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Visible light communication (VLC) has emerged as a secure, cost-effective, and green supplement to the existing radio frequency (RF) communication systems. However, the performance of a typical VLC link is degraded by the following factors: (a) inter-symbol interference (ISI), which arises due to limited modulation bandwidth of light-emitting diode (LED), (b) the dispersion due to multi-path reflections, and (c) nonlinear transfer characteristics of LED. To mitigate ISI and LED nonlinearity, existing blind post-distorters, like the Volterra modified cascaded multimodulus algorithm (MCMMA) and the Hammerstein improved multistage clustering (HIMSC) approaches, experience degradations from modeling errors due to abrupt polynomial-series truncation. To mitigate these degradations, we propose a novel random Fourier features (RFF) based improved multi-stage clustering (RFF-IMSC) algorithm for blind post-distortion. Simulations performed over standardized IEEE 802.15 PAN VLC channels indicate that the proposed RFF-RIMSC post-distorter delivers improved performance as compared to the existing blind post-distorters. Also, analytical guarantees are presented and error-rate performance are analyzed for the $\epsilon $ -optimality of this approach with respect to supervised loss-functions.

In the context of localization over ad-hoc wireless networks, the effect of non-line-of-sight (NLoS) presents a severe performance bottleneck that causes outages in the signal-to-noise ratio (SNR) of the returns and significantly increases the location estimates’ error-floor. The non-Gaussianity and the scenario-dependent distributions/statistics of the additive noise-process caused by the NLoS returns make the naive ML-based solutions sub-optimal. In this regard, information-potential (IP) based localization algorithms have recently been found viable, especially in the presence of arbitrary additive noise-processes. This letter presents analytical insights on the error-bounds of two IP based algorithms in a cooperative-localization context, namely, maximum correntropy (MCC) and the minimum error entropy with fiducial points (MEE-FP). The presented analytical results for the considered IP based approaches are validated using relevant computer-simulations assuming typical point-processes.

Reproducing Hilbert space (RKHS)-based adaptive algorithms have attracted increased attention in machine learning and nonlinear signal processing with applications in visible light communications, radar, radio frequency communications and others. However, performance of RKHS-based algorithms is highly sensitive to a suitable learning criterion. In this regard, the Versoria criterion-based adaptive filtering has gained interest in recent works due to its superior convergence characteristics as compared to the popular criterion such as minimum mean square error, and maximum correntropy criterion. Therefore, in this brief, a novel random Fourier feature (RFF)-based kernel recursive maximum Versoria criterion (KRMVC) algorithm is proposed. Convergence analysis is presented next for the proposed RFF-KRMVC algorithm as guarantees of the promised performance benefits. Lastly, the analytical results are validated by corresponding computer-simulations over practical application-scenarios considered in this brief.

Nonlinear device characteristics present a severe performance-bottleneck for several upcoming next-generation wireless communication systems and prevent them from delivering high data-rates to the end-users. In this context, reproducing kernel Hilbert space (RKHS) based signal processing methods have gained widespread deployment and have been found to outperform classical polynomial-filtering-based solutions significantly. Furthermore, recent RKHS based techniques that rely on explicit feature-maps called random Fourier features (RFF) have emerged. These techniques alleviate the dependence on learning a dictionary and avoid the computations and errors incurred in dictionary-based learning. However, the performance of existing RKHS based solutions depends on choosing a suitable kernel-width. For the widely-used Gaussian kernel, we propose a methodology of assigning kernel-bandwidths that capitalizes on a stochastic sampling of kernel-widths using an ensemble drawn from a pre-designed probability density function. The technique is found to deliver a comparable convergence/error-rate performance to the scenario when the kernel-width is chosen by brute-force trial and error for tuning it for best performance. The desirable properties of the proposed kernel-sampling technique are supported by analytical proofs and are further highlighted by computer-simulations presented in the form of case studies in the context of next-generation communication systems.

