## Chip-interleaved optical code division multiple access relying on a photon-counting iterative successive interference canceller for free-space optical channels |

Optics Express, Vol. 21, Issue 13, pp. 15926-15937 (2013)

http://dx.doi.org/10.1364/OE.21.015926

Acrobat PDF (2296 KB)

### Abstract

In this paper, we design a novel Poisson photon-counting based iterative successive interference cancellation (SIC) scheme for transmission over free-space optical (FSO) channels in the presence of both multiple access interference (MAI) as well as Gamma-Gamma atmospheric turbulence fading, shot-noise and background light. Our simulation results demonstrate that the proposed scheme exhibits a strong MAI suppression capability. Importantly, an order of magnitude of BER improvements may be achieved compared to the conventional chip-level optical code-division multiple-access (OCDMA) photon-counting detector.

© 2013 OSA

## 1. Introduction

1. V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol. **24**(12), 4750–4762 (2006) [CrossRef] .

3. Z. Wang, W. Zhong, C. Yu, and S. Fu, “Performance improvement of on-off-keying free-space optical transmission systems by a co-propagating reference continuous wave light,” Opt. Express **20**(8), 9284–9295 (2012) [CrossRef] [PubMed] .

4. X. Wang, Z. Gao, N. Kataoka, and N. Wada, “Time domain spectral phase encoding/DPSK data modulation using single phase modulator for OCDMA application,” Opt. Express **18**(10), 9879–9890 (2010) [CrossRef] [PubMed] .

7. Y. Du, S. J. B. Yoo, and Z. Ding, “Nonuniform spectral phase encoding in optical CDMA networks,” IEEE Photon. Technol. Lett. **18**(23), 2505–2507 (2006) [CrossRef] .

8. M. Jazayerifar and J. A. Salehi, “Atmospheric optical CDMA communication systems via optical orthogonal codes,” IEEE Trans. Commun. **54**(9), 1614–1623 (2006) [CrossRef] .

9. C. Goursaud, A. Vergojanne, C. Berthelemot, J. Cances, and J. Dumasl, “DS-OCDMA receiver based on parallel interference cancellation and hard limiter,” IEEE Trans. Commun. **54**(9), 1663–1671 (2006) [CrossRef] .

11. H. Mrabet, I. Dayoub, R. Attia, and S. Haxha, “Performance improving of OCDMA system using 2-d optical codes with optical SIC receiver,” J. Lightwave Technol. **27**(21), 4744–4753 (2009) [CrossRef] .

12. X. Yuan, Q. Guo, and L. Ping, “Low-complexity iterative detection in multi-user MIMO ISI channels,” IEEE Signal Processing Lett. **15**(1), 25–28 (2008) [CrossRef] .

13. H. V. Poor, “Iterative multiuser detection,” IEEE Sig. Processing Mag. **21**(1), 81–88 (2004) [CrossRef] .

*signal-independent*nature of

*additive*Gaussian noise [14

14. X. Zhou, Y. Yang, Y. Shao, and J. Liu, “Photon-counting chip-interleaved iterative PIC detector over atmospheric turbulence channels,” Chin. Opt. Lett. **10**(11), 110603 (2012) [CrossRef] .

*signal-dependent*Poissonian noise.

*the conception of an efficient chip-level iterative a posteriori probability (APP) MAI cancellation technique for the Poisson photon-counting process, namely that of the photon-counting iterative serial interference cancellation (Iter-SIC) scheme*. We will demonstrate that the Iter-SIC scheme is capable of exceeding the optimum performance of the conventional chip-level OCDMA scheme [16

16. H. Shalaby, “Complexities, error probabilities, and capacities of optical OOK-CDMA communication systems,” IEEE Trans. Commun. **50**(12), 2009–2017 (2002) [CrossRef] .

