  With the increasing sensitivity of gravitational-wave detectors, we expect to
observe multiple binary neutron-star systems through gravitational waves in the
near future. The combined analysis of these gravitational-wave signals offers
the possibility to constrain the neutron-star radius and the equation of state
of dense nuclear matter with unprecedented accuracy. However, it is crucial to
ensure that uncertainties inherent in the gravitational-wave models will not
lead to systematic biases when information from multiple detections are
combined. To quantify waveform systematics, we perform an extensive simulation
campaign of binary neutron-star sources and analyse them with a set of four
different waveform models. Based on our analysis with about 38 simulations, we
find that statistical uncertainties in the neutron-star radius decrease to $\pm
250\rm m$ ($2\%$ at $90\%$ credible interval) but that systematic differences
between currently employed waveform models can be twice as large. Hence, it
will be essential to ensure that systematic biases will not become dominant in
inferences of the neutron-star equation of state when capitalizing on future
developments.