Non-orthogonal multiple access (NOMA) has emerged as a promising multiple-access technique capable of accommodating many users over limited time-frequency resources. Among several NOMA techniques, sparse code multiple access (SCMA) has emerged as viable due to its promise of high coding-gain by appropriate codebook-design and simplistic detection using message-passing algorithm (MPA). However, the performance of classic SCMA based systems are severely impaired by impulsive noise (IN), which causes outages and therefore non-negligible degradations to the bit-error-rate (BER) performance. Exploiting the robustness of the maximum correntropy criterion (MCC) to non-Gaussian noise processes, an MPA based detector is formulated with message-functions derived from the MCC criterion. Based on the said MCC criterion, concurrent-adaptation of the MCC’s spread-parameter is proposed in this letter. Lastly, analytical results for the proposed approach’s BER performance are presented with corresponding validation by computer-simulations.

Localization has been a well-investigated problem in the past decade for several networks and is one of the most celebrated applications of adaptive signal processing. However, existing localization algorithms exhibit a significant degradation under non-line of sight (NLOS) conditions, especially in outdoor scenarios. Due to the inherent non-Gaussianity in the NLOS returns, generic mitigation of the degradations due to NLOS remains quite an open challenge. In this regard, information-theoretic learning (ITL) criteria are attractive due to their ability to adapt to arbitrary NLOS distributions and suppress NLOS-induced non-Gaussian processes. In this regard, this letter proposes the use of minimum error entropy with Fiducial points (MEE-FP) in the particular context of round-trip time of arrival (RTTOA) based localization. From the presented simulations, it is observed that the proposed MEE-FP based localization method delivers lower variance under severe NLOS conditions and is closer to the ideal maximum-likelihood solution than contemporary ITL based approaches. Lastly, analytical variance-expressions are derived for the proposed localization technique, which is validated by computer simulations.

Ultraviolet (UV) communication has emerged as a promising solution for providing non-line-of-sight (NLOS) wireless connectivity due to strong molecular and aerosol scattering at UV wavelength. However, performance of UV based communication systems is severely impaired due to nonlinear transfer-characteristics of light emitting diode (LED), which degrades the overall symbol error rate (SER) performance. In addition, UV based communication systems are also impaired by multiplicative distortion due to turbulence, that causes detrimental instantaneous outages. Hence, in this work, first an expression for the outage probability is derived for a nonlinear UV communication system via analytical characterization of the statistics of the additive distortion. Further, utilizing the proposed analytical model for additive distortion, the error rate of reproducing kernel Hilbert space (RKHS) based detectors is quantified for the nonlinear outdoor NLOS UV channel. Additionally, using the derived expression for error-rate, an RKHS based minimum symbol error rate (MSER) equalizer is formulated to mitigate the distortion due to LED nonlinearity, and to enhance the error-rate performance of the considered nonlinear NLOS UV link. Convergence of the proposed MSER equalizer is analyzed, and improvements in error-rate promised by the proposed equalizer are validated by computer simulations over typical NLOS UV channels.

Visible light communications (VLC) has emerged as a promising technology for the next-generation communication systems. For VLC, several non-orthogonal multiple access (NOMA) techniques have emerged, among which sparse-code multiple access (SCMA) is particularly viable due to promised shaping and coding gain, and typically minimal/no error propagation as compared to power-domain NOMA (PD-NOMA). In this work, we introduce using polychromatic light emitting diodes (LEDs) as transmitters, where several users are overlapped on each color using SCMA; consequently, the SCMA codewords on each color are overlapped in the color-domain before transmission. At the receiver, after color-filtering, the residual color-coupling is removed by inverting the coupling matrix. Finally, the users’ signals over each color-channel are recovered using the message passing algorithm. Further, asymptotic error-rate expressions are derived for the proposed color-domain SCMA. These expressions are validated by simulations assuming VLC channel-models for random waypoint user-mobility. The analytical results promise a potential gain in the sum-rate while supporting a larger number of users as compared to a monochromatic white-LED based SCMA system.

