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Clipping Noise Cancellation for OFDM and OFDMA Systems Using Compressed Sensing
Kee-Hoon Kim, Hosung Park, Jong-Seon No, Habong Chung
TL;DR
The paper addresses clipping noise cancellation in OFDM and OFDMA without sacrificing data rate. It uses compressed sensing on partial, reliable data tones and adapts the number of observations to noise conditions. Numerical analysis reports effective cancellation across Nyquist-rate and oversampled OFDM cases, with easy application to interleaved OFDMA.
Problem
OFDM and OFDMA clipping-noise cancellation must address severe PAPR-related distortion while avoiding data-rate loss and practical implementation difficulties.
Method
The method uses compressed sensing to reconstruct clipping noise from partial high-reliability data tones, with an adjustable number of compressed observations.
Results
Numerical analysis shows effective clipping-noise mitigation for Nyquist-rate clipping and oversampled clipping with filtering, and applicability to interleaved OFDMA.
Takeaways & Limitations
The proposed scheme provides a data-rate-preserving clipping-noise cancellation approach applicable to both OFDM and interleaved OFDMA systems.
Abstract
from arXiv · showhide
In this paper, we propose clipping noise cancellation scheme using compressed sensing (CS) for orthogonal frequency division multiplexing (OFDM) systems. In the proposed scheme, only the data tones with high reliability are exploited in reconstructing the clipping noise instead of the whole data tones. For reconstructing the clipping noise using a fraction of the data tones at the receiver, the CS technique is applied. The proposed scheme is also applicable to interleaved orthogonal frequency division multiple access (OFDMA) systems due to the decomposition of fast Fourier transform (FFT) structure. Numerical analysis shows that the proposed scheme performs well for clipping noise cancellation of both OFDM and OFDMA systems.
I. INTRODUCTION
OFDM clipping reduces peak regrowth but introduces out-of-band radiation and sparse clipping noise, while existing cancellation schemes face computational, data-rate, BER, or OFDMA implementation limitations. The proposed CS method reconstructs clipping noise from partial reliable data tones, adapts observations to noise level, and applies to OFDM and interleaved OFDMA.
- Problem: Clipping reduces OFDM peak regrowth but causes out-of-band radiation and sparse time-domain clipping noise that requires cancellation.Filtering is needed for the out-of-band radiation, while the clipping noise motivates reconstruction methods.
- Prior limitations: Prior approaches require costly iterative maximum-likelihood estimation, reserve tones that reduce data rate, or suffer poor BER under limited and noisy compressed observations.These limitations affect both conventional OFDM schemes and CS-based tone-reservation or pilot-based methods.
- Proposed approach: The proposed method reconstructs clipping noise from partial high-reliability data tones using compressed sensing, without reserved tones or data-rate loss.It exploits compressed observations underlying partial data tones rather than the whole data-tone set.
- Proposed approach: The number of compressed observations is adjustable, allowing an observation count suited to the noise level and addressing CS reconstruction weakness against noise.The scheme selects partial data tones through a parameterized reliability rule.
- Results and scope: Numerical analysis shows effective clipping-noise mitigation for Nyquist-rate clipping and oversampled clipping with filtering, with applicability to interleaved OFDMA.The OFDMA extension is enabled by the FFT structure, whereas earlier OFDMA approaches faced practical pilot-estimation or computational issues.
II. SYSTEM MODEL
The system models clipping in oversampled OFDM, transforms the clipped signal back to frequency domain, and exploits the resulting clipping-noise sparsity for compressed-sensing cancellation.
- Oversampled OFDM is generated by zero-padding the input tones with (L −1)N zeros before IDFT processing.
- Clipping and filtering limit peak regrowth and remove out-of-band radiation before frequency-domain processing.
- The clipped signal can be represented using either an additive model, x̄L(n)=xL(n)+cL(n), or an attenuated component plus clipping noise.
- At Nyquist sampling, clipping noise c(n) is K-sparse with sparsity ratio K/N, enabling compressed-sensing reconstruction.
