# Optimal Subcarrier Weighting for Mitigation of Laser Phase Noise in Optical Constant Envelope OFDM

Zahra Hourzadehgharabolagh, Vincent Choqueuse, Pascal Morel, Mihai

Telescu, Noël Tanguy, Stéphane Azou

► To cite this version:

Zahra Hourzadehgharabolagh, Vincent Choqueuse, Pascal Morel, Mihai Telescu, Noël Tanguy, et al. Optimal Subcarrier Weighting for Mitigation of Laser Phase Noise in Optical Constant Envelope OFDM. Advanced Photonics Congress (Signal Processing in Photonic Communications), OPTICA, Jul 2025, Marseille, France. SpTh3E.5, 10.1364/SPPCOM.2025.SpTh3E.5. [hal-05303666]

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Submitted on 8 Oct 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Optimal Subcarrier Weighting for Mitigation of Laser Phase Noise in Optical Constant Envelope OFDM

Zahra HOURZADEHGHARABOLAGH¹, Vincent CHOQUEUSE¹, Pascal MOREL¹,
Mihai TELESCU², Noël TANGUY² and Stéphane AZOU¹

¹ Lab-STICC, UMR CNRS 6285, ENIB, Technopôle Brest-Iroise, 29238 Brest, France

² Lab-STICC, UMR CNRS 6285, UBO, 6 Av. Victor Le Gorgeu, 29200 Brest, France

zahra hourzadehgharabolagh@enib.fr

**Abstract:** We propose a novel strategy to mitigate the impact of laser phase noise in optical constant-envelope OFDM systems by optimizing the non-zero subcarrier weights, providing a closed-form expression for them. © 2025 The Authors

**OCIS codes:** (060.1660) Coherent communications; (060.5060) Phase modulation

## 1. Introduction

Orthogonal Frequency Division Multiplexing (OFDM) has gained considerable attention in optical communications due to its high spectral efficiency, flexible resource allocation, and effective compensation for linear impairments such as Chromatic Dispersion (CD). However, the high Peak-to-Average Power Ratio (PAPR) of OFDM waveforms makes them more vulnerable to nonlinear effects in systems using components such as optical amplifiers, photodiodes, and fiber. To mitigate the influence of nonlinearities on system performance in conventional OFDM (CO-OFDM), various techniques—such as digital predistortion (DPD) [1] and PAPR reduction methods [2]—have been proposed. An alternative approach is Constant Envelope OFDM (CE-OFDM), originally developed for wireless communications [3], which eliminates the need for such compensation techniques. CE-OFDM reduces the PAPR to 0 dBm by encoding information solely in the phase of the optical signal, thereby improving resilience against nonlinear distortions. While CE-OFDM effectively mitigates nonlinearities [4], [5], it remains highly sensitive to laser phase noise. Existing phase noise mitigation strategies, such as subcarrier nulling [6] and pilot-based correction [7], help reduce this impact but come at the cost of a reduced data rate.

In this work, we propose an optimized subcarrier weighting strategy, where each subcarrier is multiplied by an optimal weight derived from a closed-form expression. This approach effectively mitigates the influence of phase noise on system performance without compromising the overall data rate, providing an efficient alternative to existing compensation techniques in a system setup that uses an SOA as a booster amplifier.

## 2. Subcarrier weight optimization

Fig. 1 illustrates the principle of CE-OFDM. Our main objective is to apply an optimal weight $W_k$ to the k-th subcarrier before the IFFT to minimize the error variance between the transmitted and received subcarriers, given by $\mathbb{E}[|\hat{x}_k - x_k|^2]$ while maintaining a fixed total power constraint, $\mathbb{E}[|W_k|^2] = 1$. This variance is primarily influenced by two noise sources: laser phase noise and channel white Gaussian noise. The spectral density of the laser phase noise is given by $\mathbb{E}[|\Theta_k|^2] = \beta(N_{sc} os)^2/(\pi F_s k^2)$ [8] where $\beta$ is the laser linewidth, $N_{sc}$ is the number of subcarriers, os is the oversampling factor and $F_s$ is the sampling frequency. Meanwhile, the white Gaussian noise is characterized by the approximated spectral density obtained after phase demodulation $\mathbb{E}[|B_k|^2] \approx 1/(2 \cdot \text{OSNR})$ as referenced in [3], where OSNR represents the optical signal-to-noise ratio, excluding laser phase noise. Through mathematical derivations, the optimal weight for the k-th subcarrier is found to be:

