We perform a computational and analytical study of how the thickness of the barrier layer in nanoheterostructures and the gate-drain capacitance C (gd) influence the microwave parameters (limiting frequency of current amplification and maximum generation frequency) and noise parameters (noise factor) of a field-effect AlGaN/GaN high electron mobility transistor. The results of complex measurements of the parameters of such transistors based on nanoheterostructures with a barrier layer thickness of 3.5-15.7 nm, which were performed within the framework of four technological routes in the range 0.1-67 GHz, are presented. It is shown that in order to reduce the noise ratio and improve the microwave parameters, it is necessary to optimize both the parameters of nanoheterostructures and the manufacturing techniques. In particular, the thickness of the barrier layer should be reduced, and the gate length should be chosen such as to maximize the product of the squared maximum current amplification frequency in the interior of the transistor and the output impedance between the drain and the source. Additionally, attention should be given to the shape of the gate to reduce the capacitance C (gd). Under certain conditions of manufacture of nitride field-effect HEMT, one can achieve a lower noise factor compared with the transistors based on arsenide nanoheterostructures.