Abstract

We provide an analytical study on the propagation effects of a directly modulated OOFDM signal through a dispersive fiber and subsequent photo-detection. The analysis includes the effects of the laser operation point and the interplay between chromatic dispersion and laser chirp. The final expression allows to understand the physics behind the transmission of a multi-carrier signal in the presence of residual frequency modulation and the description of the induced intermodulation distortion gives us a detailed insight into the diferent intermodulation products which impair the recovered signal at the receiver-end side. Numerical comparisons between transmission simulations results and those provided by evaluating the expression obtained are carried out for different laser operation points. Results obtained by changing the fiber length, laser parameters and using single mode fiber with negative and positive dispersion are calculated in order to demonstrate the validity and versatility of the theory provided in this paper. Therefore, a novel analytical formulation is presented as a versatile tool for the description and study of IM/DD OOFDM systems with variable design parameters.

© 2013 OSA

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References

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  1. W. Shieh and I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).
  2. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol.27(3), 189–204 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
  4. D-Z. Hsu, C-C. Wei, H-Y. Chen, W-Y. Li, and J. Chen, “Cost-effective 33-Gbps intensity modulation direct detection multi-band OFDM LR-PON system employing a 10-GHz-based transceiver,” Opt. Express19(18), 17546–17556 (2011).
    [CrossRef] [PubMed]
  5. W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express16(9), 6378–6386 (2008).
    [CrossRef] [PubMed]
  6. D. Visani, C. Okonkwo, S. Loquai, H. Yang, Y. Shi, H. van de Boom, T. Ditewig, G. Tartarini, B. Schmauss, J. Lee, T. Koonen, and E. Tangdiongga, “Beyond 1Gbit/s transmission over 1 mm diameter plastic optical fiber employing DMT for in-home communication systems,” J. Lightwave Technol.29(4), 622–628 (2011).
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  8. N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space pptical transmission using OFDM,” in OFC/NFOEC2008, paper OThD2.
  9. N. Cvijetic, D. Qian, J. Hu, and T. Wang, “Orthogonal frequency division multiple access PON (OFDMA-PON) for colorless upstream transmission beyond 10 Gb/s,” IEEE J. Sel. Areas Commun.28(6), 781–790 (2010).
    [CrossRef]
  10. X. Q. Jin, E. H-Salas, R. P. Giddings, J. L. Wei, J. Groenewald, and J. M. Tang, “First real-time experimental demonstrations of 11.25Gb/s optical OFDMA PONs with adaptive dynamic bandwidth allocation,” Opt. Express19(21). 20557–20570 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,” Opt. Express19(5), 4280–4293 (2011).
    [CrossRef] [PubMed]
  14. C-C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Letters36(2), 151–153 (2011).
    [CrossRef]
  15. C-C. Wei, “Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission systems,” Opt. Express20(23), 25774–25789 (2012).
    [CrossRef] [PubMed]
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    [CrossRef]
  18. E. Peral, “Large-signal theory of the effect of dispersive propagation on the intensity modulation response of semiconductor lasers,” J. Lightwave Technol.18(1), 84–89 (2000).
    [CrossRef]
  19. J. Helms, “Intermodulation distortions of broad-band modulated laser diodes,” J. Lightwave Technol.10(12), 1901–1906 (1992).
    [CrossRef]
  20. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, 1972).
  21. P. K. Vitthaladevuni, M-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun.4(6), 3039–3050 (2005).
    [CrossRef]
  22. X. Zheng, X. Q. Jin, R. P. Giddings, J. L. Wei, E. Hugues-Salas, Y. H. Hong, and J. M. Tang, “Negative power penalties of optical OFDM signal transmission in directly modulated DFB laser-based IMDD systems incorporating negative dispersion fibers,” IEEE Photon. J.2(4), 532–542 (2010).
    [CrossRef]

