Page 158 - Proceedings of the 2017 ITU Kaleidoscope

2017 ITU Kaleidoscope Academic Conference

where P b is a constant basic power consumed by CBS.
6-*0/"5-003.
The SEE of interest in this paper can be represented as [15]
40)3(+3(30,3/"5-003. "! R sec(P c , P z )
"!
η SEE = , (9)
P tot (P c , P z )
7*(3)-8/"5-003.
which evaluates the number of available secret bits transfered
!
!
from the transmitter to receiver per unit energy and band-
width.
%&
%&
"#$
"#$ We formulate an optimization problem to maximize SEE of
'()*+*,*-./01*23 the cognitive transmission under the constraints of the total
transmit power, the SR of CU and the QoS requirement of
PU, namely,
Figure 1. System model for secure communication in CRN.
log (1 + γ c ) − log (1 + γ e )
max η SEE = 2 2 (10a)
fidential and AN signal, respectively. Denote by h c ∈ C N×1 , P c ,P z P c + P z + P b
h p ∈ C N×1 and h e ∈ C N×1 the fading coefficients of the s.t. γ p ≥ γ p th (10b)
channel between CBS to CU, PU and ED, respectively. The log (1 + γ c ) − log (1 + γ e ) ≥ 0 (10c)
2
2
received signals at the PU, CU and ED can be expressed as
0 ≤ P c + P z ≤ P max , (10d)
CBS
H
H
y p = h v c x c + h v z z + n p , (1) th
p p where γ in (10b) denotes the minimal acceptable SINR for
p
the PU, (10c) specifies the minimum SR requirement, and
H
H
y c = h v c x c + h v z z + n c , (2) max
c c P in (10d) means a limit on the amount of the transmit
CBS
H
H
y e = h v c x c + h v z z + n e , (3) power for the CBS.
e
e
2
2
where n p ∼ CN(0, σ ), n c ∼ CN(0, σ ) and n e ∼
c
p
2
CN(0, σ ) denote additive white Gaussian noises (AWGN) 3. OPTIMAL SOLUTION TO SEE MAXIMIZATION
e
at PU, CU and ED, respectively, with the same variance
2
2
2
2
σ = σ = σ = σ = ∆fN 0 , where ∆f and N 0 are the In this section, we first design the normalized BF vector v c
p c e H
system bandwidth and single-sided noise spectral density, in the null space of h p , namely h v c = 0, which ensures
p
respectively. that all confidential signals would not interfere with PU, so
v c is given by [16],
Based on (1)-(3), the output signal-to-interference-plus-noise
ratios (SINRs) at PU, CU and ED can be, respectively, writ- ⊥
(I N − h )h c
p
ten as v c =
⊥
, (11)
2
(I N − h )h c
H p F
h v c P c

p
2 , (4) ⊥ H −1 H
γ p =
H 2 p where h p = h p (h h p ) h p is the orthogonal projection
h v z P z + σ
p
p
matrix of h p , I N the N × N identity matrix, and k·k the
2 F
H

h v c P c
γ c = c 2 , (5) Frobenius norm of a matrix or Euclidean norm of a vector.
H
|h v z | P z + σ 2 Meanwhile, v z is designed at the null space of h p and h c to
c c

H 2 guarantee that the artificial noise only degrades the channel
h v c P c
γ e = e 2 . (6) condition of eavesdropper. Then, a power allocation algo-
H
|h v z | P z + σ 2 e rithm is proposed to find the optimal solution of P c and P z .
e
According to (5) and (6), the available SR of the considered By substituting (11) into (10), we can obtain
CRN can be obtained as [13]
log (1 + cP c 2 ) − log (1 + eP c 2 )
2
2
+ max η SEE = dP z +σ c fP z +σ e

1 + γ c P c ,P z P c + P z + P b
R sec(P c , P z ) = log 2
1 + γ e (12a)
cP c eP c
 +
H 2 2
 2 s.t. log (1+ )−log (1+ ) ≥ 0 (12b)
|h c v c| P c (7) 2 2
1 + dP z + σ c fP z + σ e
H 2 2
 ,
= log 2 |h c v z | P z +σ c  0 ≤ P c + P z ≤ P max , (12c)

2
H
1 + |h e v c | P c CBS
2
H
|h e v z | P z +σ e 2 2 2 2
H
H
H
where a = h v c , b = h v z , c = h v c , d =
c
p

p

2
H

where [·] + is a function such that [x] + = x if x > 0 and H 2 H 2 and f = h v z .
h v z , e = h v c
c

e
e
+
[x] = 0 if x ≤ 0. Combining with the objective function (12a) and constrain-
Besides, the total power consumption at the CBS is given by t conditions (12b)-(12c), we can readily show the non-
[14] convexity of (12) due to its fractional form and logarith-
P tot (P c , P z ) = P c + P z + P b , (8) mic function. It is thus challenging to solve a non-convex
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