Performance analysis of multiple NLOS UV communication cooperative relays over turbulent channels

Ali Refaai; Mohamed Abaza; Mohamed S. El-Mahallawy; Moustafa H. Aly

doi:10.1364/OE.26.019972

1. Introduction

Ultraviolet (UV) communication has received renewed interest due to its recent advances in small size, low cost and low power as the most useful non-line-of-sight (NLOS) communication. The recent advanced technology for wireless communications using UV semiconductor sources and detectors, can be operated at solar blind NLOS communications. The transmitter emits the effective UV light beam band 200 – 280 (nm) with a certain divergence angle [1]. Hence, the light is scattered by molecules and aerosols in the atmosphere referring to Rayleigh and Mie scattering, respectively. Then, the scattered light is detected by the receiver [2]. The background noise coming from the sun rays can be mitigated due to the rejection of the ionosphere region for this specific wavelength band [3]. The characteristics of this system make communication in UV C-sub band survive in NLOS due to its inherent advantages and strong scattering characteristics that are considered as natural development for free-space optical (FSO) links, especially at short ranges for both civilian and military applications [2]. Since there is a great similarity in the characteristics of the system in terms of channel, transmitter and receiver, this provides the opportunity to rely on some studies of FSO as a guide while working in the NLOS UV communications. Serial relays NLOS UV communications are investigated in [4, 5]. Optimal relay placement and diversity analysis of relay-assisted FSO communication systems are derived in [6] which is considered a log-normal (LN) channel with a decode and forward (DF) relaying scheme. The performance of multi-hop heterodyne FSO systems with pointing errors are derived in [7] which uses a multi-hop relays with an amplify and forward (AF) relay with a fixed gain over gamma-gamma (G-G) turbulent channels. Relay assisted techniques for FSO communications are employed in [8] include a general formula for the outage probability at both serial and all-active parallel relays. Long distance NLOS UV communication channel analysis and experimental verification are investigated in [9], showing the advantage and the history of UV communication exposed to channel scattering coefficients with Rayleigh and Mie coefficients for thick, tenuous and extra thick scattering. Performance analysis of parallel relaying in FSO systems are derived in [10], where parallel relays are investigated over G-G fading with an intensity modulation direct detection (IM/DD) FSO system for a single relay considering both AF and DF relaying techniques. The obtained results show the superior improvement of parallel relays compared to serial relays in terms of outage probability, diversity gain at fixed and variable transmission rates. The single scattering model for UV communications is well explained in [11]. NLOS UV communications over turbulent channels are investigated in [4], where the UV NLOS link is studied including bit error rate (BER) performance for LN channels at short range distances assuming clear weather using on-off keying (OOK) modulation. The outage probability of UV NLOS communication using serial relays over turbulent channels is derived in [5]. It is shown that the use of relays enhances the performance as compared with direct link. However, increasing the number of relays is not necessary to enhance the system performance.

In this paper, the outage probability performance of the cooperative NLOS UV relays system is analyzed and discussed over a LN channel using the selection feature to choose the best relay at every channel time slot (assuming channel state information (CSI) for sources and receivers). Cooperative relays help to shorten the propagation distance which mitigates the effect of both turbulence and path loss effects. The best relay selection doesn’t need synchronization between the relays to avoid correlation effects at the receiver. Moreover, the best relay selection decreases the loading effect on the relays as the relays are not active all the time. This paper contains interesting results as it shows when the parallel or serial relays are better according to many factors such as the increasing number of relays, the effect of different elevation angles, and the various atmospheric model parameters. With reference to literature, the main contributions of this paper are: 1) A multi-relay UV NLOS cooperative model with N relays is proposed. 2) The outage probability for cooperative relays NLOS UV with best relay selection is considered according to the channel coefficient. 3) The proposed cooperative model based on best relay selection is compared with previous serial relays NLOS UV [5] and all-active cooperative relays including the same channel parameters. 4) Different scattering parameters such as thick and tenuous scattering are considered. 5) The required power for different field of view (FOV) is calculated. 6) The effect of elevation angle of the system is studied for different number of relays. The rest of this paper is organized as follows: In Section II, we present the system model. The UV NLOS channel is discussed in Section III. The obtained numerical results are displayed and discussed in Section IV and the paper is concluded in Section V.

