Sina Rezaei Aghdam under supervision of : Prof. Tolga M. Duman - PowerPoint PPT Presentation

Sina Rezaei Aghdam under supervision of : Prof. Tolga M. Duman Dept. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey.

Physical Layer Security • Securing the communications at the physical layer; an alternative to the conventional higher network-layer solutions for security • Basic principle: to exploit the randomness of communications channels to allow a transmitter to deliver its message to an intended receiver while guaranteeing that a third party cannot maliciously infer any information about the transmitted message. 1 • The attempt is to realize a transmission in such a way H y so as to maximize the transmission rate over the main 2 B 1 channel while keeping the eavesdropper ignorant 2 about the message. N t Bob • Secrecy Capacity: The rate at which transmitter can use the main link M so as to deliver its message to the legitimate receiver Alice 1 H in a way that the eavesdropper cannot successfully x E decode the same information . 2 z N e     max ( ; | ) ( ; | ) C I x y H I x z H Eve s B E ( ) P x X Input Mutual information Mutual information 2 distribution over Bob’s channel over Eve’s channel

Space Shift Keying (SSK) 00 0 1 11 10  … 01001110 … 01, 00, 11, 10 m  A recently proposed transmission scheme for low-complexity implementation of MIMO wireless systems  Takes advantage of the location-specific property of the wireless channel  Channel coefficients are playing the role of the “modulation unit“  Each data block is mapped to a symbol x j which is then transmitted from the j ’ th antenna.  With the knowledge of the channel state information (CSI), receiver can detect the activated channel and accordingly detect the transmitted data.  Spatial modulation (SM) is a more general form of SSK in which a conventional amplitude or phase modulation symbol is m  ˆ 10 spatially modulated (similar to the SSK) 3

Physical Layer Security for SSK • To obtain an achievable secrecy rate for SSK as      ( ; | ) ( ; | ) C R I x y H I x z H 1 s B E S  ( ) P x X M we first obtain the mutual information for SSK as: 2     2  exp( / ) 1 M M y h H ( , ,..., )   h h h    2   2 m n ( ; | , ,..., ) exp( / ) log I x y h h h y h dy B 1 2 M  b b b 1 2  M 2 m n M M    2    2 m 1 n exp( y h / )  H ( , ,..., ) y h h h   m n E 1 2 M  e e e 1 m CN h   2 P ( | , y x h ,..., h ) ( , ) Y XH | 1 M m n     1  2 ( , ) ( , | ,..., ) CN h y h n P x y h h   | 1 2 XY H M m n M   2 m d n n  1 M        ij P ( | x h ,..., h ) ( ; | , ,..., ) log log(1 exp( ) I x y h h h M E X H | 1 M 1 2 2 ( , , )    M x y H 2    j i n 1 M     ( | , ,..., ) P y x h h P ( | y h ,..., h ) where d h h Y XH | 1 m | 1 Y H m M  ij i j m 1 Precoding With an assumption that the perfect CSI of the main channel is available at the transmitter, an - Transmission rate is maximized over the main channel. appropriate precoding can be applied so as to - No gain from the eavesdropper’s perspective. maximize 4 d ij

Numerical Results Legitimate receiver’s SNR is varied while the eavesdropper’s SNR is fixed to 0 dB. Scatter plot Precoded SSK Symbols 1.4 1.4 1.5 Non-precoded SSK Symbols For A Given Channel Coefficients 1.2 1.2 1 non-precoded, N t = 2 precoded, N t = 2 1 non-precoded, N r = 4 1 non-precoded, N t = 4 0.5 precoded, N r = 4 precoded, N t = 4 Secrecy Rate (bits/s/Hz) Quadrature non-precoded, N r = 1 Secrecy Rate 0.8 0.8 precoded, N r = 1 0 -0.1853 - 0.6924i 0.6 0.6 -0.5 0.0162 - 0.5879i 0.4 0.4 -0.1853 - 0.6924i -1 0.2 0.2 0.2476 - 1.2376i -1.5 0 0 -1.5 -1 -0.5 0 0.5 1 1.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 SNR (dB) In-Phase SNR (dB) Effect of number of transmit antennas Effect of number of receive antennas An Example for Precoding on the achievable secrecy rates on the achievable secrecy rates -3 a) SNR @ Eavesdropper = 0 dB b) SNR @ Eavesdropper = 12 dB c) SNR @ Eve = 21 dB 1 x 10 1.8 0.07 MIMO, N t = 4 MIMO, N t = 4 0.9 1.6 Legitimate receiver’s SNR is varied while the SM, N t = 4 SM, N t = 4 0.06 0.8 SIMO, N t = 1 SIMO, N t = 1 1.4 eavesdropper’s SNR is fixed to 0 , 12 and 21 dB. Secrecy Rate (bit/s/Hz) 0.05 0.7 1.2 0.6 0.04 1 0.5 SM is capable of achieving a better secrecy rate with respect to 0.8 0.03 0.4 a single-antenna transmission. However, there is a gap between 0.6 0.3 the secrecy rates of SM and a general MIMO system in which all 0.02 MIMO, N t = 4 transmit antennas are activated in each time instant. 0.4 0.2 SM, N t = 4 0.01 0.2 SIMO, N t = 1 0.1 5 0 0 0 0 10 20 30 0 10 20 30 0 10 20 30 SNR (dB) SNR (dB) SNR (dB)

Conclusion  Derivation and evaluation of the secrecy capacity is one of the fundamental problems for physical layer security using which we can quantify the maximum rate at which a transmitter can send a message to an intended receiver without being decoded by an eavesdropper.  An achievable secrecy rate, i.e. a lower bound on the secrecy capacity, was derived and evaluated for SSK which is a recently proposed wireless transmission scheme for low-complexity implementation of MIMO wireless system.  A precoding scheme which maximizes the minimum Euclidean distance was proposed and the performance improvement achieved by that was evaluated for different number of transmit and receive antennas.  The framework proposed in this poster can serve as a basis for future studies on SSK in context of secure wireless communications. [1] S. R. Aghdam, T. M. Duman, M. Di Renzo, “On Secrecy Rate Analysis of Spatial Modulation and Space Shift Keying,” submitted to IEEE BlackSeaCom 2015. [2] S. R. Aghdam, T. M. Duman, “Physical Layer Security in MIMO Wiretap Channels: A Survey References on Secrecy with Imperfect Channel State Information,” submitted to IEEE Commun. Mag. [3] M. Di Renzo, H. Haas, and P. M. Grant, Spatial modulation for multiple antenna wireless systems – A survey, IEEE Commun. Mag. , vol. 49, no. 12, pp. 182-191, Dec. 2011. 6