Multivariate Extreme Value Theory Based Channel Modeling for Ultra-Reliable Communications

Attaining ultra-reliable communication (URC) in fifth-generation (5G) and beyond networks requires deriving statistics of channel in ultra-reliable region by modeling the extreme events. Extreme value theory (EVT) has been previously adopted in channel modeling to characterize the lower tail of received powers in URC systems. In this paper, we propose a multivariate EVT (MEVT)-based channel modeling methodology for tail of the joint distribution of multi-channel by characterizing the multivariate extremes of multiple-input multiple-output (MIMO) system. The proposed approach derives lower tail statistics of received power of each channel by using the generalized Pareto distribution (GPD). Then, tail of the joint distribution is modeled as a function of estimated GPD parameters based on two approaches: logistic distribution, which utilizes logistic distribution to determine dependency factors among the Frechet transformed tail sequence and obtain a bi-variate extreme value model, and Poisson point process, which estimates probability measure function of the Pickands angular component to model bi-variate extreme values. Finally, validity of the proposed models is assessed by incorporating the mean constraint on probability measure function of Pichanks coordinates. Based on the data collected within the engine compartment of Fiat Linea, we demonstrate the superiority of proposed methodology compared to the conventional extrapolation-based methods in providing the best fit to the multivariate extremes.Comment: 13 pages, 6 figure

Statistical Analysis of Geometric Algorithms in Vehicular Visible Light Positioning

Vehicular visible light positioning (VLP) methods find relative locations of vehicles by estimating the positions of intensity-modulated head/tail lights of one vehicle (target) with respect to another (ego). Estimation is done in two steps: 1) relative bearing or range of the transmitter-receiver link is measured over the received signal on the ego side, and 2) target position is estimated based on those measurements using a geometric algorithm that expresses position coordinates in terms of the bearing-range parameters. The primary source of statistical error for these non-linear algorithms is the channel noise on the received signals that contaminates parameter measurements with varying levels of sensitivity. In this paper, we present two such geometric vehicular VLP algorithms that were previously unexplored, compare their performance with state-of-the-art algorithms over simulations, and analyze theoretical performance of all algorithms against statistical channel noise by deriving the respective Cramer-Rao lower bounds. The two newly explored algorithms do not outperform existing state-of-the-art, but we present them alongside the statistical analyses for the sake of completeness and to motivate further research in vehicular VLP. Our main finding is that direct bearing-based algorithms provide higher accuracy against noise for estimating lateral position coordinates, and range-based algorithms provide higher accuracy in the longitudinal axis due to the non-linearity of the respective geometric algorithms.Comment: Technical report. 7 pages, 4 figure

Extreme Value Theory Based Rate Selection for Ultra-Reliable Communications

Ultra-reliable low latency communication (URLLC) requires the packet error rate to be on the order of $10^{-9}$-$10^{-5}$. Determining the appropriate transmission rate to satisfy this ultra-reliability constraint requires deriving the statistics of the channel in the ultra-reliable region and then incorporating these statistics into the rate selection. In this paper, we propose a framework for determining the rate selection for ultra-reliable communications based on the extreme value theory (EVT). We first model the wireless channel at URLLC by estimating the parameters of the generalized Pareto distribution (GPD) best fitting to the tail distribution of the received powers, i.e., the power values below a certain threshold. Then, we determine the maximum transmission rate by incorporating the Pareto distribution into the rate selection function. Finally, we validate the selected rate by computing the resulting error probability. Based on the data collected within the engine compartment of Fiat Linea, we demonstrate the superior performance of the proposed methodology in determining the maximum transmission rate compared to the traditional extrapolation-based approaches.Comment: 6 pages, 4 figures including 7 subfigure

Multivariate Extreme Value Theory Based Rate Selection for Ultra-Reliable Communications

Diversity schemes play a vital role in improving the performance of ultra-reliable communication systems by transmitting over two or more communication channels to combat fading and co-channel interference. Determining an appropriate transmission strategy that satisfies ultra-reliability constraint necessitates derivation of statistics of channel in ultra-reliable region and, subsequently, integration of these statistics into rate selection while incorporating a confidence interval to account for potential uncertainties that may arise during estimation. In this paper, we propose a novel framework for ultra-reliable real-time transmission considering both spatial diversities and ultra-reliable channel statistics based on multivariate extreme value theory. First, tail distribution of joint received power sequences obtained from different receivers is modeled while incorporating inter-relations of extreme events occurring rarely based on Poisson point process approach in MEVT. The optimum transmission strategies are then developed by determining optimum transmission rate based on estimated joint tail distribution and incorporating confidence intervals into estimations to cope with the availability of limited data. Finally, system reliability is assessed by utilizing outage probability metric. Through analysis of data obtained from the engine compartment of Fiat Linea, our study showcases the effectiveness of proposed methodology in surpassing traditional extrapolation-based approaches. This innovative method not only achieves a higher transmission rate, but also effectively addresses stringent requirements of ultra-reliability. The findings indicate that proposed rate selection framework offers a viable solution for achieving a desired target error probability by employing a higher transmission rate and reducing the amount of training data compared to conventional rate selection methods.Comment: 11 pages, 6 figures, submitted to the IEEE Transactions on Vehicular Technology (TVT

GANs for EVT Based Model Parameter Estimation in Real-time Ultra-Reliable Communication

The Ultra-Reliable Low-Latency Communications (URLLC) paradigm in sixth-generation (6G) systems heavily relies on precise channel modeling, especially when dealing with rare and extreme events within wireless communication channels. This paper explores a novel methodology integrating Extreme Value Theory (EVT) and Generative Adversarial Networks (GANs) to achieve the precise channel modeling in real-time. The proposed approach harnesses EVT by employing the Generalized Pareto Distribution (GPD) to model the distribution of extreme events. Subsequently, Generative Adversarial Networks (GANs) are employed to estimate the parameters of the GPD. In contrast to conventional GAN configurations that focus on estimating the overall distribution, the proposed approach involves the incorporation of an additional block within the GAN structure. This specific augmentation is designed with the explicit purpose of directly estimating the parameters of the Generalized Pareto Distribution (GPD). Through extensive simulations across different sample sizes, the proposed GAN based approach consistently demonstrates superior adaptability, surpassing Maximum Likelihood Estimation (MLE), particularly in scenarios with limited sample sizes

Incorporation of Confidence Interval into Rate Selection Based on the Extreme Value Theory for Ultra-Reliable Communications

Proper determination of the transmission rate in ultra-reliable low latency communication (URLLC) needs to incorporate a confidence interval (CI) for the estimated parameters due to the large amount of data required for their accurate estimation. In this paper, we propose a framework based on the extreme value theory (EVT) for determining the transmission rate along with its corresponding CI for an ultra-reliable communication system. This framework consists of characterizing the statistics of extreme events by fitting the generalized Pareto distribution (GPD) to the channel tail, deriving the GPD parameters and their associated CIs, and obtaining the transmission rate within a confidence interval. Based on the data collected within the engine compartment of Fiat Linea, we demonstrate the accuracy of the estimated rate obtained through the EVT-based framework considering the confidence interval for the GPD parameters. Additionally, we show that proper estimation of the transmission rate based on the proposed framework requires a lower number of samples compared to the traditional extrapolation-based approaches.Comment: 6 pages, 5 figures including 14 subfigure