ , with

C =

{12

(√4b − 3− 1

)for β < 1

23

(√3b − 2− 1

)for β = 1

produces a high-SNR rate gap of log2 b bits.

I For β > 1, if limρ→∞ τ2 = 0,

then the high-SNR rate gap is zero.

Jinhong Yuan:



Simulations

0 5 10 15 200

1

2

3

4

5

ρ [dB]

Per-usersecrecyrate

τ2 = 0

τ2 = Cρ , C for log2 b = 1

β = 1.2

β = 1

β = 0.8

Jinhong Yuan:



Outline



Performance

Upper Bounds


Ongoing Research

Jinhong Yuan:



Ongoing Research

Jinhong Yuan:



Imperfect CSIT in FDD and TDD systems

I We want a constant rate gap, compared to the case withperfect CSIT (no multiplexing gain loss)

I In a Frequency Division Duplex (FDD) system:I How many feedback bits are required by each user?

I In a Time Division Duplex (TDD) system:I How much channel training is required by each user?

Jinhong Yuan:



SDoF under Hybrid CSIT

Transmission scheme that achieves the optimal SDoF region?

Jinhong Yuan:



Acknowledgements (in alphabetical order...)

I Dr. Iain B. CollingsCSIRO ICT Centre, Sydney, Australia

I A/Prof. Romain CouilletDept. of Telecommunications, Supelec, Gif-sur-Yvette, France

I Prof. Merouane DebbahAlcatel-Lucent Chair on Flexible Radio, Supelec, Gif-sur-Yvette, France

I Malcolm EganUniversity of Sydney, Australia

I A/Prof. Mari KobayashiDept. of Telecommunications, Supelec, Gif-sur-Yvette, France

I A/Prof. Adeel RaziNED University of Engineering and Technology, Karachi, PakistanUniversity College London

Jinhong Yuan:



PublicationsConference Proceedings

I G. Geraci et al., “Secrecy sum-rates for multi-user MIMO linearprecoding,” Proc. IEEE ISWCS, 2011

I G. Geraci et al., “Large system analysis of the secrecy sum-rates withregularized channel inversion precoding,” Proc. IEEE WCNC, 2012.

Journal PapersI G. Geraci et al., “Secrecy sum-rates for multi-user MIMO regularized

channel inversion precoding,” IEEE Trans. on Commun., November 2012I G. Geraci et al., “Large system analysis of linear precoding in MISO

broadcast channels with confidential messages”, IEEE JSAC, 2012,submitted.

Book ChaptersI G. Geraci and Jinhong Yuan, “Physical Layer Security for Multiuser

MIMO Communications,” InTech Publisher, 2012, submitted.

In PreparationI G. Geraci et al., “Secrecy Sum-Rates with Regularized Channel Inversion

Precoding under Limited Feedback”, for IEEE ICASSP, 2012.

Jinhong Yuan:



Thank you!

Jinhong Yuan:


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