## 2. System description

### 2.1. Optical transmitter

*k*∈ [1,

*K*] be the user index. The information bit sequence

**d**

*= {*

_{k}*d*(

_{k}*i*),

*i*= 1, ⋯ ,

*L*} of the

_{d}*k*th user is encoded by a forward error correcting (FEC) encoder, generating the coded sequence

**c**

*= {*

_{k}*c*(

_{k}*j*),

*j*= 1, ⋯ ,

*L*}, where

_{c}*L*is the information frame length and

_{d}*L*is the encoded frame length. Then, the encoded data is interleaved by a random user-specific interleaver Π

_{c}*, producing the sequence*

_{k}**x**

*= {*

_{k}*x*(

_{k}*j*),

*j*= 1, ⋯ ,

*L*}.

_{c}**s**

*= {*

_{k}*s*(

_{k}*j*),

*j*= 1, ⋯ ,

*L*} is then used for driving the optical modulator to generate the appropriate photon counts per chip

_{c}*m*

_{0}= 0 and

*m*

_{1}=

*PT*/

_{c}*hυ*representing “0” and “1”, where

*P,T*,

_{c}*υ*and

*h*denote the transmitted power, chip duration, optical frequency and Plank’s constant, respectively. The elements of {

*x*(

_{k}*j*)} and {

*s*(

_{k}*j*)} are referred to as “chips”.

### 2.2. Poisson atmospheric channel model

*I*≥ 0 is modelled by a Gamma-Gamma distribution with the PDF given by [17

_{k}17. L. C. Andrews and R. L. Phillips, *Laser Beam Propagation Through Random Media*, 2nd ed. (SPIE Press, 2005) [CrossRef] .

*I*denotes the channel’s fading coefficient between the

_{k}*k*th user laser and the receiving photon detector (PD). The scintillation parameters

*α*> 0 and

*β*> 0 of Eq. (1) are linked to the Rytov variance

17. L. C. Andrews and R. L. Phillips, *Laser Beam Propagation Through Random Media*, 2nd ed. (SPIE Press, 2005) [CrossRef] .

18. W. Gappmair and S. S. Muhammad, “Error performance of PPM/Poisson channels in turbulent athmosphere with Gamma-Gamma distribution,” Electron. Lett. **43**(16), 880–882 (2007) [CrossRef] .

*(·) is the modified Bessel function of the second kind of order*

_{l}*l*. Finally, the scintillation index is defined as

*S.I.*=

*α*

^{−1}+

*β*

^{−1}+ (

*αβ*)

^{−1}.

*r*(

*j*) follow a Poisson distribution and is given by, where ℙ[

*λ*] denotes Poisson distribution associated with the parameter

*λ*and the received photoelectron counts are denoted by where

*k*th user in the

*j*th chip.

*η*represents the PD efficiency.

*n*=

_{b}*ηP*/(

_{b}T_{c}*hυ*) stands for the background radiation photoelectrons per chip interval.

*P*is the power incident on the PD owing to the background noise.

_{b}### 2.3. Iterative SIC algorithm

**I**= {

*I*, ∀

_{k}*k*}, the

*a posteriori*log-likelihood ratios (LLRs) of the encoded sequence {

*x*(

_{k}*j*)} are defined as

*L*

_{MUD_e}[

*x*(

_{k}*j*)] denotes the extrinsic LLR about

*x*(

_{k}*j*), and

*L*

_{MUD_a}[

*x*(

_{k}*j*)] denotes the

*a priori*LLR about

*x*(

_{k}*j*).