2. System model

The synoptic diagram of the proposed UV communication system is illustrated in Fig. 1. UV light emitting diode (LED) sources are employed in the S node using IM/DD and a photo multiplier tube (PMT) operating as a photon-counting detector in the D node. Each relay has a transceiver, where the DF relay receives the signal from the S node assuming single scattering, decodes it and resends it to the D node in order to shorten the propagation distance to enhances the system performance. These relays are located equidistant between the S and the D nodes to give the optimum performance according to [5]. The S node works as a switch to choose the preselected relay according to CSI that can be estimated by a simple signaling process due to the advantage of the slowly varying for the fading UV channel [12–14]. Hence, the active relay will be selected as [12]

j = max_{i \in 1 : N} (min (h_{{SR}_{i}}, h_{R_{i} D}))

where j is the index of the best relay, i is the relay index, h_{SR_i} = exp(2x_i) and h_{R_iD} = exp(2x_i) are the channel fading coefficients between source and the i^th relay (R_i) and between R_i and the destination, respectively. x_i is being an independent and identically distributed (i.i.d.) Gaussian random variable (RV) with a mean μ_x and a variance

σ_{x}^{2}

. To ensure that the fading channel does not attenuate or amplify the average power, the fading coefficients are normalized [14]. The distance between the source S and destination D is given by d_t.

Fig. 1 Synoptic diagram of the proposed model.

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3. UV NLOS channel model

A detailed illustration of the communication link is depicted in Fig. 2, where each NLOS link consists of two LOS paths. To clarify the proposed model, an m^th relay direct hop is chosen to explain the channel characteristics from S to D with symbols m and m + 1, respectively. In Fig. 2, d_m,m+1 is the distance between source and destination with single scattering, where short distance communications is considered that can be accurately modelled by a LN channel model of log amplitude variance $σ_{i}^{2} = 4 σ_{x}^{2} < 1.2$ [15]. A plane wave propagation is assumed and the log amplitude variance is calculated based on the Rytov theory as a function of the distance [16]. The distance between transmitter (tx) and scattering common volume is $d_{m, m + 1}^{t x}$ and it can be calculated in terms of the total hop distance d_m,m+1 with transmitter elevation angle β_Tm as

{d^{t x}}_{m, m + 1} = \frac{d_{m, m + 1} sin (β_{R_{m + 1}})}{sin (θ_{S m, m + 1})}

where β_Rm+1 is the receiver elevation angle, θ_Sm,m+1 = β_Tm + β_Rm+1 and β_tm is the transmitter elevation angle. The distance between receiver (rx) and common volume

d_{m, m + 1}^{r x}

is given by

d_{m, m + 1}^{r x} = \frac{d_{m, m + 1} sin (β_{t m})}{sin (θ_{S m, m + 1})}

where the elevation angles for both transmitter beam and the receiver FOV are β_Tm and β_Rm+1, respectively, and beam divergence for both transmitter and receiver FOV is θ_tm and θ_Rm+1, respectively. Assuming V_m is the intersection area between the transmitter cone beam and the receiver FOV and is called frustum (common volume) which can be considered small enough with respect to the total hop distance. It can be obtained by [17]

V_{m} = (\frac{π}{3}) ({D^{2}}_{m, 1} h_{m, 1} - {D^{2}}_{m, 2} h_{m, 2})

where D_m,1 = h_m,1θ_Tm/2 and D_m,2 = h_m,2θ_Tm/2 represents the radius of the bottom surface of the receiver cone and transmitter cone, respectively, the heights of the bottom surface of the receiver cone (h_m,1) and transmitter cone h_m,2 are as follows:

h_{m, 1} = {d^{t x}}_{m, m + 1} + {d^{r x}}_{m, m + 1} θ_{R m + 1} / 2 .

