Abstract

In this paper, on-off keying (OOK) differential detection with fixed threshold is proposed to deal with intensity fluctuation for satellite optical communications (SOCs). Since the intensity fluctuation is relatively slow compared to data rate, sequential symbols are in a quasi-stationary channel. Based on this characteristic, the proposed technique is implemented through the comparison between the difference of sequential symbols and the fixed threshold. The optimum fixed threshold is simply estimated with the knowledge of the channel model and noise power. The simulation results demonstrate that it overcomes the BER limitation of fixed threshold detection. Therefore, the proposed technique enables OOK detection with fixed threshold and real-time implementation in high-speed satellite optical communications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

In recent years, free space optical (FSO) communications have been actively researched due to wide bandwidth, unlicensed spectrum, high data rate, less power and high security [1,2]. For these advantages, satellite optical communications are considered for future satellite communications. Intensity modulation and direct detection (IM/DD) are generally adopted for reducing system complexity [3]. However, its performance is deteriorated by the atmospheric turbulence, which is random phenomenon caused by variation of pressure and temperature of atmospheric channel [4].

The atmospheric turbulence is main factor of system performance degradation. There are three types of atmospheric turbulence (e.g. beam wander, beam spreading and beam scintillation) [1]. Out of these three types, the beam scintillation causes the intensity fluctuation of received signal. In the IM/DD OOK system, the intensity fluctuation makes it ineffective to decide received OOK signals with fixed decision threshold [5]. The bit-error-rate (BER) floors for OOK system employing fixed decision threshold exist, then the BER cannot be small even when the signal-to-noise ratio (SNR) is high [6].

Therefore, many researches have been performed for adaptively estimating decision threshold. A symbol by symbol maximum likelihood (ML) detection and a ML sequence detection (MLSD) are introduced using channel model and temporal correlation information [5]. A symbol by symbol decision-feedback detection (DFD) is made using previous decisions and a window of received statistics [7]. A generalized likelihood ratio test (GLRT) is developed [8], which uses the GLRT-MLSD receiver for detecting data sequence and estimating channel gain. However, these methods require higher implementation complexity compared to the decision with fixed threshold due to requirement of high speed estimation. Also, this problem increases for higher data rate.

In this paper, we propose a OOK differential detection technique with fixed threshold for reducing implementation complexity and eliminating BER limitation. Based on atmospheric channel characteristic, we used difference of sequential symbols for OOK detection. In addition, the fixed threshold is used for decision threshold. We theoretically analyzed the proposed technique and the optimum fixed threshold was obtained. The OOK transmission is simulated through the generated atmospheric channel and the received signal is detected with the proposed technique for performance evaluation. The simulation results show the proposed technique overcomes the BER limitation of OOK system employing fixed threshold, which provides feasibility of a real time transmission implementation.

2. On-off keying differential detection

2.1 Concept

The temporal power spectrum of scintillation is comprised of low frequency component, and the cutoff frequency of the temporal power spectrum is smaller than several kHz [9]. Therefore, the intensity fluctuation is relatively slow compared to conventional data rate. As a result, it can be assumed that sequential symbols are in a state of quasi-stationary channel. Based on this characteristic, OOK differential detection can be implemented.

Figure 1 shows the concept of OOK differential detection. For differentially detecting OOK, difference between current symbol and previous symbol need to be calculated by receiver circuit. If the difference exists, it means current symbol is different from previous symbol, and current symbol is determined as bit ‘1’. Otherwise, just the opposite. This method requires criterion of difference, which is fixed threshold. The knowledge of noise power and channel model is only needed for estimating the optimum fixed threshold. It can be calculated through pilot transmission using continuous wave. The channel model is estimated by the intensity fluctuation which can be extracted by low-pass filtering of the received signal. In addition, the noise can be estimated by subtraction of the extracted intensity fluctuation from the received signal.

 figure: Fig. 1

Fig. 1 Concept of OOK differential detection.

