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Flip-OFDM for Unipolar Communication Systems
Nirmal Fernando, Yi Hong, Emanuele Viterbo
TL;DR
The paper addresses the limited open-literature investigation of Flip-OFDM by analyzing it in unipolar communication systems, comparing it with ACO-OFDM, and proposing a new detection scheme. It finds equivalent spectral efficiency and error performance with nearly 50% lower receiver complexity, while filtering contributes up to 3dB gain at high conditions.
Problem
Flip-OFDM had been largely ignored in the open literature, while intersymbol interference can degrade unipolar communication-system performance.
Method
The paper reviews Flip-OFDM, compares its key system parameters with ACO-OFDM, and proposes a new detection scheme with BER analysis.
Results
Equivalent spectral efficiency and error performance with ACO-OFDM were obtained, while Flip-OFDM saved nearly 50% of receiver complexity and filtering contributed up to 3dB gain at high conditions.
Takeaways & Limitations
Flip-OFDM offers comparable spectral efficiency and error performance to ACO-OFDM with lower receiver complexity, and receiver noise filtering can improve performance.
Abstract
from arXiv · showhide
Unipolar communications systems can transmit information using only real and positive signals. This includes a variety of physical channels ranging from optical (fiber or free-space), to RF wireless using amplitude modulation with non-coherent reception, to baseband single wire communications. Unipolar OFDM techniques enable to efficiently compensate frequency selective distortion in the unipolar communication systems. One of the leading examples of unipolar OFDM is asymmetric clipped optical OFDM (ACO-OFDM) originally proposed for optical communications. Flip-OFDM is an alternative approach that was proposed in a patent, but its performance and full potentials have never been investigated in the literature. In this paper, we first compare Flip-OFDM and ACO-OFDM, and show that both techniques have the same performance but different complexities (Flip-OFDM offers 50% saving). We then propose a new detection scheme, which enables to reduce the noise at the Flip-OFDM receiver by almost 3dB. The analytical performance of the noise filtering schemes is supported by the simulation results.
I. INTRODUCTION
Unipolar OFDM addresses frequency-selective distortion in systems that transmit only real, positive signals. The paper introduces Flip-OFDM, compares it with ACO-OFDM, and proposes a new detection scheme.
- Unipolar communication systems use real, positive signals across optical, non-coherent wireless, and single-wire channels.
- Channel dispersion or multipath fading can cause intersymbol interference and degrade unipolar communication performance, motivating unipolar OFDM.
- DCO-OFDM requires significant DC bias because OFDM has high PAPR, while lower bias can cause clipping, interference, and out-of-band optical power.
- ACO-OFDM avoids DC bias by using odd subcarriers and clipping negative signal parts without distorting odd-subcarrier information symbols, although amplitudes are halved.
- Flip-OFDM transmits positive and polarity-inverted negative parts in two consecutive OFDM symbols, producing an always-positive signal.
- The paper analyzes Flip-OFDM, compares it with ACO-OFDM on spectral efficiency, BER, and complexity, and proposes a new detection scheme.
II. UNIPOLAR COMMUNICATION MODEL
The paper models unipolar communication as a real, nonnegative transmit signal passed through a nonnegative channel with Gaussian noise. This framework covers optical, non-coherent RF, and single-wire baseband systems.
- The model represents transmit signal, channel impulse response, and noise through a linear baseband equivalent system.
- A unipolar system requires a real transmit signal satisfying x(t) ≥ 0 for all t.
- The equivalent received signal uses convolution with a nonnegative channel impulse response and zero-mean Gaussian noise.
- Optical communication uses a unipolar intensity signal because optical intensity is nonnegative and direct detection does not recover carrier phase.
- Other covered examples are non-coherent RF wireless with amplitude modulation and baseband digital communication over a single wire.
III. UNIPOLAR OFDM TECHNIQUES
This section compares Flip-OFDM and ACO-OFDM within the general setting of unipolar communication systems.
- The paper compares Flip-OFDM and ACO-OFDM in a general unipolar communication setting.
- The comparison focuses on key system parameters of the two unipolar OFDM techniques.
- The section frames both techniques as approaches for unipolar communication systems.
A. Flip-OFDM
Flip-OFDM constructs a real bipolar OFDM signal, separates its positive and negative parts, and transmits them in successive nonnegative subframes. The receiver removes prefixes, reconstructs the bipolar signal, and applies an FFT to detect QAM symbols.
- Flip-OFDM uses Hermitian symmetry to obtain a real time-domain signal, sacrificing half the OFDM subcarriers.
- The real bipolar signal is decomposed into positive and negative parts for separate transmission.
- The positive part is transmitted first, followed by the inverted negative part in a second subframe.
- Cyclic prefixes are added to both OFDM subframes, and the negative subframe is delayed by N + ∆ samples.
- At the receiver, prefixes are removed, the bipolar signal is reconstructed from both subframes, and FFT processing detects the transmitted QAM symbols.
B. ACO-OFDM
ACO-OFDM maps QAM symbols onto odd subcarriers and uses Hermitian symmetry to create a real signal with an odd-symmetric time-domain structure. Negative samples can then be clipped without destroying the information.
- ACO-OFDM maps QAM information symbols onto the first half of the odd subcarriers and sets the even subcarriers to zero.
- Hermitian symmetry produces a real time-domain OFDM signal with an odd-symmetry property.
- The negative time samples can be clipped after digital-to-analog conversion without destroying the original information.
