Online Extreme Learning Machine-Based Channel Estimation and Equalization for OFDM Systems

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

“…To find the output weights matrix, pilot signals are utilized. With the assistance of 1000 hidden neurons, simulations establish that compared to the previous ELM based methods [13,21], the multiple split-complex ELM owns the benefit of higher detection accuracy with a slight complexity increase. On the other hand, the multi-layer perceptron, generalized radial basis function, and robust ELM are proposed in Reference [23] for mitigating nonlinearities in CO-OFDM systems under the 16QAM signaling.…”

“…An equalizer based on the standard ELM can be robust against the multipath effects introduced by the wireless channel [13,21,22]. In our work, the improved ELM algorithm is used to increase the RF-linewidth tolerance in CO-OFDM signals, by considering pilot and data subcarriers as training and testing samples, respectively.…”

“…Therefore, the output weights in the training process simplify into a regularized least problem, and of which result comes from a closed equation. Enhancements and extensions of the standard ELM such as improving the stability [11] and compactness [12] of the ELM, ELMs for online sequential [13] and imbalanced [14] data, Bayesian [15], fuzzy [16], Wavelet [17], or complex [18,19] ELMs have been demonstrated excellent generation performance, superior efficiency, and less computational complexity, by giving solutions for regression and classification problems in diverse practical areas (medical, remote sensing, control and robotics, image/video processing, time series analysis, text classification and understanding, telecommunication, chemical process, and computer vision). Hence, the issues of convergence ability, generalization, over-fitting, local minima, and/or parameter adjustment (learning rate, learning epochs, among others) presented in support vector machines as well as back-propagation artificial neural networks do not happen in ELMs [10,20].…”

“…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].…”

“…Over a time-varying Rayleigh fading channel for the quadrature phase-shift keying (QPSK), 16-ary quadrature amplitude modulation (16QAM), and 64-ary QAM modes, the ELM exhibits significant improvement in terms of the symbol error rates and has lower computations than the following learning-based equalization schemes-the fully complex-valued ELM [25], complex-valued radial basis function network [25], complex-valued minimal resource allocation network [25], k-nearest neighbor approach [25], and back propagation [26] and stochastic gradient [27] neural networks. For QPSK-OFDM networks, an online fully-complex ELM based channel estimation and equalization scheme robust to fading channels based on the 802.11g standard and the nonlinear distortion originated from a high-power amplifier is proposed by Liu et al [13]. By combining the least square-based decision-directed channel estimation and the ELM algorithm, the received/equalized pilots may be employed to train the SSFN without pre-training and feedback connection between the transmitter and receiver.…”