Performance Analysis of Project-and-Forward Relaying in Mixed MIMO-Pinhole and Rayleigh Dual-Hop Channel

Chergui, Hatim; Benjillali, Mustapha; Saoudi, Samir

doi:10.1109/lcomm.2016.2514348

Cited by 76 publications

(43 citation statements)

References 14 publications

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“…For the first‐hop RF link, the channel is assumed to be observing a pinhole effect as in the work of Chergui et al, and the channel‐gain matrix representing small‐scale fading effects for this MIMO‐pinhole channel is expressed as

{boldH}_{S R} = {boldg}_{R} {boldg}_{S}^{H},

where

{boldH}_{S R} \in {double-struckC}^{n_{R} \times n_{S}}

is the source‐to‐relay complex channel‐gain matrix,

{boldg}_{S} \in {double-struckC}^{n_{S} \times 1}

and

{boldg}_{R} \in {double-struckC}^{n_{R} \times 1}

are the two complex independent and uncorrelated Nakagami‐ m faded vectors observed at the source and the relay, respectively, and {.} H denotes the Hermitian transpose.…”

Section: The Project and Forward Relaying Protocolmentioning

confidence: 99%

“…Instead of the actual signal, y R , the projection of this signal, ie,

ŷ_{R}

, is amplified and forwarded from the relay to the destination. Hence, the instantaneous end‐to‐end SNR for this system using modified AF relaying protocol, ie, PF relaying, can be represented as in the works of Chergui et al and Peppas et al,(eq. 1) similar to that, for a variable‐gain AF relay‐aided two‐hop link, and given as

{normalΥ}_{S R D} = \frac{{normalΥ}_{S R} {normalΥ}_{R D}}{{normalΥ}_{S R} + {normalΥ}_{R D} + 1},

where Υ SRD , Υ SR , and Υ RD represent the instantaneous SNRs for the source‐to‐relay‐to‐destination link ( S – R – D ), source‐to‐relay link ( S – R ), and relay‐to‐destination link ( R – D ), respectively.…”

Section: Snr‐statistical Characteristicsmentioning

confidence: 99%

“…To obtain the pdf of the instantaneous SNR, Υ SR , for the RF link, we firstly obtain the pdf of the

false‖ {boldh}_{R} {false‖}_{F}^{2}

, ie,

f_{false‖ {boldh}_{R} {false‖}_{F}^{2}} false(γ false)

. The pdf

f_{false‖ {boldh}_{R} {false‖}_{F}^{2}} false(γ false)

can be expressed in terms of the pdf of

false‖ {boldg}_{i} {false‖}_{F}^{2}

for i ∈ { S , R }, and is given in the work of Chergui et al as

f_{{false‖ {boldh}_{R} false‖}_{F}^{2}} false(γ false) = true \int_{0}^{\infty} u^{- 1} f_{{false‖ {boldg}_{S} false‖}_{F}^{2}} ((), \frac{γ}{u}) f_{{false‖ {boldg}_{R} false‖}_{F}^{2}} false(u false) d u .

It may be noted that the

false‖ {boldg}_{i} {false‖}_{F}^{2}

for i ∈ { S , R } is a squared Nakagami‐ m random variable that follows an Erlang distribution, and its pdf is given as

f_{{false‖ {boldg}_{i} false‖}_{F}^{2}} false(\overset{sans-serifg}{true} false) = \frac{{false(\overset{sans-serifg}{true} false)}^{m_{i} - 1}}{{false({normalΛ}_{i} false)}^{m_{i}} no...}

…”

Section: Snr‐statistical Characteristicsmentioning

confidence: 99%

“…For the first-hop RF link, the channel is assumed to be observing a pinhole effect as in the work of Chergui et al, 11 and the channel-gain matrix representing small-scale fading effects for this MIMO-pinhole channel is expressed as…”

