The present invention discloses an optimal energy efficiency-based antenna
selection method for a multi-user and large-scale antenna
relay system. The
system comprises a plurality of information source users, a plurality of information sink users and a
relay station, wherein the number of the information source users is equal to the number of the information sink users. The information source users and the information sink users are pairwise coupled and the
information transmission between the information source users and the information sink users is realized via the
relay station within two time slots. All information source users and information sink users in the
system are respectively provided with a single antenna. The relay
station is provided with an
antenna array of a large-scale number illustrated in the drawings of the abstract. According to the technical scheme of the invention, in order to realize that the energy efficiency of the system is maximal, the antenna number of the relay station is adopted as an optimization variable for the establishment of a
mathematical model. Since no clear analytical expression is available for a target function of the above
optimization problem, an approximately accurate analytical expression for the target function of the
optimization problem is figured out firstly based on the law of large numbers in the large dimensional
random matrix theory. After that, based the quasi-concave characteristics of the optimization variable in the analytical expression, an optimal antenna number closed-
form solution for realizing the optimal energy efficiency is finally solved out by means of the Lambert W function at the same time.