[Paper Review] Nonlinear Distortion Reduction in OFDM from Reliable Perturbations in Data Carriers

Ebrahim B. Al-Safadi, Tareq Y. Al-Naffouri+2 more|arXiv (Cornell University)|Jun 30, 2015

PAPR reduction in OFDM16 references3 citations

TL;DR

This paper proposes a pilotless, data-aided method for nonlinear distortion cancellation in OFDM systems using compressed sensing and sparse Bayesian recovery. By adaptively selecting reliable data carriers based on signal reliability metrics—magnitude, phase, and channel strength—it enables accurate distortion estimation without reserved tones or pilots, achieving near-oracle performance in clipping recovery while preserving spectral efficiency and reducing complexity.

ABSTRACT

A novel method for correcting the effect of nonlinear distortion in orthogonal frequency division multiplexing signals is proposed. The method depends on adaptively selecting the distortion over a subset of the data carriers, and then using tools from compressed sensing and sparse Bayesian recovery to estimate the distortion over the other carriers. Central to this method is the fact that carriers (or tones) are decoded with different levels of confidence, depending on a coupled function of the magnitude and phase of the distortion over each carrier, in addition to the respective channel strength. Moreover, as no pilots are required by this method, a significant improvement in terms of achievable rate can be achieved relative to previous work.

Motivation & Objective

• To address the limitations of existing OFDM nonlinear distortion mitigation techniques that rely on reserved tones or pilot symbols, which reduce spectral efficiency and increase complexity.
• To develop a method that enables accurate distortion estimation without requiring orthogonality between data and distortion frequency support.
• To eliminate the need for pilot tones or reserved carriers while maintaining high performance in nonlinear distortion cancellation.
• To introduce a systematic framework for selecting the most reliable data carriers for compressed sensing-based recovery.
• To optimize the trade-off between distortion tolerance, robustness to channel estimation errors, and computational complexity.

Proposed method

• The method uses a pilotless compressed sensing framework where distortion is modeled as a sparse signal in the time domain.
• It introduces a novel reliability metric that quantifies the confidence level of each data tone based on symbol magnitude, phase, constellation location, and channel strength.
• The framework employs a dual-stage tone subset selection: first minimizing the probability of incorrect measurements, then maximizing the clipping-to-noise ratio (CNR).
• A closed-form expression is derived to characterize the behavior of the reliability function, enabling geometrically inspired approximations for efficient subset selection.
• Sparse Bayesian recovery techniques are applied to reconstruct the full distortion signal from the selected reliable data carriers.
• The approach leverages the sparsity of time-domain distortion and avoids constrained transmitter-side signal shaping, reducing system complexity.

Experimental results

Research questions

• RQ1 Can nonlinear distortion in OFDM be effectively canceled without using pilot tones or reserved carriers?
• RQ2 How can the reliability of individual data carriers be quantified to guide optimal subset selection for compressed sensing?
• RQ3 What is the optimal strategy for selecting a subset of data carriers that minimizes measurement error while maximizing distortion recovery performance?
• RQ4 How does the proposed method compare to oracle-based least-squares recovery in terms of achievable rate and distortion cancellation accuracy?
• RQ5 What is the theoretical bound on the number of data carriers needed for reliable recovery without risking incorrect measurements?

Key findings

• The proposed method achieves near-oracle performance in clipping signal recovery, with a bit error rate (BER) performance very close to that of an idealized least-squares estimator with full knowledge of the distortion.
• The framework enables significant spectral efficiency gains by eliminating the need for pilot tones or reserved carriers, thus preserving all subcarriers for data transmission.
• The dual-stage tone selection process effectively reduces the probability of incorrect measurements while maximizing the CNR, leading to robust and accurate distortion recovery.
• Theoretical bounds are derived for the minimum number of data carriers required to ensure reliable recovery, providing a principled way to set system parameters without over-sampling.
• The reliability metric based on symbol magnitude, phase, and constellation geometry significantly improves the accuracy of compressed sensing recovery compared to uniform or random selection.
• Simulations confirm that the method performs favorably even under severe clipping conditions, demonstrating strong robustness and practical viability.