Power Distribution of Device-to-Device Communications Under Nakagami Fading Channel

Recently, device-to-device (D2D) communication was designated to work in cellular networks as a new standard to boost their performances. This kind of communication can occur either underlay to the existing cellular infrastructure, or overlay in the industrial scientific and medical (ISM) unused band. In this paper, we consider the case that D2D transmissions take place concurrently with the usual cellular players in the same spectrum band, and thus, controlling the interference caused by the cellular user equipments (UEs) is of crucial importance. In this work, we consider the uplink transmission of a tier of D2D users. Using network model based on stochastic geometry, we express the general cumulative distribution function (CDF) of the D2D transmit power under Nakagami fading channel. Special cases as CDF of the transmit power for Rayleigh fading and noiseless environment were derived. Besides, an upper bound of the general CDF expression is proposed. To deal with D2D lifetime, first, we express the expectation of the transmit power, then we determine the expectation of the devices lifetime and finally, we give an upper bound of this lifetime expectation. Through simulation, the obtained numerical results confirm the effectiveness of the proposed analytic schemes.