The average SER of the conventional relay system is investigated under κ−μ and η−μ fading for M-PSK modulated data. 57 3.6 Average SER versus source-to-relay distance for the relay system with equal and optimal.
An Overview of Wireless Communications
- Transmission and Reception Over Fading Channels
- Fading Channel Modeling
- Combating the Effects of Fading
- Performance Analysis
Furthermore, the sampled output of the matched filter(s) (or the output of the correlator(s)) used for the decision can be given by Depending on the number of antennas at the transmitting and receiving nodes, communication systems can be categorized as multiple-input single-output (MISO) systems, single-output multiple-input (SIMO) systems, and multiple-input multiple-output (MIMO) systems.
An Overview of Relay Systems
Three-node Relay System
In case the direct link connecting the source and destination nodes is severely faded, the relay node is useful to extend the coverage. In a relay system, the relay node uses the selective DF protocol and operates in half-duplex mode.
Wireless Energy Harvesting
Background and Technical Breakthroughs
- Near-Field Wireless EH
- Far-Field Wireless EH
It uses magnetic resonance coupling for WPT and mainly aims to provide wireless power solutions for electric vehicles. WattUp products aim to provide far-field and near-field wireless power as well [48].
Wireless Power Transfer in Communication Networks
- RF-based EH
Assuming that the data is transmitted with power P, the energy collected during the duration of the symbol can be given by [53, eq. The energy collected in a node can be used in three different ways - harvest-use, harvest-store-use, and harvest-use-storage [58].
Motivation of the Present Work
In such circumstances, wireless EH at the energy-constrained relay node can enable the participation of nodes in the communication. Under these motives, we analyze the average SER for a WPCN where energy-constrained relay node is wirelessly powered by the source node.
Thesis Contributions
The communication lifetime can be extended if the energy-limited source nodes are powered wirelessly by other nodes in the network or dedicated power transmitter(s). We consider a double-hop relay system where energy-constrained source node harvests energy using the RF signal transmitted by the relay node.
Thesis Organization
Initial Developments
In a two-hop relay system with the direct connection, full diversity cannot be utilized if a fixed-amplified DF relay is used. Chen and Laneman considered a parallel relay system and investigated optimal maximum likelihood (ML) detector for coherent and non-coherent binary FSK (BFSK) modulation schemes in [104].
Conventional AF Relay Systems
A suboptimal detector with piecewise linear (PL) combiner is used to approximate the ML detector to derive the closed-form expression for the average BER. PL detector uses the knowledge of average BER of source-to-relay link at the destination.
Conventional DF Relay Systems
In the information, theoretical performance of cognitive DF relay system under κ−µ shadow fading is investigated. The table indicates that no work is reported in the literature that provides average SER analysis of conventional DF relay system under κ−µ, η−µ, and κ−µ shadow fading for M-PSK and M-FSK modulation schemes.
WP Relay Systems
EH at Relay Node(s)
- SWIPT Networks
- WPCNs
Gu and A¨ıssa analyzed information theoretic performance of a WP DF relay system in the presence of interferences in [70]. The works in [144–147] consider generalized fading models for the analysis of WP DF relay systems.
EH at Source Node(s)
Summary
In this chapter, we consider a conventional three-node DF relay system where the direct link exists between the source and destination nodes and the fading environment is modeled using κ−µ and η−µ fading. In performance analysis of a two-hop conventional DF relay system, κ−µandη−µ fading models are investigated. Expressions of the average SER and corresponding high SNR approximations are derived for κ−µ and η−µ fading channels in Section 3.3.
System Model
When node R misdetects, then nodeD decides the data in the second slot using the decision rule.
Performance Analysis under κ − µ and η − µ Fading
Analytical Average SER
- κ − µ Fading
- η − µ Fading
Next, when the signal is perfectly detected at the relay node, the signal received at the destination node is MRC of the direct and the relayed signals. Since SD and RD links are independent, the MGF of γMRC is product of the MGFs of γSD and γRD, that is.
