Abstract

Bit-Error-Ratio (BER) of intensity modulated optical orthogonal frequency division multiplexing (OFDM) system is analytically evaluated accounting for nonlinear digital baseband distortion in the transmitter and additive noise in the photo receiver. The nonlinear distortion that is caused by signal clipping and quantization is taken into consideration. The signal clipping helps to overcome the system performance limitation related to high peak-to-average power ratio (PAPR) of the OFDM signal and to minimize the value of optical power that is required for achieving specified BER. The signal quantization due to a limited bit resolution of the digital to analog converter (DAC) causes an optical power penalty in the case when the bit resolution is too low. By introducing an effective signal to noise ratio (SNR) the optimum signal clipping ratio, system BER and required optical power at the input to the receiver is evaluated for the OFDM system with multi-level quadrature amplitude modulation (QAM) applied to the optical signal subcarriers. Minimum required DAC bit resolution versus the size of QAM constellation is identified. It is demonstrated that the bit resolution of 7 and higher causes negligibly small optical power penalty at the system BER = 10−3 when 256-QAM and a constellation of lower size is applied. The performance of the optical OFDM system is compared to the performance of the multi-level amplitude-shift keying (M-ASK) system for the same number of information bits transmitted per signal sample. It is demonstrated that in the case of the matched receiver the M-ASK system outperforms OFDM and requires 3 – 3.5 dB less of optical power at BER = 10−3 when 1 – 4 data bits are transmitted per signal sample.

© 2011 OSA

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  1. R. W. Chang, “Synthesis of band-limited orthogonal signals for multichannel data transmission,” Bell Syst. Tech. J. 45, 1775–1796 (1970).
  2. R. W. Chang, “Orthogonal frequency division multiplexing,” U.S. Patent 3 488 445, 1970.
  3. A. R. Bahai, and B. R. Saltzberg, Multi-Carrier Digital Communications: Theory and Applications of OFDM (Plenum Publishing Corp., 1999).
  4. R. van Nee, and R. Prasad, OFDM for Wireless Multimedia Communications (Artech House, 2000).
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    [CrossRef]
  10. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008).
    [CrossRef]
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    [CrossRef]
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  13. D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circuits Syst. I Regul. Pap. 53(8), 1741–1748 (2006).
    [CrossRef]
  14. S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1280–1289 (2010).
    [CrossRef]
  15. S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. Mag. 12(2), 56–65 (2005).
    [CrossRef]
  16. H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. 50(1), 89–101 (2002).
    [CrossRef]
  17. J. J. Bussgang, “Crosscorrelation functions of amplitude-distorted Gaussian signals,” Research Lab. Electron, M.I.T., Cambridge, MA, USA, Tech. Rep. 216 (March 1952).
  18. A. Papoulis, and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw Hill, 2002).
  19. S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission Theory (Prentice-Hall, Inc., 1987).
  20. J. G. Proakis, Digital Communications (McGraw-Hill, 1989).
  21. P. K. Vitthaladevuni, M.-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wirel. Comm. 4(6), 3039–3050 (2005).
    [CrossRef]

2010

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1280–1289 (2010).
[CrossRef]

2009

2008

2006

2005

S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. Mag. 12(2), 56–65 (2005).
[CrossRef]

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

2002

H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. 50(1), 89–101 (2002).
[CrossRef]

1970

R. W. Chang, “Synthesis of band-limited orthogonal signals for multichannel data transmission,” Bell Syst. Tech. J. 45, 1775–1796 (1970).

Alouini, M.-S.

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

Armstrong, J.

Breyer, F.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1280–1289 (2010).
[CrossRef]

S. C. Jeffrey Lee, F. Breyer, S. Randel, H. P. A. van den Boom, and A. M. J. Koonen, “High-speed transmission over multimode fiber using discrete multitone modulation,” J. Opt. Netw. 7(2), 183–196 (2008).
[CrossRef]

Chang, R. W.

R. W. Chang, “Synthesis of band-limited orthogonal signals for multichannel data transmission,” Bell Syst. Tech. J. 45, 1775–1796 (1970).

Dardari, D.

D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circuits Syst. I Regul. Pap. 53(8), 1741–1748 (2006).
[CrossRef]

Djordjevic, I. B.

Han, S. H.

S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. Mag. 12(2), 56–65 (2005).
[CrossRef]

Imai, H.