2012

2011

2010

N. Cvijetic, D. Qian, J. Hu, and T. Wang, “Orthogonal frequency division multiple access PON (OFDMA-PON) for colorless upstream transmission beyond 10 Gb/s,” IEEE J. Sel. Areas Commun.28(6), 781–790 (2010).
[CrossRef]

X. Zheng, X. Q. Jin, R. P. Giddings, J. L. Wei, E. Hugues-Salas, Y. H. Hong, and J. M. Tang, “Negative power penalties of optical OFDM signal transmission in directly modulated DFB laser-based IMDD systems incorporating negative dispersion fibers,” IEEE Photon. J.2(4), 532–542 (2010).
[CrossRef]

2009

2008

2005

P. K. Vitthaladevuni, M-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun.4(6), 3039–3050 (2005).
[CrossRef]

2000

1992

J. Helms, “Intermodulation distortions of broad-band modulated laser diodes,” J. Lightwave Technol.10(12), 1901–1906 (1992).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, 1972).

Agrawal, G. P.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 1993).

Alouini, M-S.

P. K. Vitthaladevuni, M-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun.4(6), 3039–3050 (2005).
[CrossRef]

Armstrong, J.

Buchali, F.

B. Franz, D. Suikat, R. Dischler, F. Buchali, and H. Buelow, “High speed OFDM data transmission over 5 km GI-multimode fiber using spatial multiplexing with 2×4 MIMO processing,” in ECOC2010, paper Tu3C4.

Buelow, H.

B. Franz, D. Suikat, R. Dischler, F. Buchali, and H. Buelow, “High speed OFDM data transmission over 5 km GI-multimode fiber using spatial multiplexing with 2×4 MIMO processing,” in ECOC2010, paper Tu3C4.

Chen, H-Y.

Chen, J.

Chen, S.

Cvijetic, N.

N. Cvijetic, D. Qian, J. Hu, and T. Wang, “Orthogonal frequency division multiple access PON (OFDMA-PON) for colorless upstream transmission beyond 10 Gb/s,” IEEE J. Sel. Areas Commun.28(6), 781–790 (2010).
[CrossRef]

N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space pptical transmission using OFDM,” in OFC/NFOEC2008, paper OThD2.

Dischler, R.

B. Franz, D. Suikat, R. Dischler, F. Buchali, and H. Buelow, “High speed OFDM data transmission over 5 km GI-multimode fiber using spatial multiplexing with 2×4 MIMO processing,” in ECOC2010, paper Tu3C4.

Ditewig, T.

Djordjevic, I.

W. Shieh and I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 1993).

Franz, B.

B. Franz, D. Suikat, R. Dischler, F. Buchali, and H. Buelow, “High speed OFDM data transmission over 5 km GI-multimode fiber using spatial multiplexing with 2×4 MIMO processing,” in ECOC2010, paper Tu3C4.

Giddings, R. P.

Groenewald, J.

Helms, J.

J. Helms, “Intermodulation distortions of broad-band modulated laser diodes,” J. Lightwave Technol.10(12), 1901–1906 (1992).
[CrossRef]

Hong, Y.

Hong, Y. H.

X. Zheng, X. Q. Jin, R. P. Giddings, J. L. Wei, E. Hugues-Salas, Y. H. Hong, and J. M. Tang, “Negative power penalties of optical OFDM signal transmission in directly modulated DFB laser-based IMDD systems incorporating negative dispersion fibers,” IEEE Photon. J.2(4), 532–542 (2010).
[CrossRef]

H-Salas, E.

Hsu, D-Z.

Hu, J.

N. Cvijetic, D. Qian, J. Hu, and T. Wang, “Orthogonal frequency division multiple access PON (OFDMA-PON) for colorless upstream transmission beyond 10 Gb/s,” IEEE J. Sel. Areas Commun.28(6), 781–790 (2010).
[CrossRef]

Hugues-Salas, E.

