Abstract

Atmospheric turbulence can cause a significant performance degradation in free space optical communication systems. An efficient solution could be to exploit the temporal diversity to improve the performance of the transmission link. Depending on the tolerable delay latency, we can benefit from some degree of time diversity that we can exploit by employing channel coding and interleaving. In this paper, we investigate the efficiency of several channel coding techniques for different time diversity orders and turbulence conditions. We show that a simple convolutional code is a suitable choice in most cases as it makes a good compromise between decoding complexity and performance. We also study the receiver performance when the channel is estimated based on some training symbols.

© 2009 Optical Society of America

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    [CrossRef]

2007

2006

2005

S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901- 1910 (2005).
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, "Free-space optical MIMO transmission with Q-ary PPM," IEEE Trans. Commun. 53, 1402-1412 (2005).
[CrossRef]

J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels," J. Opt. Net. 4, 586-601 (2005).
[CrossRef]

F. Babich and F. Vatta, "On rate-compatible punctured turbo codes design," EURASIP J. Appl. Signal Process. 6, 784-794 (2005).

2004

M. Cole and K. Kiasaleh, "Signal intensity estimators for free-space optical communications through turbulent atmosphere," IEEE Photon. Technol. Lett. 16, 2395-2397 (2004).
[CrossRef]

E. J. Lee and V. W. S. Chan, "Part 1: Optical communication over the clear turbulent atmospheric channel using diversity," IEEE J. Sel. Areas Commun. 22, 1896-1906 (2004).
[CrossRef]

D. Kedar and S. Arnon, "Urban optical wireless communication networks: the main challenges and possible solutions," IEEE Commun. Mag. 42, 2-7 (2004).
[CrossRef]

2003

S. Arnon, "Effects of atmospheric turbulence and building sway on optical wireless communication systems," Opt. Lett. 28, 129-131 (2003).
[CrossRef] [PubMed]

S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, "Understanding the performance of free-space optics," J. Opt. Net. 2, 178-200 (2003).

2002

X. Zhu and J. M. Kahn, "Pilot-symbol assisted modulation for correlated turbulent free-space optical channels," Proc. Soc. Photo-Opt. Instrum. Eng. 4489, 138-145 (2002).

X. Zhu and J. Kahn, "Free-space optical communication through atomospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1330 (2002).
[CrossRef]

2001

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

H. A. Willebrand and B. S. Ghuman, "Fiber optics without fiber," IEEE Spectrum 40, 41-45 (2001).

2000

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 5370 (2000).
[CrossRef]

1999

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. 16, 1417-1429 (1999).
[CrossRef]

1998

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 72, 72-82 (1998).
[CrossRef]

1996

J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes," IEEE Trans. Inf. Theory 42, 429-445 (1996).
[CrossRef]

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

1994

A. S. Barbulescu and S. S. Pietrobon, "Interleaver design for turbo codes," Elect. Lett. 30, 2107-2108 (1994).
[CrossRef]

1985

L. C. Andrews and R. L. Phillips, "I-K distribution as a universal propagation model of laser beams in atmospheric turbulence," J. Opt. Soc. Am. 2, 160-163 (1985).
[CrossRef]

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. 16, 1417-1429 (1999).
[CrossRef]

Andrews, L. C.

F. S. Vetelino, C. Young, L. C. Andrews, and J. Recolons, "Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence," Appl. Opt. 46, 2099-2108 (2007).
[CrossRef] [PubMed]

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 5370 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. 16, 1417-1429 (1999).
[CrossRef]

L. C. Andrews and R. L. Phillips, "I-K distribution as a universal propagation model of laser beams in atmospheric turbulence," J. Opt. Soc. Am. 2, 160-163 (1985).
[CrossRef]

Anguita, J. A.

J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels," J. Opt. Net. 4, 586-601 (2005).
[CrossRef]

Arnon, S.

D. Kedar and S. Arnon, "Urban optical wireless communication networks: the main challenges and possible solutions," IEEE Commun. Mag. 42, 2-7 (2004).
[CrossRef]

S. Arnon, "Effects of atmospheric turbulence and building sway on optical wireless communication systems," Opt. Lett. 28, 129-131 (2003).
[CrossRef] [PubMed]

Babich, F.

