Deployment of unmanned aerial vehicles (UAVs) as aerial base stations (ABSs) has been considered to be a feasible solution to provide network coverage in scenarios where the conventional terrestrial network is overloaded or inaccessible due to an emergency situation. This article studies the problem of optimal placement of the UAVs as ABSs to enable network connectivity to the users in a coverage free zone. The main contributions of this work include two approaches to position the UAVs and to assign user equipment (UE) to each UAV, such that the sum-rate and the coverage probability of the network is maximized. An approach can be selected depending on the prevailing scenario. The first approach uses clustering algorithm to determine the 2D positioning of the UAV and a matching algorithm is used for UE assignment by considering the characteristics of the air-to-ground propagation channels as well as the impact of co-channel interference from ABSs. Then it uses exhaustive search on different altitudes to find the optimal altitude. In the second approach, 2D positioning and UE assignment are done similarly to the first approach. However, the sub-optimal altitude is estimated using particle swarm optimization (PSO). The first approach is suitable for a system which has computational resource constraints or lower probability of line of sight (LoS) links. In contrast, the second approach is suitable for data rate greedy systems or a higher probability of LoS links.