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 Science and Technology, Makkah Province, Thuwal, Saudi Arabia. 2 Department of Electrical Engineering, King Fahd University of Petroleum and Minerals, Eastern Province, Dhahran, Saudi Arabia. Sparse Bayesian Clipping Recovery 1
Content Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation Sparse Bayesian Clipping Recovery 2
Content Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation Sparse Bayesian Clipping Recovery 3
OFDM ◮ OFDM is a multi-carrier modulation scheme that uses orthogonal carriers. ◮ Main Advantages include ◮ Robustness against multi-path fading. ◮ High data rate. ◮ Easy single tap equalization. ◮ The main disadvantage is High PAPR! [1] Sparse Bayesian Clipping Recovery 4
High PAPR 1011 3 + 2 1001 4 + 3 A mixture . . Transmitter based schemes . . of Sinusoids . . 1101 2 − 3 ◮ coding, partial transmit [1010 · · · 101] Incoming high PAPR sequence (PTS), selected S/P QAM IDFT data stream Signal mapping (SLM), interleaving, tone reservation (TR), tone 15 injection (TI) and active Peak Power constellation extension Amplitude 10 (ACE). Average Power ◮ Transmitter-based 5 techniques are complex. 0 0 64 128 192 256 Time Index Sparse Bayesian Clipping Recovery 5
Clipping ◮ We follow a clipping scheme ◮ clip signal above a prespecified Time Domain Signal Before Clipping Time Domain Signal After Clipping threshold γ 6 6 Amplitude Amplitude 4 4 � γe ∠ x ( i ) if | x ( i ) | > γ x p ( i ) = 2 2 x ( i ) otherwise 0 0 20 40 60 20 40 60 Sample Index Sample Index ◮ x p ( i ) = x ( i ) + c ( i ) Frequency Domain Signal Before Clipping Frequency Domain Signal After Clipping 2 2 Amplitude Amplitude 0 0 3 + 2 0 −2 −2 QAM . . 20 40 60 20 40 60 . Subcarrier Subcarrier Sparse Clipping Signal 2 − 3 0 −1 Amplitude −2 ◮ Implications: −3 ◮ Clipping signal is sparse ! 10 20 30 40 50 60 ◮ Pilot contamination. Sample Index ◮ Inter-user Interference. Sparse Bayesian Clipping Recovery 6
Content Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation Sparse Bayesian Clipping Recovery 7
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. a By Bayesian recovery, we refer to the utilized SABMP scheme [2]. Sparse Bayesian Clipping Recovery 8
Content Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation Sparse Bayesian Clipping Recovery 9
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? Geometrical representation of adopted reliability criteria. ◮ Calculate the metric [3] R = Pr ( ⌊ ˆ ˆ X a X ( i ) ⌋ = X ( i )) X 1 X × × × × × × Pr ( ⌊ ˆ X ( i ) ⌋ � = X ( i )) ˆ X 2 ⌊·⌋ denotes hard decision. × X c X b × × × × × Sparse Bayesian Clipping Recovery 10
Content Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation Sparse Bayesian Clipping Recovery 11
Phase and Likelihood Clipped with high probability ◮ Clipping operation does not 4 affect the phase. γ Amplitude c 2 x x x p 0 1 3 5 7 9 11 Sample index ◮ Phase of the clipping signal ◮ Probability of a clipping can be retrieved from the element is high, if received received clipped signal. signal is closer to threshold. ◮ This helps in increasing the ◮ Find the dominant support measurements. faster and accurately. Sparse Bayesian Clipping Recovery 12
Simulation Results 10 − 1 No Est SABMP WPA-SABMP PA-FBMP Simulation Parameters: WPAL Oracle-LS ◮ Subcarriers: 512 BER ◮ QAM Order: 64 10 − 2 ◮ Reliable Carriers: 128 Runtime ◮ Clipping Ratio: 1.61 10 0 10 − 3 15 18 21 24 27 E b /N 0 Sparse Bayesian Clipping Recovery 13
Content Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation Sparse Bayesian Clipping Recovery 14
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]. Distortion Cancellation Distortion Estimation ¯ ¯ ¯ Y 1 Φ 1 Z 1 MRC Combiner ¯ ¯ ¯ Y 2 Φ 2 Z 2 Distortion Cancellation = c + , . . . . . . . . . . . . . . . ¯ ¯ ¯ Y L Φ L Z L Distortion Cancellation Sparse Bayesian Clipping Recovery 15
Simulation Results 10 − 2 Simulation Parameters: ◮ Subcarriers: 512 10 − 3 ◮ QAM Order: 64 BER Runtime ◮ Reliable Carriers: 77 10 − 1 ◮ Eb/N0: 27 dB 10 − 4 No Est ◮ Antennas: 2 WPA-SABMP-Single WPA-SABMP-Joint Oracle-LS 10 − 5 1 . 56 1 . 61 1 . 66 1 . 71 1 . 76 CR Sparse Bayesian Clipping Recovery 16
Content Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation Sparse Bayesian Clipping Recovery 17
OFDMA System Orthogonal Channel Allocation Two Stage Recovery . . . 1 2 3 4 5 6 7 8 255 256 . . . ◮ Initially reconstruct jointly. Challenge → Distortions Overlap in Frequency Domain ◮ Form decoupled systems. 10 6 ◮ Perform individual Amplitude Distortion 4 reconstruction. 5 2 4 0 3 64 2 128 0 192 256 1 0 64 128 192 256 Users Time Index Sub-carriers Channel 1 Mobile 1 Individual Transmitter Reconstruction (1) Limiter Channel 2 Mobile 2 Individual Transmitter Receiver . Reconstruction . Reconstruction (2) . . Base Station Joint . . Decoupling . . Limiter . . . . . . P . . . . . e l . . n n a h C Mobile 3 Individual Transmitter Reconstruction (P) Limiter Sparse Bayesian Clipping Recovery 18
Simulation Results 10 − 1 Simulation Parameters: ◮ Subcarriers: 512 ◮ Users: 2 BER 10 − 2 ◮ QAM Order: 64 ◮ Reserved Tones: 75 ◮ Clipping Ratio: 1.61 No Est Joint Reconstruction Two Stage Recovery No Clipping 10 − 3 15 18 21 24 27 E b /N 0 Sparse Bayesian Clipping Recovery 19
Content Motivation Bayesian Clipping Recovery Reliable Carriers as Measurements Prior Information about clipping Multiple Antenna Receivers Multiple User System Clipped OFDM and Channel Estimation Sparse Bayesian Clipping Recovery 20
Contaminated Pilots True Pilot Sequence True Pilot Sequence Corrupted Pilot Sequence Corrupted Pilot Sequence Estimated Pilot Sequence Solutions Proposed ◮ Increase pilots. ◮ Estimate Corrupted Pilots. ◮ Data Aided pilot Estimation. ◮ Use estimated and data aided pilots together. Sparse Bayesian Clipping Recovery 21
Results − 15 Simulation Parameters: − 20 ◮ Subcarriers: 256 − 25 ◮ QAM Order: 64 MSE ◮ Pilot Tones: 16 − 30 ◮ Reliable Tones: 16 MMSE − 35 ◮ Clipping Ratio: 1.73 CPA ≈ 7 . 2dB RC CPA+RC No Clipping − 40 10 15 20 25 30 E b /N 0 Sparse Bayesian Clipping Recovery 22
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. Sparse Bayesian Clipping Recovery 23
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