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2.2 Scheme and optimum fixed threshold estimation

Figure 2 shows the block diagram of OOK transmission with the proposed technique in SOCs. At the transmitter, bit stream is modulated with the differential OOK. The optical signal generated by a laser is transmitted through atmospheric channel, which causes the intensity fluctuation. At the receiver, the received optical signal is converted to electrical signal by a photodiode, and the electrical signal is sampled at the symbol rate by sampler. The noise at the receiver is dominated by thermal noise, which can be modeled as the additive white Gaussian noise (AWGN). Therefore, the digital received signal r[k] at the receiver is expressed as

r[k]=ηI[k]s[k]+n[k],
where I[k] is the intensity fluctuation, s[k]{0, 1} is the symbol information, n[k] is AWGN with noise power σn2 and η is the optical-to-electrical conversion coefficient. We assumed that η=1 for a convenience. For the differential detection, the digital received signal r[k] is separated into two branches. One branch feeds current symbol into subtraction circuit, and the other branch feeds previous symbol into subtraction circuit with one symbol delay. The signal after subtraction process is expressed as
|r[k]r[k+1]|=|I[k]s[k]+n[k](I[k+1]s[k+1]+n[k+1])||I[k](s[k]s[k+1])+(n[k]n[k+1])|.
Because sequential symbols undergo quasi-stationary channel, it is possible that I[k]I[k+1]. The decision criterion is
|r[k]r[k+1]|d[k]=0<d[k]=1>Th,
where d[k] is decision bit and Th is fixed decision threshold, which decides whether or not current symbol is the same with previous symbol.

 figure: Fig. 2

Fig. 2 Block diagram of OOK differential detection.

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The error probability of bit ‘0’ and bit ‘1’ are respectively

P(1|0)=Pr{|r[k]r[k+1]|>Th}=Pr{|(n[k]n[k+1])|>Th},
P(0|1)=Pr{|r[k]r[k+1]|<Th}Pr{|I[k]+(n[k]n[k+1])|<Th},
where P(1|0) is the probability of decision with bit ‘1’ when bit ‘0’ is transmitted and P(0|1) is the opposite. In the case of P(1|0) and P(0|1), respectively s[k]=s[k+1] and s[k]s[k+1]. Let I, N and Z be the random variables of I[k], (n[k]n[k+1]) and Z=I+N. The density function fI(i) of I is the distribution of the intensity fluctuation. There are a variety of the distribution for the intensity fluctuation such as lognormal distribution, I-K distribution and Gamma-Gamma distribution. Because both n[k] and n[k+1] are AWGN with mean 0 and variance σn2, the density function fN(n) of N is normal distribution with mean 0 and variance 2σn2. The density function fZ(z) of Z is the convolution of fI and fN due to the sum of independent random variables.

P(1|0) and P(0|1) are respectively calculated as

P(1|0)=2ThfN(n)dn=2Th14πσn2en2σn2dn=1erf(Th2σn).
P(0|1)=ThThfZ(z)dz=12(erf(Thi2σn)erf(Thi2σn))fI(i)di.
The integration in Eq. (7) could be computed by Gauss-Hermite quadrature formula [12]
P(0|1)1πt=1kwt(Q(Thi0e2σx2+zt8σx22σn)Q(Thi0e2σx2+zt8σx22σn)),
where i0 is the mean of I, σx2 is the variance of log-amplitude fluctuation, k is the order of approximation, zt are the zeros of the kth-order Hermite polynomial, and wt are the weight factors for the kth-order approximation. The total error probability Perror=P(1|0)P(0)+P(0|1)P(1) is
Perror=12(1erf(Th2σn)+1πt=1kwt(Q(Thi0e2σx2+zt8σx22σn)Q(Thi0e2σx2+zt8σx22σn))).
The condition of the minimum error probability is satisfied with
ddThPerror=12(fZ(Th)+fZ(Th)1σnπe(Th2σn)2)=0.
Therefore, the optimum fixed threshold can be estimated by the minimum error condition with knowledge of channel model and noise power. Although the proposed technique can be applied in any channel condition, for ease of description, simulation and analysis are conducted under the weak turbulence condition where the channel model is lognormal profile.

3. Channel validation

For estimating performance of the proposed technique, we conducted transmission simulation. Because atmospheric channel which causes the intensity fluctuation is required for the simulation, we generated the intensity fluctuation. The intensity fluctuation can be generated using power spectral density (PSD) of scintillation. The PSD of log-amplitude fluctuation can be written as [10]

WA(f)=0.528π2k20LCn2(h)2πfv(h)[(κv(h))2(2πf)2]1/2κ8/3sin2(κ2γh2k)F(γκ)dκdh,
where k is the optical wave number, h is the altitude, Cn2 is the refractive index parameter, L is the propagation distance, v(h) is the wind speed, κ is the spatial wave number, γ is the propagation parameter that has the value of γ=1h/L for downlink channel and γ=h/L for uplink channel in spherical wave model, and F(γκ) is the aperture filter function [10,11]. The log-amplitude fluctuation is the logarithm of the intensity fluctuation.

