The coexistence of broadband systems with currently deployed professional mobile radio (PMR) communication systems like public protection and disaster relief has gained much deserved attention. Recently, it has been shown that a conventional orthogonal frequency division multiplexing (OFDM)-based long-term evolution (LTE) system needs sufficient guard-band or additional filtering in order to coexist in a PMR band, even without considering the radio frequency (RF) impairments of the transmitter. In practice, it is imperative to take into account the RF impairments in radio communication systems, such as the non-linear (NL) nature of a high power amplifier (PA). This paper aims at investigating some enhanced multicarrier techniques allowing the coexistence of narrowband and broadband PMR systems that can support asynchronism, have low latency, and be able to be operated with NL devices. The simulation results show that a LTE-like post-OFDM broadband system working with NL PA devices can still coexist with legacy PMR systems with high spectrum and energy efficiencies when proper PA linearisation techniques are applied in combination with effective peak-to-average power ratio reduction methods.