Performance analysis of rf energy harvesting cooperative communication networks with DF scheme

2 Km1+k−t 2  . (21)
 λ2m1 (n + 1) λ1λ2 
 n(m −1)
 N−1 1 m2−1   m1+k t n n
 X X X 1 N − 1 m1 m2φ (−1) bk N
 I(a, φ) = 1− N−1
 t! n λ1 λ2
 n=0 k=0 t=0 Γ(m1)
 ∞ `  `
 X (−1) m2φ
 × Ψ(x). (22)
 `! λ2
 `=0
 where
  m1−k+t+`  
  m1 (1+n) m1 (1+n) γth
  Γ m1 +k−t−`, ,
  λ1 λ1PS
 
 with m1 +k−t−`>1, (23a)
 
   m (1+n)γ 
  q+1 q 1 th
      exp − λ P
 (−1) m1 (1 + n) m1 (1 + n) γth 1 S gX
Ψ(x)= Ei − +  q ,
 q! λ1 λ1PS γth
  P
  S
  j j
  j m1(1+n)   γ 
  q−1 (−1) th
  X X λ1 PS
 with g = , q = m + k − t − ` < 1. (23b)
  q (q − 1) ··· (q − j) 1
  j=0
 Proof: We rewrite (13) to become an independent product of two probability com-
 2 2 2
ponents, and let X = max |h1,i| , Y = |hRnD| and Z = |hSD| be the random
 i=1,...,N
variables Gamma distribution, which are modeled as X ∼ G (m1, β1), Y ∼ G (m2, β2)
and Z ∼ G (m0, β0), respectively.
 Substituting (17) and (2) into (20), we get I (a, φ) that is showed by the equations
(24a).
 n(m −1) 
 1 m2−1 N−1    m1+k  t n n
  X X 1 X N − 1 m1 φm2 N(−1) bk 
I(a, φ) = 1− N−1 J(x)
 t! n λ1 λ2 Γ(m1)
  k=0 t=0 n=0 
 (24a)
 ∞
 Z  
 m +k−t−1 φm2 m1(n + 1)x
 where J(x) = x 1 exp − − dx. (24b)
 xλ2 λ1
 a
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 Journal of Science and Technique - Le Quy Don Technical University - No. 202 (10-2019)
 In the case of high transmit power, i.e a = γthN0 → 0, by applying [11, 3.471.9],
 PS→∞
we obtain I (a, φ) as in (21), and then by replacing back (21) into (20), we obtain the
approximation of outage probability expression as in (24b). However, this approximation
is unsuitable for low transmit power which is basically applied for EH system. To obtain
the closed-form of the outage probability expression for general case of transmit power,
 ∞
  a 
 P (−1)t  a 
t
the exponential function is expanded by Taylor algorithm: exp − x = t! x .
 t=0
Therefore, the J (x) in (24b) is rewritten as
 ∞
 ∞ `  ` Z  
 X (−1) m2φ m +k−t−`−1 m1 (1 + n) x
 J (x) = x 1 exp − dx . (25)
 `! λ2 λ1
 `=0 a
 | {z }
 Ψ(x)
Finally, by applying [11, Eq:3.351.211, Eq:3.351.4] for the integral term in (25), we
have the Ψ(x) that is given in (23a) and (23b). The proof of Proposition is completed.
4. Simulation Results
 In this section, we show the Monte - Carlo simulation results and compare them with
our theoretical analysis. We assume that the R is fixed as 1 bit/s/Hz, η = 1 (perfect
current converter), PS is constant, and α = 0.3. The distance from S to D is normalized
to unit value. We also assume that the relay node cluster is at the middle of the source
and the destination. Moreover, all channels are identical independent distribution (i.i.d).
For the sake of simplicity, the average channel gains are set as λ1i = λ2j = λ0 = 1.
 Fig. 3 illustrates the outage probability versus the average transmit power of the S.
In order to reduce complexity, we choose [m1 m2 m3] = [2 2 2], where m1, m2, m3 are
the distribution parameters of the links S-R, R-D and S-D, respectively. The number
of relays is changed within [1,5]. The result in Fig. 3 shows that the channel gain
is increased by increasing the number of relays. The reason is, the selected best relay
provides the best channel from the source to the relay in order to achieve better decoding
performance as well as higher RF EH from the source in the first phase. Furthermore,
it is clear that the theoretical analysis is perfect match with the simulation, it confirms
the correctness of the proposed analysis approach.
 Fig. 4 demonstrates the outage probability of the EH cooperative communication
system with respect to the different parameters m, while other parameters are set to
be the same as in Fig. 3. In this figure, the excellent agreement between the analytical
result and simulation result is also observed. When the parameter m is increased, the
outage probability decreases. It is explained that the other diversity is improved by
the d = min(mx , my), and then the system performance is improved significantly. In
addition, when the quality of direct link is better than that of the forward link, the
parameter m of forward link unaffects the system performance. The reason of this state
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Section on Information and Communication Technology (ICT) - No. 14 (10-2019)
 0
 10 
 −1
 10
 −2
 10
 −3
 10 Simulation
 Theoretical analysis
 −4
 10
 N=[1, 2, 3, 5]
 OutageProbability 
 −5
 10
 −6
 10
 −7
 10 
 0 5 10 15 20
 Average SNRs [dB]
 Fig. 3. The effect of relay numbers on the system performance.
is that the SNR threshold for demodulation of the destination depends on the SNR of
the direct link.
5. Conclusions
 In this paper, we derive the PDF of the order statistic for the equivalent instantaneous
SNR of the EH cooperative communication with DF protocol. The derived PDF is then
utilized to calculate the outage probability, especially the asymptotic and approximate
outage probability. The system performance is analyzed based on different parameter
m, channel gain and number of relay nodes. Our derivations are confirmed by Monte
- Carlo simulations, the significant match of both theoretical and simulation results
verifies our proposed analysis method.
 The expansion method for incomplete Gamma function provided in this paper can
be applied, and then save time for future investigations on EH DF relay systems. The
derived equations also can be integrated with Matlab or Mathematica as an useful
function to evaluate another system. Moreover, the results provided in this paper can
play an important role in the design of practical wireless networks.
 However, the system performance was theoretically analyzed while assuming the
duration time for EH is fixed. The investigation of effect and optimization of duration
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 Journal of Science and Technique - Le Quy Don Technical University - No. 202 (10-2019)
 0
 10
 [mm m ] = [2 2 1]
 SR RD SD
 −1
 10
 [mm m ] = [2 1 2]
 SR RD SD
 −2
 10
 −3
 10
 Simulation 
 Outage Probability Theoretical analysi
 −4 s
 10
 −5
 10
 m m =[2 2 2]
 SR RD SD
 −6
 10
 0 5 10 15 20
 Average SNRs [dB]
 Fig. 4. The outage probability with different values of parameter m.
time for EH is left for the future work.
Acknowledgment
 This research is funded by Vietnam National Foundation for Science and Technology
Development (NAFOSTED) under Grant No. 102.04-2017.311
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 Manuscript received 19-9-2019; Accepted 18-12-2019.
 
