Abstract

A novel approach to simultaneous wind ranging and velocimetry using low peak power, long-duration modulated laser pulse transmissions is proposed. Received signals backscattered by aerosol particles are processed by a multi-reference matched-filter (MRMF) which performs matched filter processing between the received signal and several reference signals in parallel and outputs a range-velocity profile of received power. Ranging and velocimetry are performed simultaneously by estimating received power, radial velocity, and velocity dispersion from a velocity profile at an arbitrary range in the range-velocity profile. The accuracies of the three estimates improve in proportion to the square root of pulse duration; that is, a 100 times longer pulse is equivalent to a 10-dB amplification.

© 2017 Optical Society of America

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References

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  1. C. Weitkamp, Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005).
  2. P. W. Chan and Y. F. Lee, “Application of Short-Range Lidar in Wind Shear Alerting,” J. Atmos. Ocean. Technol. 29(2), 207–220 (2012).
    [Crossref]
  3. T. Iijima, N. Matayoshi, and E. Yoshikawa, “Development and Evaluation of Low-Level Turblences Advisory Display for Aircraft Operation,” in Proceedings of 29th Congress of the International Council of the Aeronautical Sciences, (2014).
  4. R. Targ, M. J. Kavaya, R. M. Huffaker, and R. L. Bowles, “Coherent lidar airborne windshear sensor: performance evaluation,” Appl. Opt. 30(15), 2013–2026 (1991).
    [Crossref] [PubMed]
  5. H. Inokuchi, H. Tanaka, and T. Ando, “Development of an Onboard Doppler Lidar for Flight Safety,” J. Aircr. 46(4), 1411–1415 (2009).
    [Crossref]
  6. K. Asaka, T. Yanagisawa, and Y. Hirano, “1.5-μm Eye-Safe Coherent Lidar System for Wind Velocity Measurement,” Proc. SPIE 4153, 321–328 (2001).
    [Crossref]
  7. S. M. Hannon, “Pulsed Doppler Lidar for Terminal Area Monitoring of Wind and Wake Hazards,” in Proceedings of 11th Conference on Aviation, Range, and Aerospace (2004).
  8. J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).
  9. J. E. Evans, “Achieving Higher Integrity in NEXRAD Products through Multi-Sensor Integration,” in Proceedings of 8th Conference on Aviation, Range, and Aerospace Meteorology (1999).
  10. M. E. Weber, J. Y. Cho, M. Robinson, and J. E. Evans, “Analysis of Operational Alternatives to the Terminal Doppler Weather Radar (TDWR),” Project Report ATC-332, MIT Lincoln Laboratory (2007).
  11. M. Hess, P. Koepke, and I. Schult, “Optical Properties of Aerosols and Clouds: The Software Package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
    [Crossref]
  12. P. Z. Peebles, Jr., Radar Principles, (Wiley Interscience Publications, 1998).
  13. N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. 22(9), 1382–1386 (1983).
    [Crossref] [PubMed]
  14. N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, “Diode-laser random-modulation cw lidar,” Appl. Opt. 25(1), 63–67 (1986).
    [Crossref] [PubMed]
  15. C. J. Karlsson, F. A. A. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction continuous-wave coherent laser radar at 155 µm for range, speed, vibration, and wind measurements,” Appl. Opt. 39(21), 3716–3726 (2000).
    [Crossref] [PubMed]
  16. M. L. Simpson, M.-D. Cheng, T. Q. Dam, K. E. Lenox, J. R. Price, J. M. Storey, E. A. Wachter, and W. G. Fisher, “Intensity-modulated, stepped frequency cw lidar for distributed aerosol and hard target measurements,” Appl. Opt. 44(33), 7210–7217 (2005).
    [Crossref] [PubMed]
  17. O. Batet, F. Dios, A. Comeron, and R. Agishev, “Intensity-modulated linear-frequency-modulated continuous-wave lidar for distributed media: fundamentals of technique,” Appl. Opt. 49(17), 3369–3379 (2010).
    [Crossref] [PubMed]
  18. E. Brinkmeyer and T. Waterholter, “Continuous wave synthetic low-coherence wind sensing Lidar: motionless measurement system with subsequent numerical range scanning,” Opt. Express 21(2), 1872–1897 (2013).
    [Crossref] [PubMed]
  19. A. Goldsmith, Wireless Communications, (Cambridge University, 2005).
  20. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th edition, (Oxford University, 2006).
  21. R. G. Frehlich and M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30(36), 5325–5352 (1991).
    [Crossref] [PubMed]
  22. V. Banakh and I. Smalikho, Coherent Doppler Wind Lidars in a Turbulent Atmosphere, (Artech House, 2013).
  23. M. I. Skolnik, Radar Handbook, 3rd edition, (McGraw Hill, 2008).
  24. J. W. Goodman, Statistical Optics, (John Wiley & Sons, Inc., 1985).
  25. S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46(11), 1953–1962 (2007).
    [Crossref] [PubMed]

