Ensuring ubiquitous mission-critical public safety communications (PSC) to all the first responders in the public safety network is crucial at an emergency site. Recently, the use of unmanned aerial vehicles (UAVs) has received extensive interest for PSC to fill the coverage holes and establish reliable connectivity. The UAVs can be deployed as unmanned aerial base stations (UABSs) as part of a heterogeneous network (HetNet) PSC infrastructure. In this paper, we design a PSC LTE-Advanced HetNet for different path loss models and deployment mechanism for UABSs. We enhance the system-wide spectral efficiency (SE) of this PSC HetNet by apply cell range expansion (CRE) to UABSs and mitigating the inter-cell interference arising in the HetNet by applying 3GPP Release-10 enhanced inter-cell interference coordination (eICIC) and 3GPP Release-11 further-enhanced inter-cell interference coordination (FeICIC). Through Monte Carlo simulations, we compare the system-wide fifth percentile SE when UABSs are deployed on a hexagonal grid and when their locations are optimized using a genetic algorithm, while also jointly optimizing the CRE and the inter-cell interference coordination parameters. Our results show that at optimized UABS locations, reduced power subframes defined in 3GPP Release-11 can provide considerably better fifth percentile SE than the 3GPP Release-10 with almost blank subframes (eICIC).