In the context of outdoor localization over systems impaired by non-line of sight (NLoS), the minimum error entropy with fiducial points (MEE-FP) based methods have emerged as promising due to their excellent generalization and independence to statistics of NLoS. However, the performance of these approaches are well-known to depend on hyperparameters, such as, the spread parameter of the MEE-FP criterion. To enable MEE-FP based hyperparameter-free localization, we propose a modified Gauss-Newton based localization algorithm based on sampled kernel-widths. Next, analytical results are derived to demonstrate the asymptotic equivalence of the proposed kernel-width sampling based localization algorithm to its ideal fixed kernel width based counterpart. This equivalence is validated through computer simulations assuming typical non-Gaussian NLoS distributions, which motivates the hyperparameter-independence of the proposed localization algorithm and its generalization to different NLoS statistics.

Visible light communication (VLC) has emerged as a promising technology that facilitates high speed green communication for the next generation communication systems. However, some of the performance-limiting impairments in VLC include intersymbol interference (ISI), LED's nonlinearity, and multiplicative fading distortion due to user mobility, which present a significant gap between the promised and the achieved throughput of VLC based systems. To mitigate the aforementioned channel impairments, this paper proposes a random Fourier feature (RFF) based kernel minimum symbol error rate (KMSER) decision feedback equalizer (DFE) based post-distorter for VLC, which supports post distortion under finite memory budget. Furthermore, the feedforward, and feedback filter weights are jointly optimized by using a stronger minimum symbol error rate criterion as opposed to the conventional minimum mean square error criterion. Simulations 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. Lastly, an analytical bound for BER is derived for the proposed algorithm, and corroborated through simulations.

The next-generation of communication systems must be capable of serving a significantly higher traffic generated by a large number of devices. To support massive connectivity over limited time-frequency resources, several non-orthogonal multiple access (NOMA) paradigms have emerged. In this context, sparse code multiple access (SCMA) based NOMA is particularly attractive due to its robustness to error-propagation, and its potentially high coding-gain with appropriate codebook design. However, the performance of SCMA based systems is severely degraded by distortions introduced by non-ideal hardware, e.g. power-amplifier (PA) nonlinearity. To mitigate such artefacts, in this letter, a random Fourier feature (RFF) based hybrid message passing algorithm (MPA) is proposed, and validated through computer simulations. Lastly, an analytical proof is presented that indicates that the use of RFFs significantly improves the convergence of the MPA in the presence of impairments, and renders error-rate performance equivalent to that of a linear Gaussian channel under approximate MPA.

Vehicular visible light communications (VLC) has emerged as a viable supplement for high speed next-generation vehicle to vehicle (V2V) communication systems. However, performance of a V2V-VLC link is impaired due to nonlinear transfer-characteristics of light emitting diodes (LEDs), and inter-symbol interference (ISI). In this article, a low-complexity least-squares based post-distortion algorithm is formulated over reproducing kernel Hilbert space (RKHS) for a multi-hop V2V-VLC link. The impairments encountered in V2V-VLC channels are mitigated in RKHS by a minimum symbol error-rate post-distorter using a low dimensional approximation of random Fourier features (RFF) (which is a soft approximation of the feature-map to RKHS), that facilitates computationally simple post-distortion under finite memory-budget. The convergence and the BER-performance of the proposed post-distorter is analyzed over realistic V2V VLC channels obtained via ray-tracing. From the analysis, and the presented computer-simulations, the proposed post-distorter is found to exhibit equivalent convergence characteristics and error-rate over reasonable distances, with much lower computational complexity. Publisher's Version

In this article, we propose kernel maximum correntropy based nonlinear estimators for range and velocity estimation in non-Gaussian clutter and system nonlinearity. The proposed estimators are analyzed for linear frequency modulated and stepped frequency radar systems. Additionally, an adaptive update equation is derived for optimization of the kernel width, which further lowers the dictionary size and the variance of the proposed estimators. For performance evaluation of the proposed estimators, an expression is derived for the Cramer–Rao lower bound using a modified Fisher information matrix.