F. Babich and F. Vatta, "On rate-compatible punctured turbo codes design," EURASIP J. Appl. Signal Process. 6, 784-794 (2005).

Baedke, M.

S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901- 1910 (2005).
[CrossRef]

Barbulescu, A. S.

A. S. Barbulescu and S. S. Pietrobon, "Interleaver design for turbo codes," Elect. Lett. 30, 2107-2108 (1994).
[CrossRef]

Berrou, C.

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

Bloom, S.

S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, "Understanding the performance of free-space optics," J. Opt. Net. 2, 178-200 (2003).

Brandt-Pearce, M.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, "Free-space optical MIMO transmission with Q-ary PPM," IEEE Trans. Commun. 53, 1402-1412 (2005).
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901- 1910 (2005).
[CrossRef]

Cao, Q.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, "Free-space optical MIMO transmission with Q-ary PPM," IEEE Trans. Commun. 53, 1402-1412 (2005).
[CrossRef]

Cao, Q. L.

S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901- 1910 (2005).
[CrossRef]

Chan, V. W. S.

V. W. S. Chan, "Free-space optical communications," J. Lightwave Technol. 24, 4750-4762 (2006).
[CrossRef]

E. J. Lee and V. W. S. Chan, "Part 1: Optical communication over the clear turbulent atmospheric channel using diversity," IEEE J. Sel. Areas Commun. 22, 1896-1906 (2004).
[CrossRef]

Cochrane, P.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 72, 72-82 (1998).
[CrossRef]

Cole, M.

M. Cole and K. Kiasaleh, "Signal intensity estimators for free-space optical communications through turbulent atmosphere," IEEE Photon. Technol. Lett. 16, 2395-2397 (2004).
[CrossRef]

Cvijetic, N.

Djordjevic, I. B.

J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels," J. Opt. Net. 4, 586-601 (2005).
[CrossRef]

Ghuman, B. S.

H. A. Willebrand and B. S. Ghuman, "Fiber optics without fiber," IEEE Spectrum 40, 41-45 (2001).

Glavieux, A.

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

Hagenauer, J.

J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes," IEEE Trans. Inf. Theory 42, 429-445 (1996).
[CrossRef]

Heatley, D. J. T.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 72, 72-82 (1998).
[CrossRef]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 5370 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. 16, 1417-1429 (1999).
[CrossRef]

Kahn, J.

X. Zhu and J. Kahn, "Free-space optical communication through atomospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1330 (2002).
[CrossRef]

Kahn, J. M.

X. Zhu and J. M. Kahn, "Pilot-symbol assisted modulation for correlated turbulent free-space optical channels," Proc. Soc. Photo-Opt. Instrum. Eng. 4489, 138-145 (2002).

Kedar, D.

D. Kedar and S. Arnon, "Urban optical wireless communication networks: the main challenges and possible solutions," IEEE Commun. Mag. 42, 2-7 (2004).
[CrossRef]

Kiasaleh, K.

M. Cole and K. Kiasaleh, "Signal intensity estimators for free-space optical communications through turbulent atmosphere," IEEE Photon. Technol. Lett. 16, 2395-2397 (2004).
[CrossRef]

Korevaar, E.

S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, "Understanding the performance of free-space optics," J. Opt. Net. 2, 178-200 (2003).

Lee, E. J.

E. J. Lee and V. W. S. Chan, "Part 1: Optical communication over the clear turbulent atmospheric channel using diversity," IEEE J. Sel. Areas Commun. 22, 1896-1906 (2004).
[CrossRef]

Leveque, J. H.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, "Free-space optical MIMO transmission with Q-ary PPM," IEEE Trans. Commun. 53, 1402-1412 (2005).
[CrossRef]

Neifeld, M. A.

J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels," J. Opt. Net. 4, 586-601 (2005).
[CrossRef]

Neild, I.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 72, 72-82 (1998).
[CrossRef]

Offer, E.

