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Receiver-based Recovery of Clipped OFDM Signals for PAPR Reduction: A Bayesian Approach Anum Ali 1 , Abdullatif Al-Rabah 1 , Mudassir Masood 1 and Tareq Y. Al-Naffouri 1 , 2 1 Department of Electrical Engineering, King Abdullah University of

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Receiver-based Recovery of Clipped OFDM Signals for PAPR Reduction: A Bayesian Approach

Anum Ali1, Abdullatif Al-Rabah1, Mudassir Masood1 and Tareq Y. Al-Naffouri1,2

1Department of Electrical Engineering,

King Abdullah University of Science and Technology, Makkah Province, Thuwal, Saudi Arabia.

2Department of Electrical Engineering,

King Fahd University of Petroleum and Minerals, Eastern Province, Dhahran, Saudi Arabia.

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Content

Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation

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Content

Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation

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OFDM

◮ OFDM is a multi-carrier modulation scheme that uses

rthogonal carriers.

◮ Main Advantages include

◮ Robustness against multi-path fading. ◮ High data rate. ◮ Easy single tap equalization.

◮ The main disadvantage is High PAPR! [1]

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High PAPR

S/P QAM IDFT high PAPR Signal Incoming data stream [1010 · · · 101]       1011 1001 . . . 1101             3 + 2 4 + 3 . . . 2 − 3       A mixture

f Sinusoids

64 128 192 256 5 10 15 Average Power Peak Power Time Index Amplitude

Transmitter based schemes

◮ coding, partial transmit

sequence (PTS), selected mapping (SLM), interleaving, tone reservation (TR), tone injection (TI) and active constellation extension (ACE).

◮ Transmitter-based

techniques are complex.

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Clipping

◮ We follow a clipping scheme ◮ clip signal above a prespecified threshold γ xp(i) =

γe∠x(i)

if |x(i)| > γ x(i)

therwise

◮ xp(i) = x(i) + c(i) QAM      3 + 2 . . . 2 − 3      ◮ Implications:

◮ Clipping signal is sparse! ◮ Pilot contamination. ◮ Inter-user Interference.

20 40 60 2 4 6 Sample Index Amplitude Time Domain Signal Before Clipping 20 40 60 −2 2 Subcarrier Amplitude Frequency Domain Signal Before Clipping 20 40 60 2 4 6 Sample Index Amplitude Time Domain Signal After Clipping 20 40 60 −2 2 Subcarrier Amplitude Frequency Domain Signal After Clipping 10 20 30 40 50 60 −3 −2 −1 Sample Index Amplitude Sparse Clipping Signal

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Content

Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation

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Bayesian Sparse Signal Recovery

Implications of Sparsity

◮ Signal can be reconstructed using sparse signal recovery

methods.

◮ Few Measurements will be required.

Why Bayesian Recovery?a

◮ Low Complexity. ◮ Signal statistics are not required. ◮ Agnostic to distribution. ◮ Noise statistics are utilized.

aBy Bayesian recovery, we refer to the

utilized SABMP scheme [2].

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Content

Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation

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Reliable Perturbations

◮ Reserved tones reduce bandwidth efficiency. ◮ Some data carriers (called Reliable tones) can be used as

measurements.

Question

How to select the tones which are most likely to be in their correct decision region?

◮ Calculate the metric [3]

R = Pr(⌊ ˆ X(i)⌋ = X(i)) Pr(⌊ ˆ X(i)⌋ = X(i))

⌊·⌋ denotes hard decision. Geometrical representation of adopted reliability criteria.

× × × × × × × × × × × ×Xc

Xb Xa X ˆ X1 ˆ X2

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Content

Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation

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Phase and Likelihood

◮ Clipping operation does not

affect the phase.

x x c xp

◮ Phase of the clipping signal

can be retrieved from the received clipped signal.

◮ This helps in increasing the

measurements.

1 3 5 7 9 11 2 4 Sample index Amplitude Clipped with high probability γ

◮ Probability of a clipping

element is high, if received signal is closer to threshold.

◮ Find the dominant support

faster and accurately.

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Simulation Results

15 18 21 24 27 10−3 10−2 10−1 Eb/N0 BER No Est SABMP WPA-SABMP PA-FBMP WPAL Oracle-LS 100 Runtime

Simulation Parameters:

◮ Subcarriers: 512 ◮ QAM Order: 64 ◮ Reliable Carriers: 128 ◮ Clipping Ratio: 1.61

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Content

Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation

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Same clipping on all antennas

◮ Multiple receiver antennas provide more measurements for

clipping reconstruction.