Visible light communications (VLC) has emerged as a viable supplement for high speed next-generation communication systems. However, performance of a VLC link is limited by the nonlinear characteristics of light emitting diodes (LEDs), ambient light, and inter-symbol interference (ISI). In this letter, the paradigm of least-squares based post-distortion over reproducing kernel Hilbert spaces (RKHS) is considered for a visible light communication (VLC) link. The performance-limiting impairments (viz. LED nonlinearity, and ISI), are mitigated by random Fourier features (RFF) based least minimum symbol error-rate post-distorter in RKHS, which facilitates post-distortion under finite memory-budget constrained scenarios. Performance of the proposed algorithm is tested over IEEE 802.15r1 PAN VLC channels, and the proposed algorithm is observed to converge significantly faster, whilst supporting higher data rates as compared to the existing RKHS based post-distorters.

Visible light communication (VLC) has emerged as a green, low-cost, and secure supplement for existing radio frequency (RF) based systems. Although promising, the performance of VLC based systems is limited by several impairments, which degrade the achievable bit error-rate (BER) performance, viz. variations in channel-gain due to user-mobility, and channel-estimation error. Hence, in this letter, the bit error rate (BER) of maximal ratio combining is quantified over a multiple-input multiple-output (MIMO) VLC system, while considering the aforementioned impairments. Next, using the derived expressions, exact and asymptotic combiners based on the minimum bit error-rate (MBER) criterion are formulated for MIMO VLC systems impaired by user-mobility, and channel-estimation error. The accuracy of the contributed expressions for BER, and the performance of the proposed MBER combiner (MBERC) are corroborated by simulations performed over realistic MIMO VLC channels. Additionally, it is found that the proposed MBERC delivers improved BER performance in presence of channel-estimation error and user-mobility, which makes the proposed methodology viable.

Non-orthogonal multiple access (NOMA) has emerged as a promising technology that allows for multiplexing several users over limited time-frequency resources. Among existing NOMA methods, sparse code multiple access (SCMA) is especially attractive; not only for its coding gain using suitable codebook design methodologies, but also for the guarantee of optimal detection using message passing algorithm (MPA). Despite SCMA’s benefits, the bit error rate (BER) performance of SCMA systems is known to degrade due to nonlinear power amplifiers at the transmitter. To mitigate this degradation, two types of detectors have recently emerged, namely, the Bussgang-based approaches and the reproducing kernel Hilbert space (RKHS)-based approaches. This paper presents analytical results on the error-floor of the Bussgang-based MPA, and compares it with a universally optimal RKHS-based MPA using random Fourier features (RFF). Although the Bussgang-based MPA is computationally simpler, it attains a higher BER floor compared to its RKHS-based counterpart. This error floor and the BER’s performance gap are quantified analytically and validated via computer simulations.

Performance of massive multi-input multi-output (MIMO) visible light communication (VLC) link is limited by ill-conditioned massive-MIMO channel, and nonlinearity of light emitting diodes (LEDs), which degrades the bit error rate (BER) performance. In this letter, to circumvent the above limitations, we propose a hybrid solution by using a singular value decomposition based adaptive precoder and a kernel minimum symbol error rate based post-distorter. Simulations indicate that the proposed algorithm outperforms the existing algorithms in terms of BER and computational complexity. Further, for the first time, the effect of DC-bias fluctuations on BER and dictionary-size is quantified analytically, and verified through numerical simulations.

Visible light communication (VLC) has emerged as a viable supplement to the existing radio frequency based communication systems. However, its performance is severely impaired by a) nonlinear characteristics of light emitting diode (LED), which reduces the Euclidean distance between neighboring constellation points, and b) intersymbol interference (ISI) due to time-dispersive nature of VLC channel, which reduces the eye opening of the received symbols and degrades the bit error rate (BER) performance. In this paper, we propose a novel kernel least mean square (KLMS) with adaptive decision feedback equalizer based post-distorter for VLC for joint mitigation of LED nonlinearity and ISI. In this work, minimum mean square error criterion based joint optimization problem is formulated in a reproducing kernel Hilbert space for optimization of the feedforward and feedback filter coefficients. Simulations indicate that the proposed post-distorter yields better BER performance as compared to existing algorithms.

Relationship between the delay and Doppler shift with the radar return is nonlinear in nature. Therefore, a nonlinear estimator based on sparse kernel least mean square algorithm is proposed. Further, an adaptive kernel width optimization technique is proposed to lower the computational complexity and for simple implementation. An expression for the Cramer–Rao lower bound is derived and validated for the proposed estimator over linear frequency modulated, and orthogonal frequency division multiplexed radar systems.