E. Hugues-Salas, R. P. Giddings, X. Q. Jin, J. L. Wei, X. Zheng, Y. Hong, C. Shu, and J. M. Tang, “Real-time experimental demonstration of low-cost VCSEL intensity-modulated 11.25Gb/s optical OFDM signal transmission over 25km PON systems,” Opt. Express19(4), 2979–2988 (2011).
[CrossRef] [PubMed]

X. Zheng, X. Q. Jin, R. P. Giddings, J. L. Wei, E. Hugues-Salas, Y. H. Hong, and J. M. Tang, “Negative power penalties of optical OFDM signal transmission in directly modulated DFB laser-based IMDD systems incorporating negative dispersion fibers,” IEEE Photon. J.2(4), 532–542 (2010).
[CrossRef]

Jin, X. Q.

Kieffer, J. C.

P. K. Vitthaladevuni, M-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun.4(6), 3039–3050 (2005).
[CrossRef]

Koonen, T.

Lee, J.

Li, W-Y.

Loquai, S.

Lowery, A. J.

Ma, Y.

Okonkwo, C.

Peral, E.

Qian, D.

N. Cvijetic, D. Qian, J. Hu, and T. Wang, “Orthogonal frequency division multiple access PON (OFDMA-PON) for colorless upstream transmission beyond 10 Gb/s,” IEEE J. Sel. Areas Commun.28(6), 781–790 (2010).
[CrossRef]

N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space pptical transmission using OFDM,” in OFC/NFOEC2008, paper OThD2.

Schmauss, B.

Schmidt, B. J. C.

Shi, Y.

Shieh, W.

Shu, C.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, 1972).

Suikat, D.

B. Franz, D. Suikat, R. Dischler, F. Buchali, and H. Buelow, “High speed OFDM data transmission over 5 km GI-multimode fiber using spatial multiplexing with 2×4 MIMO processing,” in ECOC2010, paper Tu3C4.

Tang, J. M.

Tang, Y.

Tangdiongga, E.

Tartarini, G.

van de Boom, H.

Vanin, E.

Visani, D.

Vitthaladevuni, P. K.

P. K. Vitthaladevuni, M-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun.4(6), 3039–3050 (2005).
[CrossRef]

Wang, T.

N. Cvijetic, D. Qian, J. Hu, and T. Wang, “Orthogonal frequency division multiple access PON (OFDMA-PON) for colorless upstream transmission beyond 10 Gb/s,” IEEE J. Sel. Areas Commun.28(6), 781–790 (2010).
[CrossRef]

N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space pptical transmission using OFDM,” in OFC/NFOEC2008, paper OThD2.

Wei, C-C.

Wei, J. L.

Yang, H.

Yang, Q.

Zheng, X.

E. Hugues-Salas, R. P. Giddings, X. Q. Jin, J. L. Wei, X. Zheng, Y. Hong, C. Shu, and J. M. Tang, “Real-time experimental demonstration of low-cost VCSEL intensity-modulated 11.25Gb/s optical OFDM signal transmission over 25km PON systems,” Opt. Express19(4), 2979–2988 (2011).
[CrossRef] [PubMed]

X. Zheng, X. Q. Jin, R. P. Giddings, J. L. Wei, E. Hugues-Salas, Y. H. Hong, and J. M. Tang, “Negative power penalties of optical OFDM signal transmission in directly modulated DFB laser-based IMDD systems incorporating negative dispersion fibers,” IEEE Photon. J.2(4), 532–542 (2010).
[CrossRef]

IEEE J. Sel. Areas Commun.

N. Cvijetic, D. Qian, J. Hu, and T. Wang, “Orthogonal frequency division multiple access PON (OFDMA-PON) for colorless upstream transmission beyond 10 Gb/s,” IEEE J. Sel. Areas Commun.28(6), 781–790 (2010).
[CrossRef]

IEEE Photon. J.

