This paper concerns the feasibility of full-duplex large-scale multiple-input-multiple-output (MIMO) cellular systems. We first propose a pilot transmission scheme and assess its performance, specifically the ergodic sum-rate. The proposed scheme -- the simultaneous pilot transmission (SPT) -- enables to reduce pilot overhead, where the pilot overhead depends on the number of antennas at the base station (BS), since the self-interference channel has to be estimated. We consider two multicell scenarios-- cooperative and non-cooperative multicell systems--, and derive the analytic model of the ergodic achievable sum-rate for cell-boundary users. The model is derived by applying a simple linear filter, i.e., matched filter or zero-forcing filter, to the BS. In the analytic model, we also consider large-scale fading, pilot contamination, transmitter noise and receiver distortion. Exploiting the derived analytic model, the feasibility of full-duplex large-scale MIMO systems is shown with respect to system parameters. In the end, we confirm that our analytic model matches well the numerical results and the SPT has advantages over other pilot transmission methods.