Section: The Project and Forward Relaying Protocolmentioning

confidence: 99%

See 3 more Smart Citations

A novel project‐and‐forward relay‐assisted mixed RF‐FSO system design and its performance evaluation

Khanna

Aggarwal

Ahuja

2019

Trans Emerging Tel Tech

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The outage and error performance of a radio frequency (RF)‐free space optical (FSO) asymmetric two‐hop link using project‐and‐forward relaying protocol is evaluated in this paper. We suggest a multiple‐input–multiple‐output (MIMO)‐RF channel with multiple source and relay antennas for simultaneous transmission over the RF link followed by an FSO channel that supports point‐to‐point transmission over a single FSO link. Furthermore, the source to relay RF link is modeled by Nakagami‐m fading distribution to represent different channel fading conditions often encountered in various applications, while the FSO channel is affected by atmospheric turbulence characterized by Gamma‐Gamma fading, path loss, and misalignment errors. The performance of the system is investigated considering the impact of these parameters. We derive the mathematical expressions that are obtained in closed form for the probability density function and cumulative distribution function of the instantaneous signal‐to‐noise ratio for the Nakagami‐m faded MIMO‐RF link in terms of Meijer's G‐function. Using the aforementioned statistical results, we derive a novel closed‐form expression for the outage probability of the system. We also evaluate the average‐bit‐error‐rate performance for different coherent and noncoherent modulation schemes, and obtain novel mathematical results in closed form for the same.

show abstract

{boldH}_{S R} = {boldg}_{R} {boldg}_{S}^{H},

where

{boldH}_{S R} \in {double-struckC}^{n_{R} \times n_{S}}

is the source‐to‐relay complex channel‐gain matrix,

{boldg}_{S} \in {double-struckC}^{n_{S} \times 1}

and

{boldg}_{R} \in {double-struckC}^{n_{R} \times 1}

are the two complex independent and uncorrelated Nakagami‐ m faded vectors observed at the source and the relay, respectively, and {.} H denotes the Hermitian transpose.…”

Section: The Project and Forward Relaying Protocolmentioning

confidence: 99%

“…Instead of the actual signal, y R , the projection of this signal, ie,

ŷ_{R}

{normalΥ}_{S R D} = \frac{{normalΥ}_{S R} {normalΥ}_{R D}}{{normalΥ}_{S R} + {normalΥ}_{R D} + 1},

Section: Snr‐statistical Characteristicsmentioning

confidence: 99%

“…To obtain the pdf of the instantaneous SNR, Υ SR , for the RF link, we firstly obtain the pdf of the

false‖ {boldh}_{R} {false‖}_{F}^{2}

, ie,

f_{false‖ {boldh}_{R} {false‖}_{F}^{2}} false(γ false)

. The pdf

f_{false‖ {boldh}_{R} {false‖}_{F}^{2}} false(γ false)

can be expressed in terms of the pdf of

false‖ {boldg}_{i} {false‖}_{F}^{2}

for i ∈ { S , R }, and is given in the work of Chergui et al as

f_{{false‖ {boldh}_{R} false‖}_{F}^{2}} false(γ false) = true \int_{0}^{\infty} u^{- 1} f_{{false‖ {boldg}_{S} false‖}_{F}^{2}} ((), \frac{γ}{u}) f_{{false‖ {boldg}_{R} false‖}_{F}^{2}} false(u false) d u .

It may be noted that the

false‖ {boldg}_{i} {false‖}_{F}^{2}

for i ∈ { S , R } is a squared Nakagami‐ m random variable that follows an Erlang distribution, and its pdf is given as

f_{{false‖ {boldg}_{i} false‖}_{F}^{2}} false(\overset{sans-serifg}{true} false) = \frac{{false(\overset{sans-serifg}{true} false)}^{m_{i} - 1}}{{false({normalΛ}_{i} false)}^{m_{i}} no...}

…”

