RKHS based adaptive signal processing algorithms for visible light communication

Abstract

With the increase in high-speed-data demand for the upcoming fifth generation (5G) and beyond communication systems, visible light communication (VLC) [1] has emerged as one of the promising, secure, green, and interference free supplement to the existing ra dio frequency (RF) based communication systems. Although promising, the performance in a practical VLC system is severely impaired by the following factors: (a) nonlinear trans fer characteristics of light emitting diode (LED), (b) intersymbol interference (ISI), and (c) multiplicative fading distortion due to user-mobility. The aforementioned VLC channel impairments significantly degrade the achievable bit error rate (BER) performance, and cause a significant performance-gap between the promised and the achieved throughput of VLC based systems. Furthermore, the throughput of the existing VLC systems can be increased by deployment of massive arrays of LED at the transmitter, and photodiodes at the receiver called as massive multiple-input multiple-output (m-MIMO) VLC system. However, with the increase in number of LEDs and photodiodes per unit area, spatial channel correlation increases, thereby resulting in high condition number of the effective channel matrix. Classical polynomial series and reproducing kernel Hilbert space (RKHS) based post distortion algorithms were proposed in the existing works for mitigating LED nonlinearity. RKHS based post-distorters are found to deliver improved performance over the polyno mial series post-distorters due to its several desirable features like convexity, universal approximation, and low computational complexity achieved via sparsification. However, the conventional feedforward RKHS based post-distorters are found to deliver suboptimal performance over the multipath VLC channel impaired by high ISI, and non-Gaussian distortions. Hence, to mitigate non-Gaussian processes encountered in VLC systems due to severe ISI and other non-Gaussian additive noises, decision feedback equalizer (DFE) based post-distorters in RKHS are suggested in this thesis. Further, non-minimum mean square error (MMSE) criteria like minimum symbol error rate (MSER), and maximum Versoria criterion (MVC) are explored in this thesis to improve the performance of RKHS based post-distorters over the VLC channels impaired by non-Gaussian distortions. Fur thermore, random Fourier features (RFF) based explicit RKHS methods are suggested in this thesis, which do not require sparsification, and thus enables post-distortion under a finite memory budget. Hence, the goal of this thesis is to develop new RKHS based adaptive signal processing algorithms for post-distortion (channel equalization) for a VLC link under high ISI and non-Gaussian additive distortions. The first work in this thesis proposes a novel adaptive precoder (AP) using an expo nent based singular value decomposition (SVD) for a m-MIMO VLC link for reducing the condition number of the overall channel matrix. Further, a joint optimization problem is formulated to optimize the exponent, and to detect symbols iteratively using the minimum symbol error rate (MSER) criterion. Computer simulations performed in this work demon strates superior BER performance for the proposed AP-MSER detector over the existing channel-inversion based detection techniques with similar computational complexity, and hence is a viable technique for recovering the transmitted symbols over m-MIMO VLC channels. Analytical upper bounds for BER are also derived and validated by simulations. However, the proposed AP-MSER detector is suitable for linear m-MIMO VLC channels, and its overall performance degrades over the generic nonlinear m-MIMO channels. To further improve the performance over the m-MIMO VLC channels affected by LED nonlinearity, the second work proposes a hybrid solution by using a RKHS based AP and kernel MSER (KMSER) based post-distorter. Furthermore, the hyperparameters used in precoder, and post-distorter design like precoding index and kernel width are optimized using MSER criterion to achieve the desired performance. Lastly, the effect of DC-bias fluctuations on BER performance is quantified analytically, and verified through numerical simulations. Although the BER performance of the proposed AP-KMSER detector for nonlinear m-MIMO VLC channel asymptotically converges to the performance achieved by ideal AWGN channel, however, its performance degrades over the dispersive VLC channels with large delay spread. To address this issue, the third work proposes a novel kernel least mean square (KLMS) with adaptive DFE based post-distorter for a multipath VLC link impaired by ISI, and LED nonlinearity. Additionally, the computational complexity of the proposed KLMS DFE post-distorter is reduced by using dictionary based sparsification technique using novelty criterion, and the resulting post-distortion algorithm is termed as KLMS-DFE NC. Simulations performed over standardized IEEE 802.15 PAN VLC channel indicate that the proposed KLMS-DFE-NC post-distorter deliver improved BER performance, supports higher data rates, and converges to lower dictionary size as compared to the conventional polynomial series based Volterra-DFE, and KLMS algorithm. However, the KLMS-DFE-NC algorithm is based on MMSE criterion, which limits its performance over the VLC channels impaired by non-Gaussian additive distortions. Furthermore, the computational complexity of KLMS-DFE-NC algorithm depend on dictionaries, and cannot be predicted beforehand since cardinality of dictionary is data dependent, which limits its practical implementation under a finite memory budget. To further reduce the computational complexity of sparse RKHS based techniques, next work in this thesis proposes a fixed-budget RFF based KMSER-DFE post-distorter for a VLC link impaired by user-mobility along with ISI, and LED nonlinearity. The overall additive distortion for VLC is found to be non-Gaussian in the presence of user-mobility, which renders the MMSE criterion based algorithms suboptimal over non-Gaussian dis tortions. Therefore, the feedforward, and feedback filter weights are jointly optimized by using a stronger MSER criterion which considers higher order statistics of error as op posed to the conventional MMSE criterion. Computer simulations performed in this work indicate that the proposed RFF-KMSER-DFE based post-distorter exhibits superior BER performance and lower computational complexity over the existing dictionary based post distorters in RKHS. Lastly, using the analytical characterization of the PDF of the overall additive distortion for a nonlinear mobility impaired VLC link, an analytical expression for error-rate is quantified for the proposed RFF-KMSER-DFE post-distorter, and validated by simulations. However, the aforementioned post-distorters relies on stochastic gradient descent (SGD) methods, that has lower computational complexity but higher MSE. To further improve the convergence performance of RKHS based post-distorters, fi nally, the last work in this thesis revisits the problem of post-distortion for a VLC link by formulating a least-squares based optimization problem in RKHS which considers all past error terms as opposed to the SGD methods, which considers only the instantaneous error term. A novel RFF based kernel recursive MVC (RFF-KRMVC) algorithm is proposed, which is robust to non-Gaussian/impulsive distortions. Computer simulations performed in this work demonstrates the superior BER and convergence performance for the proposed RFF-KRMVC algorithm over the existing RKHS based SGD algorithms. The convergence analysis of the proposed RFF-KRMVC algorithm is performed, and MSE of the proposed RFF-KRMVC algorithm is analytically found to be lower than the conventional kernel recursive least squares, and kernel recursive maximum correntropy algorithm.