2013 (1)

2012 (1)

P. W. Chan and Y. F. Lee, “Application of Short-Range Lidar in Wind Shear Alerting,” J. Atmos. Ocean. Technol. 29(2), 207–220 (2012).
[Crossref]

2010 (1)

2009 (1)

H. Inokuchi, H. Tanaka, and T. Ando, “Development of an Onboard Doppler Lidar for Flight Safety,” J. Aircr. 46(4), 1411–1415 (2009).
[Crossref]

2007 (1)

2005 (1)

2001 (1)

K. Asaka, T. Yanagisawa, and Y. Hirano, “1.5-μm Eye-Safe Coherent Lidar System for Wind Velocity Measurement,” Proc. SPIE 4153, 321–328 (2001).
[Crossref]

2000 (1)

1998 (1)

M. Hess, P. Koepke, and I. Schult, “Optical Properties of Aerosols and Clouds: The Software Package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

1991 (2)

1986 (1)

1983 (1)

Agishev, R.

Ando, T.

H. Inokuchi, H. Tanaka, and T. Ando, “Development of an Onboard Doppler Lidar for Flight Safety,” J. Aircr. 46(4), 1411–1415 (2009).
[Crossref]

S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46(11), 1953–1962 (2007).
[Crossref] [PubMed]

Asaka, K.

S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46(11), 1953–1962 (2007).
[Crossref] [PubMed]

K. Asaka, T. Yanagisawa, and Y. Hirano, “1.5-μm Eye-Safe Coherent Lidar System for Wind Velocity Measurement,” Proc. SPIE 4153, 321–328 (2001).
[Crossref]

Baba, H.

Batet, O.

Bowles, R. L.

Brinkmeyer, E.

Cariou, J. P.

J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).

Chan, P. W.

P. W. Chan and Y. F. Lee, “Application of Short-Range Lidar in Wind Shear Alerting,” J. Atmos. Ocean. Technol. 29(2), 207–220 (2012).
[Crossref]

Cheng, M.-D.

Comeron, A.

Dam, T. Q.

Dios, F.

Doboue, M.

J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).

Evans, J. E.

J. E. Evans, “Achieving Higher Integrity in NEXRAD Products through Multi-Sensor Integration,” in Proceedings of 8th Conference on Aviation, Range, and Aerospace Meteorology (1999).

Fisher, W. G.

Frehlich, R. G.

Gorju, G.

J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).

Hannon, S. M.

S. M. Hannon, “Pulsed Doppler Lidar for Terminal Area Monitoring of Wind and Wake Hazards,” in Proceedings of 11th Conference on Aviation, Range, and Aerospace (2004).

Harris, M.

Hess, M.

M. Hess, P. Koepke, and I. Schult, “Optical Properties of Aerosols and Clouds: The Software Package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

Hirano, Y.

S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46(11), 1953–1962 (2007).
[Crossref] [PubMed]

K. Asaka, T. Yanagisawa, and Y. Hirano, “1.5-μm Eye-Safe Coherent Lidar System for Wind Velocity Measurement,” Proc. SPIE 4153, 321–328 (2001).
[Crossref]

Huffaker, R. M.

Iijima, T.

T. Iijima, N. Matayoshi, and E. Yoshikawa, “Development and Evaluation of Low-Level Turblences Advisory Display for Aircraft Operation,” in Proceedings of 29th Congress of the International Council of the Aeronautical Sciences, (2014).

Inokuchi, H.