*a priori*LLRs from the DEC and generates the noise estimates of

*ξ*(

_{k}*j*) for supporting the operation of the corresponding MUD block. More explicitly, the estimated noise is Let

*j*th chip for the

*k*th user, which is Thus, based on Eq. (6) and Eq. (7), we can achieve where

*L*

_{MUD_a}[

*x*(

_{k̃}*j*)] ∈ Θ

_{MUD_a}[

*x*(

_{k}*j*)], Θ

_{MUD_a}[

*x*(

_{k}*j*)] = {

*L*

_{MUD_a}[

*x*

_{1}(

*j*)],...,

*L*

_{MUD_a}[

*x*

_{k}_{−1}(

*j*)],

*L*

_{MUD_a}[

*x*

_{k}_{+1}(

*j*)],...,

*L*

_{MUD_a}[

*x*(

_{k}*j*)]} stands for the set of LLRs from interfering users. As illustrated in Fig. 1 and 2, {

*k*≤

*K*} are serially updated, where

*n*is the iteration index.

19. C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. **44**(10), 1261–1271 (1996) [CrossRef] .

*a posteriori*LLRs of the information bits {

*i*= 1, 2,...,

*L*} can be obtained by combining the

_{d}*a priori*LLRs of the encoded chips {

*L*

_{DEC_a}[

*c*(

_{k}*j*)]

*, j*= 1, 2,...,

*L*} as follows: where

_{c}*s*∈

_{z}**s**,

*N*denotes the repetition code length. The corresponding repetition code is

_{c}**d̃**

*} can be recovered by using hard decisions as*

_{k}### 2.4. Summary of the iterative SIC scheme

*k*th user can be invoked for the (

*k*+ 1)th user during the

*n*th iteration as

*Nc*− 1) additions, 2

*Nc*multiplications per bit, namely (2 − 1/

*Nc*) addition, 2 multiplications per user per chip per iteration, if repetition coding is adopted.

*Nc*) additions and 7 multiplications per user per chip per iteration.

*The Iter-SIC scheme’s computational complexity of O*(

*K*)

*per chip per iteration is modest*. By contrast, some typical CDMA MUD algorithms have a substantially higher complexity of

*O*(

*K*

^{2}) per chip per iteration, such as that of the well-known SIC-MMSE detector [15

15. X. Wang and H. V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Trans. Commun. **467**, 1046–1061 (1999) [CrossRef] .

## 3. Simulation results

### 3.1. Comparison with conventional OCDMA schemes

16. H. Shalaby, “Complexities, error probabilities, and capacities of optical OOK-CDMA communication systems,” IEEE Trans. Commun. **50**(12), 2009–2017 (2002) [CrossRef] .

*K*= 9 users.

16. H. Shalaby, “Complexities, error probabilities, and capacities of optical OOK-CDMA communication systems,” IEEE Trans. Commun. **50**(12), 2009–2017 (2002) [CrossRef] .

*R*= 1/30, which is higher than that of the spreading code rate of the conventional OCDMA schemes, such as

_{c}*R*= 1/150, hence potentially improving the bandwidth-efficiency by a factor of 5.

_{c}### 3.2. Performance over atmospheric Poisson channels

*σ*

_{R}= 0.25. The number of users supported is set to

*K*= 9 and the repetition coding rate is set to

*R*= 1/30. Our simulation results show that the proposed Iter-SIC scheme exhibits a rapid convergence after 5 iterations.

_{c}*R*= 3/10 over turbulent fading channels. As expected, the BER performance degrades upon increasing the number of users and it improves upon increasing the photon counts per bit.

_{c}K### 3.3. Convergence analysis

20. A. C. Reid, T. A. Gulliver, and D. P. Taylor, “Convergence and errors in turbo-decoding,” IEEE Trans. Commun. **49**(12), 2045–2051 (2001) [CrossRef] .

### 3.4. Impact of background light noise

*σ*

_{R}= 0.25) channels, which makes our proposed scheme suitable for employment in practical scenarios as it is resilient against the background-induced light-noise.