Visible light communication (VLC) based systems are a viable green supplement to existing radio frequency based communication systems. However, it has been found that the performance of VLC based systems is impaired in conditions when the users are mobile with respect to the transmit luminaire. The relative motion of the mobile users with respect to the luminaire renders the overall VLC channel to be time-varying. Recently, the impact of user mobility on the overall channel impulse response has been modeled by a generalized time-varying VLC channel model, which necessitates for an efficient mechanism at the receiver to tackle this phenomenon. In addition to user mobility, the inter-symbol interference, and the nonlinear characteristics of the light emitting diode are major factors that limit throughput of a VLC-based communication system. To mitigate these impairments, existing techniques such as Volterra/Hammerstein based receivers suffer from modeling error due to truncation of the polynomial kernel till second order terms. Recently, sparse reproducing kernel Hilbert space (RKHS) based methods have been suggested that guarantee universal approximation with the reasonable computational simplicity. However, the choice of a single hyper-parameter restricts its ability to model time-varying channels/systems. Therefore, this paper proposes a novel RKHS based post-distorter that adaptively learns a sparse dictionary based on the incoming observations, and monitors validity of the dictionary based on a proposed metric in RKHS. In order to mitigate the time-varying VLC channel based on this metric, a criterion for clearing the contents of the existing dictionary is proposed, and the requirement to learn a new dictionary is detected. Furthermore, the concept of mixture-adaptive kernel learning is introduced in this work for the minimum symbol error rate (MSER) criterion. From the convergence analysis presented in this paper, faster mean squared error (MSE) convergence is proved for the mixture-kernel based post-distorter. Additionally, it is also proven that for a given step-size, the proposed mixture-kernel MSER post-distorter always converges to a lower MSE as compared to the classical single-kernel MSER.

Visible light communication (VLC) has emerged as a viable complement to traditional radio frequency (RF) based systems and as an enabler for high data rate communications for beyond-5G (B5G) indoor communication systems. In particular, the emergence of new B5G-based applications with quality of service (QoS) requirements and massive connectivity has recently led to research on the required service-levels and the development of improved physical (PHY) layer methods. As part of recent VLC standards development activities, the IEEE has formed the 802.11bb “Light Communications (LC) for Wireless Local Area Networking” standardization group. This paper investigates the network requirements of 5G indoor services such as virtual reality (VR) and high-definition (HD) video for residential environments using VLC. In this paper, we consider such typical VLC scenarios with additional impairments such as light-emitting diode (LED) nonlinearity and imperfect channel feedback, and propose hyperparameter-free mitigation techniques using Reproducing Kernel Hilbert Space (RKHS) methods. In this context, we also propose using a direct current biased optical orthogonal frequency division multiplexing (DCO-OFDM)-based adaptive VLC transmission method that uses precomputed bit error rate (BER) expressions for these RKHS-based detection methods and performs adaptive BER-based modulation-order switching. Simulations of channel impulse responses (CIRs) show that the adaptive transmission method provides significantly improved error rate performance, which makes it promising for high data rate VLC-based 5G indoor services. This work was supported by the Generalitat de Catalunya, Spain [grant number 2017 SGR 1195 ] and the national program on equipment and scientific and technical infrastructure under the European Regional Development Fund (FEDER) [grant number EQC2018-005257-P ]. Publisher's Version

Visible light communications (VLC) has emerged as a high-speed, low-cost, and green supplement for the existing radio frequency (RF) based infrastructures. However, the performance of VLC based systems is found to degrade significantly due to detrimental outages caused by non-negligible variations in the VLC channel-gain, that are jointly induced by radial user-mobility and random photodetector-orientation (together designated as 3D mobility in this letter). In addition to the 3D user-mobility mentioned above, the performance of VLC based systems is further limited by imperfect channel-state information (CSI). Such degradations in the VLC-link caused by the aforementioned factors necessitate the quantification of performance-metrics for further benchmarking/receiver-design. In this work, an analytical expression for bit-error rate (BER) is derived for a single LED indoor VLC system considering the radial user-mobility, random receiver orientation, and imperfect CSI altogether. Further, the derived BER expressions are validated using computer-simulations using typical VLC channel models from the literature. A close agreement between the analytical and the simulated BER is observed, which verifies the accuracy of the presented analysis. Publisher's Version

