On the performance of cooperative cognitive networks with selection combining and proactive relay selection

UR ,
j  J 
~ (0, )jDp jDph CN
jUR and UD ,
j  J 
1 1~ (0, )SD SDh CN
US and UD 
Notation Channel coefficient between 
2 2~ (0, )jL jLh CN
jUR and L R ,
j  J 
Using (1) to rewrite (2) and (3) as 
2
1
1 1 1 1 1 1
ˆ 1LL
LL L LL L SL S L
hy x x h x n 
 

    (4) 
2
1
1 1
1 1 1 , 
ˆ 1
{ , }
Sl
Sl S Sl S
Ll L l
hy x x
h x n l D


 

 
   J
 (5) 
which result in the signal-to-interference plus 
noise ratio (SINR) at the licensed receiver and the 
unlicensed receivers in the phase 1 as 
 
2
1
1 22 2 2
1 1 0
ˆ
1
LL L
LL
LL L SL S
h P
P h P N   
 
  
 (6) 
 
2
1
1 22 2 2
1 1 0
ˆ
1
 , { , }
Sl S
Sl
Sl S Ll L
h P
P h P N
l D
   
 
  
 J
 (7) 
This paper analyzes the outage performance 
of the proactive relay selection in cooperative 
cognitive networks. According to the proactive 
relay selection criterion, the selected relay 
bUR 
is the one that obtains the largest end-to-end 
SINR, i.e. 
 1 2arg max min ,Sj jDjb   J (8) 
where 
2jD is the SINR of the signal received at 
UD from jUR in the phase 2. This signal can be 
represented in the same form as (5), i.e. 
2
2
2 2
2 2 2 
ˆ 1jD
jD j jD j
LD L D
h
y x x
h x n


 

 
 
 (9) 
where jJ , xL2 is the signal transmitted by LT 
with the power PL, and xj is the signal transmitted 
SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 
Trang 32 
by 
jUR with the power Pj . As such, 2jD can be 
computed in the same way as (7), i.e. 
 
2
2
2 22 2 2
2 2 0
ˆ
1
jD j
jD
jD j LD L
h P
P h P N   
 
  
(10) 
In the phase 2, LR also receives the desired 
signal from LT and the inference signal from 
bUR . Therefore, the SINR at LR in the phase 2 
can be expressed in the same form as (6), i.e. 
 
2
2
2 22 2 2
2 2 0
ˆ
1
LL L
LL
LL L bL b
h P
P h P N   
 
  
 (11) 
To recover the source information with low 
implementation complexity, both signals received 
from US and 
bUR can be selection-combined at
UD , which results in the total SINR at UD as 
  1 1 2max ,max min ,tot SD Sj jDj    J 
(12) 
3. POWER ALLOCATION FOR 
UNLICENSED USERS 
To guarantee QoS for LUs [10], the power of 
unlicensed transmitters must be properly allocated 
to meet the licensed outage constraint. To this 
effect, the transmit powers of US and 
bUR must 
be limited to satisfy the following two licensed 
outage constraints, correspondingly: 
  
12 1
Pr log 1 ( )
LLLL L L
F      
(13) 
  
22 2
Pr log 1 ( )
LLLL L L
F      
(14) 
where Pr{X} stands for the probability of the 
event X, 2 1LL    with L being the required 
transmission rate in the licensed network, FX(x) 
signifies the cumulative distribution function 
(cdf) of X, and  is the required outage probability 
of LUs. 
Moreover, unlicensed transmitters (i.e., US 
and 
bUR are constrained by their designed 
maximum transmit powers (i.e., PSm and Pbm). 
Therefore, the transmit powers of US and 
bUR 
are also upper-bounded by PSm and Pbm, 
respectively, i.e. 
S SmP P (15) 
b bmP P (16) 
Theorem: For the maximum transmission 
range, the transmit power of a unlicensed user 
that satisfies both the licensed outage constraint 
and the maximum transmit power constraint is 
given by 
 
2
2 0
1
2
1
1
min 1 ,
L
L LLp
L LLp
k kmN
L kLp P
P
P P
e

 