H. Inokuchi, H. Tanaka, and T. Ando, “Development of an Onboard Doppler Lidar for Flight Safety,” J. Aircr. 46(4), 1411–1415 (2009).
[Crossref]

Kameyama, S.

Karlsson, C. J.

Kavaya, M. J.

Koepke, P.

M. Hess, P. Koepke, and I. Schult, “Optical Properties of Aerosols and Clouds: The Software Package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

Lea, G.

J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).

Lee, Y. F.

P. W. Chan and Y. F. Lee, “Application of Short-Range Lidar in Wind Shear Alerting,” J. Atmos. Ocean. Technol. 29(2), 207–220 (2012).
[Crossref]

Lenox, K. E.

Letalick, D.

Machta, M.

J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).

Matayoshi, N.

T. Iijima, N. Matayoshi, and E. Yoshikawa, “Development and Evaluation of Low-Level Turblences Advisory Display for Aircraft Operation,” in Proceedings of 29th Congress of the International Council of the Aeronautical Sciences, (2014).

Olsson, F. A. A.

Price, J. R.

Sakurai, K.

Sauvage, L.

J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).

Schult, I.

M. Hess, P. Koepke, and I. Schult, “Optical Properties of Aerosols and Clouds: The Software Package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

Simpson, M. L.

Storey, J. M.

Sugimoto, N.

Takeuchi, N.

Tanaka, H.

H. Inokuchi, H. Tanaka, and T. Ando, “Development of an Onboard Doppler Lidar for Flight Safety,” J. Aircr. 46(4), 1411–1415 (2009).
[Crossref]

Targ, R.

Thobois, L.

J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).

Ueno, T.

Wachter, E. A.

Wadaka, S.

Waterholter, T.

Yanagisawa, T.

K. Asaka, T. Yanagisawa, and Y. Hirano, “1.5-μm Eye-Safe Coherent Lidar System for Wind Velocity Measurement,” Proc. SPIE 4153, 321–328 (2001).
[Crossref]

Yoshikawa, E.

T. Iijima, N. Matayoshi, and E. Yoshikawa, “Development and Evaluation of Low-Level Turblences Advisory Display for Aircraft Operation,” in Proceedings of 29th Congress of the International Council of the Aeronautical Sciences, (2014).

Appl. Opt. (8)

N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. 22(9), 1382–1386 (1983).
[Crossref] [PubMed]

N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, “Diode-laser random-modulation cw lidar,” Appl. Opt. 25(1), 63–67 (1986).
[Crossref] [PubMed]

R. Targ, M. J. Kavaya, R. M. Huffaker, and R. L. Bowles, “Coherent lidar airborne windshear sensor: performance evaluation,” Appl. Opt. 30(15), 2013–2026 (1991).
[Crossref] [PubMed]

R. G. Frehlich and M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30(36), 5325–5352 (1991).
[Crossref] [PubMed]

C. J. Karlsson, F. A. A. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction continuous-wave coherent laser radar at 155 µm for range, speed, vibration, and wind measurements,” Appl. Opt. 39(21), 3716–3726 (2000).
[Crossref] [PubMed]

M. L. Simpson, M.-D. Cheng, T. Q. Dam, K. E. Lenox, J. R. Price, J. M. Storey, E. A. Wachter, and W. G. Fisher, “Intensity-modulated, stepped frequency cw lidar for distributed aerosol and hard target measurements,” Appl. Opt. 44(33), 7210–7217 (2005).
[Crossref] [PubMed]

S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46(11), 1953–1962 (2007).
[Crossref] [PubMed]

O. Batet, F. Dios, A. Comeron, and R. Agishev, “Intensity-modulated linear-frequency-modulated continuous-wave lidar for distributed media: fundamentals of technique,” Appl. Opt. 49(17), 3369–3379 (2010).
[Crossref] [PubMed]

Bull. Am. Meteorol. Soc. (1)

M. Hess, P. Koepke, and I. Schult, “Optical Properties of Aerosols and Clouds: The Software Package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

J. Aircr. (1)

H. Inokuchi, H. Tanaka, and T. Ando, “Development of an Onboard Doppler Lidar for Flight Safety,” J. Aircr. 46(4), 1411–1415 (2009).
[Crossref]