J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes," IEEE Trans. Inf. Theory 42, 429-445 (1996).
[CrossRef]

Papke, L.

J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes," IEEE Trans. Inf. Theory 42, 429-445 (1996).
[CrossRef]

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 5370 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. 16, 1417-1429 (1999).
[CrossRef]

L. C. Andrews and R. L. Phillips, "I-K distribution as a universal propagation model of laser beams in atmospheric turbulence," J. Opt. Soc. Am. 2, 160-163 (1985).
[CrossRef]

Pietrobon, S. S.

A. S. Barbulescu and S. S. Pietrobon, "Interleaver design for turbo codes," Elect. Lett. 30, 2107-2108 (1994).
[CrossRef]

Recolons, J.

Schuster, J.

S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, "Understanding the performance of free-space optics," J. Opt. Net. 2, 178-200 (2003).

Vasic, B. V.

J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels," J. Opt. Net. 4, 586-601 (2005).
[CrossRef]

Vatta, F.

F. Babich and F. Vatta, "On rate-compatible punctured turbo codes design," EURASIP J. Appl. Signal Process. 6, 784-794 (2005).

Vetelino, F. S.

Willebrand, H.

S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, "Understanding the performance of free-space optics," J. Opt. Net. 2, 178-200 (2003).

Willebrand, H. A.

H. A. Willebrand and B. S. Ghuman, "Fiber optics without fiber," IEEE Spectrum 40, 41-45 (2001).

Wilson, S. G.

N. Cvijetic, S. G. Wilson, and R. Zarubica, "Performance evaluation of a novel converged architecture for digitalvideo transmission over optical wireless channels," J. Lightwave Technol. 25, 3366-3373 (2007).
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, "Free-space optical MIMO transmission with Q-ary PPM," IEEE Trans. Commun. 53, 1402-1412 (2005).
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901- 1910 (2005).
[CrossRef]

Wisely, D. R.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 72, 72-82 (1998).
[CrossRef]

Young, C.

Zarubica, R.

Zhu, X.

X. Zhu and J. Kahn, "Free-space optical communication through atomospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1330 (2002).
[CrossRef]

X. Zhu and J. M. Kahn, "Pilot-symbol assisted modulation for correlated turbulent free-space optical channels," Proc. Soc. Photo-Opt. Instrum. Eng. 4489, 138-145 (2002).

Appl. Opt.

Elect. Lett.

A. S. Barbulescu and S. S. Pietrobon, "Interleaver design for turbo codes," Elect. Lett. 30, 2107-2108 (1994).
[CrossRef]

EURASIP J. Appl. Signal Process.

F. Babich and F. Vatta, "On rate-compatible punctured turbo codes design," EURASIP J. Appl. Signal Process. 6, 784-794 (2005).

IEEE Commun. Mag.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 72, 72-82 (1998).
[CrossRef]

D. Kedar and S. Arnon, "Urban optical wireless communication networks: the main challenges and possible solutions," IEEE Commun. Mag. 42, 2-7 (2004).
[CrossRef]

IEEE J. Sel. Areas Commun.

E. J. Lee and V. W. S. Chan, "Part 1: Optical communication over the clear turbulent atmospheric channel using diversity," IEEE J. Sel. Areas Commun. 22, 1896-1906 (2004).
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901- 1910 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Cole and K. Kiasaleh, "Signal intensity estimators for free-space optical communications through turbulent atmosphere," IEEE Photon. Technol. Lett. 16, 2395-2397 (2004).
[CrossRef]

IEEE Spectrum

H. A. Willebrand and B. S. Ghuman, "Fiber optics without fiber," IEEE Spectrum 40, 41-45 (2001).

IEEE Trans. Commun.

X. Zhu and J. Kahn, "Free-space optical communication through atomospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1330 (2002).
[CrossRef]

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

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, "Free-space optical MIMO transmission with Q-ary PPM," IEEE Trans. Commun. 53, 1402-1412 (2005).
[CrossRef]

IEEE Trans. Inf. Theory

J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes," IEEE Trans. Inf. Theory 42, 429-445 (1996).
[CrossRef]

J. Lightwave Technol.

J. Opt. Net.

S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, "Understanding the performance of free-space optics," J. Opt. Net. 2, 178-200 (2003).