 
  


 
   
 
 
 
  
      
  
  
  

L
 (17) 
where [x]+ denotes max(x, 0) and the phase 1 
corresponds to (k, p) = (S, 1) while the phase 2 
corresponds to (k, p) = (b, 2). 
Proof: The proof for (k, p) = (S, 1) is 
presented, which is straightforwardly extended to 
(k, p) = (b, 2) for completing the whole proof of 
Theorem. 
Let 2
1
ˆ
LL LX h P and 
  22 2 21 1 01 LL L SL SY P h P N       . 
Since  1 1ˆ ~ 0,LL LLh CN and 
 1 1~ 0,SL SLh CN , the probability density 
function (pdf) of X and the pdf of Y, 
correspondingly are given by 
  1
1
1 , 0L LL
x
P
X
L LL
f x e x
P



  (18) 
TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 
 Trang 33 
 
2
1
2
1
1 ,S SL
x u
P
Y
S SL
f x e x u
P
 
 


  (19) 
where  2 21 01 LL Lu P N     . 
Given 
1 /LL X Y  in (6), it immediately 
follows that 
     
1
0
L
LL
y
L X Y
u
F f x dx f y dy




 
  
  
  (20) 
Substituting (18) and (19) into (20) and 
performing simplifications, one obtains the 
closed-form expression of  
1LL L
F  as 
 
1
1
1
2
1 1
1
L LL
LL
L LL
L
L LL L S SL
P eF
P P
 

   

   
 (21) 
where 2 2
1 0 11 /LL L L LN P      . 
Using (21), we deduce PS that meets (13) as 
1
1
2
1
1
1
L LL
L LL
S
L SL
P eP
 
   
 
   
 (22) 
When 1 1L LLe      , the right-hand side of 
(22) becomes negative. As such, the constraint in 
(13) is equivalent to 
1
1
2
1
1
1
L LL
L LL
S
L SL
P eP
 
   
 
   
 (23) 
Finally, combining (23) with (15) results in 
1
1
2
1
min 1 ,
1
L LL
L LL
S Sm
L SL
P eP P
 
   
  
      
 (24) 
To maximize the communication range, the 
equality in (24) must hold, and hence, PS is 
reduced to (17) for (k, p) = (S, 1), completing the 
proof. 
1 Due to the two-phase nature of the proactive relay selection, 
S is related to the required transmission rate, S, in the 
unlicensed network as 22 1SS
   . 
4. OUTAGE ANALYSIS 
This section presents a formula of outage 
probability, which is defined as the probability 
that the total SINR is below a predefined 1 
threshold S, i.e. 
 
  

 
1
1 1 2
1
Pr
Pr max , max min ,
Pr
tot S
SD Sj jDj
S
SD S
OP 



  
   

   
J
M
  
2
1 2Pr max min ,Sj jD Sj    J
M
 (25) 
Before presenting closed-form expressions of 
1M and 2M for completing the analytic evaluation 
of (25), we introduce the cdf of 
1S l where 
{ , }l D J . Similarly to (21), one obtains the cdf 
of 
1Sl as 
  1
1
1
1
1 , 0Sl
Sl
xSl
Sl
GF x e x
x G

   
 (26) 
where 2
1 1 1/Sl S Sl L LlG P P   and
2 2
1 0 11 /Sl S SlN P      . 
It is seen that 
1M is the cdf of 1S D 
evaluated at S, i.e. 
 
