# Extreme Learning Machines to Combat Phase Noise in RoF-OFDM Schemes
## 1 Introduction  
During the past three decades, the telecommunication industry has faced an impressive growth not only in the number of subscribers worldwide, but also in the demand for higher-speed data transmissions [1]. To this end, orthogonal frequency division multiplexing (OFDM)-based radio-over-fiber (RoF) technology, combining the benefits of optical fiber and millimeter-wave wireless links, has been proven as the solution to support secure, cost-effective, and high-capacity vehicular/mobile/wireless access for the topic generation communication systems [2]. There are two types of receiver used in the implementation of RoF-OFDM systems: direct detection [3] and coherent detection [4]. Direct detection is characterized by a simple and economical base station, but withthe cost of a worse receiving sensitivity when contrasted with coherent detection. Currently, direct detection is massively adopted because it allows using low-priced distributed feedback (DFB) lasers [5]. The reason behind DFB adoption is owed to the optical carrier and the single-sideband OFDM signal coming from the same optical source, namely the field experiment phase coherency at the central station. Nevertheless, the chromatic fiber dispersion progressively phase decorrelates optical signals as the transmission distance from the central station to a base station increases, originating phase noise at the photo-detected current. In RoF-OFDM systems, the communication from the base stations to the mobile terminals is through millimeter waves, where the system performance impairment due to phase noise is particularly detrimental [6]. In these schemes with a narrow bandwidth of the signal and a high millimeter wave, phase error leads to inter-carrier interference (ICI) and a rotation of each subcarrier, termed common phase error (CPE) [7]. By maintaining an effective information rate, as well as the simplicity of the digital signal processing, the pilot-assisted channel-correction method can efficiently correct the phase noise variations for small OFDM symbol periods [8]. This equalizer is included in most OFDM modems with the purpose of correcting the wireless channel. The complex interrelation between the chromatic dispersion effect and the feasible pilot-based equalization has been recently studied in [9], finding three different regimes as the combined tones become phase-decorrelated. The first and the second zones correspond for to case of partially phase-correlated fields. Meanwhile, the third regime occurs when there is no phase coherency between the tones. The phase noise compensator is only useful in the first zone (the OFDM symbol period does not exceed the time delay parameter that quantifies the chromatic dispersion effect). All these results are explained via a novel phase noise metric for multicarrier signals in the partial phase-decorrelation scenario, which counts the effectiveness of the equalizer. Recently, extreme learning machines (ELMs) have been reported as a promising learning algorithm for single-hidden layer feedforward neural networks (SLFNs) [10]. The weights of the input layer and the biases in the hidden layer are arbitrarily originated and, then, the weights of the output layer are analytically obtained by solving an overdetermined linear system through the Moore-Penrose pseudo-inverse [11]. Results based on real-world benchmarking function approximation and classification problems have shown that contrasted with the popular back-propagation algorithm and the support vector machines for SLFNs, the ELM algorithm is extremely simple, runs extraordinarily rapidly, and tends to provide better generalization performances [12; 10; 13; 14; 15]. With the fast development of artificial intelligence, extreme learning machines have been recently employed in communication systems for equalization purposes.