X. Zheng, X. Q. Jin, R. P. Giddings, J. L. Wei, E. Hugues-Salas, Y. H. Hong, and J. M. Tang, “Negative power penalties of optical OFDM signal transmission in directly modulated DFB laser-based IMDD systems incorporating negative dispersion fibers,” IEEE Photon. J.2(4), 532–542 (2010).
[CrossRef]

IEEE Trans. Wireless Commun.

P. K. Vitthaladevuni, M-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun.4(6), 3039–3050 (2005).
[CrossRef]

J. Lightwave Technol.

Opt. Express

D-Z. Hsu, C-C. Wei, H-Y. Chen, W-Y. Li, and J. Chen, “Cost-effective 33-Gbps intensity modulation direct detection multi-band OFDM LR-PON system employing a 10-GHz-based transceiver,” Opt. Express19(18), 17546–17556 (2011).
[CrossRef] [PubMed]

X. Q. Jin, E. H-Salas, R. P. Giddings, J. L. Wei, J. Groenewald, and J. M. Tang, “First real-time experimental demonstrations of 11.25Gb/s optical OFDMA PONs with adaptive dynamic bandwidth allocation,” Opt. Express19(21). 20557–20570 (2011).
[CrossRef] [PubMed]

C-C. Wei, “Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission systems,” Opt. Express20(23), 25774–25789 (2012).
[CrossRef] [PubMed]

Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelenth bandwidth access,” Opt. Express17(11), 9421–9427 (2009).
[CrossRef] [PubMed]

W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express16(9), 6378–6386 (2008).
[CrossRef] [PubMed]

E. Hugues-Salas, R. P. Giddings, X. Q. Jin, J. L. Wei, X. Zheng, Y. Hong, C. Shu, and J. M. Tang, “Real-time experimental demonstration of low-cost VCSEL intensity-modulated 11.25Gb/s optical OFDM signal transmission over 25km PON systems,” Opt. Express19(4), 2979–2988 (2011).
[CrossRef] [PubMed]

E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,” Opt. Express19(5), 4280–4293 (2011).
[CrossRef] [PubMed]

Opt. Letters

C-C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Letters36(2), 151–153 (2011).
[CrossRef]

Other

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 1993).

W. Shieh and I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).

B. Franz, D. Suikat, R. Dischler, F. Buchali, and H. Buelow, “High speed OFDM data transmission over 5 km GI-multimode fiber using spatial multiplexing with 2×4 MIMO processing,” in ECOC2010, paper Tu3C4.

N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space pptical transmission using OFDM,” in OFC/NFOEC2008, paper OThD2.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, 1972).

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Figures (5)

Fig. 1
Fig. 1

Schematic illustration of the simulated OOFDM system.

Fig. 2
Fig. 2

Constellations obtained by simulation of the 4-QAM IM/DD OOFDM system and evaluation of Eq. (14). (a) BW =2.5GHz, FS=32, N=14, Tpre=Tpos=0.125, L=0km, i0=40mA, Δi=0.005, α=4; (b) same as (a), but L=60km; (c) same as (b), but L=80km and i0=60mA; (d) same as (c) but BW =5.5GHz; (e) same as (d), but Δ i=0.01mA; (f) same as (e), but α=10; (g) same as (f), but FS=128, N=55 and α=4; (h) same as (g), but the nonlinear gain coefficient of the laser is equal to 3×10−23 m3, i0=80mA, Δi=0.015 and L=100km.

Fig. 3
Fig. 3

Constellations obtained by simulation of the 32-QAM IM/DD OOFDM system and evaluation of Eq. (14). BW =5.5GHz, FS=128, N=55, Tpre=Tpos=0.125, L=60km, α=4, i0=60mA and Δi=0.01mA. (a) the nonlinear gain coefficient is equal to 3×10−24 m3; (b) the nonlinear gain coefficient is equal to 3×10−23 m3; (c) same as (b) but the fiber dispersion is D=−7ps/(nm·km).