We calculated the PSD with the parameters shown in Table 1, and the result is shown in Fig. 3(a). We generated the intensity fluctuation using inverse Fourier transform process of the PSD [9], and the result of downlink channel is shown in Fig. 3(b). In addition, the density distribution, shown in Fig. 3(c), is well matched to lognormal distribution, where mean and variance of the distribution are the same with the generated intensity fluctuation. The intensity fluctuation is measured in terms of scintillation index (normalized variance of the intensity fluctuation), σI2.

Tables Icon

Table 1. Parameters for PSD

 figure: Fig. 3

Fig. 3 (a) Power spectral density, (b) generated intensity fluctuation and (c) density distribution of Table 1.

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4. Simulation and results

We simulated OOK transmission in SOCs based on previous analyses of OOK differential detection and atmospheric channel. The simulation is conducted under weak turbulence condition. BER according to SNR with varying channel parameters is demonstrated for estimating performance. The SNR is time varying due to the intensity fluctuation. Therefore, we used average SNR which is defined as SNR=E[I]2/2σn2, where E[I] denotes the average received signal intensity.

We assumed sequential symbols are in a state of quasi-stationary channel. However, this assumption is valid depending on data rate and channel condition. Figure 4(a) shows the BER performance variation according to data rate in downlink and uplink channel. Since the minimum data rate for the assumption is varied with channel condition, the data rate is set as 100 Mbps where sequential symbols are in quasi stationary channel under the weak turbulence condition. Figure 4(b) shows the BER performance variation according to ground turbulence strength and aperture diameter in downlink. Since the BER performance is influenced by various channel parameters, it can be intuitively verified by using the scintillation index. The scintillation index depends on the PSD influenced by channel parameters. Therefore, we measured the BER performance by varying scintillation index.

 figure: Fig. 4

Fig. 4 (a) The BER performance variation according to data rate of 0.1 Mbps, 0.2 Mbps, 0.4 Mbps and 1 Mbps in downlink and uplink channel. (b) The BER performance variation according to ground turbulence strength (A = 2×1011, 2×1012) and aperture diameter (D = 0.1, 1) in downlink channel.

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Figure 5 shows BER performance of OOK differential detection. The simulation results of OOK differential detection are closely matched with the theoretical BER performance from Eq. (9), as shown in Fig. 5(a). Therefore, we could know the proposed technique is operated well in weak turbulence regime. In order to evaluate the performance of the proposed scheme, the decision with instantaneous CSI and the decision with fixed threshold are used as comparison [6,12]. As shown in Fig. 5(b), the performance of the proposed scheme is better than the decision with fixed threshold from certain SNR point due to the BER limitation of OOK employing fixed threshold detection. These SNR are 16.604 dB and 13.670 dB for of 0.5 and 0.15 respectively. Since the BER limitation increases with higher scintillation index, this tendency persists and performance improvement is caused in almost every SNR. Although there is a performance gap between OOK differential detection and decision with instantaneous CSI, the results of instantaneous CSI are ideal values as it is unavailable in practical systems. Therefore, the proposed technique showed a good performance without any extra resource and possibility of real time communication in SOCs.

 figure: Fig. 5

Fig. 5 BER performance. (a) The theoretical results and the simulation results of OOK differential detection. (b) The comparison of decision with instantaneous CSI, decision with fixed threshold and OOK differential detection.

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5. Conclusion

In summary, the OOK differential detection with fixed threshold has been proposed to deal with intensity fluctuation in SOCs. We theoretically analyzed the proposed technique and the optimum fixed threshold was estimated based on atmospheric channel characteristic. The performance of the proposed technique is evaluated through the OOK transmission simulation. As a result, the proposed technique overcomes the limitation of decision with fixed threshold. In addition, real time implementation is not a problem, because it uses fixed threshold through simple calculation even in high data rate. Therefore, the OOK detection with the proposed technique can be feasible in SOCs.

Funding

National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP; Ministry of Science, ICT & Future Planning) [2017M1A3A3A02016524].