h_{m, 2} = {d^{t x}}_{m, m + 1} - {d^{r x}}_{m, m + 1} θ_{R m + 1} / 2

The total attenuation path loss consists of multiplications of the attenuation (path loss) due to scattering and turbulence [18], where the attenuation due to turbulence can be calculated as

ℓ (d_{m, m + 1}^{t}) = 10^{\frac{- α}{10}}

with

α = 2 \sqrt{(23.17 {C_{n}}^{2} k^{7 / 6})} (\sqrt{{({d^{t x}}_{m, m + 1})}^{11 / 6}} + \sqrt{{({d^{r x}}_{m, m + 1})}^{11 / 6}}) .

where k is the wave number (

k = \frac{2 π}{λ}

), λ is the wavelength and C_n² is the refractive index structure coefficient which varies according to the nature of the atmosphere and the location on the Earth’s surface. The attenuation due to scattering is given by [17]

ℓ ({d^{s}}_{m, m + 1}) = \frac{k_{s} Ψ (θ_{S m, m + 1}) A_{R} V_{m}}{(1 - cos (θ_{T m} / 2))} \frac{exp (- k_{e} ({d^{t x}}_{m, m + 1} + {d^{r x}}_{m, m + 1}))}{2 π {({d^{t x}}_{m, m + 1} {d^{r x}}_{m, m + 1})}^{2}}

where k_s is the channel atmospheric scattering, A_R is the receiver aperture area, Ψθ_Sm,m+1 is the single scattering phase function related to Rayleigh and Mie scattering phase functions [17]. The extinction coefficient k_e = k_s + k_a, k_a is the absorption coefficient related to channel path loss, and θ_Sm,m+1 = θ₁ + θ₂ where θ₁ and θ₂ are the one hop elevation angles for transmitter and receiver, respectively, θ_s is the angle between the forward direction of incident waves and the observation direction, P(u) is the scattering phase function at u = cos(θ_s) and is given by [18]

P (u) = \frac{{K_{s}}^{Ray}}{K_{s}} P^{Ray} (u) + \frac{{K_{s}}^{Mie}}{K_{s}} P^{Mie} (u)

where K_s = K_s^Ray + K_s^Mie for Rayleigh and Mie scattering, respectively. The phase functions follow the generalized Rayleigh and Henyey-Greenstein functions as [19]

P^{Ray} (u) = \frac{3 (1 + 3 γ + (1 - γ) u^{2})}{16 π (1 + 2 γ)}

and

P^{Mie} (u) = \frac{1 - g^{2}}{4 π} (\frac{1}{{(1 + g^{2} - 2 g u)}^{3 / 2}} + \frac{0.5 f (3 u^{2} - 1)}{{(1 + g^{2})}^{3 / 2}})

where γ, g, f are channel model parameters. The log amplitude variance is given by [5]

{σ_{i}}^{2} = \frac{1.23 {C_{n}}^{2} k^{7 / 6} d^{11 / 6} {(sin β_{R m})}^{11 / 6} {(sin β_{t m})}^{11 / 6}}{{(sin θ_{s})}^{11 / 6}}

where d is the total direct distance and we set the mean μ_i = −0.5σ_i² to ensure that the fading channel does not attenuate or amplify the average power [20, 21]. The instantaneous electrical received SNR for link m → m + 1 is given by [5]

γ_{m, m + 1} = \frac{{(RT P_{T} α_{m, m + 1} ℓ (d_{m, m + 1}))}^{2}}{N_{o}} .

where R is the receiver responsivity, T is the half bit interval, P_T is the total transmitted power, α_m,m+1 is the power fading factor and N_o is the one sided noise spectral density. After relay selection, the end-to-end SNR is given by [22]