- With oversampling L>1, clipping noise becomes nearly K-sparse because the remaining N−K amplitudes are close to, but not exactly, zero.
A. Formulation to CS Problem
The received OFDM model is converted into a compressed-sensing problem by selecting M frequency-domain observations and reconstructing sparse clipping noise from them.
- The received symbol follows Y(k)=H(k)(X(k)+C(k))+Z(k), with channel response H(k) and AWGN Z(k).
- A selection matrix SRR extracts M of N received components to form a reduced-dimensional observation for compressed sensing.
- Writing C=Fc makes Φ=SRRF an M×N measurement matrix, while c is the sparse clipping-noise vector.
- Subtracting the estimated selected data symbols yields a compressed observation containing the measurement of c plus data-estimation and channel-noise terms.
- Compressed-sensing reconstruction produces ĉ, whose FFT is subtracted from the equalized received symbol before final detection.
B. Selection Matrix SRR
The selection matrix uses reliable regions in the received signal space so that only higher-confidence data tones contribute to clipping-noise reconstruction.
- The reliable region is defined as a signal-space area, and KRR contains indices of received components falling within it.
- For QPSK and 16-QAM, the reliable region is the shaded area in Fig. 2; analogous regions can be defined for other modulations.
- The attenuated model has higher SCNR than the additive model because the additive model includes a signal-correlated term (α−1)X(k).
- SRR selects M identity-matrix rows indexed by KRR, and the number of compressed observations is therefore adjustable.
- Selecting tones inside the reliable region lowers the decision error of SRR X̂ as the region parameter δ increases.
C. Decision Error Probability of SRR ˆX Over an AWGN Channel
Under an AWGN channel, the analysis characterizes reliable-region membership and derives the decision error probability for the selected data symbols.
- For the attenuated model, (1/α)W(k) is modeled as zero-mean complex Gaussian with variance (1/α^2)(E[|D(k)|^2]+N0).
- The analysis assumes clipping at the Nyquist sampling rate, where all data tones experience clipping noise D(k).
- The probability that (1/α)Y(k) lies in the reliable region is used to characterize correct decisions for V^2-QAM.
- The decision error probability of SRR X̂ is obtained by substituting the reliable-region and correct-decision probabilities into the derived expression.
D. Determination of δ
The choice of δ balances estimation error against the number of compressed observations, so neither an extremely small nor large value is preferred. Simulations are used to identify an optimal δ for CS reconstruction.
- D. Determination of δ: δ trades off estimation errors against compressed-observation count: smaller values increase M but can increase estimation error, while larger values reduce observations.The two effects vary with δ and jointly determine reconstruction quality.
- D. Determination of δ: Very small δ can cause frequent estimation errors, increasing noise energy and degrading CS reconstruction, which favors larger δ from the error perspective.Thus, the preferred δ must account for both estimation accuracy and measurement quantity.
- D. Determination of δ: For fixed N and clipping noise c, larger M improves reconstruction performance, favoring smaller δ from the observation-count perspective.The compressed-observation quality is described as upper bounded for randomly selected frequency-domain observations.
- D. Determination of δ: The authors perform extensive simulations to find the δ that maximizes CS performance because both noise and compressed observations vary with δ.The section frames δ selection as an empirical optimization problem.
E. Reconstruction Algorithms in CS
The scheme uses OMP for clipping-noise recovery because it is fast and easy to implement, while acknowledging that more accurate alternatives can be more computationally expensive. The iteration process stops using a threshold or a maximum limit.
- E. Reconstruction Algorithms in CS: OMP is selected for sparse signal recovery mainly for implementation ease and speed, although basis pursuit can reconstruct better at higher computational cost.This choice prioritizes practical complexity over maximum reconstruction performance.
- E. Reconstruction Algorithms in CS: Because the receiver lacks the clipping-noise sparsity K, OMP uses a sufficiently large iteration limit and estimates nonzero components in descending amplitude order.Small-amplitude components are recovered later in the iterative process.
