## Performance improvement of FSO/CDMA systems over dispersive turbulence channel using multi-wavelength PPM signaling |

Optics Express, Vol. 20, Issue 24, pp. 26786-26797 (2012)

http://dx.doi.org/10.1364/OE.20.026786

Acrobat PDF (886 KB)

### Abstract

Previous studies show that, compared to on-off keying (OOK) signaling, pulse-position modulation (PPM) is favorable in FSO/CDMA systems thanks to its energy efficiency and simple detection. Nevertheless, when the system bit rate increases and the transmission distance is far, the FSO/CDMA systems using PPM signaling critically suffer from the impact of pulse broadening caused by dispersion, especially when the modulation level is high. In this paper, we therefore propose to use multi-wavelength PPM (MWPPM) signaling to overcome the limitation of PPM. To further improve the system performance, avalanche photodiode (APD) is also used. The performance of the proposed system is theoretically analyzed using a realistic model of Gaussian pulse propagation. To model the impact of intensity fluctuation caused by the atmospheric turbulence, the log-normal channel is used. We find that, by using MWPPM, the effects of both intensity fluctuation and pulse broadening are mitigated, the BER is therefore significantly improved. Additionally, we quantitatively show that the system performance is further improved by using APD, especially when the average APD gain is chosen properly.

© 2012 OSA

## 1. Introduction

1. H. A. Willebrand and B. S. Ghuman, “Fiber optics without fiber,” IEEE Spectrum **38**, 40–45 (2001). [CrossRef]

2. Q. Liu, C. Qiao, G. Mitchell, and S. Stanton, “Optical wireless communication networks for first- and last-mile broadband access [Invited],” J. Opt. Netw. **4**, 807–828 (2005). [CrossRef]

3. T. Ohtsuki, “Performance analysis of atmospheric optical PPM CDMA systems,” J. Lightwave Technol. **21**, 406–411 (2003). [CrossRef]

7. A. T. Pham, T. A. Luu, and N. T. Dang, “Performance bound for Turbo-coded 2-D FSO/CDMA systems over atmospheric turbulence channel,” IEICE Trans. Fundamentals. **E93-A**, 1745–1337 (2010). [CrossRef]

8. A. Stok and E. H. Sargent, “The role of optical CDMA in access networks,” IEEE Commun. Mag. **40**, 83–87 (2002). [CrossRef]

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

11. C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt **37**, 7655–7660 (1998). [CrossRef]

*M*-ary pulse-position modulation (

*M*-PPM) as an energy-efficient transmission [3

3. T. Ohtsuki, “Performance analysis of atmospheric optical PPM CDMA systems,” J. Lightwave Technol. **21**, 406–411 (2003). [CrossRef]

7. A. T. Pham, T. A. Luu, and N. T. Dang, “Performance bound for Turbo-coded 2-D FSO/CDMA systems over atmospheric turbulence channel,” IEICE Trans. Fundamentals. **E93-A**, 1745–1337 (2010). [CrossRef]

*M*-PPM also avoids adaptive threshold adjustment required in on-off keying (OOK). Previous studies, which ignore the pulse broadening effect, show that

*M*-PPM is effective in reducing intensity fluctuation. However, to provide a comprehensive performance analysis of FSO/CDMA systems, the effect of pulse broadening should be evaluated. Moreover, its effect will be considerable and cannot be ignored since FSO systems, and especially FSO/CDMA systems using

*M*-PPM, require to send high chip rate (i.e., short pulse) through turbulence channel.

*M*-PPM with high-level modulation (i.e.,

*M*is large), we propose to use multi-wavelength PPM (MWPPM), which is a combination of wavelength shift keying (WSK) [12

12. H. Hemmati, *Deep Space Optical Communications* (John Wiley and Sons, 2006). [CrossRef]

*L*) and the number of positions (

*M*). In a

*L*-

*M*-MWPPM, an optical pulse representing one of

*N*symbols can be transmitted in one of

*M*time slot at one of

*L*wavelengths as shown in Fig. 1, where

*N*=

*L*×

*M*. As a result, thanks to the use of

*L*wavelengths, the modulation level of

*M*-PPM can be increased

*L*times without increasing the chip rate. In addition, MWPPM avoids the linear increase in required average laser power with data rate that is characteristic of WSK [12

12. H. Hemmati, *Deep Space Optical Communications* (John Wiley and Sons, 2006). [CrossRef]

## 2. Atmospheric turbulence channel model

### 2.1. Log-normal channel model

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

14. T. A. Tsiftsis, H.G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Comm. **8**, 951–957 (2009). [CrossRef]

15. E. Bayaki, R. Schober, and R.K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Comm. **57**, 3415–3424 (2009). [CrossRef]