◮ Use measurements from all antennas together to improve

clipping mitigation [4].      ¯ Y1 ¯ Y2 . . . ¯ YL      =      ¯ Φ1 ¯ Φ2 . . . ¯ ΦL      c+      ¯ Z1 ¯ Z2 . . . ¯ ZL      ,

Distortion Estimation Distortion Cancellation Distortion Cancellation Distortion Cancellation

. . . . . .

MRC Combiner

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Simulation Results

1.56 1.61 1.66 1.71 1.76 10−5 10−4 10−3 10−2 CR BER No Est WPA-SABMP-Single WPA-SABMP-Joint Oracle-LS 10−1 Runtime

Simulation Parameters:

◮ Subcarriers: 512 ◮ QAM Order: 64 ◮ Reliable Carriers: 77 ◮ Eb/N0: 27 dB ◮ Antennas: 2

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Content

Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation

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OFDMA System

Orthogonal Channel Allocation

1 2 3 4 5 6 7 8 . . . . . . 255 256

Challenge→ Distortions Overlap in Frequency Domain

64 128 192 256 5 10 Time Index Amplitude 64 128 192 256 1 2 3 4 2 4 6 Sub-carriers Users Distortion

Two Stage Recovery

◮ Initially reconstruct

jointly.

◮ Form decoupled

systems.

◮ Perform individual

reconstruction.

. . .

Mobile 1 Transmitter Mobile 2 Transmitter

. . .

Mobile 3 Transmitter Limiter Limiter

. . .

Limiter Channel 1 Channel 2 C h a n n e l P Base Station Receiver .

. .

Joint Reconstruction .

. . Decoupling

Individual Reconstruction (1) Individual Reconstruction (2)

. . .

Individual Reconstruction (P)

. . .

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Simulation Results

15 18 21 24 27 10−3 10−2 10−1 Eb/N0 BER No Est Joint Reconstruction Two Stage Recovery No Clipping

Simulation Parameters:

◮ Subcarriers: 512 ◮ Users: 2 ◮ QAM Order: 64 ◮ Reserved Tones: 75 ◮ Clipping Ratio: 1.61

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Content

Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation

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Contaminated Pilots

True Pilot Sequence Corrupted Pilot Sequence

Solutions

◮ Increase pilots. ◮ Data Aided pilot Estimation.

True Pilot Sequence Corrupted Pilot Sequence Estimated Pilot Sequence

Proposed

◮ Estimate Corrupted Pilots. ◮ Use estimated and data

aided pilots together.

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Results

10 15 20 25 30 −40 −35 −30 −25 −20 −15 ≈ 7.2dB Eb/N0 MSE MMSE CPA RC CPA+RC No Clipping

Simulation Parameters:

◮ Subcarriers: 256 ◮ QAM Order: 64 ◮ Pilot Tones: 16 ◮ Reliable Tones: 16 ◮ Clipping Ratio: 1.73

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References

[1] S. H. Han and J. H. Lee, An overview of peak-to-average power ratio reduction techniques for multicarrier transmission, IEEE Wireless Commun., vol. 12, no. 2, pp. 5665, 2005. [2] M. Masood and T. Y. Al-Naffouri, “Sparse Reconstruction Using Distribution Agnostic Bayesian Matching Pursuit,” IEEE Trans. Signal Process., vol. 61, no. 21, pp. 52985309, 2013. [3] E. B. Al-Safadi and T. Y. Al-Naffouri, “Pilotless Recovery of Nonlinearly Distorted OFDM Signals by Compressive Sensing over Reliable Data Carriers,” in Proc. IEEE Int. Workshop on Signal Process. Advances in Wireless Commun. (SPAWC), 2012. [4] A. Ali, A. Al-Zahrani, T. Y. Al-Naffouri, “Receiver Based PAPR Reduction in OFDMA”, in Proc. IEEE Int. Conf. Acoust. Speech Signal Process., 2014.

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For more information...

◮ Email:

tareq.alnaffouri@kaust.edu.sa

◮ For details and relevant papers:

http://faculty.kfupm.edu.sa/ee/naffouri/publications.html

THANK YOU!

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