References

1. H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017). [CrossRef]  

2. H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

3. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: a communication theory perspective,” IEEE Commun. Surveys Tuts. 16(4), 2231–2258 (2014). [CrossRef]  

4. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through RandomMedia (SPIE Press, 2005).

5. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002). [CrossRef]  

6. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007). [CrossRef]  

7. M. L. B. Riediger, R. Schober, and L. Lampe, “Decision–Feedback Detection for Free–Space Optical Communications,” in Vehicular Technology Conference (IEEE, 2007), pp. 1193–1197.

8. T. Song and P.-Y. Kam, “A robust GLRT receiver with implicit channel estimation and automatic threshold adjustment for the free space optical channel with IM/DD,” J. Lightwave Technol. 32(3), 369–383 (2014). [CrossRef]  

9. M. Toyoshima, H. Takenaka, and Y. Takayama, “Atmospheric turbulence-induced fading channel model for space-to-ground laser communications links,” Opt. Express 19(17), 15965–15975 (2011). [CrossRef]   [PubMed]  

10. H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330, 160–164 (2014). [CrossRef]  

11. C. Chen and H. Yang, “Role of location-dependent transverse wind on root-mean-square bandwidth of temporal light-flux fluctuations in the turbulent atmosphere,” J. Opt. Soc. Am. A 34(11), 2070–2076 (2017). [CrossRef]   [PubMed]  

12. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Commun. 6(8), 2813–2819 (2007). [CrossRef]  

References

  • View by:

  1. H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017).
    [Crossref]
  2. H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).
  3. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: a communication theory perspective,” IEEE Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
    [Crossref]
  4. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through RandomMedia (SPIE Press, 2005).
  5. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
    [Crossref]
  6. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
    [Crossref]
  7. M. L. B. Riediger, R. Schober, and L. Lampe, “Decision–Feedback Detection for Free–Space Optical Communications,” in Vehicular Technology Conference (IEEE, 2007), pp. 1193–1197.
  8. T. Song and P.-Y. Kam, “A robust GLRT receiver with implicit channel estimation and automatic threshold adjustment for the free space optical channel with IM/DD,” J. Lightwave Technol. 32(3), 369–383 (2014).
    [Crossref]
  9. M. Toyoshima, H. Takenaka, and Y. Takayama, “Atmospheric turbulence-induced fading channel model for space-to-ground laser communications links,” Opt. Express 19(17), 15965–15975 (2011).
    [Crossref] [PubMed]
  10. H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330, 160–164 (2014).
    [Crossref]
  11. C. Chen and H. Yang, “Role of location-dependent transverse wind on root-mean-square bandwidth of temporal light-flux fluctuations in the turbulent atmosphere,” J. Opt. Soc. Am. A 34(11), 2070–2076 (2017).
    [Crossref] [PubMed]
  12. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Commun. 6(8), 2813–2819 (2007).
    [Crossref]

2017 (2)

2014 (3)

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330, 160–164 (2014).
[Crossref]

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: a communication theory perspective,” IEEE Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

T. Song and P.-Y. Kam, “A robust GLRT receiver with implicit channel estimation and automatic threshold adjustment for the free space optical channel with IM/DD,” J. Lightwave Technol. 32(3), 369–383 (2014).
[Crossref]

2011 (1)

2007 (2)

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Commun. 6(8), 2813–2819 (2007).
[Crossref]

2002 (1)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through RandomMedia (SPIE Press, 2005).

Chen, C.

Fan, C.

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330, 160–164 (2014).
[Crossref]

Jain, V. K.

H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017).
[Crossref]

Kahn, J. M.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

Kam, P.-Y.

Kar, S.

H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

Kaushal, H.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017).
[Crossref]

H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

Kavehrad, M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Commun. 6(8), 2813–2819 (2007).
[Crossref]

Khalighi, M. A.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: a communication theory perspective,” IEEE Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

Lampe, L.

M. L. B. Riediger, R. Schober, and L. Lampe, “Decision–Feedback Detection for Free–Space Optical Communications,” in Vehicular Technology Conference (IEEE, 2007), pp. 1193–1197.

Li, J.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Liu, J. Q.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Navidpour, S. M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Commun. 6(8), 2813–2819 (2007).
[Crossref]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through RandomMedia (SPIE Press, 2005).

Riediger, M. L. B.