Section: Snr‐statistical Characteristicsmentioning

confidence: 99%

Section: The Project and Forward Relaying Protocolmentioning

confidence: 99%

See 2 more Smart Citations

A novel project‐and‐forward relay‐assisted mixed RF‐FSO system design and its performance evaluation

Khanna

Aggarwal

Ahuja

2019

Trans Emerging Tel Tech

View full text Add to dashboard Cite

show abstract

“…Further, it may be noted that the term

P_{3}

in is same as

P_{2 a}

in , and, hence, its high SNR series expansion is given by

{scriptP}_{2 a}^{\infty}

in . The asymptotic expression at high SNR for

P_{4}

in is obtained by using the residue method as in the work of Chergui et al First, we express the BMGF represented by

P_{4}

in terms of Mellin‐Barnes integrals as in the work of Ansari et al, ie,

P_{4} = \frac{1}{{false(2 π j false)}^{2}} \int_{L_{1}} \int_{L_{2}} \frac{((), \prod_{l = 1}^{3} normalΓ ((), c_{1}^{false(l false)} - s)) ((), \prod_{l = 1}^{7} normalΓ (() c_{3}^{(l)} - t))}{normalΓ (() 1 - s - t) \prod_{l = 1}^{2} normalΓ (() c_{2}^{(l)} - t)} \times {℧_{1}}^{s} {℧_{2}}^{t} d s d t,

where

j = \sqrt{- 1},

c_{1}^{false(l false)}

c_{2}^{false(l false)}

, and

c_{3}^{false(l false)}

are the l th element in { c 1 }, { c 2 }, and { c 3 }, respectively, defined in , and ℧ 2 =Φ γ th . The residue at the corresponding integrands is then evaluated at the pole that is closest to the contour.…”

Section: High Snr Outage and Error Performance Evaluationmentioning

confidence: 99%

Further results on the performance improvement in mixed RF‐FSO systems using hybrid DF/AF (HDAF) relaying

Khanna

Aggarwal

Ahuja

2018

Trans Emerging Tel Tech

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This paper presents the performance of a dual‐hop mixed radio frequency (RF)‐free space optical (FSO) system employing a hybrid‐decode/amplify‐and‐forward (HDAF) relaying protocol. The RF link forms the first hop and the FSO link is the second hop for the proposed system model. The assumption of the absence of the direct FSO and RF link between the source transmitter and the destination receiver ends is made for the analysis. The RF link is affected by short‐term multipath fading and long‐term shadowing phenomena and is characterized by the generalized‐K fading distribution, whereas the FSO link is modeled by the gamma‐gamma fading, representing moderate to strong turbulence scenarios. We assume pointing error‐induced misalignment fading to be significantly present over the FSO link. We analyze the outage probability for the system employing amplify‐and‐forward, decode‐and‐forward, and HDAF relaying protocols and show the benefits of using HDAF relaying in mixed RF‐FSO systems. The optimum relay position that results in the best outage performance is investigated. Furthermore, the bit error rate performance for a q‐ary phase shift keying (q‐PSK) modulated signal and the channel capacity for the proposed system employing HDAF relaying protocol are also evaluated. The expressions in closed form for the outage probability, bit error rate, and channel capacity are derived. The asymptotic outage and error performance at high signal‐to‐noise ratio is also evaluated. Furthermore, the performance of the system is demonstrated by numerical plots.

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Physical-Layer Security for Ambient Backscattering Internet-of-Things

ElHalawany

El-Banna

2020

Internet of Things

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Performance Analysis of Project-and-Forward Relaying in Mixed MIMO-Pinhole and Rayleigh Dual-Hop Channel

Cited by 76 publications

References 14 publications

A novel project‐and‐forward relay‐assisted mixed RF‐FSO system design and its performance evaluation

A novel project‐and‐forward relay‐assisted mixed RF‐FSO system design and its performance evaluation

Further results on the performance improvement in mixed RF‐FSO systems using hybrid DF/AF (HDAF) relaying

Physical-Layer Security for Ambient Backscattering Internet-of-Things

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