Visible light communication (VLC) has emerged as a promising supplement to existing radio frequency-based communication systems. Recently, the use of massive light emitting diodes (LED) and photodetector (PD) arrays have been proposed to increase the capacity of the overall VLC link. At the receiver, the signals received by the PD arrays are combined to enhance the achievable data rates. However, successful combining and subsequent detection depends on accurate channel estimation. In this paper, we consider a typical massive multiple input multiple output VLC scenario with maximal ratio combining, and derive an asymptotic analytical expression for the probability density function (p.d.f) of the residual additive distortion for mobile users. Since the minimum error entropy (MEE)-based learning paradigm outperforms the traditional Bussgang approaches due to the incorporation of order statistics, we derive an MEE-based channel estimator using the analytical expression for the p.d.f of the additive distortion. Simulations are carried out for various LED array-sizes, and under various LED transmit half angles. Furthermore, using the analytically derived p.d.f, the proposed MEE-criterion-based channel estimator achieves lower bit error rate, and faster convergence, as compared to existing minimum mean square error based channel estimator.

Visible light communication (VLC) has emerged as a promising, green, and interference-free supplement to existing radio frequency-based communication systems. To enhance the capacity of existing VLC-based systems, using massive arrays of light emitting diodes (LEDs) at the transmitter and photodiodes at the receiver has been proposed recently, resulting in a massive multiple-input multiple-output (m-MIMO) VLC system. However, by increasing LED array pitch in m-MIMO, the VLC channel matrices are generally ill conditioned which makes them sensitive to small perturbations and degrades the overall bit error rate (BER) performance. To reduce the condition number of the overall channel matrix, a novel precoder using an exponent-based singular value decomposition is proposed for m-MIMO VLC system. Furthermore, a joint optimization problem is formulated to optimize the exponent and to detect symbols iteratively using the minimum symbol error rate criterion. Simulations show that the proposed adaptive precoding technique exhibits superior BER performance over existing techniques. Analytical upper bounds for BER are also derived and validated by simulations.

One of the proposed solutions to meet the ever growing demand for data rates in 5G communication systems is to use large number of antennas (100–1000) in a massive multiple input multiple output (MIMO) communication system. Performing multi-user (MU) detection over massive-MIMO systems presents many challenges, prime among them being: large-dimensionality of the received dataset which can increase the computational complexity of traditional algorithms, and susceptibility to device impairments like power amplifier (PA) nonlinearity. Due to these factors, detection of the users’ symbols over uplink-MU massive-MIMO systems in a fast and computationally efficient way is an open problem. In this work, a reproducing kernel Hilbert space (RKHS) based block symbol detector is proposed for uplink-MU massive-MIMO systems that works on decomposed blocks of the observations, and selectively decides the use of an incoming observation, thereby rendering the detector to be computationally tractable, and robust to PA-nonlinearity encountered in uplink-MU massive-MIMO. Simulations have been carried out in this work that demonstrate superior performance of the proposed approach as compared to batch/iterative least squares based algorithms.

In the context of beyond-5G indoor communication systems, visible light communication (VLC) has emerged as a viable supplement for existing RF-based systems and as an enabler for high datarate communications. However, the existing indoor VLC systems are limited by detrimental outages caused by fluctuations in the VLC channel-gain due to user-mobility. Furthermore, the nonlinear characteristics of the light-emitting diode (LED) degrade the performance of VLC systems in the highpower regime by warping the input constellation. Additional performance-limits are introduced by inter-symbol interference (ISI) due to finite modulation-bandwidth of LEDs, and reflections from walls. In this paper, a random Fourier feature (RFF) based post-distorter is considered for mitigating the LED nonlinearity, and relevant expressions for the signal to noise ratio (SNR) are derived for a direct current biased optical orthogonal frequency division multiplexing (DCO-OFDM) system. Based on the derived expressions for SNR, the effects of user-mobility and ISI are mitigated by a DCO-OFDM based adaptive VLC transmission technique, which varies the transmission-rate/modulation-order under a specified error-rate constraint. Simulations are presented over channels obtained by ray-tracing, which indicates that the proposed algorithm achieves superior data-rates with a significantly lower error-rate. Publisher's Version