$$W_k = C_W \cdot \sqrt{\mathbb{E}[|\hat{x}_k - x_k|^2]} = C_W \cdot \frac{1}{2\pi h \cdot C} \sqrt{\left(\frac{\beta(N_{sc} os)^2}{\pi F_s} \cdot \frac{1}{k^2} + \frac{1}{2 \cdot \text{OSNR}}\right)} \quad (1)$$

Here, $C_W$ is a normalization constant ensuring a fixed total power, while $2\pi h$ represents the phase modulation index, and $C$ is the power normalization factor of the real OFDM-modulated signal $x(t)$. At the receiver, the inverse of the applied weight $W_k^{-1}$ is used to compensate for the weighting applied at the transmitter.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Block diagram of CE-OFDM with subcarrier weighting and a booster SOA.</figcaption></figure>
### 3. Simulation parameters and results

To demonstrate the benefits of our approach, we simulated the optical chain described in Fig. 1. The system was simulated in Python, except for the SOA, which was implemented in ADS using the model developed in [9]. We map 4-QAM symbols onto 256 subcarriers, where 3 subcarriers are set to zero around the carrier frequency and 6 at the left band edge and 5 at the right. The signal follows Hermitian symmetry. The system operates with a 10 GHz bandwidth and an oversampling factor of 4, resulting in a 40 GHz sampling rate and a total data rate of 35 Gb/s. Both the transmitter and receiver lasers have a 100 kHz linewidth. The first scenario (Fig. 2) considers optical back-to-back transmission over an AWGN channel, without the SOA and fiber chromatic dispersion. The Kerr effect is negligible in this scenario. A total of 1000 OFDM symbols are generated, with the first serving as a synchronization reference under the same allocation scheme. Each OFDM symbol includes a 16-sample cyclic prefix. Fig. 2a compares the EVM per subcarrier for uniform and optimized weighting schemes. Note that, due to the normalization constraint, the mean EVM remains unchanged before and after weight optimization. For the optimized weighting scheme, we observe that the EVM of subcarriers near the carrier frequency is significantly reduced, while that of distant subcarriers slightly increases. In terms of performance, the proposed strategy produces a cleaner constellation (Fig. 2b, Fig. 2c) and achieves a tenfold reduction in BER (from $10^{-4}$ to $10^{-5}$).

<figure><img src="image_3.png" /><figcaption>Fig. 2: a) EVM per subcarrier, received data constellation b) before and c) after weight optimization.</figcaption></figure>

The second scenario evaluates phase modulation indices and SOA input power in an AWGN channel for 100 OFDM symbols. The setup includes a booster SOA, 80 km of SSMF, and compares subcarrier sizes of 256 and 512. Fig. 3a (–10 dBm SOA input, $I_{bias}$ = 150 mA, 16 dB gain) shows BER improvement via weight optimization, peaking near $2\pi h = 0.6$. Fig. 3b (fixed $2\pi h = 0.6$) reveals a two-order BER improvement for $N_{SC}$ = 256 and one-order for $N_{SC}$ = 512 across input power levels.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Impact of (a) phase modulation index and (b) booster SOA input power on BER after 80 km of SSMF.</figcaption></figure>

### 4. Conclusion

We introduced a laser phase noise compensation strategy by optimizing subcarrier weights in CE-OFDM. Our results show that while the mean EVM remains unchanged, the BER is reduced by at least a factor of 10, all while maintaining the overall data rate. This approach could eliminate the need for dedicated laser phase noise compensation algorithms.

**Acknowledgments:** This work was supported by the European Union through the European Regional Development Fund (ERDF), the Ministry of Higher Education and Research, the Région Bretagne, the Département du Finistère, and Brest Métropole through the Contrat de Plan État-Région (CPER) Project PhotBreizh.

### References

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