  This paper explores a novel integrated localization and communication (ILAC)
system using the affine Fourier transform multicarrier (AFT-MC) waveform.
Specifically, we consider a multiple-input multiple-output (MIMO) AFT-MC system
with ILAC and derive a continuous delay and Doppler shift channel matrix model.
Based on the derived signal model, we develop a two-step algorithm with low
complexity for estimating channel parameters. Furthermore, we derive the
Cram\'er-Rao lower bound (CRLB) of location estimation as the fundamental limit
of localization. Finally, we provide some insights about the AFT-MC parameters
by explaining the impact of the parameters on localization performance.
Simulation results demonstrate that the AFT-MC waveform is able to provide
significant localization performance improvement compared to orthogonal
frequency division multiplexing (OFDM) while achieving the CRLB of location
estimation.
