Performance evaluation of cognitive multi-hop networks to assist building system

ncrease is the main target. Each node is possible of MRC (Maximal Radio 
Combining) on the frame included multiple time slots. They gave out the algorithm to find 
the best power vector in terms of LOS (Ligh of Sight) or Non-LOS. However, the multi-hop 
network occupies its own spectrum. In [16], the authors propose the cognitive network 
model in which the secondary multi-hop network is constrained power by the multiple 
antenna primary network. Solved the multi-antenna system by TAS/SC diversity (Transmit 
Antenna Selection/Selection Combining), the authors calculate the optimal of the OP of 
primary network that it assists in enhancing the OP on the multi-hop network. Nevertheless, 
the Rician fading is modeled in the data link. Whereas, the work in [13] use Rayleigh fading 
for its proposal to derive the SOP with the i.n.i.d primary node distribution. Having said that 
all aforementioned papers did not show clearly map supports to directly network design. 
To the best of our knowledge, hardly papers fully cover the multiple primary users’ 
impact on the outage of the secondary multi-hop network and show the foot-print form to 
support the design of new cognitive multi-hop networks except [5]. Ignoring the security, 
this work concentrates on the multi-hop outage performance in CRNs via building the map 
directly to assist designers and operators on a new network. Furthermore, the hardware 
imperfection is also concerned in our analysis. 
2. SYSTEM ANALYSIS 
2.1. Network model 
Figure 1 shows the structure of the proposed cognitive networks. The primary network 
has L PUs, which has more priority in communication. Hence, to avoid suffering from 
others, PUs define their own interference threshold P
iI so that other transmitters have to 
adjust to satisfy these thresholds. Besides, the secondary multi-hop network has a source 
0ST that transfers data to its destination STK with the assistance of 1K relays 
1 1ST ...STK via K orthogonal time slots. Source 0ST transmits the signal to 1ST in the 
first slot, exploited Decode-and-Forward (DF) protocol. Next, 
1ST similarly transmits 
signal to 
2ST in the second time slot. The process is repeated until the data send over K 
time slots. It is assumed that all channels in the proposed model are subject to slowly varying 
Rayleigh fading. 
Figure 1. Network model 
Performance evaluation of cognitive multi-hop networks to assist building system 
17 
2.2. Performance evaluation 
2.2.1. Limitation of the secondary transmit power due to the multiple interference constraints 
To avoid the inteference between the PUs and secondary transmitter 
1STk , all the 
secondary nodes has to adjust their power as long as the PUs can decode their signals. 
According to the formula 13.26 [17], the transmit power of the 
1STk relates to 
,1 1 P ,
i
k kg Q I (1) 
where 
1kQ is the real transmit power of -1STk , and 
1
P P,...,
LI I are the maximum interference 
levels at the respective 
1PU ,...,PU .L For the sake of simplicity, we assume that every 
interference threshold 1P P,...,
LI I is equal to 
P .I Hence, the domain that is satisfied all 
inequalities in (1) can be writen to 
1, 1 P
1
max ,k i k
i L
g Q I (2) 
P
1
1,
1
.
max
k
k i
i L
I
Q
g
 (3) 
It is also assumed that we have L PUs, which located in the form of a cluster, and takes 
account into path-loss, we have the maximum allowable normalized power following 
1 P
1
0 0 1,
1
,
max
k k
k
k i
i L
Q I
P
N N
 (4) 
where 1,PUk kd . More clearly, the 1,PUkd is the distance between the -1STk and PUs. is 
the path loss exponent. Similarily, we have 1,k k kd is of the -thk hop. 
2.2.2. Performance evaluation of the secondary multi-hop network 
Because of cluster form in the primary network, we denote max 1,
1
maxk k i
i L
V , where 
1,k i is the channel gain from -1STk to PUi . When it comes to the secondary network, the 
instantaneous signal-to-noise ratio (SNR) at a secondary receiver expresses by 
1 max
1
1 max
1
. /
,
1 . / 1
k k k k k k
k
k k k k k k
P AB V
P AB V
 (5) 
where 
1kP is in (4), and k is the normalized channel coefficient of -1STk to STk link. The 
 is respective harware impairment level, as defined in [18, 19]. Also, we symbolize 
P 0/A I N , / .k k kB Thus, the outage of the -thk hop is given to 
max
th thmax
. /
OP Pr Pr ,
. / 1
k k k
k k
k k k
AB V
AB V
 (6) 
where 
th
 is the target rate. 
Remarkably, the interference channels suffer from slow Rayleigh fading and have the 
same distances, we have 
 max 1,
1
P maxr 1 ,k
k
k i
iV L
L
x
F x x e (7) 
Ngo Hoang An, Tran Minh Hong, Le Van Hung, Pham Minh Nam 
18 
and max
1
1
1
0
. .. 1
k
L
ii
L
i
i x
V
Cf x L e (8) 
Back to (6), the outage rewrites to 
 max
th th th thOP Pr Pr 1 . / .k k k k kAB V (9) 
With the 1 , the probability is absolutely right. Hence, we only consider the 
otherwise. In that case, the (9) changes to 
max
maxth
th
th
th
th
0
O P
1
.
P r
1k kV
k k k
k
k
F f
V
AB
y y
AB
dy
 (10) 
After some algebra manipulations, we have the outage of the -thk hop as follows 
1
th
th 1
0 th th
1 . .