 Hoang Duc Vinh received B.E degree in Electronics and Communications Engineering from
 University of Transport and Communications in 2004, M.E degree in Radio-Electronics En-
 gineering of Le Quy Don Technical University in 2011. He had worked at Department of
 Information and Communications of Nghe An province from 2005 to 2011, and at Ministry of
 Information and Communications of Viet Nam from 2011 to 2016. Now he is a Ph.D candidate
 of Le Quy Don Technical University, Hanoi, Vietnam. His reseach interests lie in the area of
 physical layer and spectrum management of wireless systems..
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Journal of Science and Technique - Le Quy Don Technical University - No. 202 (10-2019)
 Vu Van Son received the B.E.E. degree from the Le Quy Don Technical University, in
 2004; received the Ph.D. degree in Radio-physics, Electronic and Medicine Engineering from
 the Vladimir State University, Russia, in 2009. His previous research interests have included
 stochastic processes, wireless communications, pattern recognition, and neural networks. His
 current work is mainly focused on wireless communications, with special emphasis on model-
 ing, estimation, and efficient simulation of wireless channels, and system performance analysis.
 Bui Anh Duc received the B.S. in 2013 in Telecommunication University and M.S from Le
 Quy Don University, Ha Noi, Vietnam in 2017. His research interests include wireless body
 area network cooperative communication.
 Tran Manh Hoang received the B.S. degree in Communication Command from Telecom-
 munications University, Ministry of Defense, Vietnam, in 2002, and the B. Eng. degree in
 Electrical Engineering from Le Quy Don Technical University, Ha Noi, Vietnam, in 2006. He
 obtained the M.Eng. degree in Electronics Engineering from Posts and Telecommunications,
 Institute of Technology, (VNPT), Vietnam, in 2013. He is currently pursuing the Ph.D degree
 at Le Quy Don Technical University, Hanoi, Vietnam. His research interests include energy
 harvesting, Non-orthogonal Multiple Access, and signal processing for wireless cooperative
 communications.
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Section on Information and Communication Technology (ICT) - No. 14 (10-2019)
 Pham Thanh Hiep received the B.E degree in Communications Engineering from National
 Defence Academy, Japan, in 2005; received the M.E and Ph.D degree in Physics, Electrical
 and Computer Engineering from Yokohama National University, Japan, in 2009 and 2012,
 respectively. He was an associate researcher at Center for Future Medical Social Infrastructure
 Based on Information Communications (MICT cener) of Yokohama National University during
 2012-2015. He is currently working as lecturer at Le Quy Don Technical University, Ha Noi,
 Viet Nam. His reseach interests lie in the area of wireless information and communications
 technologies.
 PHÂN TÍCH HIỆU NĂNG HỆ THỐNG HỢP TÁC
 GIẢI MÃ CHUYỂN TIẾP ỨNG DỤNG THU THẬP
 NĂNG LƯỢNG VÔ TUYẾN
 Tóm tắt
 Bài báo phân tích hoạt động truyền tải thông tin và năng lượng đồng thời cho mạng
 truyền thông hợp tác. Trong hệ thống này, một nút nguồn truyền thông tin tới một nút đích
 thông qua đường truyền trực tiếp hoặc thông qua nút chuyển tiếp được lựa chọn. Giao thức
 giải mã và chuyển tiếp (DF: decode and forward) được sử dụng tại nút chuyển tiếp, và kĩ
 thuật lựa chọn kết hợp (SC: selection combination) được áp dụng tại nút nguồn để lựa chọn
 nút chuyển tiếp tốt nhất. Phẩm chất hệ thống được đánh giá qua xác suất dừng trên kênh có
 phân bố Nakagami-m. Phân tích giải tích và các phương trình gần đúng được đề xuất, tính
 toán và so sánh với mô phỏng Monte-Carlo. Kết quả mô phỏng tương đồng với kết quả tính
 toán, điều này chứng minh tính chính xác của phương pháp tính toán của chúng tôi.
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