Performance Analysis of Physical Layer Security over Fluctuating Beckmann Fading Channels

In this paper, we analyse the performance of physical layer security over Fluctuating Beckmann (FB) fading channel, which is an extended model of both the κ - μ shadowed and the classical Beckmann distributions. Specifically, the average secrecy capacity (ASC), secure outage probability (SOP), the lower bound of SOP (SOPL), and the probability of strictly positive secrecy capacity (SPSC) are derived using two different values of the fading parameters, namely, m and μ which represent the multipath and shadowing severity impacts, respectively. Firstly, when the fading parameters are arbitrary values, the performance metrics are derived in exact expressions in terms of the extended generalised bivariate Fox's H-function (EGBFHF) that has been widely implemented in the open literature. In the second case, to obtain simple mathematically tractable expressions in terms of analytic functions as well as to gain more insight on the behaviour of the physical layer security over Fluctuating Beckmann fading channel models, m and μ are assumed to be integer and even numbers, respectively. In addition, the asymptotic behaviour for all the studied performance metrics has been provided. The numerical results of this analysis are verified via Monte Carlo simulations

Метод стробирования данных АЗН-В и его вероятностные модели

The article developed a gating technique that allows us to validate ADS-B data without the necessity to verify using the secondary surveillance radar or multilateration. Probabilistic models of the ADS-B data gating technique, as well as the algorithm for applying these models were proposed. Benchmark cases that occur when aircraft (A/C) positioning by ADS-B systems, determined by threshold values of navigation and pilot’s errors, were analyzed. The first benchmark case assumes not exceeding of navigation and pilot’s errors the bounds of the tolerance limits, which allows us to draw up a conclusion concerning the ADS-B data validation. The second one assumes exceeding of a pilot’s error the bounds of the tolerance limits under an allowable navigational error. Herewith, the air traffic controller (ATC) obtains a message about the proper ADS-B operation and the necessity to issue instructions to the pilot to correct a flight. The third benchmark case assumes exceeding of a navigation error the bounds of the tolerance limits under an allowable or not allowable pilot’s error. In this case, the ATC obtains a message about not valid ADS-B data and the incapability to use these systems. The simulation of the given benchmark cases was performed. In addition, the Rayleigh and Rice distributions were applied to implement the ADS-B data gating technique. The simulation results allow us to assess the required amount of accumulated ADS-B data for the evaluation. Thus, it was found that during the estimate based on the Rayleigh distribution, it is sufficient to accumulate 15–20 measurements, which, when transmitting 2 messages per second and under the condition of the normal ADS-B equipment operation, will take 8–10 s. During the estimate, using the Rice distribution, an accumulation of 25–30 measurements is sufficient, which will take 13–20 s. The developed method will allow the use of ADS-B systems at regional aerodromes with the low intensity of air traffic as the primary or sole surveillance means. В статье разработан метод стробирования, который позволяет оценить достоверность данных АЗН-В без необходимости проверки с помощью вторичного радиолокатора или многопозиционной системы наблюдения. Предложены вероятностные модели метода стробирования данных АЗН-В, а также алгоритм применения данных моделей. Проанализированы типовые ситуации, возникающие при определении местоположения воздушного судна с помощью систем АЗН-В, определяемые пороговыми значениями погрешностей навигации и пилотирования. Первая типовая ситуация предполагает невыход погрешностей пилотирования и навигации за пределы допуска, что позволяет сделать вывод о подтверждении достоверности данных АЗН-В. Вторая типовая ситуация предполагает выход погрешности пилотирования за пределы допуска при допустимой погрешности навигации, при этом диспетчер получает сообщение о корректной работе АЗН-В и о необходимости выдачи команды пилоту на корректировку полета. Третья типовая ситуация предполагает выход погрешности навигации за пределы допуска при допустимой или недопустимой погрешности пилотирования; в этом случае диспетчер получает сообщение о том, что достоверность данных АЗН-В не подтверждается и применять эти системы нельзя. Выполнено моделирование этих типовых ситуаций, при этом для реализации метода стробирования данных АЗН-В применялись распределения Рэлея и Райса. Результаты моделирования позволяют оценить требуемое количество накопленных данных АЗН-В для проведения достоверной оценки. Так, было установлено, что при выполнении оценки с применением распределения Рэлея достаточно накопления 15–20 измерений, что при передаче двух сообщений в секунду и при условии штатной работы оборудования АЗН-В потребует 8–10 с. При выполнении оценки с применением распределения Райса достаточно накопления 25–30 измерений, что потребует 13–20 с. Разработанный метод позволит применять системы АЗН-В на региональных аэродромах с низкой интенсивностью полетов как основное или единственное средство наблюдения.

Ratio of Products of Mixture Gamma Variates with Applications to Wireless Communications Systems

The fading scenario of many realistic wireless communication transmission systems, such as, multi-hop communications and spectrum sharing in cognitive radio networks (CRNs), can be modelled by the product and the ratio of the product of the random variables (RVs) of the channel distribution. However, there is no work has been investigated in the literature to provide unified statistics of the product and the ratio of the products that can be used for a wide range of non-composite and composite fading conditions. Accordingly, in this paper, the statistical properties, namely, probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) of the product and the ratio of the product of independent and non-identically distributed (i.n.d.) mixture Gamma (MG) RVs are derived. A MG distribution has been widely employed to approximate with high accuracy most of the conventional fading models, for example, Rayleigh, Nakagami-m, Nakagami-q (Hoyt), and Nakagami-n (Rician) as well as the generalised composite fading channels, such as, generalised- (),− /gamma, − /gamma, and − /gamma. Hence, the derived PDF, CDF, and MGF are utilized for the Beaulieu–Xie and −−− shadowed fading channels that have not been yet presented by the previous works due to mathematical intractability of their statistics. Thus, the equivalent parameters of a MG distribution for these channels are given. To this end, simple closed-form mathematically tractable expressions of the performance metrics are obtained. The derived statistics are applied to analyse the outage probability (OP), the average error probability for different modulation schemes, the effective rate (ER) of wireless communication systems and the average area under the receiver operating characteristics (AUC) curve of energy detection over cascaded fading channels. Moreover, the OP of the multi-hop communications systems with co-channel interference (CCI), both the lower bound of secure OP (SOPL) and probability of non-zero secrecy capacity (PNSC) of the physical layer security (PLS), and the outage and delay-limited capacities of CRNs are studied via using the statistics of the ratio of the product of MG variates. A comparison between the numerical results and the Monte Carlo simulations is presented to verify the validation of our analysis