*B*has a log-normal distribution if the random variable

*A*= ln

*B*has a normal (i.e., Gaussian) distribution. Thus, if the amplitude of the random path gain

*B*is

*I*, the optical intensity

*I*=

*B*

^{2}is also lognormally distributed in this case. Consequently, the fading channel coefficient, which models the channel from the transmit aperture to the receive aperture, is given by where,

*I*is the signal light intensity, actually at the transmitter, without turbulence;

_{m}*I*is the signal light intensity, actually at the receiver, with turbulence. Log-amplitude

*X*, which is the identically distributed normal random variable with mean

*μ*and standard deviation

_{x}*σ*, can be expressed as

_{x}*h*)=1. Doing so requires the choice of

16. I. Djordjevic, W. Ryan, and B. Vasic, *Coding for Optical Channels* (Springer, 2010). [CrossRef]

*λ*is the wavelength and

*z*is the link distance in meters.

### 2.2. Pulse propagation model

*P*and

_{p}*T*

_{0}are the peak power and the half-width (at the 1/

*e*point) of the input pulse, respectively.

*z*(km) from the transmitter can be expressed as where

*A*is receiver aperture area.

*θ*and

*β*are beam divergence angle in mrad and attenuation coefficient in km

^{−1}, respectively. The parameter

*α*is given by [11

11. C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt **37**, 7655–7660 (1998). [CrossRef]

*L*

_{0}is the outer scale of turbulence and

*c*is the light velocity. In Eq. (7),

*z*is the link distance in meters.

## 3. Multi-wavelength PPM signaling

*L*-

*M*-MWPPM is a combination of

*L*-WSK and

*M*-PPM, where

*L*is the number of transmitted wavelengths and

*M*is the modulation level of PPM. In this technique, each block of

*b*= log

_{2}

*N*data bits is mapped to one of

*N*possible symbols (

*s*

_{0},

*s*

_{1},...,

*s*

_{N}_{−1}). In each

*b*-bit block, the first log

_{2}

*L*bits are used for WSK and the remaining log

_{2}

*M*ones for PPM, as shown in Fig. 2. The symbol intervals,

*T*, are divided into

_{w}*M*time-disjoint time slots and an optical pulse with constant power is sent in one of these

*M*time slots while remaining

*M*− 1 time slots are empty. Moreover, the optical pulse can take on any of

*L*disjoint wavelengths. Therefore, the dimensionality of the signal-space has been increased from

*M*dimensions for PPM to

*L*×

*M*dimensions.

*b*

_{1}

*b*

_{2}) decide the wavelength of the optical pulse while the last two bits (

*b*

_{3}

*b*

_{4}) govern the position (or time slot, TS) that the pulse is transmitted. For example, if the 4-bit input data is 0111, the 4-4-MWPPM modulator will send an optical pulse at time slot 3 of the symbol interval and on wavelength

*λ*

_{1}.

## 4. FSO/CDMA systems using MWPPM

*L*-

*M*-MWPPM is shown in Fig. 3. For illustrative purposes, the principle of the FSO/CDMA system using 2-2-MWPPM is explained in detail.

*b*= log

_{2}

*N*data bits is first sent to a MWPPM modulator, whose block diagram is illustrated in Fig. 4(a). At the MWPPM modulator, the first log

_{2}

*L*bits of the

*b*-bit block are detected by a WSK modulator to decide the wavelength of the MWPPM symbol by sending the remaining bits to its corresponding output. The remaining bits are entered into a PPM modulator to govern the position, i.e., time slot, of the transmitted pulse during a symbol interval (

*T*). Finally, optical pulse representing for a MWPPM symbol is encoded by an OCDMA encoder, where it is spread into a chip sequence including chip “1” and “0”. A chip “1” is an optical pulse while a chip “0” is no pulse. The number of chips in a sequence is equal to the code length (

_{w}*F*) of the signature code generated by the code generator. Each chip “1” is assumed as a Gaussian pulse, which will be affected by pulse broadening effect and attenuation during propagation over dispersive turbulence channel.

*M*outputs which contain the electrical currents corresponding the intensity of the received signal at

*M*time slots of a symbol interval. Finally, at symbol detector, integrated photocurrents over

*N*=

*L*×

*M*inputs corresponding to

*N*symbols, are compared. The input with the highest current determines the transmitted symbol and recovers the binary data.

