6. Summary and Discussions
⋆
Conventional relay systems: The work in Chapter 3 can be further explored in the following directions.• Average BER of conventional multihop DF relay system under κ−µ and η−µ fading for M-QAM scheme is analyzed in [119, 120]. In [121], outage probability is examined for conventional parallel DF relay system underκ−µandη−µfading. Outage probability under κ−µshadowed fading is analyzed for conventional parallel AF and DF relay systems in [112].
In [81], average SER of parallel DF relay system under η−µ fading is analyzed for M- PSK and M-QAM modulation schemes. Average BER/SER of conventional parallel relay systems under κ−µ and/or κ−µ shadowed fading can be analyzed for M-ary modulation schemes.
• Outage probability and average BER of dual-hop DF relay system under η−µ fading in the presence of co-channel interference are examined in [118]. Binary modulation schemes are considered for the analysis. To the best of our knowledge, investigation of the average BER/SER for dual-hop, multihop, and/or parallel relay systems in the presence of co- channel interference is not reported in the literature for M-ary modulation schemes and generalized fading models. Because it can have mathematical challenges. The analysis can be simplified with the help of mathematical tools, such as Meijer-G function, Fox-H function, Mellin transform, etc.
• In [86], average BER of full-duplex dual-hop relay system under Rayleigh and Nakagami- m fading is analyzed for BPSK scheme. The analysis can be extended for higher order modulation schemes underκ−µ,η−µ, and/or κ−µshadowed fading.
⋆
WP relay systems: The analysis for WP relay systems in Chapters 4 and 5 can be extended to following possible future directions.• In [146], the average BER is investigated for binary modulation schemes under κ−µ and η−µfading. The analysis can be extended forM-ary modulation schemes. Though, it may incur mathematical difficulties, which can be tackled with the help of mathematical tools, namely, Meijer-Gfunction, Fox-H function, and Mellin transform.
• Instead of a single relay node, multiple relay nodes can be considered between source and destination. This would improve the diversity gain of the system. Full-duplex mimicking
6.2 Suggestions for Future Work
[32] can be considered to improve the throughput. The analysis can be further extended for the system having nodes equipped with multiple antennas. Effects due to the presence of interference can also be investigated. In [141, 142], analysis of SWIPT networks in the presence of co-channel interferences in presented.
• In this thesis, we have made assumptions to simplify the analysis of the WP relay systems.
The main assumptions are i) negligible power consumption in elementary circuitries, such as encoder, decoder, modulator, demodulator, etc., ii) linear EH model, and iii) harvest-use approach to process the incoming energy flow. In practical scenarios, power consumption in these circuitries cannot be neglected [148], and EH model is nonlinear [59, 175, 176].
Moreover, due to small RF-based energy arrival at harvester, the harvest-store-use approach for processing harvested energy can be more desirable [131]. This approach enables energy- constrained nodes to accumulate energy until a minimum amount of energy is stored. Then the accumulated energy can be used for data transmission. By considering these facts, the analysis can be extended to incorporate more practical scenarios.
• Performance analysis of WP heterogeneous cellular networks using stochastic geometry is also an interesting area of research [74, 139, 143]. In such networks, nodes are considered to be randomly deployed and their location is modeled using a Poisson point process. Perfor- mance of a system comprising one source, one destination, and multiple energy-constrained random relay nodes is analyzed in [143]. The transmission technique considered in Chap- ter 4 can be investigated for such systems on incorporating the appropriate modifications.
6. Summary and Discussions
A
Derivation of P e, EGC , PDF f γ EGC ( γ EGC ) and Its Asymptotic Approximation
Contents
A.1 Product of Two Nakagami-m Distributed Random Variables . . . . 132 A.2 PDF fγEGC(γEGC). . . . 133 A.3 Simplification of Pe,EGC . . . . 134 A.4 Asymptotic Approximation of PDFfγEGC(γEGC). . . . 134
A. Derivation of Pe,EGC, PDF fγEGC(γEGC) and Its Asymptotic Approximation
A.1 Product of Two Nakagami-m Distributed Random Variables
The cumulative distribution function (CDF) of the random variable t2 =ν2|hSR||hRD|, which is a scaled version of the product of two Nakagami-m distributed random variables, can be obtained by solving
Ft2(t2) = Pr[ν2|hSR||hRD| ≤t2]
= Z ∞
0
Pr
|hSR| ≤ t2 ν2|hRD|
f|hRD|(|hRD|)d|hRD|. (A.1)
Equation (A.1) can be simplified using the PDF of |hRD|in (4.9) and the CDF of|hSR|given as F|hSR|(|hSR|) = 1
Γ(mSR)γ
mSR,mSR
λSR|hSR|2 ,
where γ(·) is lower incomplete gamma function. Thus, (A.1) is Ft2(t2) =
Z ∞
0
1
Γ(mSR)γ mSR, mSR (ν2)2λSR
t2
|hRD| 2!
×2(mRD)mRD|hRD|2mRD−1 Γ(mRD)(λRD)mRD exp
−mRD|hRD|2 λRD
d|hRD|. (A.2)
Using (B.2), the incomplete gamma function in (A.2) can be represented in terms of Meijer-Gfunction, which on employing (4.13) can be written in integral form. Hence, on changing the order of integration (A.2) can be rewritten as
Ft2(t2) = 2(mRD)mRD
Γ(mSR)Γ(mRD)(λRD)mRD 1
2π
Z
C
Γ(mSR+p)Γ(−p) Γ(1−p)
mSR (ν2)2λSR(t2)2
−p
× Z ∞
0 |hRD|2mRD+2p−1exp
−mRD|hRD|2 λRD
d|hRD|dp. (A.3)
Now, on employing (B.7), the inner integral in (A.3) can be simplified in the terms of gamma function, thence (A.3) is written as
Ft2(t2) = 1
Γ(mSR)Γ(mRD) 1
2π
Z
C
Γ(mSR+p)Γ(mRD+p)Γ(−p) Γ(1−p)
mSRmRD
¯
γ2 (t2)2 −p
dp, (A.4)
where ¯γ2 =λSRλRD(ν2)2. The PDF of t2 is obtained by differentiating (A.4) with respect to t2 and using the relation x= Γ(1 +x)/Γ(x) as
ft2(t2) = 2mSRmRDt2
Γ(mSR)Γ(mRD)¯γ2 1
2π
Z
C
Γ(mSR+p)Γ(mRD+p)
mSRmRD
¯
γ2 (t2)2 −p−1
dp .(A.5)