J. Atmos. Ocean. Technol. (1)

P. W. Chan and Y. F. Lee, “Application of Short-Range Lidar in Wind Shear Alerting,” J. Atmos. Ocean. Technol. 29(2), 207–220 (2012).
[Crossref]

Opt. Express (1)

Proc. SPIE (1)

K. Asaka, T. Yanagisawa, and Y. Hirano, “1.5-μm Eye-Safe Coherent Lidar System for Wind Velocity Measurement,” Proc. SPIE 4153, 321–328 (2001).
[Crossref]

Other (12)

S. M. Hannon, “Pulsed Doppler Lidar for Terminal Area Monitoring of Wind and Wake Hazards,” in Proceedings of 11th Conference on Aviation, Range, and Aerospace (2004).

J. P. Cariou, L. Sauvage, L. Thobois, G. Gorju, M. Machta, G. Lea, and M. Doboue, “Long Range Scanning Pulsed Coherent Lidar for Real Time Wind Monitoring in the Planetary Boundary Layer,” in Proceedings of 16th Conference on Coherent Laser Radar (2011).

J. E. Evans, “Achieving Higher Integrity in NEXRAD Products through Multi-Sensor Integration,” in Proceedings of 8th Conference on Aviation, Range, and Aerospace Meteorology (1999).

M. E. Weber, J. Y. Cho, M. Robinson, and J. E. Evans, “Analysis of Operational Alternatives to the Terminal Doppler Weather Radar (TDWR),” Project Report ATC-332, MIT Lincoln Laboratory (2007).

T. Iijima, N. Matayoshi, and E. Yoshikawa, “Development and Evaluation of Low-Level Turblences Advisory Display for Aircraft Operation,” in Proceedings of 29th Congress of the International Council of the Aeronautical Sciences, (2014).

V. Banakh and I. Smalikho, Coherent Doppler Wind Lidars in a Turbulent Atmosphere, (Artech House, 2013).

M. I. Skolnik, Radar Handbook, 3rd edition, (McGraw Hill, 2008).

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

A. Goldsmith, Wireless Communications, (Cambridge University, 2005).

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th edition, (Oxford University, 2006).

P. Z. Peebles, Jr., Radar Principles, (Wiley Interscience Publications, 1998).

C. Weitkamp, Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005).

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Figures (5)

Fig. 1
Fig. 1

Block diagram of system example.

Fig. 2
Fig. 2

Processing flow of MRMF approach.

Fig. 3
Fig. 3

a) Range and b) velocity profiles of a signal received from a single particle.

Fig. 4
Fig. 4

Accuracies of a) received power, b) radial velocity, and c) velocity dispersion estimates. std. denotes standard deviation.

Fig. 5
Fig. 5

Range profiles of a signal received from a single particle by the conventional and proposed wind lidars.

Tables (3)

Tables Icon

Table 1 Configuration of Proposed Wind Lidar in Range-Velocity Profile Simulation