11 SD S
F M (27) 
We rewrite 
2M in (25) as 
 

2
2
2 1 2
2
2
maxmin ,Pr
LD
Sj jDh j
S LDh

  

E
J
M
SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 
Trang 34 
 

 
2
2
2
2
1 2
2
2
Pr min ,
1
LD
LD
Sj jDh
j
S LD
j jh
j
h


  

 
  
 





E
E
J
J
Q T
 (28) 
where 
   
11
P r 1
S jj S j S S
F     Q (29) 
 22 2Prj jD S LDh  T 
(30) 
Using (10) to compute 
jT in (30) as 
2
2
2 2
2
L
S jD LD
jD j
P h
P
j e

 

 
   
 
 T (31) 
where Pj has the same form as (17) with 
changing k to j and 
2
2 0
2
2
1jD
jD j
N
P

 

   (32) 
Using the fact that 
   
 
1 2 1 1
1 1 2
1 1 1 1
1 1 1
1
i i
J
j j
j j
J J i J i J
i
j
i w w w w w j
u u
u

 
    
      
   
 
 
    
J J
K
 (33) 
where       1 2, , . . . , iw w wK J J J
2, to 
expand the product in (28), one obtains 
 
 
1 2 1 1
2
1 1 2
1 1 1 1
1 1
1
i i
J
J J i J i J
i
i w w w w w 
    
     
    
    
J
K
M
 (34) 
where  ,C KJ and 
 2
2LD
j jh
j
 
   
 
EC
C
Q T (35) 
2  jJ is the value of the jth element in the J set. 
To complete the derivation of the exact 
closed-form representation of 2M , we firstly 
substitute (31) into (35): 
2
2
2 2
2
2
2
2
2
2
2 2
2
2
L
S jD LD
jD j
LD
LD S L
jD jj S jD
LD
P h
P
jh
j
h P
P
jh
j
e
e e

 



  
 
    
 




 
 
   
  
  
  
  


E
E C
C
C
C
Q
Q
(36) 
Since  2 2~ 0,LD LDh CN , the pdf of 
2
2LDh is   22
2
/
2/LD
LD
x
LDh
f x e   , 0x  . 
Using this fact in (36), one then obtains 
 
2
2 2
2
2
2
2
2 2
2
0
/
20
2
2
2
1
S L
jD jj S jD
LD
S L LD
jD jj S jD
S jD
x P
P
jh
j
x P x
P
j
jLD
j
j
S LD L
j jD j
e f x dx e
ee dx e
e
P
P


  

 
  
 


 



 


  






 








C
C
C
C
C
C
C
Q
Q
Q
 (37) 
Plugging (37) into (34) and then, inserting the 
result together with (27) into (25), one obtains the 
exact closed-form representation of OP. 
5. ILLUSTRATIVE RESULTS 
This section presents various results with 
arbitrary fading powers as  52 1 11.775 ,7jD j  
11.6284,5.0188,11.9693,9.2398 , 
1 2LD LD  0.6905 , 
  52 1 3.5696,1.6902,jL j  
TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 
 Trang 35 
4.1890, 5.3979, 3.6321 , 
1 2LL LL  
14.2668, 
  51 1 1.7106, 0.9601, 2.5613,Lj j  
2.1784, 1.8496 , 
  51 1 5.5479, 4.6852,Sj j  
11.8926, 4.6987, 6.7476 , 
1 1.2761SL  , 
1 1SD  ; , { , }km mP P k S   J ; L = 0.5 
bits/s/Hz and S = 0.2 bits/s/Hz. In the sequel, 
three different relay sets 
1({ }UR , 
3
1{ }j jUR , 
5
1{ } )j jUR are illustrated for J = 1, 3, 5, 
correspondingly. 
Figure 2 illustrates OP with respect to the 
variation of ρ for PL/N0 = 16 dB, Pm/N0 = 14 dB, 
 = 0.05. It is observed that the simulation and the 
analysis are in a perfect agreement. Also, the 
unlicensed network is complete in outage for a 
wide range of  (e.g.,  < 0.935 in Figure 2). 
When the channel estimation is better (e.g.,   
0.935 in Figure 2), the outage performance of the 
unlicensed network is dramatically enhanced. 
Moreover, the increase in the number of relays 
significantly improves the outage performance. 
This comes from the fact that the larger J, the 
higher chance to select the best relay, and hence, 
the smaller the outage probability. 
Figure 2. Outage probability versus  
Figure 3 demonstrates OP with respect to the 
variation of  for Pm/N0 = 14 dB,  = 0.97, PL/N0 
= 16 dB. It is observed that the analysis perfectly 
matches the simulation. Additionally, the system 
performance is significantly better with larger 
number of relays. Moreover, some interesting 
comments are observed as follows: 
 The high QoS (e.g.,   0.025 in Figure 3) 
requirement in the licensed network causes 
the unlicensed network to be complete in 
outage. 
 When the licensed network requires the 
moderate QoS (e.g., 0.025 <   0.08 in 
Figure 3), the outage performance of the 
unlicensed network is drastically improved 
with the increase in . 
 When the licensed network is not stringent 
in the QoS (i.e., low QoS requirement), the 
unlicensed network suffers error floor for 
large values of  (e.g.,  > 0.08 in Figure 3). 
Figure 3. Outage probability versus  
The results in Figure 3 demonstrate that better 
performance of the licensed network (i.e., lower 
values of ) induces worse performance of the 
unlicensed network (i.e., larger values of OP) and 
vice versa. Therefore, the performance trade-off 
between the unlicensed network and the licensed 
network should be accounted when designing 
cooperative cognitive networks. 
Figure 4 illustrates OP with respect to the 
variation of PL/N0 for Pm/N0 = 14 dB,  = 0.97, and 
 = 0.05. Results expose a perfect agreement 
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1
10
-4
10
-3
10-2
10
-1
10
0