Asymptotic Average SER
- κ − µ Fading
- η − µ Fading
Performance Analysis under Mixed κ − µ and η − µ Fading
Optimal Power Allocation and Diversity Order
Optimal Power Allocation
For 2µSD≥µRD, the optimal power allocated to the source node will always be greater than P/2, while for 2µSD <. Solving (3.62), we can obtain the optimal power allocated at the source and the relay node. For µij = 1, all channels are Rician faded and the optimal power at the source and relay node is given by (3.65) in which.
Diversity Order
The connection with the result that exists in the literature: When all connections are κ−µ decay, then instead of 2µSD in (3.57) we have µSD. Expressions of optimal power for any value of attenuation parameters inκ−µ,η−µ, and mixed κ−µ and η−µ faded channel can be obtained after appropriate changes in (3.62) and its solution in mathematical software such as MATHEMATICS, MAPLE, and MATLAB.
Numerical Results
In Figure 3.2 (a), the average SER is plotted for fixed µSD and κij and varying µSR and µRD. In Figure 3.3 (a), the average SER is plotted for fixed µij and ηSD and varying ηSR and ηRD. Figure 3.4 shows the average SER results for a relay system with uniform and optimal power distribution.
Conclusion
In such a scenario, end-to-end communication is inhibited if the batteries in the participating relay node(s) are depleted between communications. If the direct link exists and is considered for the analysis, the performance of the system can be significantly improved by using diversity combining schemes at the destination node. Analytical expressions for the average SER are derived for M-PSK modulated data under the Nakagami-m fading environment.
System Model
In the kth time window, the baseband equivalent of the received RF signal at node j is given by The ratio of the power exponent of the equivalent signal and noise components in (4.3) gives the equivalent instantaneous SNR at node D. The average link SNRs for the SR, RD, and SD links are obtained by taking the expectation of .
Performance Analysis
Analytical Average SER
- With SD Link
- Without SD Link
We analyze the average end-to-end SER for the case when the SDlink assists in data transmission and the signals received from SDandRDlinks are combined using the EGC principle (4.7) at the destination. We analyze the average end-to-end SER for the system when the SDlink is deeply degraded. An approximate and efficient computational expression for the average SER of link RD can be analyzed by substituting (4.31) into (4.26) for φ=RD.
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Asymptotic Average SER
- With SD Link
- Without SD Link
To determine Pe,EGC∞, we approximate the PDF and MGF of γEGC at high SNR. Since EGC combines the signal received via independent SD and RD links, the PDF and MGF of γEGCare is approximated with high SNR for each link individually. The high SNR approximation of the end-to-end SER in (4.29) is given by. where Pe,SR∞ and Pe,RD∞ are the high SNR approximation of Pe,SR and Pe,RD, respectively.
Resources Optimization
If the system is Rayleigh fade, the corresponding asymptotic expression of the average SER can be realized by setting mij = 1 in (4.52) and (4.53) for the system with and without SDlink, respectively. We can see that the coefficients for the SD-link system are independent of the SDlink channel quality. Furthermore, the suboptimal resource allocation for the system without SDlink is independent of aM, that is, of modulation or.
Diversity Order and Throughput
Diversity Order
Since the suboptimal value for the fraction of the total energy consumed in T1 and T2 is known, the suboptimal power and time for the respective slot can be found using (4.12). Similar to the optimal resource allocation in the case of Nakagami-m fading, we consider two cases where i) the three time slots are equally divided, i.e. T1 =T2 =T3=T /3 or τ = 1/3 and ii) power transmitted in slots T1 and T2 are the same, i.e. P1=P2.
Throughput
Numerical Results
In Figure 4.3 it is observed that the average SER decreases with increase inmij, which implies improvement in performance of the system. We see from Figure 4.8 that the optimal relay location lies close to the source node for all values of ζ. Similar analysis follows for the system without SD link and the systems enabled with optimal resource allocation.
