Extreme Learning Machines to Combat Phase Noise in RoF-OFDM Schemes

Abstract

Radio-over-fiber (RoF) orthogonal frequency division multiplexing (OFDM) systems have been revealed as the solution to support secure, cost-effective, and high-capacity wireless access for the future telecommunication systems. Unfortunately, the bandwidth-distance product in these schemes is mainly limited by phase noise that comes from the laser linewidth, as well as the chromatic fiber dispersion. On the other hand, the single-hidden layer feedforward neural network subject to the extreme learning machine (ELM) algorithm has been widely studied in regression and classification problems for different research fields, because of its good generalization performance and extremely fast learning speed. In this work, ELMs in the real and complex domains for direct-detection OFDM-based RoF schemes are proposed for the first time. These artificial neural networks are based on the use of pilot subcarriers as training samples and data subcarriers as testing samples, and consequently, their learning stages occur in real-time without decreasing the effective transmission rate. Regarding the feasible pilot-assisted equalization method, the effectiveness and simplicity of the ELM algorithm in the complex domain are highlighted by evaluation of a QPSK-OFDM signal over an additive white Gaussian noise channel at diverse laser linewidths and chromatic fiber dispersion effects and taking into account several OFDM symbol periods. Considering diverse relationships between the fiber transmission distance and the radio frequency (for practical design purposes) and the duration of a single OFDM symbol equal to 64 ns, the fully-complex ELM followed by the real ELM outperform the pilot-based correction channel in terms of the system performance tolerance against the signal-to-noise ratio and the laser linewidth.

Relaxation of the Radio-Frequency Linewidth for Coherent-Optical Orthogonal Frequency-Division Multiplexing Schemes by Employing the Improved Extreme Learning Machine

“…Based on the setting of References [4,6,7,24,37,43] (common values for CO-OFDM signals), the employed parameters in this work are summarized in Table 2. Various constellations are considered in order to rigorously analyze the benefits and limitations of the SLFN subject to the RC-ELM algorithm to diminish amplitude and phase noises.…”

“…This situation makes strict sense if the RF is much greater than the bandwidth of the OFDM signal [24,30], which is very common for OFDM signals in the optical domain. Besides, our study is focused on the introduction of the improved ELM to enhance the CO-OFDM performance affected by laser phase noises; consequently, linear distortions (chromatic dispersion) and non-linear impairments (fiber non-linearity, intra-channel nonlinearity, among others) [36] are discarded.…”

“…By assuming a perfect time and frequency synchronization at the demodulation process, the OFDM symbol is under-sampled with the fixed sampling rate to simulate the ADC process, CP is removed, and FFT is performed, see Figure 1b. The kth received information symbol can be expressed as follows [24,38]:…”

“…The merits owned by the ELM algorithm make it a suitable alternative to perform channel equalization in OFDM schemes in wireless [13,21,22] and optical fiber [23,24] communications. On the one hand, a fully real-valued ELM to perform equalization and symbol detection processes in OFDM-based systems is introduced in Reference [21].…”

“…While the Wilcoxon robust ELM possesses a good generalization capability and fast training speed, the Wilcoxon generalized radial basis function gives the highest value of Q-factor among the rest of the algorithms as well as non-robust approaches based on minimization of least square error principle. ELMs in the real and complex planes for decreasing the chromatic dispersion effect in direct-detection OFDM-based radio-over-fiber systems are revealed by Zabala-Blanco et al [24]. Immediately, its ELM algorithm is summarized.…”