### 3.5. Impact of the number of users with different repetition coding rates

*K*= 3, 6, 9 users, Fig. 8(a) also shows an approximately linear BER vs photon counts relationship. The reason is likely to because the multiuser interference is essentially eliminated and the multiuser scenario becomes similar to the single-user case. Thus, the BER curve exhibits an approximately linear trend. Moreover, the shot-noise is signal-dependent, which constitutes the reason for the performance gaps among the

*K*= 3, 6, 9 cases, although the multiuser interference was substantially mitigated. By contrast, in the presence of multiuser interference, the BER curve of conventional chip-level OOC exhibits an error-floor, as shown in the dashed line marked by cross of Fig. 8(a). In turbulence fading channels associated with

*α*= 4.1,

*β*= 2.0, the error-floor occurs at a high BER level for both single-user and multiuser scenarios, as seen in Fig. 8(b).

## 4. Discussions on the employment in practical scenarios

## 5. Conclusions

## Acknowledgments

## References and links

1. | V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol. |

2. | L. Hanzo, H. Haas, S. Imre, D. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE |

3. | Z. Wang, W. Zhong, C. Yu, and S. Fu, “Performance improvement of on-off-keying free-space optical transmission systems by a co-propagating reference continuous wave light,” Opt. Express |

4. | X. Wang, Z. Gao, N. Kataoka, and N. Wada, “Time domain spectral phase encoding/DPSK data modulation using single phase modulator for OCDMA application,” Opt. Express |

5. | J. Jiang, D. Wu, and P. Fan, “General constructions of optimal variable-weight optical orthogonal codes,” IEEE Trans. Inf. Theory |

6. | G. C. Yang, C. H. Chen, and W. C. Kwong, “Accurate analysis of double-weight optical CDMA with power control,” IEEE Trans. Commun. |

7. | Y. Du, S. J. B. Yoo, and Z. Ding, “Nonuniform spectral phase encoding in optical CDMA networks,” IEEE Photon. Technol. Lett. |

8. | M. Jazayerifar and J. A. Salehi, “Atmospheric optical CDMA communication systems via optical orthogonal codes,” IEEE Trans. Commun. |

9. | C. Goursaud, A. Vergojanne, C. Berthelemot, J. Cances, and J. Dumasl, “DS-OCDMA receiver based on parallel interference cancellation and hard limiter,” IEEE Trans. Commun. |

10. | A. O. M’foubat, I. Dayoub, J. M. Rouvaen, W. Hamouda, and A. Mazen, “Approach to interference cancellation in DS-CDMA optical networks,” J. Opt. Commun. Netw. |

11. | H. Mrabet, I. Dayoub, R. Attia, and S. Haxha, “Performance improving of OCDMA system using 2-d optical codes with optical SIC receiver,” J. Lightwave Technol. |

12. | X. Yuan, Q. Guo, and L. Ping, “Low-complexity iterative detection in multi-user MIMO ISI channels,” IEEE Signal Processing Lett. |

13. | H. V. Poor, “Iterative multiuser detection,” IEEE Sig. Processing Mag. |

14. | X. Zhou, Y. Yang, Y. Shao, and J. Liu, “Photon-counting chip-interleaved iterative PIC detector over atmospheric turbulence channels,” Chin. Opt. Lett. |

15. | X. Wang and H. V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Trans. Commun. |

16. | H. Shalaby, “Complexities, error probabilities, and capacities of optical OOK-CDMA communication systems,” IEEE Trans. Commun. |

17. | L. C. Andrews and R. L. Phillips, |

18. | W. Gappmair and S. S. Muhammad, “Error performance of PPM/Poisson channels in turbulent athmosphere with Gamma-Gamma distribution,” Electron. Lett. |

19. | C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. |

20. | A. C. Reid, T. A. Gulliver, and D. P. Taylor, “Convergence and errors in turbo-decoding,” IEEE Trans. Commun. |

**OCIS Codes**

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(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: April 23, 2013

Revised Manuscript: June 11, 2013

Manuscript Accepted: June 11, 2013

Published: June 26, 2013

**Citation**

Xiaolin Zhou, Xiaowei Zheng, Rong Zhang, and Lajos Hanzo, "Chip-interleaved optical code division multiple access relying on a photon-counting iterative successive interference canceller for free-space optical channels," Opt. Express **21**, 15926-15937 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15926