γ_{i} = \frac{γ_{{SR}_{i}} γ_{R_{i} D}}{1 + γ_{{SR}_{i}} + γ_{R_{i} D}}

where γ_{SR_i} and γ_{R_iD} are the SNR of S-R and R-D, respectively. The outage probability is defined as the probability that information rate is less than the threshold required information rate. If SNR exceeds the threshold level of SNR (γ_th), no outage occurs and signal is decoded with error probability. If multiple branches of dual-hop exist, the outage probability for the best relay selection can be obtained as [23]

{P_{out}}^{m, m + 1} = \Pr (γ_{m, m + 1} < γ_{t h}) = \Pr (α_{m, m + 1} < \frac{(M + 1) P_{t h}}{L_{m, m + 1} P_{T}}) .

where power margin is defined as P_M = P_T/P_th. P_th denotes the threshold transmitted power required to ensure that no outage occurs at single scattering techniques at free transmission direct fading from S to D. L_m,m+1 is the total normalized attenuation function of scattering and path loss attenuation and M is the number of relays. Therefore, the outage probability can be written using the cumulative distribution function (CDF) of the LN distribution. Then, the outage probability for the total link with DF relaying is given by [5]

P_{out} = 1 - \prod_{m = 0}^{M} (1 - Q (\frac{ln (L_{m, m + 1} P_{M} / (M + 1)) + μ_{{NLOS}_{m, m + 1}}}{σ_{{NLOS}_{m, m + 1}}})) .

where μ_{NLOS_m,m+1} and σ_{NLOS_m,m+1} are mean and variance for one UV NLOS direct hop, respectively. where

Q (x) = (\frac{1}{\sqrt{2 π}}) \int_{x}^{\infty} exp (\frac{- t^{2}}{2}) d t

is the Gaussian Q-function. According to our proposed model, the outage probability in case of best relay selection for N number of relays is given by

P_{out} = {(1 - \prod_{m = 0}^{1} (1 - Q (\frac{ln (L_{m, m + 1} P_{M} / (2)) + μ_{{NLOS}_{m, m + 1}}}{σ_{{NLOS}_{m, m + 1}}})))}^{N} .

at d_m,m+1 = d_t/2.

The end-to-end outage probability for a parallel scheme is given by [8]

P_{out} = {\sum^{2^{N}}}_{i = 1} [\prod_{m \in S (i)} (1 - z) \times \prod_{m \notin S (i)} z] Q (\frac{ln (\frac{P_{M} exp (μ_{ξ})}{2 N})}{σ_{ξ} (d_{S} (i))}) .

where z is the outage probability for one hop [5, eqn. (9)]. However the power margin is divided by the number of transmitters in the relays, 2N, as in [8, eqn. (32)]. Therefore

z = Q (\frac{ln (L_{m, m + 1} P_{M} / (2 N)) + μ_{{NLOS}_{m, m + 1}}}{σ_{{NLOS}_{m, m + 1}}})

where the variance

σ_{ξ}^{2}

and the mean μ_ξ of the log-amplitude factor ξ are functions of d_S(i) which is the set of all the distances between the decoding relays and D [8]

σ_{ξ}^{2} = ln (1 + \frac{\sum_{i \in D} L_{i, N + 1}^{2} (exp (σ_{{NLOS}_{m, m + 1}}^{2}) - 1)}{{(\sum_{i \in D} L_{i, N + 1})}^{2}}) .

μ_{ξ} = ln \sum_{i \in D} L_{i, N + 1} - σ_{ξ}^{2} / 2

The outage probability is investigated at different types of atmospheric model conditions: tenuous, thick, thick plus and extra thick which that correspond to clear, overcast, foggy and dense foggy atmosphere, respectively as given in Table 1.

Fig. 2 One link model for NLOS ultraviolet channel.

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Table 1. Various Types of Atmosphere Model Parameters [24].

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4. Numerical results

In this section, we verify the obtained numerical results for our proposed model with Monte-Carlo (MC) simulation using 10⁶ samples with system configuration as given in Table 2.

Table 2. System Configuration [5, 25].