J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels," J. Opt. Net. 4, 586-601 (2005).
[CrossRef]

J. Opt. Soc. Am.

L. C. Andrews and R. L. Phillips, "I-K distribution as a universal propagation model of laser beams in atmospheric turbulence," J. Opt. Soc. Am. 2, 160-163 (1985).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. 16, 1417-1429 (1999).
[CrossRef]

Opt. Eng.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

X. Zhu and J. M. Kahn, "Pilot-symbol assisted modulation for correlated turbulent free-space optical channels," Proc. Soc. Photo-Opt. Instrum. Eng. 4489, 138-145 (2002).

Waves Random Media

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 5370 (2000).
[CrossRef]

Other

Digital Video Broadcasting (DVB); Framing Structure, Channel Coding and Modulation for Digital Terrestrial Television (ETSI EN 300 744 V1.5.1, European Standard (Telecommunications series), 2004).

F. Xu, M. A. Khalighi, P. Caussé, and S. Bourennane, "Performance of coded time-diversity free-space optical links," Proc. Queen’s 24th Biennial Symp. Commun. (QSBC) pp. 146-149 (2008). Kingston, Canada.

R. M. Gagliardi and S. Karp, Optical Communications (John Wiley & Sons, 1995), 2nd ed.

J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985). New York.

A. Harris, J. J. Sluss, H. H. Refai, and P. G. LoPresti, "Alignment and tracking of a free-space optical communications link to a UAV," Proc. Digital Avionics Syst. Conf. (DASC) 1.C, 2.1-2.9 (2005).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover Publications Inc., 1968). New York.

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

J. G. Proakis, Digital Communications (McGraw-Hill, 5th edition, 2008).

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Figures (9)

Fig. 1.
Fig. 1.

System block diagram.

Fig. 2.
Fig. 2.

Pilot insertion for channel estimation purpose; example of two fading blocks per frame of NF symbols, NF = 2(M + MP ).

Fig. 3.
Fig. 3.

Concatenation of RS and convolutional codes. ENCODING and DECODING correspond to the “Channel Encoder” and “Channel Decoder” blocks in Fig. 1, respectively.

Fig. 4.
Fig. 4.

Turbo encoder block diagram.

Fig. 5.
Fig. 5.

Weak turbulence conditions, (α = 51.9, β = 49.1), no time diversity, perfect CSI.

Fig. 6.
Fig. 6.

Weak turbulence conditions, (α = 51.9, β = 49.1), PTDO = 2, perfect CSI.

Fig. 7.
Fig. 7.

Moderate turbulence conditions, (α = 4.39, β = 2.56), PTDO = 2 and 4, perfect CSI.

Fig. 8.
Fig. 8.

Strong turbulence conditions, (α = 5.49, β = 1.12), PTDO = 2, 4, and 8, perfect CSI.

Fig. 9.
Fig. 9.

BER versus the number of pilots per fading block. PTDO = 2, strong and weak turbulence conditions, BER=10-5 for perfect channel knowledge, NF = 4080.

Equations (13)

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p(h)=2(αβ)(α/β)/2Γ(α)Γ(β) h(α+β)/21 Kαβ [2(αβh)1/2] , h>0
α=1σx2=[exp(0.49χ2(1+1.11χ12/5)7/6)1]1
β=1σy2=[exp(0.51χ2(1+0.69χ12/5)5/6)1]1
re=η(I+Ia)+n
r=ηI+n.
I=h I0
{H0:r=hs0+nH1:r=hs1+n
P(r|s)=12πσn2 exp ((rhs)22σn2) .
ŝ=argmaxsP(r|s)P(s)
ŝ=argmaxsP(rs).
LR=P(r|s1)P(r|s0)=exp ((rhs1)2+(rhs0)22σn2)=exp(2hrh22σn2).
LLR=2hrh22σn2 H0H1
ĥ=1MP i=1MPri .

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