Trends in Digital Signal Processing

May 29, 2015 16:1 PSP Book - 9in x 6in 15-Yong-Ching-Lim-c15

466 Multiple Antennas for Physical Layer Secrecy

Proposition 15.1 When both H

R

and H

E

are perfectly known, the

secrecy capacity of the MIMO wiretap channel is defined as

C

s

 max

Q0, Tr(Q)≤1

C

s

(Q), (15.4)

where

C

s

(Q) = log det(I + ρH

R

QH

†

R

) − log det(I + ρH

E

QH

†

E

) (15.5)

and ρ = P /σ

2

.

For a general MIMO channel, finding C

s

via a polynomial time

algorithm is still an open problem and requires a global optimization

technique such as the branch-and-bound algorithm (Liu et al., 2009).

15.3.1 Conditions for Positive Secrecy Capacity, Convexity,

and Solution

An important question is when the secrecy capacity ...