- E. Reconstruction Algorithms in CS: OMP stops when the latest reconstructed component falls below a predetermined threshold or the maximum iteration count is reached, reducing unnecessary computation.The stopping rule targets components whose amplitudes are negligible.
- E. Reconstruction Algorithms in CS: The evaluation covers clipping at the Nyquist rate, clipping and filtering, and K-largest-peaks reduction variants.The K-largest-peaks method scales exactly K large-amplitude signal components to 80% of the (K+1)-th largest amplitude.
IV. CLIPPING NOISE CANCELLATION FOR INTERLEAVED OFDMA DOWNLINK SYSTEMS
The OFDMA extension exploits interleaved subcarrier allocation and FFT decomposition to reconstruct only the clipping noise associated with a user's data tones. This reduces measurement-matrix size but increases sparsity ratio, which can degrade reconstruction.
- IV. CLIPPING NOISE CANCELLATION FOR INTERLEAVED OFDMA DOWNLINK SYSTEMS: User-specific data-tone estimation is possible because each user needs only its own tones, avoiding dependence on other users' data tones.This modifies the OFDM formulation for the OFDMA downlink.
- IV. CLIPPING NOISE CANCELLATION FOR INTERLEAVED OFDMA DOWNLINK SYSTEMS: Interleaved OFDMA allocation partitions subcarriers into user groups from which smaller FFT blocks can be extracted from the N-point FFT.The method exploits this FFT structure to adapt clipping-noise cancellation to OFDMA.
- IV. CLIPPING NOISE CANCELLATION FOR INTERLEAVED OFDMA DOWNLINK SYSTEMS: The reduced OFDMA clipping-noise vector remains sparse with maximum K sparsity but has fewer dimensions, increasing its sparsity ratio relative to OFDM.The increased sparsity ratio may degrade reconstruction performance.
- IV. CLIPPING NOISE CANCELLATION FOR INTERLEAVED OFDMA DOWNLINK SYSTEMS: The receiver reconstructs only the clipping noise associated with the target user's data tones rather than the entire clipping-noise vector.For user 1, four reduced components are reconstructed instead of all eight original components in the illustrative N = 8 case.
V. NUMERICAL ANALYSIS
Numerical analysis evaluates the proposed cancellation scheme across OFDM and interleaved OFDMA settings, clipping conditions, modulation formats, and system sizes. The results show strong BER improvement in several settings, while reconstruction is limited by noise, sparsity, and parameter choice.
- V. NUMERICAL ANALYSIS: The proposed scheme provides a large BER benefit over no clipping-noise cancellation, while K > 8 prevents performance from approaching original OFDM in the K-largest-peaks setting.The comparison is reported for N = 64 with the proposed scheme and the scheme in [13].
- V. NUMERICAL ANALYSIS: δ = 0.4–0.5 gives the best BER for Nyquist-rate clipping, whereas smaller or larger values cause decision errors or insufficient compressed observations.At CR = 0 dB, K can exceed the OMP limit of 8, preventing complete clipping-noise reconstruction.
- V. NUMERICAL ANALYSIS: Using the largest eight IDFT components for reconstructed clipping noise gives almost the same BER as CS reconstruction when δ = 0.At δ = 0, M = N, so CS reconstruction is unnecessary.
- V. NUMERICAL ANALYSIS: With clipping and filtering at L = 4, the method has limited performance because the clipping noise is nearly sparse, although larger N yields nearly the same BER as smaller N.The δ giving best BER is also unchanged for large N, and its best value is mainly affected by CR and modulation rate.
VI. CONCLUSION
The paper proposes compressed-sensing clipping-noise cancellation that uses selected data tones and extends to OFDMA through FFT decomposition. Numerical analysis shows improved BER performance for both OFDM and OFDMA compared with conventional schemes.
- Partial data tones are exploited to reconstruct clipping noise instead of using all data tones.Rate reduction is avoided, and RR selects the partial data tones.
- Numerical analysis indicates that a proper value of δ must be chosen.
- The proposed scheme applies easily to OFDMA systems because of the FFT structure.
- BER performance improves compared with conventional schemes for both OFDM and OFDMA systems.