Achievable Data Rate Analysis of Clipped Flip-OFDM in ...Achievable Data Rate Analysis of Clipped...
Transcript of Achievable Data Rate Analysis of Clipped Flip-OFDM in ...Achievable Data Rate Analysis of Clipped...
Achievable Data Rate Analysis of Clipped Flip-OFDM inOptical Wireless Communication
Zhenhua Yu1 Robert J. Baxley2 G. Tong Zhou1
1Center for Signal and Image ProcessingGeorgia Institute of Technology
2Georgia Tech Research Institute
Dec. 3 2012
Acknowledgement: This work was supported in part by the Texas Instrument DSP
Leadership University Program.
(Georgia Tech) Dec. 3 2012 1 / 25
Outline
1 System model
2 Achievable Data Rate Analysis
3 Numerical Results
4 Conclusion
(Georgia Tech) Dec. 3 2012 2 / 25
Outline
1 System model
2 Achievable Data Rate Analysis
3 Numerical Results
4 Conclusion
(Georgia Tech) Dec. 3 2012 3 / 25
OFDM for Optical Wireless Communication (OWC)
Intensity modulation (IM) and direct detection (DD) schemes requirethe electric signal to be real-valued and unipolar (positive-valued)
Hermitian symmetricBipolar-unipolar conversion
Real-valued unipolar OFDM signal for OWC
DC biased optical OFDM (DCO-OFDM) [Hranilovic, 2005]Asymmetrically clipped optical OFDM (ACO-OFDM)[Armstrong and Lowery, 2006]Flip-OFDM [Yong, 2007] [Fernando et al., 2011]Unipolar OFDM (U-OFDM) [Tsonev et al., 2012]
Disadvantage of OFDM: high peak-to-average-power ratio (PAPR)
The OFDM signal often has to be double-sided clipped in order to fitthe linear range of LED [Mesleh et al., 2011][Dimitrov et al., 2011][Yu et al., 2012][Dimitrov et al., 2012]Introduces nonlinear distortions
(Georgia Tech) Dec. 3 2012 4 / 25
OFDM for OWC (Continued)
Subcarrier Assignment
N-point IDFT
DPDData in Bipolar-
UnipolarConversion
DAC
HermitianSymmetry
Electrical to Optical Conversion (LED)
O ti l Symmetry Optical Channel
Subcarrier Extraction
N-point DFT ADC
Data out Optical to Electrical Conversion (PD or
Image Sensor)
r[n] = y[n]⊗ h[n] + w[n]
Assume that the digital pre-distortion (DPD) has perfectly linearizedthe LED between the interval [PL, PH ] [Elgala et al., 2009].
(Georgia Tech) Dec. 3 2012 5 / 25
Flip-OFDM [Fernando et al., 2011]
The unipolar signal y[n] is composed of a positive part and a negativepart from x[n]
x[n] = x+[n] + x−[n],
where the positive part x+[n] and the negative part x−[n] areobtained as
x+[n] =
{x[n], x[n] > 0
0, x[n] < 0
x−[n] =
{x[n], x[n] < 0
0, x[n] > 0
(Georgia Tech) Dec. 3 2012 6 / 25
Flip-OFDM (Continued) [Fernando et al., 2011]
At the receiver, assume the channel h[n] is constant over two frames,the two received components can be expressed as
r+[n] = x+[n]⊗ h[n] + w+[n],
r−[n] = −x−[n]⊗ h[n] + w−[n]
Then the bipolar signal is reconstructed as
r[n] = r+[n]− r−[n]
= (x+[n] + x−[n])⊗ h[n] + w+[n] + w−[n]
= x[n]⊗ h[n] + w?[n],
w?[n] = w+[n] + w−[n]: has power 2σ2w; can be further reduced with
noise filtering scheme [Fernando et al., 2012].