- The clipped unipolar OFDM symbol receives a cyclic prefix before transmission.
- At the receiver, direct detection is followed by cyclic-prefix removal, serial-to-parallel conversion, FFT processing, and detection of symbols on odd subcarriers.
C. System Comparisons
Flip-OFDM and ACO-OFDM are compared under matched channel and symbol conditions. They achieve the same spectral efficiency, SNR, and BER, while Flip-OFDM provides a receiver-complexity advantage.
- Flip-OFDM and ACO-OFDM use the same bandwidth, cyclic prefix, and channel delay-spread conditions for comparison.
- Spectral Efficiency: The two schemes have the same spectral efficiency because Flip-OFDM combines two subframes while carrying twice as many information symbols per OFDM symbol.
- Symbol Energy: Flip-OFDM carries twice the information-symbol energy of ACO-OFDM for a given transmitted power.Flip-OFDM spreads energy across positive and negative subframes and recombines it, whereas ACO-OFDM loses energy through clipping.
- Equivalent SNR: The equivalent SNRs of Flip-OFDM and ACO-OFDM are the same despite their different signal-energy and noise-power distributions.
- Bit Error Rates: Both systems have the same BER performance, including under the compared optical wireless channel conditions.
- Complexity: 50% of receiver complexity is saved by Flip-OFDM compared with ACO-OFDM, while transmitter complexities are nearly the same for large N.
IV. ENHANCED DETECTION FOR FLIP-OFDM
The enhanced Flip-OFDM detector uses two nonlinear time-domain noise-filtering stages before FFT-based detection. It assumes a strong LOS channel with AWGN characteristics.
- The proposed detector adds two nonlinear noise-filtering stages for Flip-OFDM time-domain samples.
- A negative clipper follows direct detection, forcing negative received samples to zero.
- A threshold-based noise filter provides the second stage to further improve BER performance.
- The preprocessed time samples are then sent to the FFT for detection.
A. Negative Clipper
The negative-clipper stage exploits the fact that signal samples are nonnegative while Gaussian noise can produce negative received samples. Its analysis derives the resulting equivalent noise and SNR improvement.
- Although transmitted samples are positive, Gaussian noise can make received samples negative, motivating negative clipping.
- The positive and negative Flip-OFDM subframes share one bipolar OFDM frame, so only one paired sample contains the signal component.
- The negative clipper sets negative samples to zero before reconstruction of the bipolar OFDM sample.
- The resulting equivalent noise and improved equivalent SNR are used to derive the first-stage theoretical BER performance.
B. Threshold Based Noise Filtering Algorithm
The threshold-based filter chooses how to reconstruct each bipolar sample by comparing the two clipped subframe samples. Its threshold controls a trade-off between noise reduction and incorrect decisions.
- The filter assumes the signal component is in one of the two clipped subframe samples and reconstructs the bipolar sample accordingly.
- The binary decision compares the difference between the two clipped samples with threshold c.
- When the sample difference is below threshold, both noise components contribute to the reconstructed output.
- When the signal-containing sample is correctly identified, the output uses that sample and achieves significantly reduced noise power.
- An incorrect threshold decision can destroy the signal estimate and increase output noise power.
- The probabilities of the decision cases depend on the signal value and threshold, which is tuned for best BER performance.
C. Design of the optimal threshold and performance analysis
The section develops an optimized threshold-based noise filter after negative clipping and evaluates its SNR and BER benefits. The combined processing provides almost 3dB SNR gain at high SNR and 2.5dB gain at BER 10^-4.
- Threshold design: The threshold-based algorithm minimizes overall noise power by tuning threshold c after the negative clipper.The analysis fixes the signal value, derives equivalent noise power, and selects copt numerically or through an SNR-based approximation.
- Threshold design: When SNR < 4.5dB, copt is infinite and the algorithm does not bring any gain.For SNR > 4.5dB, copt is finite and there is a significant SNR gain.
- SNR performance: At higher SNRs of 25–30dB, the negative clipper and threshold-based algorithm together provide almost 3dB overall SNR gain.The negative clipper contributes most at low SNR, while its gain decreases and the algorithm's gain increases with SNR.
- BER analysis: The theoretical BER expression remains valid because the FFT operation whitens the non-Gaussian noise in the frequency domain for large N.The comparison uses 16-QAM and evaluates simulated and theoretical BER at each noise-filtering stage.
- BER analysis: The measured BER curves accurately reflect the SNR gains, yielding 2.5dB gain at BER of 10^-4 versus the original system.This result uses both the negative clipper and the proposed threshold-based algorithm.
V. CONCLUSION
The paper analyzes Flip-OFDM as a unipolar OFDM technique and compares it with ACO-OFDM. It finds equivalent spectral efficiency and error performance, nearly 50% lower receiver complexity, and up to 3dB high-SNR gain from joint noise filtering.
- Conclusion: Flip-OFDM is equivalent to ACO-OFDM in spectral efficiency and error performance while saving nearly 50% of receiver complexity.This is the paper's main comparison between the two unipolar OFDM techniques.
- Conclusion: A noise filtering algorithm is applied immediately after the negative clipper at the receiver.The conclusion presents the filter as an additional receiver-processing stage.
- Conclusion: Negative clipping and noise filtering jointly contribute up to 3dB gain at high SNRs.The reported gain is a combined result of the two receiver operations.
- Conclusion: Future work will examine the potential of Flip-OFDM for non-coherent RF wireless communications.The paper identifies this as a future research direction.