Resumen
In this paper, we obtain a low-complexity closed-form formula for the outage probability of the energy-harvested decode-and-forward (DF) relay-aided underlay Device-to-device (D2D) communications in Nakagami fading channel. By proposing a new idea which finds the power splitting factor in simultaneous wireless information and power transfer (SWIPT) energy-harvesting system such that the transmit power of the relay node in the second time slot is fixed in a pre-defined value, the obtained closed-form expression is valid for both energy-harvested and non-energy-harvested scenarios. This formula is based on n-point generalized Gauss-Laguerre and m-point Gauss-Legendre solutions. It is shown that n is more effective than m for reducing the formula complexity. In addition to a good agreement between the simulation results and numerical analysis based on normalized mean square error (NMSE), it is indicated that (n, m)=(1, 4) and (n, m)=(1, 2) are the appropriate choices, respectively for 0.5= µ <0.7 and µ =0.7, where µ is the fading factor. As shown in this investigation, increasing the average distance between D2D pairs and cellular user (lower interference), is the reason for decreasing the outage probability. Furthermore, it is clear that increasing the Nakagami fading factor is the reason for decreasing the outage probability.