(Georgia Tech) Dec. 3 2012 7 / 25
Outline
1 System model
2 Achievable Data Rate Analysis
3 Numerical Results
4 Conclusion
(Georgia Tech) Dec. 3 2012 8 / 25
Clipping and Biasing Model[Dimitrov et al., 2011, Yu et al., 2012]
Clipping Biasing
In order to fit the signal within the optical power constraints of thetransmitter
y[n] =
cu − cl, y[n] > cuy[n]− cl, cl ≤ x[n] ≤ cu
0, x[n] < cl
(Georgia Tech) Dec. 3 2012 9 / 25
Definitions
Clipping ratio γ and Biasing ratio ς
γ ,(cu − cl)/2
σ, ς ,
−clcu − cl
where σ denotes the standard deviation of x[n]Average optical power
Oy , E{y[n]}Optical signal to noise power ratio (OSNR)
OSNR ,Oyσw
Dynamic optical power
Gy , max (y[n])−min (y[n])
Dynamic signal to noise power ratio (DSNR)
DSNR ,Gyσw
(Georgia Tech) Dec. 3 2012 10 / 25
Clipping and Biasing for Flip-OFDM
After the clipping and biasing, the two components of Flip-OFDMcan be expressed as
x+[n] =
cu − cl, x+[n] > cu
x+[n]− cl, cl ≤ x+[n] ≤ cu0, x+[n] < cl
− x−[n] =
cu − cl, −x−[n] > cu
−x−[n]− cl, cl ≤ −x−[n] ≤ cu0, −x−[n] < cl
Average optical power of y[n] is reduced to
Oy = σ
(φ(2γς)− φ (2γ(1− ς))− 2γςΦ (−2γς)
+2γ(1− ς)Φ (−2γ(1− ς)) + 2γς
)(Georgia Tech) Dec. 3 2012 11 / 25
Clipping and Biasing for Flip-OFDM (Continued)
Dynamic optical power of y[n] is reduced to
Gy = max (y[n])−min (y[n]) = cu − cl = 2σγ
At the receiver, we can obtain the reconstructed signal
r[n] = x[n]⊗ h[n] + w?[n],
where
x[n] = x+[n] + x−[n]
=
cu − cl, x[n] > cux[n]− cl, cl ≤ x[n] ≤ cu
0, −cl < x[n] < clx[n] + cl, −cu ≤ x[n] ≤ −clcl − cu, x[n] ≤ −cu
(Georgia Tech) Dec. 3 2012 12 / 25
System Constraints
Average optical power constraint PA (limit on power consumption,eye safety regulation, dim illumination requirement, etc.)
Oy ≤ PA
OSNR constraint ηOSNR , PA/σw
Dynamic optical power constraint PH − PL (dynamic range of theLED)
Gy ≤ PH − PLDSNR constraint ηDSNR , (PH − PL)/σw
The maximum σ/σw value can be obtained as
σ
σw= min
(ηOSNROy/σ
,ηDSNRGy/σ
)
(Georgia Tech) Dec. 3 2012 13 / 25
Signal to Distortion Ratio
Auto-SDR
IDFT DFTcorrelation calculation
SDR calculation
Bussgang’s Theorem [Bussgang, 1952]
x[n] = α · x[n] + d[n], n = 0, . . . , N − 1
The output auto-correlation function Rxx[m] is related to the inputauto-correlation function Rxx[m] via [Davenport and Root, 1987]
Rxx[m] =
∞∑`=0
b2``!
[Rxx[m]
σ2
]`The SDR at the kth subcarrier
SDRk =E [|α ·Xk|2]
E [|Dk|2]=α2PX,kPD,k
=α2PX,k
PX,k − α2PX,k
(Georgia Tech) Dec. 3 2012 14 / 25
Achievable Data Rate
The signal-to-noise-and-distortion ratio (SNDR) for the kth subcarrier
SNDRk =
((SDRk)
−1 +2β(N − 2)
Nα2|Hk|2·max
(O2y/σ
2
η2OSNR
,G2y/σ
2
η2DSNR
))−1
The achievable data rate
R (γ, ς, ηOSNR, ηDSNR,H)
=1
2N
N/2−1∑k=1
log2 (1 + SNDRk)bits
subcarrier
For given ηOSNR, ηDSNR values and channel response H, we canobtain a pair of optimum clipping ratio γ‡ and optimum biasing ratioς‡ that maximize the achievable data rate by
(γ‡, ς‡) = argmax(γ,ς)
R|ηOSNR,ηDSNR,H,
and the corresponding achievable data rate.
(Georgia Tech) Dec. 3 2012 15 / 25
Outline
1 System model
2 Achievable Data Rate Analysis
3 Numerical Results
4 Conclusion
(Georgia Tech) Dec. 3 2012 16 / 25
Optimal clipping ratio and biasing ratio
0 5 10 15 20 252
4
6
8
10
ηOSNR (dB)
Opt
imum
clip
ping
rat
io (
dB) (a)
0 5 10 15 20 25
−0.04
−0.02
0
0.02
ηOSNR (dB)
Opt
imum
bia
sing
rat
io
(b)
N = 512. AWGN channel.