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### References

- V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol.24(12), 4750–4762 (2006). [CrossRef]
- L. Hanzo, H. Haas, S. Imre, D. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE100(special centennial issue), 1853–1888 (2012). [CrossRef]
- Z. Wang, W. Zhong, C. Yu, and S. Fu, “Performance improvement of on-off-keying free-space optical transmission systems by a co-propagating reference continuous wave light,” Opt. Express20(8), 9284–9295 (2012). [CrossRef] [PubMed]
- X. Wang, Z. Gao, N. Kataoka, and N. Wada, “Time domain spectral phase encoding/DPSK data modulation using single phase modulator for OCDMA application,” Opt. Express18(10), 9879–9890 (2010). [CrossRef] [PubMed]
- J. Jiang, D. Wu, and P. Fan, “General constructions of optimal variable-weight optical orthogonal codes,” IEEE Trans. Inf. Theory57(7), 4488–4496 (2011). [CrossRef]
- G. C. Yang, C. H. Chen, and W. C. Kwong, “Accurate analysis of double-weight optical CDMA with power control,” IEEE Trans. Commun.60(2), 322–327 (2012). [CrossRef]
- Y. Du, S. J. B. Yoo, and Z. Ding, “Nonuniform spectral phase encoding in optical CDMA networks,” IEEE Photon. Technol. Lett.18(23), 2505–2507 (2006). [CrossRef]
- M. Jazayerifar and J. A. Salehi, “Atmospheric optical CDMA communication systems via optical orthogonal codes,” IEEE Trans. Commun.54(9), 1614–1623 (2006). [CrossRef]
- C. Goursaud, A. Vergojanne, C. Berthelemot, J. Cances, and J. Dumasl, “DS-OCDMA receiver based on parallel interference cancellation and hard limiter,” IEEE Trans. Commun.54(9), 1663–1671 (2006). [CrossRef]
- A. O. M’foubat, I. Dayoub, J. M. Rouvaen, W. Hamouda, and A. Mazen, “Approach to interference cancellation in DS-CDMA optical networks,” J. Opt. Commun. Netw.1(3), 204–212 (2009). [CrossRef]
- H. Mrabet, I. Dayoub, R. Attia, and S. Haxha, “Performance improving of OCDMA system using 2-d optical codes with optical SIC receiver,” J. Lightwave Technol.27(21), 4744–4753 (2009). [CrossRef]
- X. Yuan, Q. Guo, and L. Ping, “Low-complexity iterative detection in multi-user MIMO ISI channels,” IEEE Signal Processing Lett.15(1), 25–28 (2008). [CrossRef]
- H. V. Poor, “Iterative multiuser detection,” IEEE Sig. Processing Mag.21(1), 81–88 (2004). [CrossRef]
- X. Zhou, Y. Yang, Y. Shao, and J. Liu, “Photon-counting chip-interleaved iterative PIC detector over atmospheric turbulence channels,” Chin. Opt. Lett.10(11), 110603 (2012). [CrossRef]
- X. Wang and H. V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Trans. Commun.467, 1046–1061 (1999). [CrossRef]
- H. Shalaby, “Complexities, error probabilities, and capacities of optical OOK-CDMA communication systems,” IEEE Trans. Commun.50(12), 2009–2017 (2002). [CrossRef]
- L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE Press, 2005). [CrossRef]
- W. Gappmair and S. S. Muhammad, “Error performance of PPM/Poisson channels in turbulent athmosphere with Gamma-Gamma distribution,” Electron. Lett.43(16), 880–882 (2007). [CrossRef]
- C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun.44(10), 1261–1271 (1996). [CrossRef]
- A. C. Reid, T. A. Gulliver, and D. P. Taylor, “Convergence and errors in turbo-decoding,” IEEE Trans. Commun.49(12), 2045–2051 (2001). [CrossRef]

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