Fig. 4
Fig. 4

Comparison of the carrier to interference power ratio obtained through simulation of an IM/DD OOFDM system and that obtained through numerical computation of Eq. (14), and carrier to different interfering terms power ratios for a dispersive fiber link of length (a) 20 km, (b) 40 km, (c) 60 km, and (d) 80 km.

Fig. 5
Fig. 5

Comparison of the BER obtained through numerical simulations and calculated by the obtained expression Eq. (14) for standard and negative dispersion fibers.

Tables (1)

Tables Icon

Table 1 Laser Parameters

Equations (21)

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s ( t ) k = 1 N | X k | cos ( Ω k t + φ x k )
d p ( t ) d t = [ Γ v g a g n ( t ) n t 1 + ε n l p ( t ) 1 τ p ] p ( t ) + ζ Γ B n 2 ( t ) d n ( t ) d t = i ( t ) e V A n B n 2 C n 3 v g a g n ( t ) n t 1 + ε n l p ( t ) p ( t ) d ϕ d t = 1 2 α Γ v g a g ( n ( t ) n t )
E ( t , z = 0 ) = P ( t ) exp ( j ϕ 1 ( t ) ) exp ( j ω 0 t )
ϕ 1 ( t ) = k = 1 N m k sin ( Ω k t + φ m k )
H ( ω ) = exp ( j β ( ω ) L ) = exp ( j ( β 0 + β 1 ( ω ω 0 ) + 1 2 β 2 ( ω ω 0 ) 2 ) L )
E ( t , z = L ) = F T 1 { F T { E ( t , z = 0 ) } H ( ω ) }
I p h ( t ) = 𝔕 | E ( t , z = L ) | 2
i ( t ) = i 0 + k = 1 N 2 i k cos ( Ω k t + φ i k )
P ( t ) P 0 + P 1 ( t ) + P 2 ( t ) + P 11 ( t ) = P 0 + k = 1 N 2 p k cos ( Ω k t + φ p k ) + k = 1 N 2 p 2 k cos ( 2 Ω k t + φ p 2 k ) + k = 1 N l = 1 k 1 2 p k l cos ( ( Ω k + Ω t ) t + φ p k l ) + k = 1 N l = 1 k 1 2 p k _ l cos ( ( ( Ω k Ω l ) + φ p k _ l ) )
p k exp ( j φ p k ) = H p 1 ( Ω k ) i k exp ( j φ i k ) p 2 k exp ( φ p 2 k ) = H p 2 ( Ω k ) i k 2 exp ( j 2 φ i k ) p k l exp ( j φ p k l ) = H p 11 ( ( Ω k , Ω l ) ) i k i l exp ( j ( φ i k + φ i l ) ) p k _ l exp ( j φ p k _ l ) = H p 11 ( ( Ω k , Ω l ) ) i k i l exp ( j ( φ i k φ i l ) )
| E ( t ) | = a + b P 1 ( t ) + c P 2 ( t ) + c P 11 ( t ) + d k = 1 N l = 1 l k N 2 p k p l cos ( ( Ω k + Ω l ) t + φ p k + φ p l ) + d k = 1 N l = 1 l k N 2 p k p l cos ( ( Ω k Ω l ) t + φ p k φ p l ) + d k = 1 N 2 p k 2 cos ( 2 ( Ω k t + φ p k ) )
a = P 0 1 2 , b = c = 1 2 P 0 1 2 , d = 1 8 P 0 3 2
