This paper addresses the per-link power and bandwidth allocation problem with the objective of maximizing energy efficiency (EE) related metrics under a per-link minimum goodput constraint when only statistical channel state information is available. We consider a parallel (i.e., without multiuser interference) Rician channel model, which encompasses both Rayleigh and additive white Gaussian noise channels as special cases. We also consider Type-I hybrid automatic repeat request with practical modulation and coding schemes. The addressed problems are the maximization of the sum of the user's EE, the maximization of the EE of the user with the lowest EE and the maximization of the EE of the network. We derive the optimal solutions of these problems in closed form using fractional programming and a convex optimization framework. We show that substantial gains can be achieved by taking into account the line of sight between the transmitter and the receiver instead of only considering the average channel power.