Conclusion
In addition, the energy allocations and the corresponding average SER in the SD offline system are independent of the modulation order. The average SER and throughput of a direct-connected system is always better than that of a non-direct-connected system for a given energy allocated to each slot or at an optimal resource allocation. In this chapter, the average SER of the system is derived considering that the fading environment is modeled by the Nakagami-m distribution, which is then expanded for κ−µshaded fading.
System model
PDF and MGF of Instantaneous SNRs
- Nakagami-m Fading
- κ − µ Shadowed Fading
The PDF of the power variation for κ−µshadow fading switching gains is given by [12, eq. To simplify the derivation, we use the series form representation of the PDF1 given in [173]. 1Another serial form representation of the PDF is provided in [15, cf. 12)] which calculation of Nmoments ofh[15, cf. 11)], where is the number of terms in the series.
Performance Analysis under Nakagami-m Fading
- Analytical Average SER
- M-PSK
- Orthogonal M -FSK
- Asymptotic Average SER
- M-PSK
- Orthogonal M -FSK
- Optimal Relay Location
- Diversity Order
The average end-to-end correct detection probability can be obtained by expecting the conditional probability in (5.28) given by . The average error probability Pe,SR can be obtained by expecting (5.37) using the PDF in (5.16). At high SNRs, the end-to-end average SER term in (5.32) can be approximated as
Performance Analysis under κ − µ Shadowed Fading
- Analytical average SER
- M-PSK
- Orthogonal M -FSK
- Asymptotic Average SER
- M-PSK
- Orthogonal M -FSK
- Optimal Relay Location
- Diversity order
To obtain Pe∞ in (5.68), the approximate PDF expression fγSR(γSR) is used to derive Pe,SR∞. The considered approximation of the average SER is good for κij →0 and deviates as the value of κij increases. In order to get a better approximation for higher values of κij, it is necessary to include more terms in the series, which increases with increasing κij. The method used to approximate κij →0 can be followed when κij is large by choosing an appropriate number of terms in the set that depends on κij.
Numerical Results
Nakagami-m Fading
Similarly, in Figure 5.3 (b) and 5.4 (b), the optimal location of the relay is near node D for small mRD and when mRD increases, it moves towards node S. The optimal relay location in the case of 4-PSK and orthogonal 2-FSK modulation schemes can be obtained by applying the golden section search method in (5.62) and (5.63), respectively. The optimal dSR for|mRS−mSR|>0 can be obtained using (5.62) and (5.63) for the orthogonal M-PSK and M-FSK modulation schemes, respectively.
Next, we consider |mRS −mSR| = 0.1 in Figure 5.7(b) and note that the asymptotic mean SER is a loose bound for small value of |mRS -mSR|. Further, in Figure 5.7(c) with |mRS -mSR| = 0.7, the graph corresponding to the asymptotic mean SER is relatively close to the analytical results. In Figure 5.10, we plot the average SER versus source-relay distance for 4-PSK with variation in µij.
Conclusion
High SNR approximations of the average SER are also obtained for each system to simplify the analysis. We have conducted an in-depth review of the available literature on the performance analysis of relay systems. A high SNR approximation of the average SER is also obtained to analyze the DO of the system and allocate optimal power to the source and relay node.
Suggestions for Future Work
The average BER/SER of conventional parallel relay systems under κ−µ and/or κ−µ shadow fading can be analyzed for M-ary modulation schemes. The analysis can be extended for higher order modulation schemes with κ−µ, η−µ and/or κ−µshadowed fading. The analysis can be further extended for a system that has nodes equipped with multiple antennas.
PDF f γ EGC (γ EGC )
Simplification of P e,EGC
Asymptotic Approximation of PDF f γ EGC (γ EGC )
Performance analysis of conventional DF relay systems
Performance analysis of WP DF relay systems: EH at relay node(s)
Performance analysis of WP DF relay systems: EH at source node(s)