E ( t ) = | E ( t ) | exp ( j k = 1 N m k sin ( Ω k t + φ m k ) )
I p h ( t ) 𝔕 n 1 n N = J n 1 ( μ 1 ) J n N ( μ N ) ( a 2 + 2 b 2 k = 1 N p k 2 cos ( 2 θ k ) + T 0 2 a b k = 1 N p k J n k ( μ k ) cos ( θ k ) ( J n k + 1 ( μ k ) exp ( j ( Δ φ k + π 2 ) ) + J n k 1 ( μ k ) exp ( j ( Δ φ k + π 2 ) ) ) T 1 + 2 a c k = 1 N p 2 k J n k ( μ k ) cos ( 2 θ k ) ( J n k + 2 ( μ k ) exp ( j ( 2 φ m k φ p 2 k + π ) ) + J n k 2 ( μ k ) exp ( j ( 2 φ m k φ p 2 k + π ) ) ) T 2 + 2 a c k = 1 N l = 1 k 1 p k l J n k ( μ k ) J n l ( μ l ) cos ( θ k + θ l ) ( J n k + 1 ( μ k ) J n l + 1 ( μ l ) exp ( j ( φ m k + φ m l φ p k l + π ) ) ) + T 3 J n k 1 ( μ k ) J n l 1 ( μ l ) exp ( j ( φ m k + φ m l φ p k l + π ) ) + 2 a c k = 1 N l = 1 k 1 p k _ l J n k ( μ k ) J n l ( μ l ) cos ( θ k θ l ) T 3 ( J n k + 1 ( μ k ) J n l 1 ( μ l ) exp ( j ( φ m k φ m l φ p k _ l ) ) + J n k 1 ( μ k ) J n l + 1 ( μ l ) exp ( j ( φ m k φ m l φ p k _ l ) ) ) T 3 + k = 1 N l = 1 l k N p k p l J n k ( μ k ) J n l ( μ l ) ( J n k + 1 ( μ k ) J n l + 1 ( μ l ) exp ( j ( Δ φ k + Δ φ l + π ) ) + J n k 1 ( μ k ) J n l 1 ( μ l ) ) T 4 exp ( j ( Δ φ k + Δ φ l + π ) ) ) ( 2 a d cos ( θ k + θ l ) + b 2 ) + k = 1 N l = 1 l k N p k p l J n k ( μ k ) J n l ( μ l ) ( J n k + 1 ( μ k ) J n l 1 ( μ l ) T 4 exp ( j ( Δ φ k Δ φ l ) ) + J n k 1 ( μ k ) J n l + 1 ( μ l ) exp ( j ( Δ φ k Δ φ l ) ) ) ( 2 a d cos ( θ k θ l ) + b 2 ) T 4 + k = 1 N p k 2 ( J n k + 2 ( μ k ) exp ( j 2 ( Δ φ k + π 2 ) ) + J n k 2 ( μ k ) exp ( j 2 ( Δ φ k + π 2 ) ) J n k ( μ k ) ( 2 a d cos ( 2 θ k + b 2 ) ) T 5 ) exp ( j ( Ω imp t + k = 1 N n k ( φ m k + π 2 ) ) )
Err y [ k ] = | Y rec sim [ k ] Y rec theo [ k ] | 2 | Y rec sim [ k ] | 2 × 100
CIPR Ω k = Information Signal Power at Ω k Interference Power at Ω k
H p 1 ( Ω k ) = C p 1 e V ψ X M E Ψ Ω k 2 + j Ω k ( X + M ) H p 2 ( Ω k ) = C p v g a g 1 + ε n l p 0 ( ψ Γ ( 2 j Ω k + X ) ) ( P j Ω k ψ ) X M E Ψ 4 Ω k 2 + 2 j Ω k ( X + M ) ( H p 1 ( Ω k ) C p ) 2 H p 1 , 1 ( Ω k , Ω l ) = C p v g a g 1 + ε n l p 0 ( ψ Γ ( j ( Ω k + Ω l ) + X ) ) ( 2 P j Ω k + Ω l ψ ) X M E ψ ( Ω k + Ω l ) 2 + j ( Ω k + Ω l ) ( X + M ) H p 1 ( Ω k ) C p H p 1 ( Ω l ) C p