Visible light communication (VLC) is one of the main technologies driving the future 5G communication systems due to its ability to support high data rates with low power consumption, thereby facilitating high speed green communications. To further increase the capacity of VLC systems, a technique called non-orthogonal multiple access (NOMA) has been suggested to cater to increasing demand for bandwidth, whereby users’ signals are superimposed prior to transmission and detected at each user equipment using successive interference cancellation. Some recent results on NOMA exist which greatly enhance the achievable capacity as compared with the orthogonal multiple access techniques. However, one of the performance-limiting factors affecting VLC systems is the nonlinear characteristics of a light emitting diode (LED). This paper considers the nonlinear LED characteristics in the design of pre-distorter for cognitive radio inspired NOMA in VLC, and proposes singular value decomposition-based Chebyshev precoding to improve performance of nonlinear multiple-input multiple-output NOMA-VLC. A novel and generalized power allocation strategy is also derived in this paper, which is valid even in scenarios when users experience similar channels. Additionally, in this paper, analytical upper bounds for the bit error rate of the proposed detector are derived for square $M$ -quadrature amplitude modulation.

In this letter, a visible light communication (VLC) link affected by the light emitting diode (LED) nonlinearity and dispersion due to the IEEE 802.15 PAN channel impulse response is considered. To mitigate severe intersymbol interference and LED nonlinearity, computationally complex classical post-distortion techniques fall short in terms of applicability to massively connected 5G deployments (as in a VLC attocell) due to increased demand on resources and intractability of implementation. To address these issues, this letter proposes a low-complexity reproducing kernel Hilbert space-based post-distorter using a better sparsification technique equipped with an adaptive kernel width optimized by a minimum symbol error rate (MSER) criterion. Use of the proposed MSER metric for kernel width optimization reduces the computational complexity at the receiver, without compromising on the bit error rate. An upper bound on step-size to guarantee convergence of the proposed post-distorter is analytically derived, and the steady-state mean square error is also analyzed theoretically and validated by simulations. Furthermore, analytical upper bounds for bit error rate and steady-state dictionary size are also derived.

Adaptive channel equalization is a signal processing technique to mitigate inter-symbol interference in a time dispersive channel. For adaptive equalization, minimum mean square error (MMSE) criterion-based reproducing kernel Hilbert spaces (RKHS) approaches such as the kernel least mean squares (KLMS) algorithm and its variants have been suggested in the literature for nonlinear channels. Another optimality criterion, based on minimum bit/symbol error rate (MBER/MSER), is a better choice for adapting an equalizer as compared to MMSE criterion. A kernel-based minimum symbol error rate (KMSER) equalization algorithm combines minimum symbol error rate (MSER)-based approaches with RKHS techniques. However, most algorithms in RKHS such as KMSER/KLMS require infinite storage requirement and hence cannot be practically implemented. To curtail the infinite memory requirement, and make adaptive algorithm suitable for implementation with finite memory and processing power, we propose quantized KMSER (QKMSER) and fixed-budget quantized KMSER (FBQKMSER)-based equalizers in this paper. In this paper, we derive the dynamical equation for MSE evolution of the QKMSER and FBQKMSER and find their performance to be asymptotically close to the MSE behavior of the KMSER. Also, it is found via simulations that the tracking performance of FBQKMSER is better than all the compared algorithms in this paper which is particularly useful for non-stationary channels.

