  The Laser Interferometer Space Antenna (LISA) is a European Space Agency
mission that aims to measure gravitational waves in the millihertz range. The
three-spacecraft constellation forms a nearly-equilateral triangle, which
experiences flexing along its orbit around the Sun. These time-varying and
unequal armlengths require to process measurements with time-delay
interferometry (TDI) to synthesize virtual equal-arm interferometers, and
reduce the otherwise overwhelming laser frequency noise. Algorithms compatible
with such TDI combinations have recently been proposed in order to suppress the
phase fluctuations of the onboard ultra-stable oscillators (USO) used as
reference clocks.
  In this paper, we propose a new method to cancel USO noise in TDI
combinations. This method has comparable performance to existing algorithms,
but is more general as it can be applied to most TDI combinations found in the
literature. We compute analytical expressions for the residual clock noise
before and after correction, accounting for the effect of time-varying beatnote
frequencies, previously neglected. We present results of numerical simulations
that are in agreement with our models, and show that clock noise can be
suppressed below required levels. The suppression algorithm introduces a new
modulation noise, for which we propose a partial mitigation. This modulation
noise remains the limiting effect for clock-noise suppression, setting strict
timing requirements on the sideband generation.
