PAPR Reduction of OFDM Signals using Hybrid Clipping ...

International Conference on Applied Electronics Pilsen, Czech – AE 2011

PAPR Reduction of OFDM Signals using Hybrid Clipping-Companding Scheme with Sigmoid Functions Victor Cuteanu, Alexandru Isar

Orthogonal Frequency Division-Multiplexing ƒ popular technologies used in broadband wireless communication systems like WiMAX, DVB-T or DAB. ƒ is a form of multi-carrier modulation, where spectra overlap but signals are orthogonal.

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Block Diagram of Base-band OFDM Transmitter ƒ

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Nonlin. Comp.

D/A LPF

HPA

IFFT

Cyclic Prefix

S/P

Guard Insertion

MOD

Pilot Insertion

Data

P/S

channel

Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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High Power Amplifier (HPA) ƒ The HPA nonlinearity ( Saleh Memory-less Model ) ƒ The amplitude and phase are influenced. ƒ Saturation threshold should not be exceeded.

A[u ] =

αa ⋅ u 1 + βa ⋅ u2

Φ[u ] =

αϕ ⋅ u 2 1 + βϕ ⋅ u 2

HPA

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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OFDM & PAPR ƒ Important drawback of OFDM communication system is PAPR. ƒ Peak to Average Power Ratio (PAPR) is given by:

PAPR ( x ) =

x (t ) =

1 N

(

max x (t )

[

E x (t ) N −1

∑X n =0

n

2

2

]

)

e j 2πf nt

ƒ where the sub-carriers are chosen to be orthogonal: f n = n ⋅ Δf

Δf = 1 / T 12/13/2011

Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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PAPR Reduction Techniques ƒ For the PAPR Reduction Problem, different solutions proposed: ƒNonlinear methods: ƒClipping ƒCompression / Companding ( A-law, exponential, … ) ƒLinear methods: ƒSelective Mapping / Partial Transmit Sequence ƒMultiple Signal Representations ( Constellation derivatives ) ƒTone Reservation: ƒOne Tone – One Peak (OTOP) ƒOne-by-One iteration. ƒ The PAPR of a given OFDM signal is evaluated with the complementary cumulative distribution function (CCDF):

CCDF (Y ) = Pr (PAPR > Y ) = 1 − Pr (PAPR < Y ) 12/13/2011

Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Proposed Hybrid Technique for PAPR Reduction ƒ The proposed PAPR reduction technique: ƒ Represents a combination of two standard methods: ƒ Clipping (with filtering); ƒ Companding (@Tx) with Expanding (@Rx). ƒ Performs nonlinear and quasi-nonlinear signal processing.

P/S

Frequency Domain Filtering

HPA

IFFT

Clipping

S/P

Companding (Compression)

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Zero Padding

MOD

Data

channel

Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Clipping with Filtering ƒ By clipping, time domain signal amplitude is limited to a given threshold. ƒ The clipping ratio is defined as the clipping level A divided by the rootmean-square power σ of the unclipped base-band signal. ƒ The input vector is padded by inserting N(p-1) zeros in its middle, resulting time domain signal trigonometric interpolation. ƒ Filtering can also cause peak re-growth, but less than before clipping. a0,…,aN/2-1 N(p-1) zeroes

Inverse DFT

aN/2,…,aN-1

⎛ A⎞ CR = 20 ⋅ log10 ⎜ ⎟ ⎝σ ⎠

Non-linear processing (Clipping)

Forward DFT

Signal Zero Padding

Inverse DFT

Frequency domain filtering

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Zero Padding in the Frequency Domain ƒOFDM zero-padded signal after expanding (in frequency domain). ƒSignal’s noise level is affected (slightly increased)

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Effects in Time Domain ƒ Signal processing by clipping and filtering (before & after). ƒ Signal peaks level decreased => smaller PAPR

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Companding/Expanding ƒSignal is amplified/attenuated with a factor which depends by signal level. ƒDifferent conversion laws are considered: μ-law ⎧ x⎞ ⎛ A ⋅ sign( x ) ⋅ ln⎜1 + μ ⎟ ⎪ A ⎠ ⎝ ⎪ y (x ) = ⎪ ln (1 + μ ) ⎨ ⎪ ⎛ y ⋅ ln (1 + μ ) ⎞ ⎞ A ⋅ sign( y ) ⎛⎜ ⎪ x( y ) = ⎟ − 1⎟ ⋅ exp⎜⎜ ⎟ ⎟ ⎜ μ A ⎪⎩ ⎝ ⎠ ⎠ ⎝ proposed

⎧ ⎪⎪ y ( x ) = ⎨ ⎪ x( y ) = ⎪⎩ 12/13/2011

exponential x ⎧ ⎛ −b⋅ ⎞ ⎪ y ( x ) = A ⋅ sign( x ) ⋅ ⎜⎜1 − e A ⎟⎟ ⎪ ⎠ ⎝ ⎨ y⎞ ⎛ A ⋅ sign( y ) ⎪ ⋅ log⎜⎜1 − ⎟⎟ ⎪ x( y ) = −b A⎠ ⎝ ⎩

simplified

a⋅x+b c⋅x +d b− y⋅d y⋅c − a

x ⎧ ⎪⎪ y ( x ) = c ⋅ x + d ⎨ ⎪ x( y ) = d ⋅ y ⎪⎩ 1− c ⋅ y

Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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A Comparison in Time Domain ƒCompanding functions changes signal’s mean value => new PAPR.