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As a benchmark, the outage probability of the direct transmission is also included in the numerical results (N = M = 0), where M and N are the number of relays for serial relays and cooperative relays, respectively. In Fig. 3, the outage probability of cooperative relays UV system is illustrated at different numbers of relays (N = 0, 1, 2, 3, 4) at β′ = 70° under the condition of equidistant with best relay selection technique which can enhance the performance based on the max-min SNR criterion at every time slot [13, 14, 26]. It is observed that the performance gain is highly dependent on system configuration. At outage probability of 10⁻⁶, increasing the number of relays enhances the system performance by 7 dB, 11 dB, 13 dB and 14 dB for N = 1, N = 2, N = 3 and N = 4, respectively compared with the direct link. At a higher number of relays, the system performance has small improvement due to the proximity of the distance between the relays. Figure 4 demonstrates the UV NLOS cooperative relays performance at β = β′ = 30°. At outage probability of 10⁻⁶, increasing the number of relays enhances the system performance by 16 dB, 19 dB, 20 dB and 21 dB for N = 1, N = 2, N = 3 and N = 4, respectively compared with the direct link. By controlling the parameters of the system such as elevation angle and number of relays, the system can be enhanced. This means that a good cooperative relays system design is required to reach optimum number of relays that tends to gain an optimum system cost. The incoming light for UV receiver is collected by a lens and is focused onto the detection area, which depends on the aperture size and the receiver FOV. The relation between receiver angle and required power margin is shown in Fig. 5. It is clear that increasing the FOV angle decreases the required power at the same target of outage probability. This is because UV receiver with a large FOV angle collects more received light and improves the system performance. Cooperative relays are also compared with serial relays with the same channel characteristics considering the case of node elevation angles β′ = 70°, 30° [5] as shown in Figs. (6) and (7), respectively. In Fig. 6, it is observed that, the cooperative relays at N=2 conserve up to 10.5 dB of power transmitter and about 8 dB at N=3 compared to serial relays at M=2, M=3, respectively. This value decreases to 3.2 dB at N=4. Figure 7 demonstrates that a different effect is observed when decreasing the elevation angle to β′ = 30°. The obtained results show that using the serial relays is better than using cooperative relays by 3 dB, 4.5 dB and 5 dB for two, three and four relays, respectively. In Figs. (8) and (9), the proposed cooperative based on best relay selection is compared with all-active relays for different values of elevation angle. Figure 8 shows that for β′ = 70°, increasing the number of relays for the case of all-active relays degrades the performance by 1.6 dB, 4.7 dB and 6.3 dB at N=2, N=3, N=4, respectively, as compared with best relay selection scenario. While in Fig. 9, increasing the number of relays does not enhance the performance of the system and increasing the number of relays degrades the performance by 7 dB, 9 dB and 12 dB at N=2, N=3, N=4, respectively, as compared with best relay selection scenario.

Fig. 3 Outage probability of cooperative relays UV system for different numbers of relays at β′ = 70°.

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Fig. 4 Outage probability of cooperative relays UV system for different numbers of relays at β′ = 30°.

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Fig. 5 Relation between receiver FOV angle and required power at outage probability 10⁻⁶ and β′ = 30°.

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Fig. 6 Comparison between serial and cooperative best relays for different numbers of relays at β′ = 70°.

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Fig. 7 Comparison between serial and cooperative best relays for different numbers of relays at β′ = 30°.

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Fig. 8 Comparison between all-active and cooperative best relays for different numbers of relays at β′ = 70°.

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Fig. 9 Comparison between all-active and cooperative best relays for different numbers of relays at β′ = 30°.

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Due to the path loss depends on the scattering parameters and absorbtion coefficient K_a, the atmospheric scattering is studied at different weather conditions as stated in Table 1. To make our system more realistic to different weather conditions, two types of atmospheric models (tenuous and thick) are considered in Fig. 10. There is a 4 dB enhancing in the system performance between tenuous and thick models due to increasing the values of scattering parameters that increases the scattering particles concentration leading to enhancement of the system performance. Figure 11 shows the effect of node elevation angle β′ for N = 0, 1, 2, 3, 4, on the system outage probability. It is observed that in order to get the same outage probability, the threshold values of node elevation angle at power margin P_M = 4 dB are 42°, 56°, 65° and 70° for N =1, 2, 3 and 4, respectively. Therefore, at the same transmitted power margin, increasing the number of relays requires a higher elevation angle β′ to achieve the same outage probability.