M. L. B. Riediger, R. Schober, and L. Lampe, “Decision–Feedback Detection for Free–Space Optical Communications,” in Vehicular Technology Conference (IEEE, 2007), pp. 1193–1197.

Schober, R.

M. L. B. Riediger, R. Schober, and L. Lampe, “Decision–Feedback Detection for Free–Space Optical Communications,” in Vehicular Technology Conference (IEEE, 2007), pp. 1193–1197.

Shen, H.

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330, 160–164 (2014).
[Crossref]

Song, T.

Takayama, Y.

Takenaka, H.

Taylor, D. P.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Toyoshima, M.

Uysal, M.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: a communication theory perspective,” IEEE Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Commun. 6(8), 2813–2819 (2007).
[Crossref]

Yang, H.

Yu, L.

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330, 160–164 (2014).
[Crossref]

Zhu, X.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

IEEE Comm. Surv. and Tutor. (1)

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017).
[Crossref]

IEEE Commun. Surveys Tuts. (1)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: a communication theory perspective,” IEEE Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

IEEE Trans. Commun. (2)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

IEEE Trans. Wirel. Commun. (1)

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Commun. 6(8), 2813–2819 (2007).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330, 160–164 (2014).
[Crossref]

Opt. Express (1)

Other (3)

M. L. B. Riediger, R. Schober, and L. Lampe, “Decision–Feedback Detection for Free–Space Optical Communications,” in Vehicular Technology Conference (IEEE, 2007), pp. 1193–1197.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through RandomMedia (SPIE Press, 2005).

H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

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Figures (5)

Fig. 1
Fig. 1 Concept of OOK differential detection.
Fig. 2
Fig. 2 Block diagram of OOK differential detection.
Fig. 3
Fig. 3 (a) Power spectral density, (b) generated intensity fluctuation and (c) density distribution of Table 1.
Fig. 4
Fig. 4 (a) The BER performance variation according to data rate of 0.1 Mbps, 0.2 Mbps, 0.4 Mbps and 1 Mbps in downlink and uplink channel. (b) The BER performance variation according to ground turbulence strength (A = 2× 10 11 , 2× 10 12 ) and aperture diameter (D = 0.1, 1) in downlink channel.
Fig. 5
Fig. 5 BER performance. (a) The theoretical results and the simulation results of OOK differential detection. (b) The comparison of decision with instantaneous CSI, decision with fixed threshold and OOK differential detection.

Tables (1)

Tables Icon

Table 1 Parameters for PSD

Equations (11)

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r[k]=ηI[k]s[k]+n[k],
| r[k]r[k+1] |=| I[k]s[k]+n[k](I[k+1]s[k+1]+n[k+1]) | | I[k](s[k]s[k+1])+(n[k]n[k+1]) |.
| r[k]r[k+1] | d[k]=0 < d[k]=1 > Th,
P(1|0)=Pr{| r[k]r[k+1] |>Th}=Pr{| (n[k]n[k+1]) |>Th},
P(0|1)=Pr{| r[k]r[k+1] |<Th}Pr{| I[k]+(n[k]n[k+1]) |<Th},
P(1|0)=2 Th f N (n)dn=2 Th 1 4π σ n 2 e n 2 σ n 2 dn=1erf( Th 2 σ n ) .
P(0|1)= Th Th f Z (z)dz = 1 2 (erf( Thi 2 σ n )erf( Thi 2 σ n )) f I (i)di.
P(0|1) 1 π t=1 k w t (Q( Th i 0 e 2 σ x 2 + z t 8 σ x 2 2 σ n )Q( Th i 0 e 2 σ x 2 + z t 8 σ x 2 2 σ n )),
P error = 1 2 (1erf( Th 2 σ n )+ 1 π t=1 k w t (Q( Th i 0 e 2 σ x 2 + z t 8 σ x 2 2 σ n )Q( Th i 0 e 2 σ x 2 + z t 8 σ x 2 2 σ n ))).
d dTh P error = 1 2 ( f Z (Th)+ f Z (Th) 1 σ n π e ( Th 2 σ n ) 2 )=0.
W A (f)=0.528 π 2 k 2 0 L C n 2 (h) 2πf v(h) [ (κv(h)) 2 (2πf) 2 ] 1/2 κ 8/3 sin 2 ( κ 2 γh 2k ) F(γκ)dκdh,

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