1)
1
OP 1
( 1
L
i ki
k L
i k
AB
C
A
L
i B
 (11) 
By exploiting the DF protocol to transfer data from the source to destination, we finally 
obtain the closed form of the end-to-end outage probability of the secondary multi-hop 
network under multiple interference constraints and present to following 
1
th
th 1
1 0 th th
1
OP 1 1
( 1
.
1)
LK
i ki
L
k i k
L
AB
C
i AB
 (12) 
3. SIMULATION RESULTS AND DISCUSSION 
3.1. Verification of the theoretical derivation 
On the XY plane, we set the source at 0,0 and the destination at 1,0 . All the relays 
are located at the source and destination gap so that its communication distance is the same as 
others. For example, when 2,K 1 0,0.5ST , and when 3,K 1 20,0.33 0,0.67ST , ST . 
The PUs were installed at P P,x y . 
Figure 2. OP as a function of A when 5,L 0,
th 1, P P 0.3.x y 
Performance evaluation of cognitive multi-hop networks to assist building system 
19 
As seen in Figure 2, the end-to-end OP goes down when the 
P 0/I N rises. It is because 
the 
P 0/I N looser, the multi-hop transmitters can transmit with higher power at that time. It 
leads to OP reduction. When it comes to the number of secondary hops, we observe that the 
OP is a lower value where the number of hops increases. It relates to the shorten distance on 
each hop. 
Figure 3. OP as a function of τ when 4,K ( )10 dB ,A th 1, P P 0.3.x y 
Figure 3 shows the OP as a function of various hardware imperfections. In fact, when 
the imperfect level increases to one, the transmission is unsuccessful because of OP = 1 
regardless of other factors. Compared to the model [14] which exists power beacons and 
primary users, the hardware impairment tolerance is higher where OP = 1 due to the fact that 
its transmit power is not constrained in this case. Besides, more PUs results in higher OP value. 
3.2. Building footprints of the desired network 
Figure 4. OP on the PU’s location map when 4,K 5,L 0,01, th 1, ( )10 dBA 
Ngo Hoang An, Tran Minh Hong, Le Van Hung, Pham Minh Nam 
20 
We determine the end-to-end multi-hop outage with the verified derivation above in 
terms of fixed 4,K 5L on half of the vicinity in Figure 4. As seen, OP is the highest when 
the PU is nearest the transmitter or receiver. Compared to [10], [20, 21], and [22] with simply 
sliding the Eavesdropper, the Relay, and the Power Beacon respectively in one direction (1D), 
the Figure above indicates that the multi-hop network is not only severely affected 
performance by PU’s location on the horizontal direction but also significantly changed on the 
vertical PU’s moving. Back to [5] with a 2D optimal relay map, Figure 4 clearly shows the 
map which indicates the effect of PUs on the performance of the secondary multi-hop 
network. Based on this map, it is recommended that setting a new network install the multi-
hop transceiver positions in the condition that the PUs are placed farther the multi-hop 
network. 
4. CONCLUSION 
In this paper, we evaluate the performance of the secondary multi-hop network in the 
underlay CRNs paradigm. Our research shows that the multi-hop topology has better 
performance when compared to dual-hop in the same condition. Many more PUs results in 
low multi-hop QoS. The hardware imperfection can influent the end-to-end OP, but it is 
significant if the level is 1. Based on the PU’s location map, we suggest that the multi-hop 
transceiver needs farther away from the PUs if it’s possible. 
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Ngo Hoang An, Tran Minh Hong, Le Van Hung, Pham Minh Nam 
22 
TÓM TẮT 
ĐÁNH GIÁ HIỆU NĂNG MẠNG ĐA CHẶNG NHẬN THỨC 
NHẰM HỖ TRỢ XÂY DỰNG HỆ THỐNG MẠNG 
Ngô Hoàng Ấn1*, Trần Minh Hồng2, 
Lê Văn Hùng2, Phạm Minh Nam2 
1Trường Đại học Công nghiệp Thực phẩm TP.HCM (HUFI) 
2Trường Đại học Công nghiệp TP.HCM (IUH) 
*Email: annh@hufi.edu.vn 
Trong những năm gần đây, mạng chuyển tiếp nhận thức (CRNs) đã được quan tâm 
như một xu hướng nghiên cứu mới. Đặc tính của mạng nhận thức có thể hỗ trợ thiết lập một 
mạng truyền thông mới bằng kỹ thuật chia sẻ phổ tần. Tuy nhiên, hầu hết các bài báo trước 
đây chỉ dừng lại ở việc nghiên cứu hiệu năng của mạng thứ cấp với sơ đồ hai chặng 
(dual-hop). Bài báo này đánh giá hiệu năng của mô hình mạng đa chặng bằng cách đưa ra 
công thức xác suất dừng từ đầu cuối đến đầu cuối. Từ đó, mô phỏng kiểm chứng tính chính 
xác của các kết quả đưa ra. Ngoài ra, kết quả mô phỏng cho thấy những ảnh hưởng của một 
số yếu tố liên quan khác đến xác suất dừng của mạng đa chặng thứ cấp. Chúng tôi đặc biệt 
đưa ra được biểu đồ xác xuất dừng hệ thống trong mối tương quan ở dạng footprint nhằm hỗ 
trợ trực tiếp các nhà thiết kế và vận hành mạng. 
Từ khoá: Mạng chuyển tiếp đa chặng, mạng nhận thức, xác suất dừng.