O
ut
ag
e 
pr
ob
ab
ili
ty
Sim.: J=1
Ana.: J=1
Sim.: J=3
Ana.: J=3
Sim.: J=5
Ana.: J=5
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11
10-4
10
-3
10
-2
10-1
100

O
ut
ag
e 
pr
ob
ab
ilit
y
Sim.: J=1
Ana.: J=1
Sim.: J=3
Ana.: J=3
Sim.: J=5
Ana.: J=5
SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 
Trang 36 
between the analysis and the simulation. 
Additionally, the outage performance is 
significantly enhanced with larger number of 
relays as expected. Moreover, some interesting 
comments are observed as follows: 
 For small values of PL (e.g., PL/N0  15 dB 
in Figure 4), the increase in PL substantially 
enhances the outage performance. This can 
be interpreted as follows. According to (17), 
PL is proportional to L while the power of 
unlicensed transmitters is controlled by the 
minimum of L and Pm, and hence, at small 
values of PL and the fixed value of Pm, the 
power of unlicensed transmitters is 
proportional to PL, ultimately improving the 
performance of the unlicensed network as PL 
increases and the interference caused by the 
licensed network to the unlicensed network 
is not significant (due to small PL). 
 For large values of PL (e.g., PL/N0 > 15 dB 
in Figure 4), the L term in (17) is larger 
than Pm and hence, the transmit power of 
unlicensed users is fixed at the value of Pm 
(e.g., Pm/N0 = 14 dB in Figure 4). 
Meanwhile, as PL is large and increases, the 
interference that the licensed network 
imposes on the unlicensed network 
dramatically increases, ultimately 
deteriorating the performance of the 
unlicensed network (i.e., increasing the 
outage probability). At the very large values 
of PL (e.g., PL/N0  37 dB in Figure 4), the 
unlicensed network is complete in outage. 
Figure 4. Outage probability versus PL/N0 
Figure 5. Outage probability versus Pm/N0 
Figure 5 demonstrates OP with respect to the 
variation of Pm/N0 for PL/N0 = 16 dB,  = 0.05, 
and  = 0.97. It is seen that the analysis and the 
simulation are in a perfect agreement. Also, the 
increase in J dramatically enhances the system 
performance. Furthermore, the system 
performance is significantly improved with the 
increase in Pm. This can be interpreted as follows. 
Since Pm upper bounds the power of unlicensed 
transmitters (e.g., (17)) and hence, the larger Pm, 
the larger the transmit power, ultimately 
remedying the corresponding outage probability. 
Nevertheless, the unlicensed network experiences 
performance saturation at large values of Pm/N0 
(e.g., Pm/N0  15 dB in Figure 5). This comes from 
the fact that the power of unlicensed transmitters 
in (17) is controlled by the minimum of Pm and PL 
and hence, as Pm is larger than a certain level (e.g., 
Pm/N0  15 dB in Figure 5), the power of 
unlicensed transmitters is completely determined 
0 5 10 15 20 25 30 35 40 45
10-4
10-3
10-2
10-1
10
0
PL/N0 (dB)
O
ut
ag
e 
pr
ob
ab
ili
ty
Sim.: J=1
Ana.: J=1
Sim.: J=3
Ana.: J=3
Sim.: J=5
Ana.: J=5
0 2 4 6 8 10 12 14 16
10-4
10-3
10-2
10-1
100
Pm/N0 (dB)
O
ut
ag