H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. 50(1), 89–101 (2002).
[CrossRef]

Jansen, S. L.

Jeffrey Lee, S. C.

Kieffer, J. C.

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

Koonen, A. M. J.

Lee, J. H.

S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. Mag. 12(2), 56–65 (2005).
[CrossRef]

Lee, S. C. J.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1280–1289 (2010).
[CrossRef]

Lowery, A.

Lowery, A. J.

Morita, I.

Ochiai, H.

H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. 50(1), 89–101 (2002).
[CrossRef]

Randel, S.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1280–1289 (2010).
[CrossRef]

S. C. Jeffrey Lee, F. Breyer, S. Randel, H. P. A. van den Boom, and A. M. J. Koonen, “High-speed transmission over multimode fiber using discrete multitone modulation,” J. Opt. Netw. 7(2), 183–196 (2008).
[CrossRef]

Schenk, T. C. W.

Schmidt, B. J. C.

Shore, K. A.

Takeda, N.

Tanaka, H.

Tang, J. M.

van den Boom, H. P. A.

Vasic, B.

Vitthaladevuni, P. K.

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

Walewski, J. W.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1280–1289 (2010).
[CrossRef]

Bell Syst. Tech. J.

R. W. Chang, “Synthesis of band-limited orthogonal signals for multichannel data transmission,” Bell Syst. Tech. J. 45, 1775–1796 (1970).

IEEE J. Sel. Top. Quantum Electron.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1280–1289 (2010).
[CrossRef]

IEEE Trans. Circuits Syst. I Regul. Pap.

D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circuits Syst. I Regul. Pap. 53(8), 1741–1748 (2006).
[CrossRef]

IEEE Trans. Commun.

H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. 50(1), 89–101 (2002).
[CrossRef]

IEEE Trans. Wirel. Comm.

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

IEEE Wireless Commun. Mag.

S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. Mag. 12(2), 56–65 (2005).
[CrossRef]

J. Lightwave Technol.

J. Opt. Netw.

Opt. Express

Other

R. W. Chang, “Orthogonal frequency division multiplexing,” U.S. Patent 3 488 445, 1970.

A. R. Bahai, and B. R. Saltzberg, Multi-Carrier Digital Communications: Theory and Applications of OFDM (Plenum Publishing Corp., 1999).

R. van Nee, and R. Prasad, OFDM for Wireless Multimedia Communications (Artech House, 2000).

W. Shieh, and I. Djordjevic, OFDM for Optical Communications (Academic Press, 2010).

J. J. Bussgang, “Crosscorrelation functions of amplitude-distorted Gaussian signals,” Research Lab. Electron, M.I.T., Cambridge, MA, USA, Tech. Rep. 216 (March 1952).

A. Papoulis, and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw Hill, 2002).

S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission Theory (Prentice-Hall, Inc., 1987).

J. G. Proakis, Digital Communications (McGraw-Hill, 1989).

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Figures (6)

Fig. 1
Fig. 1

(Color online) Schematic of IM optical OFDM system with digital baseband distortion. Dots on the analog waveforms shown in the inset B indicate values of digital signal samples.

Fig. 2
Fig. 2

(Color online) Effective signal to noise ratio S N R e f f specified by Eq. (14) versus clipping ratio for various values of parameter S 0 . Dashed curve in red shows S N R e f f at optimum clipping ratio.

Fig. 3
Fig. 3

(Color online) Effective signal to noise ratio S N R e f f specified by Eq. (18) versus clipping ratio for S 0 = 45 dB and DAC bit resolution N b i t equal to 2, 3, 4, 5, 6 and 8, respectively. Dashed curve in red shows S N R e f f at optimum clipping ratio (the same as shown in Fig. 2). Solid curve in bold black is the same as shown in Fig. 2 for S 0 = 45 dB .

Fig. 4
Fig. 4

(Color online) BER versus clipping ratio for (a) 16-QAM, S 0 = 28 dB , N b i t = 4 (b) 64-QAM, S 0 = 3 6 dB , N b i t = 5 , and (c) 256-QAM, S 0 = 44 dB , N b i t = 6 . Solid lines show the results of analytical evaluation. Symbols display the results of brute-force numerical simulations with direct error counting for FFT size (total number of subcarriers) equal to 16 (dots in blue), 64 (crosses in red), and 128 (triangles in green).