ηDSNR/ηOSNR = (PH − PL)/PA = 18 dB
(Georgia Tech) Dec. 3 2012 17 / 25
Achievable data rate (ηDSNR/ηOSNR = 6 dB)
0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
ηOSNR (dB)
Ach
ieva
ble
data
rat
e (b
its/s
ubca
rrie
r)
AWGN channelCeiling bounce channel
DCO−OFDM
Flip−OFDM
Figure : Achievable data rate with optimal clipping ratio and optimal biasing ratiofor ηOSNR = 0, 1, ..., 25 dB (in step size of 1 dB), and ηDSNR/ηOSNR = 6 dB.
(Georgia Tech) Dec. 3 2012 18 / 25
Achievable data rate (ηDSNR/ηOSNR = 18 dB)
0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
ηOSNR (dB)
Ach
ieva
ble
data
rat
e (b
its/s
ubca
rrie
r)
AWGN channelCeiling bounce channel
DCO−OFDM
Flip−OFDM
Figure : Achievable data rate with optimal clipping ratio and biasing ratio forηOSNR = 0, 1, ..., 25 dB (in step size of 1 dB), and ηDSNR/ηOSNR = 18 dB.
(Georgia Tech) Dec. 3 2012 19 / 25
Achievable data rate (no ηDSNR constraint)
0 5 10 15 20 250
0.5
1
1.5
2
2.5
3
ηOSNR (dB)
Ach
ieva
ble
data
rat
e (b
its/s
ubca
rrie
r)
AWGN channelCeiling bounce channel
Flip−OFDM
DCO−OFDM
Figure : Achievable data rate with optimal clipping ratio and biasing ratio forηOSNR = 0, 1, ..., 25 dB (in step size of 1 dB), and no ηDSNR constraint.
(Georgia Tech) Dec. 3 2012 20 / 25
Outline
1 System model
2 Achievable Data Rate Analysis
3 Numerical Results
4 Conclusion
(Georgia Tech) Dec. 3 2012 21 / 25
Summary
Derived the achievable data rate of clipped Flip-OFDM
Investigated the trade-off between the optical power constraint anddistortion
Analyzed the optimum clipping ratio and biasing ratio and comparedthe performance of Flip-OFDM and DCO-OFDM techniques
Numerical results showed that DCO-OFDM outperforms theFlip-OFDM for most of the optical power constraint scenarios
(Georgia Tech) Dec. 3 2012 22 / 25
References I
Armstrong, J. and Lowery, A. J. (2006).Power efficient optical OFDM.Electronics Letters, 42(6):370–372.
Bussgang, J. (1952).Crosscorrelation functions of amplitude-distorted gaussian signals.NeuroReport, 17(2).
Davenport, W. and Root, W. (1987).An introduction to the theory of random signals and noise.IEEE Press.
Dimitrov, S., Sinanovic, S., and Haas, H. (2011).A comparison of OFDM-based modulation schemes for OWC with clipping distortion.In Proc. IEEE GLOBECOM Workshop on OWC, pages 787 –791.
Dimitrov, S., Sinanovic, S., and Haas, H. (2012).Signal shaping and modulation for optical wireless communication.Journal of Lightwave Technology, 30(9):1319–1328.
Elgala, H., Mesleh, R., and Haas, H. (2009).Non-linearity effects and predistortion in optical OFDM wireless transmission using LEDs.International Journal of Ultra Wideband Communications and Systems, 1(2):143–150.
(Georgia Tech) Dec. 3 2012 23 / 25
References II
Fernando, N., Hong, Y., and Viterbo, E. (2011).Flip-OFDM for optical wireless communications.In Proc. IEEE Information Theory Workshop, pages 5–9. IEEE.
Fernando, N., Hong, Y., and Viterbo, E. (2012).Flip-OFDM for unipolar communication systems.IEEE Transactions on Communications.
Hranilovic, S. (2005).On the design of bandwidth efficient signalling for indoor wireless optical channels.International Journal of Communication Systems, 18(3):205–228.
Mesleh, R., Elgala, H., and Haas, H. (2011).On the performance of different ofdm based optical wireless communication systems.Journal of Optical Communications and Networking, 3(8):620–628.
Tsonev, D., Sinanovic, S., and Haas, H. (2012).Novel unipolar orthogonal frequency division multiplexing (U-OFDM) for optical wirelesscommunication.In Proc. IEEE VTC 2012-Spring.
Yong, J. (2007).Modulation and demodulation apparatuses and method for wired / wirelesscommunication.
(Georgia Tech) Dec. 3 2012 24 / 25
References III
Yu, Z., Baxley, R. J., and Zhou, G. T. (2012).EVM and achievable data rate analysis of clipped OFDM signals in visible lightcommunication.EURASIP Journal on Wireless Communications and Networking.
(Georgia Tech) Dec. 3 2012 25 / 25