Achievable Data Rate Analysis of Clipped Flip-OFDM in ...Achievable Data Rate Analysis of Clipped Flip-OFDM in Optical Wireless Communication Zhenhua Yu1 Robert J. Baxley2 G. Tong

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

[email protected]

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


Outline

1 System model


3 Numerical Results

4 Conclusion


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


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].


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


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].


Outline

1 System model


3 Numerical Results

4 Conclusion


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


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


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


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

)


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


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.


Outline

1 System model


3 Numerical Results

4 Conclusion


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


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.


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)


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.


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)


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.


Outline

1 System model


3 Numerical Results

4 Conclusion


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


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.


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.


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.


Documents

Achievable Data Rate Analysis of Clipped Flip-OFDM in ...Achievable Data Rate Analysis of Clipped Flip-OFDM in Optical Wireless Communication Zhenhua Yu1 Robert J. Baxley2 G. Tong