ψ = Γ v g a g p 0 1 + ε n l p 0 + 2 β B Γ n 0 M = Γ v g a g n 0 n t 1 + ε n l p 0 ( ε n l p 0 1 + ε n l p 0 1 ) + 1 τ p X = A + 2 B n 0 + 3 C n 0 2 + v g a g p 0 1 + ε n l p 0 E = v g a g n 0 n t 1 + ε n l p 0 ( p 0 1 + ε n l p 0 1 ) P = n 0 n t 1 + ε n l p 0 ε n l M ψ
s c ( t ) = k = N / 2 N / 2 1 X k exp ( Ω k t )
s ( t ) = Re { s c ( t ) exp ( Ω r f t ) } = k = N / 2 N / 2 1 | X k | cos ( ( Ω r f + Ω k ) t + φ X k )
I p h ( t ) 𝔕 n N / 2 n N / 2 1 = J n N / 2 ( μ N / 2 ) J n N / 2 1 ( μ N / 2 1 ) ( a 2 + 2 b 2 k = N / 2 N / 2 1 p k 2 cos ( 2 θ k ) + 2 a b k = N / 2 N / 2 1 p k J n k ( μ k ) cos ( θ k ) ( J n k + 1 ( μ k ) exp ( j ( Δ φ k + π 2 ) ) + J n k 1 ( μ k ) exp ( j ( Δ φ k + π 2 ) ) ) + 2 a c k = N / 2 N / 2 1 p 2 k J n k ( μ k ) cos ( 2 θ k ) ( J n k + 2 ( μ k ) exp ( j ( 2 φ m k φ p 2 k + π ) ) + J n k 2 ( μ k ) exp ( j ( 2 φ m k φ p 2 k + π ) ) ) + 2 a c k = N / 2 N / 2 1 l = N / 2 k 1 p k l J n k ( μ k ) J n l ( μ l ) cos ( θ k + θ l ) ( J n k + 1 ( μ k ) J n l + 1 ( μ l ) exp ( j ( φ m k + φ m l φ p k l + π ) ) + J n k 1 ( μ k ) J n l 1 ( μ l ) exp ( j ( φ m k + φ m l φ p k l + π ) ) ) + 2 a c k = N / 2 N l = N / 2 k 1 p k _ l J n k ( μ k ) J n l ( μ l ) cos ( θ k θ l ) ( J n k + 1 ( μ k ) J n l 1 ( μ l ) exp ( j ( φ m k φ m l φ p k _ l ) ) + J n k 1 ( μ k ) J n l + 1 ( μ l ) exp ( j ( φ m k φ m l φ p k _ l ) ) ) + k = N / 2 N / 2 1 l = N / 2 l k N / 2 1 p k p l J n k ( μ k ) J n l ( μ l ) ( J n k + 1 ( μ k ) J n l + 1 ( μ l ) exp ( j ( Δ φ k + Δ φ l + π ) ) + J n k 1 ( μ k ) J n l 1 ( μ l ) exp ( j ( Δ φ k + Δ φ l + π ) ) ) ( 2 a d cos ( θ k + θ l ) + b 2 ) + k = N / 2 N / 2 1 l = N / 2 l k N / 2 1 p k p l J n k ( μ k ) J n l ( μ l ) ( J n k + 1 ( μ k ) J n l 1 ( μ l ) exp ( j ( Δ φ k Δ φ l ) ) + J n k 1 ( μ k ) J n l + 1 ( μ l ) exp ( j ( Δ φ k Δ φ l ) ) ) ( 2 a d cos ( θ k θ l ) + b 2 ) + k = N / 2 N / 2 1 p k 2 ( J n k + 2 ( μ k ) exp ( j 2 ( Δ φ k + π 2 ) ) + J n k 2 ( μ k ) exp ( j 2 ( Δ φ k + π 2 ) ) J n k ( μ k ) ( 2 a d cos ( 2 θ k ) + b 2 ) ) ) exp ( j ( Ω imp t + k = N / 2 N / 2 1 n k ( φ m k + π 2 ) ) )

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