Tables Icon

Table 2 Wind parameters for evaluation of ranging and velocimetry

Tables Icon

Table 3 Configuration Examples of Conventional and Proposed Wind Lidar

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

s T ( t )= a T s M ( t ) s I ( t ),
s M ( t )={ exp( j2π u( t ) U t ); 0t<T 0; otherwise ,
u( t )= u k ; k K Tt< k+1 K T .
s I ( t )=exp{ j( 2π f I t+ θ I ) },
s TC ( t ) s T ( t )exp( j2π f C t+ θ C ),
s RC (i) ( t )= s TC ( t τ (i) ) x (i) exp{ j2π f D (i) ( t τ (i) ) },
x= a P g l r 2 ,
r= cτ 2 ,
f D = 2v c f C .
s R (i) ( t ) s RC (i) ( t )exp{ ( j2π f C t+ θ T ) } = a T x (i) exp( j2π f C τ (i) ) s MD ( t τ (i) , f D (i) ) s I ( t τ (i) ),
s MD ( t, f D )= s M ( t )exp( j2π f D t ).
s R ( t )= iΝ s R (i) ( t ) = a T iΝ x (i) exp( j2π f C τ (i) ) s MD ( t τ (i) , f D (i) ) s I ( t τ (i) ) ,
c R ( r( τ ^ ),v( f ^ D ) )= s R ( t ) s T ( t τ ^ , f ^ D ) * dt ,
s T ( t, f D )= s MD ( t, f D ) s I ( t ).
c R ( r( τ ^ ),v( f ^ D ) ) a T iΝ { x (i) exp( j2π f C τ (i) ) τ ^ τ ^ +T s MD ( t τ (i) , f D (i) ) s MD ( t τ ^ , f ^ D ) * dt } ,
c R (i) ( r( τ ^ ),v( f ^ D ) ) = a T x (i) exp( j2π f C τ (i) ) τ ^ τ ^ +T s MD ( t τ (i) , f D (i) ) s MD ( t τ ^ , f ^ D ) * dt .
c R (i) ( r( τ ^ ),v( f D (i) ) ) = a T x (i) exp( j2π f C τ (i) ) τ ^ τ ^ +T s MD ( t τ (i) , f D (i) ) s MD ( t τ ^ , f D (i) ) * dt ,
Δr c 2B .
c R (i) ( r( τ (i) ),v( f ^ D ) ) = a T x (i) exp( j2π f C τ (i) ) τ (i) τ (i) +T | s M ( t τ (i) ) | 2 exp{ j2π( f D (i) f ^ D )( t τ (i) ) }dt .
Δv c 2T f C .
s R+N ( t ) = a T iΝ x (i) exp( j2π f C τ (i) ) s MD ( t τ (i) , f D (i) ) s I ( t τ (n) )+ a N s N ( t ) ,
c R+N ( r( τ ^ ),v( f ^ D ) )= c R ( r( τ ^ ),v( f ^ D ) )+ c N ( r( τ ^ ),v( f ^ D ) ),
c N ( r( τ ^ ),v( f ^ D ) )= a N τ τ+T s N ( t ) s T ( t τ ^ , f ^ D ) * dt .
E[ | c R ( r( τ ^ ),v( f ^ D ) ) | 2 ] 1 2 a T 2 T 2 | x( r( τ ^ ),v( f ^ D ) ) | 2 ¯ N( r( τ ^ ),v( f ^ D ) ),
| x( r( τ ),v( f D ) ) | 2 ¯ = 1 N( r( τ ),v( f D ) ) iN( r( τ ),v( f D ) ) | x (i) exp( j2π f C τ (i) ) | 2 ,
N( r( τ ),v( f D ) )ΔrΔvn( r( τ ),v( f D ) ),
E[ | c N ( r( τ ^ ),v( f ^ D ) ) | 2 ] a N 2 T.
SNR( r( τ ^ ),v( f ^ D ) )= E[ | c R ( r( τ ^ ),v( f ^ D ) ) | 2 ] E[ | c N ( r( τ ^ ),v( f ^ D ) ) | 2 ] c 2 8 a T 2 a N 2 B f C | x( r( τ ^ ),v( f ^ D ) ) | 2 ¯ n( r( τ ^ ),v( f ^ D ) ).
c 1+SNR =G( s )+ n c ,
c 1+SNR [ | c R+N ( v (1) ) | 2 E[ | c N ( v (1) ) | 2 ] | c R+N ( v (2) ) | 2 E[ | c N ( v (2) ) | 2 ] | c R+N ( v ( M v ) ) | 2 E[ | c N ( v ( M v ) ) | 2 ] ] T .
G( s )= [ g( s, v (1) ) g( s, v (2) ) g( s, v ( M v ) ) ] T ,
g( s, v (m) )= M v Δv s 0 2π s 2 exp{ ( v (m) s 1 ) 2 2 s 2 2 }+1,
s= [ s 0 s 1 s 2 ] T .
n s ( G s ) + n c ,
σ( n s (o) )= m=1 M v { g + (o,m) σ( n c (o) ) } 2 ; ( o=0,1,2 ),
σ( n c (m) ) 1 L E[ | c R+N ( v (m) ) | 2 ] E[ | c N ( v (m) ) | 2 ] ,
σ ˜ ( n s (0) )= σ( n s (0) ) | [dB] 10log( s 0 +1 ) ,
σ( n s (0) ) | [dB] =10log{ exp( σ( n s (0) ) s 0 +1 ) },

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