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Implementation ƒ Variety of companding (and corresponding expanding) functions has been proposed. ƒ Their nonlinearity may be static (constant) or dynamically (variable) from an OFDM frame to another ƒ Variable parameters imply additional information to be sent to receiver. ƒ The computational effort depends by the mathematical complexity of the respective formula: ƒ Logarithms, ƒ Exponentials, ƒ Polynomial ratios. ƒ Due to necessary operation of signal amplitude expanding, noise level increases. 12/13/2011

Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Companding Examples ƒ Signal is amplified with a factor which depends by signal level.

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Expanding examples ƒ Signal is attenuated with a factor which depends by signal level.

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Simulation Scenario

Data Tx

BER(SNR) Evaluation

M-QAM M-PSK

OFDM block

Clipping & Filtering

Companding (Compression)

parameters PAPR Evaluator

Data Rx

M-QAM M-PSK

Expanding (Decompression)

AWGN

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CCDF Evaluator

Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Numerical Results. 16 QAM ƒThe CCDF of PAPR for a 16-QAM based OFDM, 128 data carriers. ƒDifferent compression laws applied (after clipping).

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Distortions ƒThe BER(SNR) for a 16-QAM based OFDM, 128 data carriers, AWGN channel. ƒDifferent compression laws applied (after clipping).

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Numerical Results. 16 PSK ƒThe CCDF of PAPR for a 16-PSK based OFDM, 128 data carriers. ƒDifferent compression laws applied (after clipping).

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Distortions ƒThe BER(SNR) for a 16-PSK based OFDM, 128 data carriers, AWGN channel. ƒDifferent compression laws applied (after clipping).

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Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Conclusions ƒ Characteristics of the new PAPR Reduction technique: ƒ Is a combination of two methods: ƒ Clipping (with filtering); ƒ Companding (Compression). ƒ Overall provides advantages of ‘less nonlinearity’ (companding) and reduced computation complexity (from Clipping). ƒ Performance of the new PAPR Reduction technique: ƒ Better PAPR reduction; ƒ Slight BER(SNR) degradation at low SNR; ƒ Improved BER(SNR) at higher SNR. ƒ Variations of the new PAPR Reduction technique: ƒ Different companding functions; ƒ Provide different PAPR/BER(SNR) performances. 12/13/2011

Eugen Victor Cuteanu, Alexandru Isar - Pilsen, Czech - AE2011

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Bibliography ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ

J. Armstrong, “New OFDM Peak-to-Average Power Reduction Scheme”, IEEE VTC'2001 May 2001, Rhodes, Greece. Xiao Huang, Jianhua Lu, Junli Zheng, Jun Gu, "Piecewise-scales transform for the reduction of PAPR of OFDM signals", IEEE Global Telecommunications Conference, 2002. GLOBECOM '02 C. Tellambura, “A Coding Technique For Reducing Peak-To-Average Power Ration in OFDM”, IEEE, 1998. Seung Hee Han and Jae Hong Lee, "Reduction of PAPR of an OFDM Signal by Partial Transmit Sequence Technique with Reduced Complexity", IEEE Global Telecommunications Conference, 2003. GLOBECOM '03. X. Wang, T. T. Yjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of OFDM system using a companding technique,” IEEE Trans. Broadcast., vol. 45, no. 9, pp. 303-307, Sept. 1999. M. Malkin, T. Magesacher, J. M. Cioffi, "Dynamic Allocation of Reserved Tones for PAR Reduction," in OFDM Workshop, Aug 2008, Hamburg, Germany. Brian Scott Krongold and Douglas L. Jones, "PAR Reduction in OFDM via Active Constellation Extension", IEEE Transactions On Broadcasting, Vol. 49, No. 3, September 2003 X. Wang, T. T. Tjhung, C. S. Ng and A. A. Kassim, “On the SER Analysis of A-Law Companded OFDM System”, in Proc. IEEE GLOBECOM’00, vol.2, pp.756-760, 2000. Jiao, Y.Z., Liu, X.J., Wang, X.A., "A Novel Tone Reservation Scheme with Fast Convergence for PAPR Reduction in OFDM Systems", Consumer Communications and Networking Conference, 2008. Marc Deumal, Carles Vilella, Joan Lluis Pijoan, Pau Bergadà, “Partially Clipping (PC) Method For The Peak-ToAverage Power Ratio (PAPR) Reduction In OFDM”, Personal, Indoor and Mobile Radio Communications, 2004. PIMRC 2004. Jaewoon Kim and Yoan Shin, "An Effective Clipped Companding Scheme for PAPR Reduction of OFDM Signals", IEEE International Conference on Communications, 2008. ICC '08. Taleb Moazzeni, Henry Selvaraj, Yingtao Jiang, "A novel Multi-Exponential Function-based Companding Technique for Uniform Signal Compression over Channels with Limited Dynamic Range", Intl. Journal of Electronics and Telecommunications, Vol. 56, No.2, pp. 125-128, 2010 Tao Jiang, Yang Yang, and Yong-Hua Song, "Companding Technique for PAPR Reduction in OFDM Systems Based on An Exponential Function", IEEE Global Telecommunications Conference, 2005. GLOBECOM '05. S. H. Muller and J. B. Huber, “A Novel Peak Power Reduction scheme for OFDM,” Proc. of IEEE PIMPC’97, Helsinki, Finland, pp. 1090-1094, Sep. 1997.

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Thank You Very Much for Your Attention!

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