I’m using the LTE-A system level simulator and i try to implement energy efficient algorithms with tilt optimisation . However I am unable to find a mathematical relationship that links the Power received at the receiving antenna of the UE and the Power transmitted by the eNode B antenna, taking into account the tilt angle.
Right now I can calculate my received power,Pr, using the Power transmit,Pt, the Gain of the transmit antenna,Gt, the Gain of the receive antenna , Gr, and the path loss, Lp.
Antenna types that our simulator supports are given in +antennas and not all of them include the tilt angle. Regarding received power, you can look at the pathloss maps generated from pathloss model and antenna gain. In general with the simulator pathloss maps are generated (including antenna gain), and this is added on top of the channel matrix (small-scale fading).