Fig. 10 Outage probability versus required power for different types of atmospheric models (tenuous and thick).

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Fig. 11 Relation between nodes elevation angle β′ and outage probability for different numbers of relays N=0, 1, 2, 3, 4.

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5. Conclusions

In this paper, the performance of cooperative relays UV NLOS over LN turbulent channel with best relay selection technique is investigated. The system performance is discussed for the proposed model with compatibility for analytically and MC simulation methods, based on the system parameters such as elevation angle and different atmospheric parameters. The obtained results demonstrate that increasing the number of relays leads to enhancing the system performance at large elevation angles. However, this turns upside down at small elevation angles compared with serial relays UV NLOS system. In addition, the obtained results show that the best relay selection outperforms all-active relay for the same number of relays for small and large elevation angles. In large elevation angles, increasing the number of relays for all-active method enhances the performance of the system. However, for small elevation angles, increasing the number of relays degrades the system performance. For the same system configurations, increasing the receiver FOV angles enhances the system performance to a specified level according to system design. Moreover, the values of atmosphere parameters have a great effect on system performance. Increasing the sources of scattering leads to enhancing the system performance. At UV NLOS cooperative relays, the node elevation angle has a great effect on the system performance which must be considered when designing an UV NLOS communications system. A future work includes the investigation of the non-coplanar geometries of the cooperative NLOS UV. The aim of this future study is to avoid the limitation that the S, the relays and the D cone axes lie in the same plane.

References and links

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Atmosphere	K_S^Ray(km⁻¹)	K_S^Mie(km⁻¹)	K_a(km⁻¹)
Tenuous	0.266	0.286	0.972
Thick	0.292	1.431	1.531
Thick plus	1.101	4.530	1.602
Extra thick	1.912	7.648	1.684

Parameter	Symbol	Value
Extinction coefficient	k_e	1.352 km⁻¹
Atmospheric scattering	k_s	0.55 km⁻¹
Refractive index coefficient	C_n ²	5 × 10⁻¹⁵ m^−2/3
Operating wavelength	λ	260 nm
Channel model parameters	γ, g, f	0.017, 0.72, 0.5
The receiver area	A_R	1.77 cm²
Transmitter beam divergence	θ_tm	8 mrad
Receiver FOV	θ _Rm+1	45°
Transmitter elevation angle	β	30°
Receiver elevation angle	β	30°
Total link distance	d_t	1 km

Atmosphere	K_S^Ray(km⁻¹)	K_S^Mie(km⁻¹)	K_a(km⁻¹)
Tenuous	0.266	0.286	0.972
Thick	0.292	1.431	1.531
Thick plus	1.101	4.530	1.602
Extra thick	1.912	7.648	1.684

Parameter	Symbol	Value
Extinction coefficient	k_e	1.352 km⁻¹
Atmospheric scattering	k_s	0.55 km⁻¹
Refractive index coefficient	C_n ²	5 × 10⁻¹⁵ m^−2/3
Operating wavelength	λ	260 nm
Channel model parameters	γ, g, f	0.017, 0.72, 0.5
The receiver area	A_R	1.77 cm²
Transmitter beam divergence	θ_tm	8 mrad
Receiver FOV	θ _Rm+1	45°
Transmitter elevation angle	β	30°
Receiver elevation angle	β	30°
Total link distance	d_t	1 km

Performance analysis of multiple NLOS UV communication cooperative relays over turbulent channels

Abstract

1. Introduction

2. System model

3. UV NLOS channel model

4. Numerical results

5. Conclusions

References and links

Cited By

Figures (11)

Tables (2)

Equations (21)

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