## 5. Performance analysis

### 5.1. Signal and noise

*A*(

_{i}*t*), representing for chip “1” based on system’s parameters. For the bit rate of

*R*bit per second, the

_{b}*L*-

*M*-MWPPM symbol intervals have a duration of

*T*= log

_{w}_{2}

*N/R*, and the duration of time slots is written as

_{b}*T*=

_{s}*T*/

_{w}*M*. As

*F*chips is send in each time slot, the chip duration can be expressed as

*T*=

_{c}*T*/

_{s}*F*. The relation between the half-width of Gaussian pulse (

*T*

_{0}) and its full-width (

*T*) can be expressed as [17]

_{c}*P*. The relation between

_{s}*P*and

_{c}*P*is given by

_{s}*P*=

_{c}*M*(log

_{2}

*N*)

*P*/

_{s}*w*. In addition, the peak power of transmitted Gaussian pulse (

*P*) can be computed as The derivation of Eq. (9) is presented in detail in the Appendix.

_{p}*w*pulses from the desired user, which is equal to the code weight. As well, each interfering user contributes at most

*γ*pulses corresponding to the cross-correlation value between two different codes.

*a*= 1 when the desired transmitter send a symbol at the time slot

*u*on wavelength

*λ*(0 ≤

_{v}*u*≤

*M*− 1 and 0 ≤

*v*≤

*L*− 1), otherwise

*a*is equal to zero.

*h*and

_{d}*h*denote the intensity fluctuation caused by atmospheric turbulence on the desired user and interfering user

_{k}*k*.

*κ*

^{(u,v)}is the total of number of interfering pulses at the time slot

*u*and wavelength

*λ*. In addition,

_{v}*ω*

_{λv}and

*ϕ*

_{λv}are the optical frequency and phase of the optical carrier corresponding to the wavelength

*λ*, respectively.

_{v}*u*can be expressed as where and

*g*̄ are the responsivity and average gain of APD, respectively.

*P*̄

*is the average power per chip considering pulse broadening effect, whose value can be computed as*

_{c}*e*is the electron charge;

*k*is Boltzmann constant;

_{B}*T*is the absolute temperature; and

*R*is the load resistance.

_{L}*P*denotes optical background power and Δ

_{b}*f*=

*B*/2 is the effective noise bandwidth with

_{e}*B*=

_{e}*MR*/ log

_{b}_{2}

*N. F*is the excess noise factor of the APD, which is given by where

_{a}*ζ*denotes the ionization factor.

### 5.2. Bit error rate

*L*-

*M*-MWPPM and APD. It is worth noting that

*M*-PPM and

*L*-WSK are the special cases of

*L*-

*M*-MWPPM with

*L*= 1 and

*M*= 1, respectively. Denoting

*P*as the symbol error probability, the bit error rate of the system then can be derived as

_{e}*s*

_{0}is transmitted and there is no pulse interfering to this symbol (upper bound case), by using union bound technique, the upper bound to the instantaneous symbol error probability over a

*K*user channel can be expressed as [7

7. A. T. Pham, T. A. Luu, and N. T. Dang, “Performance bound for Turbo-coded 2-D FSO/CDMA systems over atmospheric turbulence channel,” IEICE Trans. Fundamentals. **E93-A**, 1745–1337 (2010). [CrossRef]

*s*represents the transmitted symbol.

*κ*

^{(1,0)}is the total number of pulses interfering to symbol

*s*

_{1}.

*γ*is the maximum cross-correlation between two users’ signature codes.

*I*

^{(0,0)}and

*I*

^{(1,0)}are the photocurrent representing symbols

*s*

_{0}and

*s*

_{1}, respectively.

*w/F*. On the other hand, the probability that this pulse will overlap another pulse from an interfering user is again equal to

*w/F*. This result leads to the probability of a single chip interference (overlap) between any two codes at chip duration being equal to

*w*

^{2}/

*F*

^{2}. Hence,

*κ*

^{(1,0)}can be modeled as a binomial random variable with probability

*w*

^{2}

*/F*

^{2}. As a result, the first term in Eq. (16) can be expressed as The last term in Eq. (16) is calculated by

*Q*(.) is the

*Q*function.

*μ*

_{I(0,0)},

*μ*

_{I(1,0)}, and

*I*

^{(0,0)}and

*I*

^{(1,0)}, respectively. Based on Eqs. (11) and (13) and under assumption that there are no MAI pulses interfering to symbol

*s*

_{0}, i.e., the worst performance as the impact of MAI on symbol

*s*

_{0}is positive, their values can be expressed as

## 6. Numerical results

*p*) has the code length of

_{s}*w*=

*p*, and the cross-correlation between two any codes of

_{s}*γ*= 2 [18]. The system parameters and constants used in the analysis are shown in Table 1.

