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In this research work, we investigate the secrecy rate and optimal power allocation schemes for a half-duplex (HD) wire-tap Rayleigh fading channel in which a source wishes to communicate securely to a destination in the presence of an eavesdropper and under the aid of an amplify-and-forward (AF) relay. The secrecy capacity and the corresponding optimal power allocation schemes are examined under both individual and joint power constraints. Due to the absence of an insightful expression of the secrecy rate for a given power allocation scheme, determining such secrecy capacity is challenging. To overcome this issue, we first propose a novel method to calculate the expectation of an exponentially distributed random variable using the exponential integral function. By exploiting this calculation, we then establish the average secrecy rate of the considered AF relay channel in closed-form. By examining the quasi-concavity of the optimal power allocation problem, it is then concluded that the problem is quasi-concave. As such, the globally optimal solution exists and is unique for both individual and joint power constraints. A simple root finding method then can be applied into the derived close-formed formula to approximately calculate the optimal power allocation scheme to achieve the secrecy capacity. Numerical results are then provided to confirm the accuracy of the derived formula and the optimality of the proposed power allocation.

This paper studies a wire-tap channel in which a source node wants to communicate securely to a destination node in the presence of an eavesdropper and under the aid of an amplify-and-forward (AF) relay operating in full-duplex (FD) mode. The residual self-interference due to FD transmission is explicitly taken into account. The secrecy capacity and the respective optimal power allocation schemes for this system are examined under both individual and joint power constraints. At first, the related optimization problems are shown to be quasiconcave. As such, the globally optimal solution exists and is unique. Due to the non-linearity of the derivative, we apply a simple bisection method for root finding and obtain a simple expression for the optimal power allocation scheme. To further provide some insight on the solutions, we apply the method of dominant balance to analyze the capacity and power allocations in different high power regions. It is then demonstrated that full relay power is only needed when the power at the relay is sufficiently small compared to the power at the source. Comparisons with half-duplex (HD) relaying also revealed that FD can achieve a significantly higher secrecy capacity. Finally, numerical results are presented to confirm the optimality of the solutions.

Wetlands provide resources, regulate the environment, and stabilize shorelines; however, they are among the most vulnerable ecosystems in the world. Managing and monitoring wetland ecosystems are important for the development and maintenance of ecosystem services and their sustainable use in the context of climate change. We used Phantom 4 multispectral unmanned aerial vehicles (UAVs) to collect data from wetland areas in the Dong Rui Commune, which is one of the most diverse and valuable wetland ecosystems in northern Vietnam. A tree-species classification map was constructed through a combination of the visual classification method and spectral reflectance values of each plant species, and the characteristic distributions of mangrove plants, including Bruguiera gymnorrhiza, Rhizophora stylosa, and Kandelia obovata, were determined with an overall accuracy of 91.11% and a kappa coefficient (K) of 0.87. Universal reflectance graphs of each mangrove plant species were constructed for five wave channels, including blue, green, red, red edges, and near-infrared and the normalized difference vegetation index (NDVI). An experiment was conducted to map plant taxonomy in the same area based only on a graph of spectral reflectance values at five single-spectral bands and constructed NDVI values, resulting in an overall accuracy of 78.22% and a K of 0.67. The constructed map is useful for classifying, monitoring, and evaluating the structure of each group of mangroves, thereby enabling the efficient management and conservation of the Dong Rui Commune wetlands.

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