In recent times, there has been a surge in research on visible light communications (VLC). In VLC systems, normal light emitting diode (LED) lamps are used as transmitters by modulating the optical power of the LED with the input current. All this is done at a high frequency, so that the fluctuations are not visible to the naked eye. It is a well known fact that the LED characteristics are not linear. Such nonlinearities degrade the performance of VLC. In the literature, a predistorter using a linear adaptive scaling parameter is proposed as a predistorter, which uses the well known normalized least mean squares (NLMSs) algorithm as the learning mechanism. However, to correct a nonlinearity, we need a nonlinear mapping/predistorter. This letter proposes a Chebyshev regression-based nonlinear predistorter to correct the nonlinear characteristics of LED by learning a polynomial expansion of the input electrical signal so as to mitigate the LED nonlinearity. Simulations have been carried out to validate the performance of the algorithm against existing adaptive predistortion techniques, such as NLMS-based predistortion and post-distortion techniques, such as Volterra and Hammerstein filters.

Visible light communication (VLC) has emerged as a promising supplement to the existing radio frequency (RF) technology, which facilitates high speed communication for next generation communication systems. Although promising, the performance in a practical VLC system is severely impaired by ambient light interference. Furthermore, nonlinearity of light emitting diodes (LEDs) and imperfect/oudated channel state information (CSI) are other factors that degrade the achievable bit error rate (BER) performance. In this work, an analytical framework for analyzing the expression for BER of a wide class of modulation techniques is derived for an impaired VLC system considering: (a) ambient light interference, (b) LED nonlinearity, and (c) imperfect and outdated CSI. The derived analytical expressions for BER are validated through extensive computer simulations performed over typical VLC channels. Lastly, the utility of the derived analytical framework is demonstrated in the context of high data-rate VLC systems, wherein the performance of DC biased optical orthogonal frequency division multiplexing (DCO-OFDM) is quantified for VLC links impaired by the aforementioned degradations.

Visible light communications (VLC) has emerged as one of the prominent technologies to cater to the ever-increasing high-speed-data demand for proposed fifth-generation (5G) systems. However, two main issues affect the performance of VLC in an indoor environment: a) nonlinearity of light-emitting diode, which renders the overall system nonlinear; and b) intersymbol interference due to the propagation channel, which closes the eye diagram of the transmit constellation and, hence, causes it to be unsuitable for detection. To counter these artifacts, complex post-distortion receivers such as the Volterra-decision feedback equalizer (DFE) have been proposed to recover the transmit symbols. In this paper, the use of a reproducing kernel Hilbert space-based minimum symbol error rate equalizer is proposed that provides performance comparable to a long Volterra-DFE, with much less computational cost. Simulations have been carried over IEEE 802.15 personal area network (PAN) channels, which suggest that the proposed approach gives equivalent performance in an indoor VLC channel, as compared with Volterra-DFE with far fewer computations. An analytical expression for mean square error dynamics over these channels is also derived, and it is observed that the theoretically derived expression matches the simulation results for the considered IEEE 802.15 PAN indoor VLC channels.

A new blind equalisation algorithm is presented for multi-level quadrature amplitude modulation schemes. The presented technique provides faster convergence and improved performance in terms of mean square error, which is demonstrated through various simulations. A mathematical analysis is also presented for the steady-state mean square error, which verifies the better performance of the proposed scheme over the conventional ones. The performance is also compared on the basis of inter-symbol interference metric. A computationally efficient implementation of the proposed algorithm is also presented. Simulations are done with various types of fading channels ranging from highly degrading Hoyt fading channels to moderate Rayleigh fading channels.

The improved multi-stage clustering (IMSC)-based blind equalisation algorithm proposed by Mitra and colleagues in 2011 gave rise to significant improvements in terms of performance metrics as compared with its state-of-the-art counterparts. However, the present authors' research studies show that IMSC performance degrades significantly for multiple access interference (MAI) in code-division multiplexing access (CDMA) systems. To mitigate MAI, code filtering by orthogonal Hadamard codes is a popular practice to minimise the interference. Code-filtering techniques have been used in the past in which a de-correlating transform (inverse of an orthonormal Hadamard matrix) has been incorporated into the cost function of the parent algorithm (which can be any traditional equalisation algorithm). A hybrid equalisation scheme is suggested which combines IMSC and code-filtering, so as to mitigate interference in CDMA environments. The code-filtered IMSC shows better performance than any of the previously proposed algorithms.