*M*-PPM, and

*L*-

*M*-MWPPM versus the transmitted power per bit when

*z*= 1.5 km,

*K*= 32 users, and

*R*= 1 Gbps. It is seen that the system performance is significantly improved by using either PPM or MWPPM. However, we find that

_{b}*M*-PPM with

*M*> 16 does not help to reduce system’s BER. BER of FSO/CDMA system using 32-PPM is even worse than that of the one using 8-PPM. This is because the system using 32-PPM has higher chip rate and thus pulse broadening effect is dominant compared to intensity fluctuation one.

*M*-PPM can be overcome by using

*L*-

*M*-MWPPM, which has an ability of mitigating both intensity fluctuation and pulse broadening effects, simultaneously. Figure 5 shows that the required transmitted-power per bit to achieve the same BER of the system using 2–8-MWPPM is about 3 dB lower than that of the one using 8-PPM. The power gain of 2–8-MWPPM compared to 8-PPM comes from the fact that 2–8-MWPPM helps to reduce the power loss caused by pulse broadening effect thanks to the increase of the pulse width compared with 8-PPM. Actually, according to Eq. (8), the pulse width of the system using 2–8-MWPPM is equal to 4/3 the pulse width of the one using 8-PPM.

*P*= 0 dBm and investigate the BER versus the link distance for OOK, PPM, WSK, and MWPPM systems. The number of simultaneous users and the user bit rate are kept the same as in Fig. 5 while the modulation level is fixed to 16. Thanks to the reduction of pulse broadening effect, the link distance in the FSO/CDMA system using MWPPM can be extended in comparison to the one using OOK or PPM. For example, the maximum link distance in the 8-2-MWPPM system is 0.4 km longer than that of the 16-PPM system. Also, 8-2-MWPPM overcomes 16-WSK (i.e., 16-1-MWPPM) in terms of maximum link distance since WSK, although can also reduce the pulse broadening effect, requires more transmitted power per bit than that of MWPPM.

_{s}*z*= 1.5 km,

*K*= 32 users, and

*P*= 0 dBm. We can observe that the increase of atmospheric turbulence effects (i.e.,

_{s}*L*-

*M*-MWPPM can support higher bit rate per user compared to the one using

*M*-PPM. More specifically, when

^{−6}) is about 1.35 Gbps. By using 4-4-MWPPM, more than double bit rate per user (i.e., 3.0 Gbps) can be achieved. When

^{−6}) of the system using 16-PPM drops below 1 Gbps while it is 1.5 Gbps for the one using 4-4-MWPPM.

*P*= −2 dBm. It is seen that BER of FSO/CDMA systems with APD receiver are significantly reduced in comparison with the ones without APD receiver (i.e.,

_{s}*g*̄ = 1). The optimum average APD gain, at which BER is smallest, is around 30. When APD gain is larger than 30, APD shot noise becomes considerable thus the system performance is degraded, i.e., BER increases.

## 7. Conclusion

*M*-PPM with

*M*> 16 should not be used as it requires to send short pulse, which is more affected by pulse broadening effect. By using MWPPM, the effect of both intensity fluctuation and pulse broadening can be mitigated thus the system’s BER is reduced. In addition, we found that the system performance is significantly improved by using APD, especially when the average APD gain is chosen properly.

## Appendix

*P*, is defined as We assume that the amplitude of transmitted Gaussian pulse is decreased so that the borders of the chip duration, −

_{c}*T*/2 and

_{c}*T*/2, can be replaced by −∞ and ∞ as integration limits. Equation (19) can be written as where

_{c}## Acknowledgment

## References and links

1. | H. A. Willebrand and B. S. Ghuman, “Fiber optics without fiber,” IEEE Spectrum |

2. | Q. Liu, C. Qiao, G. Mitchell, and S. Stanton, “Optical wireless communication networks for first- and last-mile broadband access [Invited],” J. Opt. Netw. |

3. | T. Ohtsuki, “Performance analysis of atmospheric optical PPM CDMA systems,” J. Lightwave Technol. |

4. | K. Ohba, T. Hirano, T. Miyazawa, and I. Sasase, “A symbol decision scheme to mitigate effects of scintillations and MAIs in optical atmospheric PPM-CDMA systems,” in |

5. | M. Jazayerifar and J. A. Salehi, “Atmospheric optical CDMA communication systems via optical orthogonal godes,” J. Lightwave Technol. |

6. | T. Miyazawa and I. Sasase, “BER performance analysis of spectral phase-encoded optical atmospheric PPM-CDMA communication systems,” J. Lightwave Technol. |