e 
pr
ob
ab
ili
ty
Sim.: J=1
Ana.: J=1
Sim.: J=3
Ana.: J=3
Sim.: J=5
Ana.: J=5
TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 
 Trang 37 
by PL, making the outage performance unchanged 
regardless of any increase in Pm. However, the 
error floor level is drastically reduced with respect 
to the increase in J. 
6. CONCLUSION 
This paper analyzes the outage performance 
of cooperative cognitive networks with the 
proactive relay selection and the selection 
combining under channel information error, 
licensed users’ interference, i.n.i fading channels, 
licensed outage constraint and maximum transmit 
power constraint. To meet these power constraints 
and account for channel information error and 
licensed users’ interference, we proposed an 
appropriate power allocation scheme for 
unlicensed users. Then, to analytically assess the 
system performance in key operation parameters 
without exhaustive simulations, we suggested an 
exact closed-form outage probability formula. 
Various results demonstrate that i) mutual 
interference between the licensed network and the 
unlicensed network establishes a performance 
trade-off between them; ii) channel information 
error dramatically degrades system performance; 
iii) the unlicensed network suffers the error floor; 
iv) the relay selection plays an important role in 
system performance improvement as well as 
system resource savings. 
ACKNOWLEDGEMENT 
This research is funded by Vietnam National 
Foundation for Science and Technology 
Development (NAFOSTED) under grant number 
102.04-2014.42. 
Hiệu năng của mạng nhận thức hợp tác có 
chọn lựa relay chủ động và kết hợp chọn 
lọc 
 Hồ Văn Khương 
 Võ Quế Sơn 
 Lưu Thanh Trà 
Trường Đại học Bách Khoa – ĐHQG-HCM, Việt Nam 
 Phạm Hồng Liên 
Đại học Sư phạm Kỹ Thuật, TP. Hồ Chí Minh, Việt Nam 
TÓM TẮT 
Bài báo này đề xuất một khung phân tích 
xác suất dừng cho mạng nhận thức hợp tác 
có chọn lựa relay chủ động và kết hợp chọn 
lọc dưới ràng buộc xác suất dừng sơ cấp, 
ràng buộc công suất phát tối đa, phân bố 
fading không đồng nhất, thông tin kênh 
SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 
Trang 38 
truyền sai, và can nhiễu của người dùng sơ 
cấp. Hướng đến mục tiêu này, trước hết 
chúng tôi đề xuất phân bổ công suất cho các 
máy phát thứ cấp để đảm bảo các ràng buộc 
công suất và tính đến thông tin kênh truyền 
sai và can nhiễu của người dùng sơ cấp. Sau 
đó, chúng tôi đề xuất một biểu thức xác suất 
dừng chính xác dạng kín cho mạng thứ cấp 
để đánh giá nhanh hiệu năng hệ thống và 
cung cấp các hiểu biết hữu ích về giới hạn 
hiệu năng. Nhiều kết quả cho thấy sự tương 
nhượng hiệu năng giữa mạng sơ cấp và 
mạng thứ cấp, nền lỗi trong mạng thứ cấp, sự 
suy giảm hiệu năng hệ thống đáng kể do 
thông tin kênh truyền sai và can nhiễu của 
người dùng sơ cấp, và sự cải thiện hiệu năng 
đáng kể do sự gia tăng về số lượng relay.
Từ khóa: Chọn lựa relay chủ động, Thông tin kênh truyền sai, Cognitive radio. 
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