Fig. 5
Fig. 5

(Color online) Top: Parameter S 0 defined by Eq. (15) versus effective signal to noise ratio S N R e f f at optimum clipping ratio and DAC bit resolution N b i t equal to 2 ÷ 8 and infinity (no quantization). Bottom: System BER (solid curves) for various size of QAM constellation and optimum clipping ratio (dashed curve in red) versus S N R e f f .

Fig. 6
Fig. 6

(Color online) BER versus received optical power for IM optical OFDM system (infinite DAC bit resolution) with M-QAM modulated subcarriers (in red) and for the system with multi-level ASK (in blue). The performance of OFDM and ASK systems is compared in terms of required optical power at BER = 10−3 for the same number of data bits transmitted per signal sample.

Tables (1)

Tables Icon

Table 1 Optical Receiver Parameters

Equations (20)

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x k = 1 N n = 1 N 2 1 X n exp { 2 π i k n / N } + c . c . ,       k = 0 , 1 , ... N 1 ,
z k = ρ P 0 ( 1 + y k x D C ) + d k | t h e r m + d k | s h o t ,
Q ( x ) Q C ( x ) = { x , i f     | x | < x 0 x 0 s i g n ( x ) , i f     | x | x 0
Q ( x ) Q C & Q ( x ) = { x s , i f     | x x s | < Δ x / 2 x 0 s i g n ( x ) , i f     | x | x 0 Δ x / 2
y = α x + d .
α = < x y > < x 2 > = 1 2 π σ x 3 + x Q ( x ) exp { x 2 2 σ x 2 }     d x .
I s i g n a l     C & Q 2 = ( ρ P 0 x D C α σ x ) 2 .
I n o i s e     C & Q 2 = ( ρ P 0 x D C ) 2 ( < y 2 > α 2 σ x 2 )     ,
< y 2 > = 1 2 π σ x + Q 2 ( x ) exp { x 2 2 σ x 2 }     d x     .
S N R e f f = I s i g n a l     C & Q 2 I n o i s e     C & Q 2 + I t h e r m 2 + I s h o t 2 = ( ρ P 0 x D C α σ x ) 2 ( ρ P 0 x D C ) 2 ( < y 2 > α 2 σ x 2 ) + S t h 2 Δ f + 2 q ρ P 0 Δ f ,
B E R M Q A M = 2 l o g 2 M ( 1 1 M )       erfc     ( 3     S N R e f f 2     ( M 1 ) )     .
α = 1 erfc ( R c l / 2 )     ,
< y 2 > = σ x 2 ( 1 erfc ( R c l / 2 ) + R c l erfc ( R c l / 2 ) 2 R c l / π exp { R c l / 2 } )     ,
S N R e f f = S 0 ( 1 erfc ( R c l / 2 ) ) 2 R c l + S 0 ( ( 1 + R c l ) erfc ( R c l / 2 ) erfc 2 ( R c l / 2 ) 2 R c l / π exp { R c l / 2 } ) ,
S 0 = ( x 0 x D C ) 2 ( ρ P 0 ) 2 ( S t h 2 + 2 q ρ P 0 ) Δ f .
α = 2 R c l π ( exp { R c l 2 β 2 ( 1 / 2 ) }                                                   + k = 1 2 N b i t 1 1 β ( k )     [ exp { R c l 2 β 2 ( k + 1 / 2 ) } exp { R c l 2 β 2 ( k 1 / 2 ) } ] )     ,
< y 2 > = σ x 2 R c l ( erfc { R c l 2 β ( 1 / 2 ) } +                                                 + k = 1 2 N b i t 1 1 β 2 ( k ) [ erfc { R c l 2 β ( k + 1 / 2 ) } erfc { R c l 2 β ( k 1 / 2 ) } ] )     ,
S N R e f f = S 0 α 2 R c l + S 0 ( < y 2 > σ x 2 α 2 )     .
z k = 2 ρ P 0 m 1 M 1 + d k | t h e r m + d k | s h o t ,               m = 1 , 2 , ... M ,
B E R M A S K M 1 M log 2 M Pr ( | z k 2 ρ P 0 m 1 M 1 | > ρ P 0 M 1 ) M 1 M log 2 M erfc ( 1 2 ( M 1 ) ( ρ P 0 ) 2 ( S t h 2 + 2 q ρ P 0 ) Δ f )     .

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