7. | A. T. Pham, T. A. Luu, and N. T. Dang, “Performance bound for Turbo-coded 2-D FSO/CDMA systems over atmospheric turbulence channel,” IEICE Trans. Fundamentals. |

8. | A. Stok and E. H. Sargent, “The role of optical CDMA in access networks,” IEEE Commun. Mag. |

9. | X. Zhu and J. M. Khan, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. |

10. | C. C. Davis and I. Smolyaninov, “The effect of atmospheric turbulence on bit-error-rate in an on-off keyed optical wireless system,” in Proceedings of SPIE Free-Space Laser Commun. Laser Imaging , (1997), pp. 126–137. |

11. | C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt |

12. | H. Hemmati, |

13. | S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Comm. |

14. | T. A. Tsiftsis, H.G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Comm. |

15. | E. Bayaki, R. Schober, and R.K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Comm. |

16. | I. Djordjevic, W. Ryan, and B. Vasic, |

17. | G. Agrawal, |

18. | G. C. Yang and W. C. Kwong, |

**OCIS Codes**

(060.4510) Fiber optics and optical communications : Optical communications

(060.2605) Fiber optics and optical communications : Free-space optical communication

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 21, 2012

Revised Manuscript: November 5, 2012

Manuscript Accepted: November 6, 2012

Published: November 13, 2012

**Citation**

Ngoc T. Dang and Anh T. Pham, "Performance improvement of FSO/CDMA systems over dispersive turbulence channel using multi-wavelength PPM signaling," Opt. Express **20**, 26786-26797 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-26786

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### References

- H. A. Willebrand and B. S. Ghuman, “Fiber optics without fiber,” IEEE Spectrum38, 40–45 (2001). [CrossRef]
- Q. Liu, C. Qiao, G. Mitchell, and S. Stanton, “Optical wireless communication networks for first- and last-mile broadband access [Invited],” J. Opt. Netw.4, 807–828 (2005). [CrossRef]
- T. Ohtsuki, “Performance analysis of atmospheric optical PPM CDMA systems,” J. Lightwave Technol.21, 406–411 (2003). [CrossRef]
- K. Ohba, T. Hirano, T. Miyazawa, and I. Sasase, “A symbol decision scheme to mitigate effects of scintillations and MAIs in optical atmospheric PPM-CDMA systems,” in Proceedings of IEEE GLOBECOM, (St. Louis, 2005), pp. 1999–2003.
- M. Jazayerifar and J. A. Salehi, “Atmospheric optical CDMA communication systems via optical orthogonal godes,” J. Lightwave Technol.54, 1614–1623 (2006).
- T. Miyazawa and I. Sasase, “BER performance analysis of spectral phase-encoded optical atmospheric PPM-CDMA communication systems,” J. Lightwave Technol.25, 2992–3000 (2007). [CrossRef]
- A. T. Pham, T. A. Luu, and N. T. Dang, “Performance bound for Turbo-coded 2-D FSO/CDMA systems over atmospheric turbulence channel,” IEICE Trans. Fundamentals.E93-A, 1745–1337 (2010). [CrossRef]
- A. Stok and E. H. Sargent, “The role of optical CDMA in access networks,” IEEE Commun. Mag.40, 83–87 (2002). [CrossRef]
- X. Zhu and J. M. Khan, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun.50, 1293–1300 (2002). [CrossRef]
- C. C. Davis and I. Smolyaninov, “The effect of atmospheric turbulence on bit-error-rate in an on-off keyed optical wireless system,” in Proceedings of SPIE Free-Space Laser Commun. Laser Imaging, (1997), pp. 126–137.
- C. Y. Young, L. C. Andrews, and A. Ishimaru, “Time-of-arrival fluctuations of a space-time Gaussian pulse in weak optical turbulence: an analytic solution,” Appl. Opt37, 7655–7660 (1998). [CrossRef]
- H. Hemmati, Deep Space Optical Communications (John Wiley and Sons, 2006). [CrossRef]
- S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Comm.6, 2813–2819 (2007). [CrossRef]
- T. A. Tsiftsis, H.G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Comm.8, 951–957 (2009). [CrossRef]
- E. Bayaki, R. Schober, and R.K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Comm.57, 3415–3424 (2009). [CrossRef]
- I. Djordjevic, W. Ryan, and B. Vasic, Coding for Optical Channels (Springer, 2010). [CrossRef]
- G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006).
- G. C. Yang and W. C. Kwong, Prime Code with Application to CDMA Optical and Wireless Networks (Artech House, 2002).

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